Subgroups — C₂₃×#61255 #19208881

Order 5888.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3355	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3347	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3346	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3339	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#553	—	2	1	no	—
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#553	C₂²	1	2	yes	—
35	C₂₃×#553	C₂²	1	2	yes	—
36	C₂₃×#553	C₂²	1	2	yes	—
37	C₂₃×#553	C₂²	1	2	yes	—
38	C₂₃×#553	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#553	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#552	—	2	1	no	—
41	C₂₃×#552	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#552	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#551	—	2	1	no	—
44	C₂₃×#551	—	2	1	no	—
45	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#546	—	2	1	no	—
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂₃×#529	—	2	1	no	—
49	C₂₃×#529	—	2	1	no	—
50	C₂₃×#529	—	2	1	no	—
51	C₂×C₂₃×#126	—	2	1	no	—
52	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
53	C₂₃×#525	C₂²	1	1	yes	characteristic
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#123	—	2	1	no	—
56	C₂×C₂₃×#121	—	2	1	no	—
57	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
59	C₄×#41×C₂₃	—	2	1	no	—
60	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₂₃	—	2	1	no	—
62	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
67	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
68	C₂₃×#501	C₂²	1	2	yes	complemented
69	C₂₃×#501	C₂²	1	2	yes	complemented
70	C₂₃×#499	C₂²	1	2	yes	complemented
71	C₂₃×#499	C₂²	1	2	yes	complemented
72	C₂₃×#485	C₂²	1	2	yes	complemented
73	C₂₃×#485	C₂²	1	2	yes	complemented
74	C₂₃×#484	C₂²	1	2	yes	complemented
75	C₂₃×#483	C₂²	1	2	yes	complemented
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#482	C₂²	1	2	yes	complemented
78	C₂₃×#482	C₂²	1	2	yes	complemented
79	C₂₃×#482	C₂²	1	2	yes	complemented
80	C₂₃×#482	C₂²	1	2	yes	complemented
81	C₂₃×#482	C₂²	1	2	yes	complemented
82	C₂₃×#481	C₂²	1	2	yes	complemented
83	C₂₃×#481	C₂²	1	2	yes	complemented
84	C₂₃×#481	C₂²	1	2	yes	complemented
85	C₂₃×#480	C₂²	1	2	yes	complemented
86	C₂₃×#480	C₂²	1	2	yes	complemented
87	C₂₃×#480	C₂²	1	2	yes	complemented
88	C₂₃×#479	C₂²	1	2	yes	complemented
89	C₂₃×#479	C₂²	1	2	yes	complemented
90	C₂₃×#478	C₂²	1	2	yes	complemented
91	C₂₃×#478	C₂²	1	2	yes	complemented
92	C₂₃×#478	C₂²	1	2	yes	complemented
93	C₂₃×#478	C₂²	1	2	yes	complemented
94	C₂₃×#476	C₂²	1	2	yes	complemented
95	C₂₃×#474	C₂²	1	2	yes	complemented
96	C₂₃×#469	C₂²	1	2	yes	complemented
97	C₂₃×#469	C₂²	1	2	yes	complemented
98	C₂₃×#468	C₂²	1	2	yes	complemented
99	C₂₃×#468	C₂²	1	2	yes	complemented
100	C₂₃×#466	C₂²	1	2	yes	complemented
101	C₂₃×#466	C₂²	1	2	yes	complemented
102	C₂₃×#465	C₂²	1	2	yes	complemented
103	C₂₃×#465	C₂²	1	2	yes	complemented
104	C₂₃×#442	C₂²	1	2	yes	complemented
105	C₂₃×#440	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
107	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
108	C₂₃×#436	C₂²	1	2	yes	complemented
109	C₂₃×#435	C₂²	1	2	yes	complemented
110	C₂₃×#435	C₂²	1	2	yes	complemented
111	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
112	C₂₃×#428	C₂²	1	1	yes	characteristic
113	C₂₃×#428	C₂²	1	1	yes	characteristic
114	C₂₃×#428	C₂²	1	1	yes	characteristic
115	C₂₃×#428	C₂²	1	1	yes	characteristic
116	C₂₃×#428	C₂²	1	1	yes	characteristic
117	C₂₃×#428	C₂²	1	1	yes	characteristic
118	C₂₃×#428	C₂²	1	1	yes	characteristic
119	C₂₃×#428	C₂²	1	1	yes	characteristic
120	C₂₃×#428	C₂²	1	1	yes	characteristic
121	C₂₃×#428	C₂²	1	2	yes	complemented
122	C₂₃×#428	C₂²	1	2	yes	complemented
123	C₂₃×#428	C₂²	1	2	yes	complemented
124	C₂₃×#428	C₂²	1	2	yes	complemented
125	C₂₃×#427	C₂²	1	2	yes	complemented
126	C₂₃×#427	C₂²	1	2	yes	complemented
127	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
129	C₂₃×#423	C₂²	1	1	yes	characteristic
130	C₂₃×#418	C₂²	1	1	yes	characteristic
131	C₂₃×#418	C₂²	1	1	yes	characteristic
132	C₂₃×#418	C₂²	1	1	yes	characteristic
133	C₂₃×#417	C₂²	1	1	yes	characteristic
134	C₂₃×#417	C₂²	1	1	yes	characteristic
135	C₂₃×#417	C₂²	1	1	yes	characteristic
136	C₂₃×#407	C₂²	1	1	yes	characteristic
137	C₂₃×#407	C₂²	1	1	yes	characteristic
138	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₂₃	—	2	1	no	—
142	C₂²×D₄×C₂₃	—	2	1	no	—
143	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
144	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₂₃	—	2	1	no	—
146	C₂³×C₄×C₂₃	—	2	1	no	—
147	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×D₈×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	—	2	4	no	—
153	C₂×M₁₆×C₂₃	—	2	4	no	—
154	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₃×#126	—	2	1	no	—
165	C₂₃×#126	—	2	1	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	1	no	—
171	C₂₃×#126	—	2	1	no	—
172	C₂₃×#126	—	2	1	no	—
173	C₂₃×#126	—	2	1	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	—	2	1	no	—
176	C₂₃×#125	—	2	1	no	—
177	C₂₃×#125	—	2	1	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	C₂³	1	1	yes	characteristic
180	C₂₃×#125	C₂³	1	1	yes	characteristic
181	C₂₃×#125	C₂³	1	2	yes	—
182	C₂₃×#125	C₂³	1	2	yes	—
183	C₂₃×#124	—	2	1	no	—
184	C₂₃×#124	—	2	1	no	—
185	C₂₃×#124	—	2	1	no	—
186	C₂₃×#123	—	2	1	no	—
187	C₂₃×#123	—	2	1	no	—
188	C₂₃×#123	—	2	1	no	—
189	C₂₃×#123	—	2	1	no	—
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	1	no	—
192	C₂₃×#123	—	2	1	no	—
193	C₂₃×#123	—	2	1	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×C₂²⋊Q₈	—	2	1	no	—
199	C₂₃×C₂²⋊Q₈	—	2	1	no	—
200	C₂₃×C₂²⋊Q₈	—	2	1	no	—
201	C₂₃×C₂²⋊Q₈	—	2	1	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂₃×#121	—	2	2	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	2	no	—
210	C₂₃×#121	—	2	2	no	—
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	1	no	—
213	C₂₃×#121	—	2	1	no	—
214	C₂₃×#121	—	2	1	no	—
215	C₂₃×#121	—	2	1	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	C₂³	1	1	yes	characteristic
219	C₂₃×#121	C₂³	1	1	yes	characteristic
220	C₂₃×#121	C₂³	1	2	yes	—
221	C₂₃×#121	C₂³	1	2	yes	—
222	C₂₃×#121	C₂³	1	2	yes	—
223	C₂₃×#121	C₂³	1	2	yes	—
224	C₂₃×#121	C₂³	1	1	yes	characteristic
225	C₂₃×#121	C₂³	1	1	yes	characteristic
226	C₂₃×#120	—	2	1	no	—
227	C₂₃×#120	—	2	1	no	—
228	C₄×Q₈×C₂₃	—	2	1	no	—
229	C₄×Q₈×C₂₃	—	2	1	no	—
230	C₄×Q₈×C₂₃	—	2	1	no	—
231	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	1	no	—
237	C₄×D₄×C₂₃	—	2	1	no	—
238	C₄×D₄×C₂₃	—	2	1	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
249	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
250	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
251	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
252	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	1	no	—
263	C₂₃×#117	—	2	1	no	—
264	C₂₃×#117	—	2	1	no	—
265	C₂₃×#117	—	2	1	no	—
266	C₂₃×#117	—	2	1	no	—
267	C₂₃×#117	—	2	1	no	—
268	C₂₃×#117	—	2	1	no	—
269	C₂₃×#117	—	2	1	no	—
270	C₂₃×#117	C₂³	1	1	yes	characteristic
271	C₂₃×#117	C₂³	1	1	yes	characteristic
272	C₂₃×#117	C₂³	1	2	yes	—
273	C₂₃×#117	C₂³	1	2	yes	—
274	C₂₃×#117	C₂³	1	1	yes	characteristic
275	C₂₃×#117	C₂³	1	1	yes	characteristic
276	C₂₃×#117	C₂³	1	1	yes	characteristic
277	C₂₃×#117	C₂³	1	1	yes	characteristic
278	C₂₃×#117	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
300	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₂₃	—	2	1	no	—
303	C₂×C₄²×C₂₃	—	2	1	no	—
304	C₂×C₄²×C₂₃	—	2	1	no	—
305	C₂×C₄²×C₂₃	—	2	1	no	—
306	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
307	C₂₃×#107	C₂³	1	2	yes	—
308	C₂₃×#107	C₂³	1	2	yes	—
309	C₂₃×#107	C₂³	1	2	yes	—
310	C₂₃×#107	C₂³	1	2	yes	—
311	C₂₃×#107	C₂³	1	2	yes	—
312	C₂₃×#107	C₂³	1	2	yes	—
313	C₂₃×#107	C₂³	1	2	yes	—
314	C₂₃×#107	C₂³	1	2	yes	—
315	C₂₃×#107	C₂³	1	2	yes	—
316	C₂₃×#106	C₂³	1	2	yes	—
317	C₂₃×#106	C₂³	1	2	yes	—
318	C₂₃×#106	C₂³	1	2	yes	—
319	C₂₃×#106	C₂³	1	2	yes	—
320	C₂₃×#106	C₂³	1	2	yes	—
321	C₂₃×#106	C₂³	1	2	yes	—
322	C₂₃×#106	C₂³	1	2	yes	—
323	C₂₃×#106	C₂³	1	2	yes	—
324	C₂₃×#106	C₂³	1	2	yes	—
325	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
326	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
327	C₂₃×#103	C₂³	1	2	yes	—
328	C₂₃×#103	C₂³	1	2	yes	—
329	C₂₃×#103	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	2	yes	—
331	C₂₃×#102	C₂³	1	2	yes	—
332	C₂₃×#102	C₂³	1	2	yes	—
333	C₂₃×#102	C₂³	1	2	yes	—
334	C₂₃×#102	C₂³	1	2	yes	—
335	C₂₃×#102	C₂³	1	2	yes	—
336	C₂₃×#102	C₂³	1	2	yes	—
337	C₂₃×#102	C₂³	1	2	yes	—
338	C₂₃×#102	C₂³	1	2	yes	—
339	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₂₃×#97	C₂³	1	2	yes	—
344	C₄×C₈×C₂₃	C₂³	1	2	yes	—
345	C₂⁴×C₂₃	—	2	1	no	—
346	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
348	#41×C₂₃	—	2	2	no	—
349	#41×C₂₃	—	2	2	no	—
350	#41×C₂₃	—	4	4	no	—
351	C₂×Q₈×C₂₃	—	2	1	no	—
352	C₂×Q₈×C₂₃	—	2	1	no	—
353	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₂₃	—	2	1	no	—
355	C₂×D₄×C₂₃	—	2	1	no	—
356	C₂×D₄×C₂₃	—	2	1	no	—
357	C₂×D₄×C₂₃	—	2	2	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	2	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	4	2	no	—
367	C₂×D₄×C₂₃	—	4	4	no	—
368	C₂×D₄×C₂₃	—	8	2	no	—
369	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₂₃	—	2	2	no	—
376	C₂²×C₄×C₂₃	—	2	2	no	—
377	C₂²×C₄×C₂₃	—	2	2	no	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	1	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	1	no	—
385	C₂²×C₄×C₂₃	—	2	1	no	—
386	C₂²×C₄×C₂₃	—	2	2	no	—
387	C₂²×C₄×C₂₃	—	2	2	no	—
388	C₂²×C₄×C₂₃	—	2	1	no	—
389	C₂²×C₄×C₂₃	—	2	1	no	—
390	C₂²×C₄×C₂₃	—	2	1	no	—
391	C₂²×C₄×C₂₃	—	2	2	no	—
392	C₂²×C₄×C₂₃	—	2	2	no	—
393	C₂²×C₄×C₂₃	—	8	2	no	—
394	C₂²×C₄×C₂₃	—	8	2	no	—
395	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	SD₁₆×C₂₃	—	2	4	no	—
409	D₈×C₂₃	—	2	4	no	—
410	M₁₆×C₂₃	—	2	2	no	—
411	M₁₆×C₂₃	—	2	2	no	—
412	M₁₆×C₂₃	—	2	2	no	—
413	M₁₆×C₂₃	—	2	4	no	—
414	M₁₆×C₂₃	—	2	4	no	—
415	M₁₆×C₂₃	#41	1	4	yes	complemented
416	C₂×C₈×C₂₃	—	2	4	no	—
417	C₂×C₈×C₂₃	—	2	4	no	—
418	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
421	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	2	no	—
425	C₄⋊C₄×C₂₃	—	2	2	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	—	2	1	no	—
435	C₄⋊C₄×C₂₃	—	2	1	no	—
436	C₄⋊C₄×C₂₃	—	2	1	no	—
437	C₄⋊C₄×C₂₃	—	2	1	no	—
438	C₄⋊C₄×C₂₃	—	2	1	no	—
439	C₄⋊C₄×C₂₃	—	2	1	no	—
440	C₄⋊C₄×C₂₃	—	2	1	no	—
441	C₄⋊C₄×C₂₃	—	2	1	no	—
442	C₄⋊C₄×C₂₃	—	2	1	no	—
443	C₄⋊C₄×C₂₃	—	2	1	no	—
444	C₄⋊C₄×C₂₃	—	2	1	no	—
445	C₄⋊C₄×C₂₃	—	2	1	no	—
446	C₄⋊C₄×C₂₃	—	2	1	no	—
447	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
458	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
459	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
460	C₂²⋊C₄×C₂₃	—	2	1	no	—
461	C₂²⋊C₄×C₂₃	—	2	1	no	—
462	C₂²⋊C₄×C₂₃	—	2	1	no	—
463	C₂²⋊C₄×C₂₃	—	2	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	—	2	1	no	—
466	C₂²⋊C₄×C₂₃	—	2	1	no	—
467	C₂²⋊C₄×C₂₃	—	2	1	no	—
468	C₂²⋊C₄×C₂₃	—	2	1	no	—
469	C₂²⋊C₄×C₂₃	—	2	1	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	2	no	—
474	C₂²⋊C₄×C₂₃	—	2	2	no	—
475	C₂²⋊C₄×C₂₃	—	2	2	no	—
476	C₂²⋊C₄×C₂₃	—	2	2	no	—
477	C₂²⋊C₄×C₂₃	—	2	2	no	—
478	C₂²⋊C₄×C₂₃	—	2	2	no	—
479	C₂²⋊C₄×C₂₃	—	2	1	no	—
480	C₂²⋊C₄×C₂₃	—	2	1	no	—
481	C₂²⋊C₄×C₂₃	—	2	1	no	—
482	C₂²⋊C₄×C₂₃	—	2	1	no	—
483	C₂²⋊C₄×C₂₃	—	2	1	no	—
484	C₂²⋊C₄×C₂₃	—	2	1	no	—
485	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₂₃	—	2	1	no	—
494	C₄²×C₂₃	—	2	1	no	—
495	C₄²×C₂₃	—	2	1	no	—
496	C₄²×C₂₃	—	2	1	no	—
497	C₄²×C₂₃	—	2	1	no	—
498	C₄²×C₂₃	—	2	1	no	—
499	C₄²×C₂₃	—	2	2	no	—
500	C₄²×C₂₃	—	2	2	no	—
501	C₄²×C₂₃	—	2	1	no	—
502	C₄²×C₂₃	—	2	1	no	—
503	C₄²×C₂₃	—	2	1	no	—
504	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
505	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
507	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
508	#61255	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂³×C₂₃	—	2	2	no	—
510	C₂³×C₂₃	—	2	2	no	—
511	C₂³×C₂₃	—	2	2	no	—
512	C₂³×C₂₃	—	2	1	no	—
513	C₂³×C₂₃	—	2	2	no	—
514	C₂³×C₂₃	—	4	1	no	—
515	C₂³×C₂₃	—	4	1	no	—
516	C₂³×C₂₃	—	4	1	no	—
517	C₂³×C₂₃	—	4	2	no	—
518	C₂³×C₂₃	—	4	2	no	—
519	C₂³×C₂₃	—	4	2	no	—
520	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
521	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
525	Q₈×C₂₃	—	2	1	no	—
526	Q₈×C₂₃	—	2	1	no	—
527	Q₈×C₂₃	—	4	2	no	—
528	Q₈×C₂₃	—	8	1	no	—
529	D₄×C₂₃	—	2	2	no	—
530	D₄×C₂₃	—	2	2	no	—
531	D₄×C₂₃	—	2	1	no	—
532	D₄×C₂₃	—	2	2	no	—
533	D₄×C₂₃	—	2	2	no	—
534	D₄×C₂₃	—	2	1	no	—
535	D₄×C₂₃	—	4	1	no	—
536	D₄×C₂₃	—	4	1	no	—
537	D₄×C₂₃	—	4	4	no	—
538	D₄×C₂₃	—	4	2	no	—
539	D₄×C₂₃	—	4	2	no	—
540	D₄×C₂₃	—	4	4	no	—
541	D₄×C₂₃	—	4	2	no	—
542	D₄×C₂₃	—	4	2	no	—
543	D₄×C₂₃	—	8	1	no	—
544	D₄×C₂₃	—	8	1	no	—
545	D₄×C₂₃	—	8	2	no	—
546	D₄×C₂₃	—	8	2	no	—
547	C₂×C₄×C₂₃	—	2	2	no	—
548	C₂×C₄×C₂₃	—	2	2	no	—
549	C₂×C₄×C₂₃	—	2	2	no	—
550	C₂×C₄×C₂₃	—	2	2	no	—
551	C₂×C₄×C₂₃	—	2	2	no	—
552	C₂×C₄×C₂₃	—	2	2	no	—
553	C₂×C₄×C₂₃	—	2	1	no	—
554	C₂×C₄×C₂₃	—	2	1	no	—
555	C₂×C₄×C₂₃	—	2	1	no	—
556	C₂×C₄×C₂₃	—	2	1	no	—
557	C₂×C₄×C₂₃	—	2	1	no	—
558	C₂×C₄×C₂₃	—	2	1	no	—
559	C₂×C₄×C₂₃	—	2	1	no	—
560	C₂×C₄×C₂₃	—	2	1	no	—
561	C₂×C₄×C₂₃	—	2	1	no	—
562	C₂×C₄×C₂₃	—	2	1	no	—
563	C₂×C₄×C₂₃	—	2	1	no	—
564	C₂×C₄×C₂₃	—	2	2	no	—
565	C₂×C₄×C₂₃	—	2	1	no	—
566	C₂×C₄×C₂₃	—	2	1	no	—
567	C₂×C₄×C₂₃	—	2	1	no	—
568	C₂×C₄×C₂₃	—	2	1	no	—
569	C₂×C₄×C₂₃	—	2	2	no	—
570	C₂×C₄×C₂₃	—	2	2	no	—
571	C₂×C₄×C₂₃	—	4	1	no	—
572	C₂×C₄×C₂₃	—	4	1	no	—
573	C₂×C₄×C₂₃	—	4	2	no	—
574	C₂×C₄×C₂₃	—	4	2	no	—
575	C₂×C₄×C₂₃	—	4	2	no	—
576	C₂×C₄×C₂₃	—	4	2	no	—
577	C₂×C₄×C₂₃	—	4	2	no	—
578	C₂×C₄×C₂₃	—	4	2	no	—
579	C₂×C₄×C₂₃	—	4	2	no	—
580	C₂×C₄×C₂₃	—	8	1	no	—
581	C₂×C₄×C₂₃	—	8	2	no	—
582	C₂×C₄×C₂₃	—	8	2	no	—
583	C₂×C₄×C₂₃	—	8	1	no	—
584	C₂×C₄×C₂₃	—	8	1	no	—
585	C₂×C₄×C₂₃	—	8	2	no	—
586	C₂×C₄×C₂₃	—	8	2	no	—
587	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
597	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
598	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
599	C₈×C₂₃	—	2	2	no	—
600	C₈×C₂₃	—	2	2	no	—
601	C₈×C₂₃	—	2	2	no	—
602	C₈×C₂₃	C₂×#41	1	4	yes	—
603	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
604	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
605	#3355	C₂×C₂₃	1	2	yes	complemented
606	#3351	C₂×C₂₃	1	2	yes	complemented
607	#3350	C₂×C₂₃	1	2	yes	complemented
608	#3347	C₂×C₂₃	1	2	yes	complemented
609	#3346	C₂×C₂₃	1	2	yes	complemented
610	#3345	C₂×C₂₃	1	2	yes	complemented
611	#3339	C₂×C₂₃	1	2	yes	complemented
612	#3337	C₂×C₂₃	1	2	yes	complemented
613	#3166	C₂×C₂₃	1	1	yes	characteristic, complemented
614	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
615	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
616	#3093	C₂×C₂₃	1	1	yes	characteristic, complemented
617	#3092	C₂×C₂₃	1	1	yes	characteristic, complemented
618	#3080	C₂×C₂₃	1	1	yes	characteristic, complemented
619	#3077	C₂×C₂₃	1	1	yes	characteristic, complemented
620	#3055	C₂×C₂₃	1	1	yes	characteristic, complemented
621	#3055	C₂×C₂₃	1	1	yes	characteristic, complemented
622	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
623	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
624	#2911	C₂×C₂₃	1	1	yes	characteristic, complemented
625	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
626	C₂²×C₂₃	—	2	1	no	—
627	C₂²×C₂₃	—	2	1	no	—
628	C₂²×C₂₃	—	2	1	no	—
629	C₂²×C₂₃	—	2	1	no	—
630	C₂²×C₂₃	—	2	1	no	—
631	C₂²×C₂₃	—	2	1	no	—
632	C₂²×C₂₃	—	2	1	no	—
633	C₂²×C₂₃	—	2	1	no	—
634	C₂²×C₂₃	—	2	1	no	—
635	C₂²×C₂₃	—	2	1	no	—
636	C₂²×C₂₃	—	2	1	no	—
637	C₂²×C₂₃	—	2	1	no	—
638	C₂²×C₂₃	—	2	1	no	—
639	C₂²×C₂₃	—	4	4	no	—
640	C₂²×C₂₃	—	4	2	no	—
641	C₂²×C₂₃	—	4	1	no	—
642	C₂²×C₂₃	—	4	1	no	—
643	C₂²×C₂₃	—	4	2	no	—
644	C₂²×C₂₃	—	4	1	no	—
645	C₂²×C₂₃	—	4	2	no	—
646	C₂²×C₂₃	—	8	2	no	—
647	C₂²×C₂₃	—	8	4	no	—
648	C₂²×C₂₃	#547	1	2	yes	—
649	C₂²×C₂₃	#575	1	2	yes	—
650	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
651	C₄×C₂₃	—	2	1	no	—
652	C₄×C₂₃	—	2	1	no	—
653	C₄×C₂₃	—	2	1	no	—
654	C₄×C₂₃	—	2	1	no	—
655	C₄×C₂₃	—	2	1	no	—
656	C₄×C₂₃	—	2	1	no	—
657	C₄×C₂₃	—	2	1	no	—
658	C₄×C₂₃	—	2	1	no	—
659	C₄×C₂₃	—	4	2	no	—
660	C₄×C₂₃	—	4	2	no	—
661	C₄×C₂₃	—	4	1	no	—
662	C₄×C₂₃	—	4	1	no	—
663	C₄×C₂₃	—	4	1	no	—
664	C₄×C₂₃	—	4	1	no	—
665	C₄×C₂₃	—	4	1	no	—
666	C₄×C₂₃	—	4	2	no	—
667	C₄×C₂₃	—	4	1	no	—
668	C₄×C₂₃	—	4	1	no	—
669	C₄×C₂₃	#547	1	2	yes	—
670	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
671	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
672	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
673	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
674	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
675	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#553	—	2	1	no	—
679	#553	—	2	1	no	—
680	#553	—	2	1	no	—
681	#553	—	2	1	no	—
682	#553	C₂²×C₂₃	1	2	yes	—
683	#553	C₂²×C₂₃	1	2	yes	—
684	#553	C₂²×C₂₃	1	2	yes	—
685	#553	C₂²×C₂₃	1	2	yes	—
686	#553	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#553	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	#552	—	2	1	no	—
689	#552	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#552	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#551	—	2	1	no	—
692	#551	—	2	1	no	—
693	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#546	—	2	1	no	—
695	#533	C₂²×C₂₃	1	1	yes	characteristic
696	#529	—	2	1	no	—
697	#529	—	2	1	no	—
698	#529	—	2	1	no	—
699	C₂×#126	—	2	1	no	—
700	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
701	#525	C₂²×C₂₃	1	1	yes	characteristic
702	#525	C₂²×C₂₃	1	1	yes	characteristic
703	C₂×#123	—	2	1	no	—
704	C₂×#121	—	2	1	no	—
705	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
706	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
707	C₄×#41	—	2	1	no	—
708	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
709	C₂×C₄×D₄	—	2	1	no	—
710	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
711	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
712	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
713	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
714	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
715	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
716	#501	C₂²×C₂₃	1	2	yes	complemented
717	#501	C₂²×C₂₃	1	2	yes	complemented
718	#499	C₂²×C₂₃	1	2	yes	complemented
719	#499	C₂²×C₂₃	1	2	yes	complemented
720	#485	C₂²×C₂₃	1	2	yes	complemented
721	#485	C₂²×C₂₃	1	2	yes	complemented
722	#484	C₂²×C₂₃	1	2	yes	complemented
723	#483	C₂²×C₂₃	1	2	yes	complemented
724	#482	C₂²×C₂₃	1	2	yes	complemented
725	#482	C₂²×C₂₃	1	2	yes	complemented
726	#482	C₂²×C₂₃	1	2	yes	complemented
727	#482	C₂²×C₂₃	1	2	yes	complemented
728	#482	C₂²×C₂₃	1	2	yes	complemented
729	#482	C₂²×C₂₃	1	2	yes	complemented
730	#481	C₂²×C₂₃	1	2	yes	complemented
731	#481	C₂²×C₂₃	1	2	yes	complemented
732	#481	C₂²×C₂₃	1	2	yes	complemented
733	#480	C₂²×C₂₃	1	2	yes	complemented
734	#480	C₂²×C₂₃	1	2	yes	complemented
735	#480	C₂²×C₂₃	1	2	yes	complemented
736	#479	C₂²×C₂₃	1	2	yes	complemented
737	#479	C₂²×C₂₃	1	2	yes	complemented
738	#478	C₂²×C₂₃	1	2	yes	complemented
739	#478	C₂²×C₂₃	1	2	yes	complemented
740	#478	C₂²×C₂₃	1	2	yes	complemented
741	#478	C₂²×C₂₃	1	2	yes	complemented
742	#476	C₂²×C₂₃	1	2	yes	complemented
743	#474	C₂²×C₂₃	1	2	yes	complemented
744	#469	C₂²×C₂₃	1	2	yes	complemented
745	#469	C₂²×C₂₃	1	2	yes	complemented
746	#468	C₂²×C₂₃	1	2	yes	complemented
747	#468	C₂²×C₂₃	1	2	yes	complemented
748	#466	C₂²×C₂₃	1	2	yes	complemented
749	#466	C₂²×C₂₃	1	2	yes	complemented
750	#465	C₂²×C₂₃	1	2	yes	complemented
751	#465	C₂²×C₂₃	1	2	yes	complemented
752	#442	C₂²×C₂₃	1	2	yes	complemented
753	#440	C₂²×C₂₃	1	2	yes	complemented
754	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
755	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
756	#436	C₂²×C₂₃	1	2	yes	complemented
757	#435	C₂²×C₂₃	1	2	yes	complemented
758	#435	C₂²×C₂₃	1	2	yes	complemented
759	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
760	#428	C₂²×C₂₃	1	1	yes	characteristic
761	#428	C₂²×C₂₃	1	1	yes	characteristic
762	#428	C₂²×C₂₃	1	1	yes	characteristic
763	#428	C₂²×C₂₃	1	1	yes	characteristic
764	#428	C₂²×C₂₃	1	1	yes	characteristic
765	#428	C₂²×C₂₃	1	1	yes	characteristic
766	#428	C₂²×C₂₃	1	1	yes	characteristic
767	#428	C₂²×C₂₃	1	1	yes	characteristic
768	#428	C₂²×C₂₃	1	1	yes	characteristic
769	#428	C₂²×C₂₃	1	2	yes	complemented
770	#428	C₂²×C₂₃	1	2	yes	complemented
771	#428	C₂²×C₂₃	1	2	yes	complemented
772	#428	C₂²×C₂₃	1	2	yes	complemented
773	#427	C₂²×C₂₃	1	2	yes	complemented
774	#427	C₂²×C₂₃	1	2	yes	complemented
775	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
776	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
777	#423	C₂²×C₂₃	1	1	yes	characteristic
778	#418	C₂²×C₂₃	1	1	yes	characteristic
779	#418	C₂²×C₂₃	1	1	yes	characteristic
780	#418	C₂²×C₂₃	1	1	yes	characteristic
781	#417	C₂²×C₂₃	1	1	yes	characteristic
782	#417	C₂²×C₂₃	1	1	yes	characteristic
783	#417	C₂²×C₂₃	1	1	yes	characteristic
784	#407	C₂²×C₂₃	1	1	yes	characteristic
785	#407	C₂²×C₂₃	1	1	yes	characteristic
786	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
787	C₂×C₂₃	—	2	2	no	—
788	C₂×C₂₃	—	2	2	no	—
789	C₂×C₂₃	—	4	1	no	—
790	C₂×C₂₃	—	4	1	no	—
791	C₂×C₂₃	—	4	1	no	—
792	C₂×C₂₃	—	8	1	no	—
793	C₂×C₂₃	—	8	2	no	—
794	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
795	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
796	C₂×C₂₃	#3585	1	1	yes	characteristic
797	C₂×#41	—	2	1	no	—
798	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
799	C₂²×D₄	—	2	1	no	—
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
802	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
803	C₂³×C₄	—	2	1	no	—
804	C₂³×C₄	—	2	1	no	—
805	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
806	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
807	AGL(1,ℤ/8)	—	2	4	no	—
808	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
809	C₂×D₈	C₂³×C₂₃	1	2	yes	—
810	C₂×M₁₆	—	2	4	no	—
811	C₂×M₁₆	—	2	4	no	—
812	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
813	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
814	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
815	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
816	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
817	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
818	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
819	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
820	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
821	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
822	#126	—	2	2	no	—
823	#126	—	2	2	no	—
824	#126	—	2	2	no	—
825	#126	—	2	2	no	—
826	#126	—	2	1	no	—
827	#126	—	2	1	no	—
828	#126	—	2	1	no	—
829	#126	—	2	1	no	—
830	#126	—	2	1	no	—
831	#126	—	2	1	no	—
832	#125	—	2	1	no	—
833	#125	—	2	1	no	—
834	#125	—	2	1	no	—
835	#125	—	2	1	no	—
836	#125	—	2	1	no	—
837	#125	C₂³×C₂₃	1	2	yes	—
838	#125	C₂³×C₂₃	1	2	yes	—
839	#125	C₂³×C₂₃	1	1	yes	characteristic
840	#125	C₂³×C₂₃	1	1	yes	characteristic
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	—	2	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	1	no	—
853	#123	—	2	1	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
864	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
865	#121	—	2	2	no	—
866	#121	—	2	2	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	C₂³×C₂₃	1	2	yes	—
877	#121	C₂³×C₂₃	1	2	yes	—
878	#121	C₂³×C₂₃	1	2	yes	—
879	#121	C₂³×C₂₃	1	2	yes	—
880	#121	C₂³×C₂₃	1	1	yes	characteristic
881	#121	C₂³×C₂₃	1	1	yes	characteristic
882	#121	C₂³×C₂₃	1	1	yes	characteristic
883	#121	C₂³×C₂₃	1	1	yes	characteristic
884	#120	—	2	1	no	—
885	#120	—	2	1	no	—
886	C₄×Q₈	—	2	1	no	—
887	C₄×Q₈	—	2	1	no	—
888	C₄×Q₈	—	2	1	no	—
889	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	—	2	2	no	—
901	C₄×D₄	—	2	2	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
907	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
908	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
909	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₂₃	1	2	yes	—
911	C₄×D₄	C₂³×C₂₃	1	2	yes	—
912	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
913	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
916	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
918	#117	—	2	1	no	—
919	#117	—	2	1	no	—
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	—	2	1	no	—
923	#117	—	2	1	no	—
924	#117	—	2	1	no	—
925	#117	—	2	1	no	—
926	#117	—	2	1	no	—
927	#117	—	2	1	no	—
928	#117	C₂³×C₂₃	1	1	yes	characteristic
929	#117	C₂³×C₂₃	1	1	yes	characteristic
930	#117	C₂³×C₂₃	1	1	yes	characteristic
931	#117	C₂³×C₂₃	1	1	yes	characteristic
932	#117	C₂³×C₂₃	1	1	yes	characteristic
933	#117	C₂³×C₂₃	1	2	yes	—
934	#117	C₂³×C₂₃	1	2	yes	—
935	#117	C₂³×C₂₃	1	1	yes	characteristic
936	#117	C₂³×C₂₃	1	1	yes	characteristic
937	C₂×C₄⋊C₄	—	2	1	no	—
938	C₂×C₄⋊C₄	—	2	1	no	—
939	C₂×C₄⋊C₄	—	2	1	no	—
940	C₂×C₄⋊C₄	—	2	1	no	—
941	C₂×C₄⋊C₄	—	2	1	no	—
942	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
946	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
947	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
952	C₂×C₂²⋊C₄	—	2	1	no	—
953	C₂×C₂²⋊C₄	—	2	1	no	—
954	C₂×C₂²⋊C₄	—	2	1	no	—
955	C₂×C₂²⋊C₄	—	2	1	no	—
956	C₂×C₂²⋊C₄	—	2	1	no	—
957	C₂×C₂²⋊C₄	—	2	1	no	—
958	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
959	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
960	C₂×C₄²	—	2	1	no	—
961	C₂×C₄²	—	2	1	no	—
962	C₂×C₄²	—	2	1	no	—
963	C₂×C₄²	—	2	1	no	—
964	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
965	#107	C₂³×C₂₃	1	2	yes	—
966	#107	C₂³×C₂₃	1	2	yes	—
967	#107	C₂³×C₂₃	1	2	yes	—
968	#107	C₂³×C₂₃	1	2	yes	—
969	#107	C₂³×C₂₃	1	2	yes	—
970	#107	C₂³×C₂₃	1	2	yes	—
971	#107	C₂³×C₂₃	1	2	yes	—
972	#107	C₂³×C₂₃	1	2	yes	—
973	#107	C₂³×C₂₃	1	2	yes	—
974	#106	C₂³×C₂₃	1	2	yes	—
975	#106	C₂³×C₂₃	1	2	yes	—
976	#106	C₂³×C₂₃	1	2	yes	—
977	#106	C₂³×C₂₃	1	2	yes	—
978	#106	C₂³×C₂₃	1	2	yes	—
979	#106	C₂³×C₂₃	1	2	yes	—
980	#106	C₂³×C₂₃	1	2	yes	—
981	#106	C₂³×C₂₃	1	2	yes	—
982	#106	C₂³×C₂₃	1	2	yes	—
983	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
984	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
985	#103	C₂³×C₂₃	1	2	yes	—
986	#103	C₂³×C₂₃	1	2	yes	—
987	#103	C₂³×C₂₃	1	2	yes	—
988	#102	C₂³×C₂₃	1	2	yes	—
989	#102	C₂³×C₂₃	1	2	yes	—
990	#102	C₂³×C₂₃	1	2	yes	—
991	#102	C₂³×C₂₃	1	2	yes	—
992	#102	C₂³×C₂₃	1	2	yes	—
993	#102	C₂³×C₂₃	1	2	yes	—
994	#102	C₂³×C₂₃	1	2	yes	—
995	#102	C₂³×C₂₃	1	2	yes	—
996	#102	C₂³×C₂₃	1	2	yes	—
997	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
998	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
999	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1000	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
1001	#97	C₂³×C₂₃	1	2	yes	—
1002	C₄×C₈	C₂³×C₂₃	1	2	yes	—
1003	C₂₃	#61255	1	1	yes	characteristic, direct product factor, Sylow
1004	C₂⁴	—	2	1	no	—
1005	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1006	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
1007	#41	—	2	2	no	—
1008	#41	—	2	2	no	—
1009	#41	—	4	4	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	—	2	1	no	—
1012	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	2	no	—
1025	C₂×D₄	—	4	2	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	—	8	2	no	—
1028	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1030	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1031	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1032	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1033	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	2	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	2	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	8	2	no	—
1053	C₂²×C₄	—	8	2	no	—
1054	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1067	SD₁₆	—	2	4	no	—
1068	D₈	—	2	4	no	—
1069	M₁₆	—	2	2	no	—
1070	M₁₆	—	2	2	no	—
1071	M₁₆	—	2	2	no	—
1072	M₁₆	—	2	4	no	—
1073	M₁₆	—	2	4	no	—
1074	M₁₆	#41×C₂₃	1	4	yes	complemented
1075	C₂×C₈	—	2	4	no	—
1076	C₂×C₈	—	2	4	no	—
1077	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1080	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1108	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1109	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1111	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1112	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1113	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1114	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1116	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1117	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1118	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1147	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1148	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1149	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1150	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1152	C₄²	—	2	1	no	—
1153	C₄²	—	2	1	no	—
1154	C₄²	—	2	1	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	1	no	—
1157	C₄²	—	2	1	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	—	2	2	no	—
1160	C₄²	—	2	1	no	—
1161	C₄²	—	2	1	no	—
1162	C₄²	—	2	1	no	—
1163	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1164	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1165	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1166	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1167	C₂³	—	2	2	no	—
1168	C₂³	—	2	2	no	—
1169	C₂³	—	2	2	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	4	1	no	—
1173	C₂³	—	4	1	no	—
1174	C₂³	—	4	1	no	—
1175	C₂³	—	4	2	no	—
1176	C₂³	—	4	2	no	—
1177	C₂³	—	4	2	no	—
1178	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1179	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1180	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1181	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1182	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	1	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	8	1	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	2	2	no	—
1189	D₄	—	2	1	no	—
1190	D₄	—	2	2	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	1	no	—
1193	D₄	—	4	1	no	—
1194	D₄	—	4	1	no	—
1195	D₄	—	4	4	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	4	4	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	8	2	no	—
1202	D₄	—	8	2	no	—
1203	D₄	—	8	1	no	—
1204	D₄	—	8	1	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	4	1	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	2	no	—
1238	C₂×C₄	—	8	2	no	—
1239	C₂×C₄	—	8	2	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	1	no	—
1244	C₂×C₄	—	8	1	no	—
1245	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1251	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1252	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1254	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1255	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1256	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₈	—	2	2	no	—
1260	C₈	C₂×#41×C₂₃	1	4	yes	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	4	4	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	1	no	—
1278	C₂²	—	4	2	no	—
1279	C₂²	—	4	2	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	8	2	no	—
1282	C₂²	—	8	4	no	—
1283	C₂²	C₂₃×#547	1	2	yes	—
1284	C₂²	C₂₃×#575	1	2	yes	—
1285	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	2	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	2	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	C₂₃×#547	1	2	yes	—
1305	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1306	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1307	C₂	—	2	2	no	—
1308	C₂	—	2	2	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	4	1	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	8	2	no	—
1313	C₂	—	8	1	no	—
1314	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
1315	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1316	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3475	C₂	semidirect
2. C₂×C₂₃×#553	C₂	semidirect
3. C₂₃×#3355	C₂	semidirect
4. C₂₃×#3351	C₂	semidirect
5. C₂₃×#3350	C₂	semidirect
6. C₂₃×#3347	C₂	semidirect
7. C₂₃×#3346	C₂	semidirect
8. C₂₃×#3345	C₂	semidirect
9. C₂₃×#3339	C₂	semidirect
10. C₂₃×#3337	C₂	semidirect
11. C₂₃×#3166	C₂	semidirect
12. C₂₃×#3094	C₂	semidirect
13. C₂₃×#3094	C₂	semidirect
14. C₂₃×#3093	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂₃×#3080	C₂	semidirect
17. C₂₃×#3077	C₂	semidirect
18. C₂₃×#3055	C₂	semidirect
19. C₂₃×#3055	C₂	semidirect
20. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
21. D₄×M₁₆×C₂₃	C₂	semidirect
22. C₂₃×#2911	C₂	semidirect
23. C₂×C₂₃×#428	C₂	semidirect
27. C₂₃×#556	C₂²	semidirect
28. C₂₃×#555	C₂²	semidirect
29. C₂₃×#554	C₂²	semidirect
38. C₂₃×#553	C₂²	semidirect
39. C₂₃×#553	C₂²	semidirect
41. C₂₃×#552	C₂²	semidirect
42. C₂₃×#552	C₂²	semidirect
45. C₂₃×#547	C₂²	semidirect
68. C₂₃×#501	C₂²	semidirect
69. C₂₃×#501	C₂²	semidirect
70. C₂₃×#499	C₂²	semidirect
71. C₂₃×#499	C₂²	semidirect
72. C₂₃×#485	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
74. C₂₃×#484	C₂²	semidirect
75. C₂₃×#483	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#482	C₂²	semidirect
78. C₂₃×#482	C₂²	semidirect
79. C₂₃×#482	C₂²	semidirect
80. C₂₃×#482	C₂²	semidirect
81. C₂₃×#482	C₂²	semidirect
82. C₂₃×#481	C₂²	semidirect
83. C₂₃×#481	C₂²	semidirect
84. C₂₃×#481	C₂²	semidirect
85. C₂₃×#480	C₂²	semidirect
86. C₂₃×#480	C₂²	semidirect
87. C₂₃×#480	C₂²	semidirect
88. C₂₃×#479	C₂²	semidirect
89. C₂₃×#479	C₂²	semidirect
90. C₂₃×#478	C₂²	semidirect
91. C₂₃×#478	C₂²	semidirect
92. C₂₃×#478	C₂²	semidirect
93. C₂₃×#478	C₂²	semidirect
94. C₂₃×#476	C₂²	semidirect
95. C₂₃×#474	C₂²	semidirect
96. C₂₃×#469	C₂²	semidirect
97. C₂₃×#469	C₂²	semidirect
98. C₂₃×#468	C₂²	semidirect
99. C₂₃×#468	C₂²	semidirect
100. C₂₃×#466	C₂²	semidirect
101. C₂₃×#466	C₂²	semidirect
102. C₂₃×#465	C₂²	semidirect
103. C₂₃×#465	C₂²	semidirect
104. C₂₃×#442	C₂²	semidirect
105. C₂₃×#440	C₂²	semidirect
106. C₄×SD₁₆×C₂₃	C₂²	semidirect
107. C₄×D₈×C₂₃	C₂²	semidirect
108. C₂₃×#436	C₂²	semidirect
109. C₂₃×#435	C₂²	semidirect
110. C₂₃×#435	C₂²	semidirect
111. C₈×D₄×C₂₃	C₂²	semidirect
121. C₂₃×#428	C₂²	semidirect
122. C₂₃×#428	C₂²	semidirect
123. C₂₃×#428	C₂²	semidirect
124. C₂₃×#428	C₂²	semidirect
125. C₂₃×#427	C₂²	semidirect
126. C₂₃×#427	C₂²	semidirect
127. C₂×C₂₃×#107	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
415. M₁₆×C₂₃	#41	semidirect
508. #61255	C₂₃	direct (N × H)
603. #3475	C₂×C₂₃	semidirect
604. C₂×#553	C₂×C₂₃	semidirect
605. #3355	C₂×C₂₃	semidirect
606. #3351	C₂×C₂₃	semidirect
607. #3350	C₂×C₂₃	semidirect
608. #3347	C₂×C₂₃	semidirect
609. #3346	C₂×C₂₃	semidirect
610. #3345	C₂×C₂₃	semidirect
611. #3339	C₂×C₂₃	semidirect
612. #3337	C₂×C₂₃	semidirect
613. #3166	C₂×C₂₃	semidirect
614. #3094	C₂×C₂₃	semidirect
615. #3094	C₂×C₂₃	semidirect
616. #3093	C₂×C₂₃	semidirect
617. #3092	C₂×C₂₃	semidirect
618. #3080	C₂×C₂₃	semidirect
619. #3077	C₂×C₂₃	semidirect
620. #3055	C₂×C₂₃	semidirect
621. #3055	C₂×C₂₃	semidirect
622. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
623. D₄×M₁₆	C₂×C₂₃	semidirect
624. #2911	C₂×C₂₃	semidirect
625. C₂×#428	C₂×C₂₃	semidirect
675. #556	C₂²×C₂₃	semidirect
676. #555	C₂²×C₂₃	semidirect
677. #554	C₂²×C₂₃	semidirect
686. #553	C₂²×C₂₃	semidirect
687. #553	C₂²×C₂₃	semidirect
689. #552	C₂²×C₂₃	semidirect
690. #552	C₂²×C₂₃	semidirect
693. #547	C₂²×C₂₃	semidirect
716. #501	C₂²×C₂₃	semidirect
717. #501	C₂²×C₂₃	semidirect
718. #499	C₂²×C₂₃	semidirect
719. #499	C₂²×C₂₃	semidirect
720. #485	C₂²×C₂₃	semidirect
721. #485	C₂²×C₂₃	semidirect
722. #484	C₂²×C₂₃	semidirect
723. #483	C₂²×C₂₃	semidirect
724. #482	C₂²×C₂₃	semidirect
725. #482	C₂²×C₂₃	semidirect
726. #482	C₂²×C₂₃	semidirect
727. #482	C₂²×C₂₃	semidirect
728. #482	C₂²×C₂₃	semidirect
729. #482	C₂²×C₂₃	semidirect
730. #481	C₂²×C₂₃	semidirect
731. #481	C₂²×C₂₃	semidirect
732. #481	C₂²×C₂₃	semidirect
733. #480	C₂²×C₂₃	semidirect
734. #480	C₂²×C₂₃	semidirect
735. #480	C₂²×C₂₃	semidirect
736. #479	C₂²×C₂₃	semidirect
737. #479	C₂²×C₂₃	semidirect
738. #478	C₂²×C₂₃	semidirect
739. #478	C₂²×C₂₃	semidirect
740. #478	C₂²×C₂₃	semidirect
741. #478	C₂²×C₂₃	semidirect
742. #476	C₂²×C₂₃	semidirect
743. #474	C₂²×C₂₃	semidirect
744. #469	C₂²×C₂₃	semidirect
745. #469	C₂²×C₂₃	semidirect
746. #468	C₂²×C₂₃	semidirect
747. #468	C₂²×C₂₃	semidirect
748. #466	C₂²×C₂₃	semidirect
749. #466	C₂²×C₂₃	semidirect
750. #465	C₂²×C₂₃	semidirect
751. #465	C₂²×C₂₃	semidirect
752. #442	C₂²×C₂₃	semidirect
753. #440	C₂²×C₂₃	semidirect
754. C₄×SD₁₆	C₂²×C₂₃	semidirect
755. C₄×D₈	C₂²×C₂₃	semidirect
756. #436	C₂²×C₂₃	semidirect
757. #435	C₂²×C₂₃	semidirect
758. #435	C₂²×C₂₃	semidirect
759. C₈×D₄	C₂²×C₂₃	semidirect
769. #428	C₂²×C₂₃	semidirect
770. #428	C₂²×C₂₃	semidirect
771. #428	C₂²×C₂₃	semidirect
772. #428	C₂²×C₂₃	semidirect
773. #427	C₂²×C₂₃	semidirect
774. #427	C₂²×C₂₃	semidirect
775. C₂×#107	C₂²×C₂₃	semidirect
776. C₂×#106	C₂²×C₂₃	semidirect
1003. C₂₃	#61255	direct (N × H)
1074. M₁₆	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3475	2
C₂×C₂₃×#553	2
C₂₃×#3355	2
C₂₃×#3351	2
C₂₃×#3350	2
C₂₃×#3347	2
C₂₃×#3346	2
C₂₃×#3345	2
C₂₃×#3339	2
C₂₃×#3337	2
C₂₃×#3166	2
C₂₃×#3094	2
C₂₃×#3093	2
C₂₃×#3092	2
C₂₃×#3080	2
C₂₃×#3077	2
C₂₃×#3055	2
C₄×C₂₃×AGL(1,ℤ/8)	2
D₄×M₁₆×C₂₃	2
C₂₃×#2911	2
C₂×C₂₃×#428	2
#61255	23

Subgroups — C23×#61255 #19208881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61255 #19208881