Subgroups — C₂₃×#61449 #19209075

Order 5888.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3347	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3309	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3268	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3100	C₂	1	2	yes	maximal, complemented
21	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
23	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
26	C₂₃×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#555	—	2	1	no	—
29	C₂₃×#555	—	2	2	no	—
30	C₂₃×#555	C₂²	1	1	yes	characteristic
31	C₂₃×#555	C₂²	1	2	yes	complemented
32	C₂₃×#554	C₂²	1	1	yes	characteristic
33	C₂₃×#554	C₂²	1	1	yes	characteristic
34	C₂₃×#553	—	2	1	no	—
35	C₂₃×#553	C₂²	1	2	yes	—
36	C₂₃×#551	—	2	2	no	—
37	C₂₃×#550	—	2	1	no	—
38	C₂₃×#550	C₂²	1	1	yes	characteristic
39	C₂₃×#550	C₂²	1	2	yes	complemented
40	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#546	C₂²	1	2	yes	—
43	D₄²×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#532	—	2	1	no	—
45	C₂₃×#532	—	2	2	no	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#532	C₂²	1	2	yes	complemented
49	C₂₃×#529	—	2	1	no	—
50	C₂₃×#529	C₂²	1	2	yes	—
51	C₂₃×#525	—	2	2	no	—
52	C₄×#41×C₂₃	—	2	1	no	—
53	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₂₃	—	2	1	no	—
58	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
59	C₂₃×#501	C₂²	1	2	yes	complemented
60	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#496	C₂²	1	2	yes	complemented
62	C₂₃×#493	C₂²	1	1	yes	characteristic
63	C₂₃×#490	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#486	C₂²	1	1	yes	characteristic
66	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#482	C₂²	1	2	yes	—
69	C₂₃×#482	C₂²	1	2	yes	complemented
70	C₂₃×#482	C₂²	1	2	yes	complemented
71	C₂₃×#480	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#476	C₂²	1	1	yes	characteristic
78	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#474	C₂²	1	2	yes	—
80	C₂₃×#474	C₂²	1	2	yes	complemented
81	C₂₃×#469	C₂²	1	2	yes	—
82	C₂₃×#469	C₂²	1	2	yes	—
83	C₂₃×#468	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#466	C₂²	1	2	yes	complemented
86	C₂₃×#466	C₂²	1	2	yes	complemented
87	C₂₃×#464	C₂²	1	2	yes	complemented
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#460	C₂²	1	1	yes	characteristic
90	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#459	C₂²	1	2	yes	—
92	C₂₃×#459	C₂²	1	1	yes	characteristic
93	C₂₃×#459	C₂²	1	1	yes	characteristic
94	C₂₃×#459	C₂²	1	2	yes	complemented
95	C₂₃×#452	C₂²	1	2	yes	complemented
96	C₂₃×#449	C₂²	1	2	yes	—
97	C₂₃×#449	C₂²	1	2	yes	—
98	C₂₃×#449	C₂²	1	2	yes	complemented
99	C₂₃×#447	C₂²	1	2	yes	—
100	C₂₃×#447	C₂²	1	2	yes	—
101	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#442	C₂²	1	2	yes	—
104	C₂₃×#442	C₂²	1	2	yes	complemented
105	C₂₃×#440	C₂²	1	2	yes	—
106	C₂₃×#440	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
115	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₂₃	C₂²	1	2	yes	—
118	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
120	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic
122	C₂₃×#436	C₂²	1	1	yes	characteristic
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₂₃×#431	C₂²	1	2	yes	complemented
126	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#428	C₂²	1	2	yes	complemented
128	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#418	C₂²	1	2	yes	—
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂₃×#416	C₂²	1	1	yes	characteristic
132	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	—	2	2	no	—
138	C₂×#41×C₂₃	—	2	1	no	—
139	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
140	C₂×#41×C₂₃	C₂³	1	2	yes	—
141	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₂₃	—	2	1	no	—
144	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₂₃	—	2	2	no	—
146	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
147	C₂₃×#135	—	2	4	no	—
148	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₂₃	C₂³	1	2	yes	—
155	C₂×D₈×C₂₃	C₂³	1	2	yes	—
156	C₂×D₈×C₂₃	C₂³	1	2	yes	—
157	C₂×D₈×C₂₃	C₂³	1	2	yes	—
158	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	—	2	1	no	—
163	C₂₃×C₄⋊Q₈	—	2	2	no	—
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₂₃×#127	—	2	1	no	—
168	C₂₃×#127	—	2	2	no	—
169	C₂₃×#127	C₂³	1	1	yes	characteristic
170	C₂₃×#127	C₂³	1	2	yes	—
171	C₂₃×#127	C₂³	1	1	yes	characteristic
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#126	—	2	2	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	C₂³	1	2	yes	—
176	C₂₃×#124	—	2	1	no	—
177	C₂₃×#124	—	2	2	no	—
178	C₂₃×#124	—	2	2	no	—
179	C₂₃×#124	—	2	2	no	—
180	C₂₃×#124	—	2	1	no	—
181	C₂₃×#124	—	2	1	no	—
182	C₂₃×#124	—	2	2	no	—
183	C₂₃×#124	C₂³	1	2	yes	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	—	2	2	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	1	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×#121	—	2	1	no	—
193	C₂₃×#121	—	2	2	no	—
194	C₂₃×#121	—	2	2	no	—
195	C₂₃×#121	—	2	1	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	1	no	—
198	C₂₃×#121	—	2	1	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	1	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#121	C₂³	1	2	yes	—
209	C₂₃×#121	C₂³	1	2	yes	—
210	C₂₃×#120	—	2	2	no	—
211	C₂₃×#120	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	1	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	—	2	2	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	2	no	—
235	C₄×D₄×C₂₃	—	2	1	no	—
236	C₄×D₄×C₂₃	—	2	2	no	—
237	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
238	C₄×D₄×C₂₃	D₄	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	2	yes	—
242	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₂₃	C₂³	1	2	yes	—
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₃	C₂³	1	2	yes	—
247	C₄×D₄×C₂₃	C₂³	1	2	yes	—
248	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₂₃	C₂³	1	2	yes	—
250	C₂₃×#117	—	2	1	no	—
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	1	no	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	—	2	2	no	—
255	C₂₃×#117	—	2	2	no	—
256	C₂₃×#117	D₄	1	2	yes	—
257	C₂₃×#117	D₄	1	1	yes	characteristic
258	C₂₃×#117	C₂³	1	1	yes	characteristic
259	C₂₃×#117	C₂³	1	2	yes	—
260	C₂₃×#117	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄²×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂×C₄²×C₂₃	—	2	2	no	—
268	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	1	yes	characteristic
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	2	yes	—
273	C₂₃×#107	C₂³	1	2	yes	—
274	C₂₃×#107	C₂³	1	2	yes	—
275	C₂₃×#107	C₂³	1	2	yes	—
276	C₂₃×#106	C₂³	1	1	yes	characteristic
277	C₂₃×#106	C₂³	1	1	yes	characteristic
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#102	C₂³	1	1	yes	characteristic
291	C₂₃×#102	C₂³	1	1	yes	characteristic
292	C₂₃×#102	C₂³	1	1	yes	characteristic
293	C₂₃×#102	C₂³	1	1	yes	characteristic
294	C₂₃×#102	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	C₂⁴×C₂₃	—	2	2	no	—
315	#41×C₂₃	—	2	2	no	—
316	#41×C₂₃	—	2	4	no	—
317	#41×C₂₃	—	2	2	no	—
318	#41×C₂₃	—	4	2	no	—
319	#41×C₂₃	—	4	1	no	—
320	#41×C₂₃	—	4	1	no	—
321	#41×C₂₃	—	4	2	no	—
322	#41×C₂₃	—	4	4	no	—
323	#41×C₂₃	—	8	4	no	—
324	#41×C₂₃	—	8	2	no	—
325	#41×C₂₃	—	8	2	no	—
326	C₂×Q₈×C₂₃	—	2	1	no	—
327	C₂×Q₈×C₂₃	—	2	2	no	—
328	C₂×Q₈×C₂₃	—	2	1	no	—
329	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₂₃	—	2	4	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	2	no	—
339	C₂×D₄×C₂₃	—	2	2	no	—
340	C₂×D₄×C₂₃	—	2	2	no	—
341	C₂×D₄×C₂₃	—	2	2	no	—
342	C₂×D₄×C₂₃	—	2	1	no	—
343	C₂×D₄×C₂₃	—	2	2	no	—
344	C₂×D₄×C₂₃	—	2	1	no	—
345	C₂×D₄×C₂₃	—	2	1	no	—
346	C₂×D₄×C₂₃	—	2	2	no	—
347	C₂×D₄×C₂₃	—	2	1	no	—
348	C₂×D₄×C₂₃	—	4	2	no	—
349	C₂×D₄×C₂₃	—	4	4	no	—
350	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
354	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	2	1	no	—
358	C₂²×C₄×C₂₃	—	2	1	no	—
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	2	no	—
361	C₂²×C₄×C₂₃	—	2	2	no	—
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	1	no	—
365	C₂²×C₄×C₂₃	—	2	2	no	—
366	C₂²×C₄×C₂₃	—	2	2	no	—
367	C₂²×C₄×C₂₃	—	2	2	no	—
368	C₂²×C₄×C₂₃	—	2	2	no	—
369	C₂²×C₄×C₂₃	—	8	4	no	—
370	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
376	Q₁₆×C₂₃	—	2	2	no	—
377	SD₁₆×C₂₃	—	2	4	no	—
378	SD₁₆×C₂₃	—	2	2	no	—
379	SD₁₆×C₂₃	—	4	2	no	—
380	SD₁₆×C₂₃	#41	1	4	yes	complemented
381	D₈×C₂₃	—	2	2	no	—
382	D₈×C₂₃	—	2	4	no	—
383	D₈×C₂₃	—	2	4	no	—
384	D₈×C₂₃	—	4	2	no	—
385	D₈×C₂₃	—	4	2	no	—
386	M₁₆×C₂₃	—	2	4	no	—
387	M₁₆×C₂₃	—	4	2	no	—
388	C₂×C₈×C₂₃	—	2	2	no	—
389	C₂×C₈×C₂₃	—	4	1	no	—
390	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	1	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	1	no	—
404	C₄⋊C₄×C₂₃	—	2	1	no	—
405	C₄⋊C₄×C₂₃	—	2	1	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	—	2	2	no	—
408	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	1	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	1	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	1	no	—
434	C₂²⋊C₄×C₂₃	—	2	1	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	2	no	—
437	C₂²⋊C₄×C₂₃	—	2	2	no	—
438	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	—	2	1	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	1	no	—
447	C₄²×C₂₃	—	2	1	no	—
448	C₄²×C₂₃	—	2	1	no	—
449	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₂₃	C₂×D₄	1	2	yes	—
451	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₂₃	C₂×D₄	1	2	yes	—
453	C₄²×C₂₃	C₂⁴	1	2	yes	—
454	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
456	#61449	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂³×C₂₃	—	2	1	no	—
458	C₂³×C₂₃	—	2	2	no	—
459	C₂³×C₂₃	—	2	2	no	—
460	C₂³×C₂₃	—	2	1	no	—
461	C₂³×C₂₃	—	4	4	no	—
462	C₂³×C₂₃	—	4	4	no	—
463	C₂³×C₂₃	—	8	2	no	—
464	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
465	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₂₃	—	2	2	no	—
467	Q₈×C₂₃	—	2	1	no	—
468	Q₈×C₂₃	—	2	1	no	—
469	Q₈×C₂₃	—	2	1	no	—
470	Q₈×C₂₃	—	8	2	no	—
471	Q₈×C₂₃	—	8	1	no	—
472	Q₈×C₂₃	—	8	1	no	—
473	Q₈×C₂₃	C₂×#41	1	2	yes	—
474	D₄×C₂₃	—	2	2	no	—
475	D₄×C₂₃	—	2	2	no	—
476	D₄×C₂₃	—	2	2	no	—
477	D₄×C₂₃	—	2	1	no	—
478	D₄×C₂₃	—	2	1	no	—
479	D₄×C₂₃	—	2	2	no	—
480	D₄×C₂₃	—	2	1	no	—
481	D₄×C₂₃	—	2	2	no	—
482	D₄×C₂₃	—	4	2	no	—
483	D₄×C₂₃	—	4	4	no	—
484	D₄×C₂₃	—	4	2	no	—
485	D₄×C₂₃	—	4	4	no	—
486	D₄×C₂₃	—	4	4	no	—
487	D₄×C₂₃	—	4	2	no	—
488	D₄×C₂₃	—	4	4	no	—
489	D₄×C₂₃	—	4	2	no	—
490	D₄×C₂₃	—	4	2	no	—
491	D₄×C₂₃	—	8	2	no	—
492	D₄×C₂₃	—	8	1	no	—
493	D₄×C₂₃	—	8	1	no	—
494	D₄×C₂₃	—	8	2	no	—
495	D₄×C₂₃	—	8	2	no	—
496	D₄×C₂₃	—	8	2	no	—
497	D₄×C₂₃	—	8	2	no	—
498	D₄×C₂₃	C₂×#41	1	2	yes	—
499	C₂×C₄×C₂₃	—	2	1	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	4	no	—
502	C₂×C₄×C₂₃	—	2	2	no	—
503	C₂×C₄×C₂₃	—	2	1	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	2	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	1	no	—
510	C₂×C₄×C₂₃	—	2	1	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	2	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	4	2	no	—
515	C₂×C₄×C₂₃	—	4	2	no	—
516	C₂×C₄×C₂₃	—	4	4	no	—
517	C₂×C₄×C₂₃	—	4	2	no	—
518	C₂×C₄×C₂₃	—	4	4	no	—
519	C₂×C₄×C₂₃	—	4	2	no	—
520	C₂×C₄×C₂₃	—	4	2	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	4	no	—
523	C₂×C₄×C₂₃	—	4	2	no	—
524	C₂×C₄×C₂₃	—	4	4	no	—
525	C₂×C₄×C₂₃	—	8	2	no	—
526	C₂×C₄×C₂₃	—	8	2	no	—
527	C₂×C₄×C₂₃	—	8	2	no	—
528	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
537	C₈×C₂₃	—	2	1	no	—
538	C₈×C₂₃	—	2	2	no	—
539	C₈×C₂₃	—	2	1	no	—
540	C₈×C₂₃	—	2	1	no	—
541	C₈×C₂₃	—	2	2	no	—
542	C₈×C₂₃	C₂×#41	1	2	yes	—
543	#3483	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3481	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#3399	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3385	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3375	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3366	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3357	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#3347	C₂×C₂₃	1	2	yes	complemented
551	#3333	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#3319	C₂×C₂₃	1	2	yes	complemented
554	#3309	C₂×C₂₃	1	2	yes	complemented
555	#3274	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3268	C₂×C₂₃	1	2	yes	complemented
557	#3171	C₂×C₂₃	1	2	yes	complemented
558	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
561	#3102	C₂×C₂₃	1	2	yes	complemented
562	#3100	C₂×C₂₃	1	2	yes	complemented
563	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
564	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
565	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
566	C₂²×C₂₃	—	2	1	no	—
567	C₂²×C₂₃	—	2	2	no	—
568	C₂²×C₂₃	—	2	2	no	—
569	C₂²×C₂₃	—	2	1	no	—
570	C₂²×C₂₃	—	2	2	no	—
571	C₂²×C₂₃	—	2	2	no	—
572	C₂²×C₂₃	—	2	1	no	—
573	C₂²×C₂₃	—	4	1	no	—
574	C₂²×C₂₃	—	4	1	no	—
575	C₂²×C₂₃	—	4	2	no	—
576	C₂²×C₂₃	—	4	1	no	—
577	C₂²×C₂₃	—	4	2	no	—
578	C₂²×C₂₃	—	4	2	no	—
579	C₂²×C₂₃	—	4	1	no	—
580	C₂²×C₂₃	—	4	2	no	—
581	C₂²×C₂₃	—	4	2	no	—
582	C₂²×C₂₃	—	4	1	no	—
583	C₂²×C₂₃	—	4	2	no	—
584	C₂²×C₂₃	—	8	8	no	—
585	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	2	no	—
588	C₄×C₂₃	—	2	2	no	—
589	C₄×C₂₃	—	2	1	no	—
590	C₄×C₂₃	—	2	2	no	—
591	C₄×C₂₃	—	2	2	no	—
592	C₄×C₂₃	—	2	1	no	—
593	C₄×C₂₃	—	4	1	no	—
594	C₄×C₂₃	—	4	1	no	—
595	C₄×C₂₃	—	4	1	no	—
596	C₄×C₂₃	—	4	1	no	—
597	C₄×C₂₃	—	4	2	no	—
598	C₄×C₂₃	—	4	1	no	—
599	C₄×C₂₃	—	4	2	no	—
600	C₄×C₂₃	#575	1	2	yes	—
601	C₄×C₂₃	#576	1	2	yes	—
602	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
603	C₄×C₂₃	#585	1	1	yes	characteristic
604	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
605	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
606	#559	C₂²×C₂₃	1	1	yes	characteristic
607	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
608	#555	—	2	1	no	—
609	#555	—	2	2	no	—
610	#555	C₂²×C₂₃	1	1	yes	characteristic
611	#555	C₂²×C₂₃	1	2	yes	complemented
612	#554	C₂²×C₂₃	1	1	yes	characteristic
613	#554	C₂²×C₂₃	1	1	yes	characteristic
614	#553	—	2	1	no	—
615	#553	C₂²×C₂₃	1	2	yes	—
616	#551	—	2	2	no	—
617	#550	—	2	1	no	—
618	#550	C₂²×C₂₃	1	1	yes	characteristic
619	#550	C₂²×C₂₃	1	2	yes	complemented
620	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	#546	—	2	1	no	—
622	#546	C₂²×C₂₃	1	2	yes	—
623	D₄²	C₂²×C₂₃	1	1	yes	characteristic
624	#532	—	2	1	no	—
625	#532	—	2	2	no	—
626	#532	C₂²×C₂₃	1	1	yes	characteristic
627	#532	C₂²×C₂₃	1	2	yes	complemented
628	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#529	—	2	1	no	—
630	#529	C₂²×C₂₃	1	2	yes	—
631	#525	—	2	2	no	—
632	C₄×#41	—	2	1	no	—
633	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
634	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
635	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
636	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
637	C₂×C₄×D₄	—	2	1	no	—
638	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
639	#501	C₂²×C₂₃	1	2	yes	complemented
640	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	#496	C₂²×C₂₃	1	2	yes	complemented
642	#493	C₂²×C₂₃	1	1	yes	characteristic
643	#490	C₂²×C₂₃	1	2	yes	complemented
644	#489	C₂²×C₂₃	1	2	yes	complemented
645	#486	C₂²×C₂₃	1	1	yes	characteristic
646	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	#485	C₂²×C₂₃	1	2	yes	complemented
648	#482	C₂²×C₂₃	1	2	yes	—
649	#482	C₂²×C₂₃	1	2	yes	complemented
650	#482	C₂²×C₂₃	1	2	yes	complemented
651	#480	C₂²×C₂₃	1	2	yes	complemented
652	#480	C₂²×C₂₃	1	2	yes	complemented
653	#479	C₂²×C₂₃	1	2	yes	complemented
654	#478	C₂²×C₂₃	1	2	yes	complemented
655	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	#476	C₂²×C₂₃	1	1	yes	characteristic
658	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#474	C₂²×C₂₃	1	2	yes	—
660	#474	C₂²×C₂₃	1	2	yes	complemented
661	#469	C₂²×C₂₃	1	2	yes	—
662	#469	C₂²×C₂₃	1	2	yes	—
663	#468	C₂²×C₂₃	1	2	yes	complemented
664	#468	C₂²×C₂₃	1	2	yes	complemented
665	#466	C₂²×C₂₃	1	2	yes	complemented
666	#466	C₂²×C₂₃	1	2	yes	complemented
667	#464	C₂²×C₂₃	1	2	yes	complemented
668	#463	C₂²×C₂₃	1	2	yes	complemented
669	#460	C₂²×C₂₃	1	1	yes	characteristic
670	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#459	C₂²×C₂₃	1	2	yes	—
672	#459	C₂²×C₂₃	1	1	yes	characteristic
673	#459	C₂²×C₂₃	1	1	yes	characteristic
674	#459	C₂²×C₂₃	1	2	yes	complemented
675	#452	C₂²×C₂₃	1	2	yes	complemented
676	#449	C₂²×C₂₃	1	2	yes	—
677	#449	C₂²×C₂₃	1	2	yes	—
678	#449	C₂²×C₂₃	1	2	yes	complemented
679	#447	C₂²×C₂₃	1	2	yes	—
680	#447	C₂²×C₂₃	1	2	yes	—
681	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#442	C₂²×C₂₃	1	2	yes	—
684	#442	C₂²×C₂₃	1	2	yes	complemented
685	#440	C₂²×C₂₃	1	2	yes	—
686	#440	C₂²×C₂₃	1	2	yes	complemented
687	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
691	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
694	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
696	C₄×D₈	C₂²×C₂₃	1	2	yes	—
697	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
698	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
699	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
700	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
701	#436	C₂²×C₂₃	1	1	yes	characteristic
702	#436	C₂²×C₂₃	1	1	yes	characteristic
703	#435	C₂²×C₂₃	1	2	yes	complemented
704	#435	C₂²×C₂₃	1	2	yes	complemented
705	#431	C₂²×C₂₃	1	2	yes	complemented
706	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#428	C₂²×C₂₃	1	2	yes	complemented
708	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	#418	C₂²×C₂₃	1	2	yes	—
710	#417	C₂²×C₂₃	1	2	yes	complemented
711	#416	C₂²×C₂₃	1	1	yes	characteristic
712	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
714	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
715	C₂×C₂₃	—	4	1	no	—
716	C₂×C₂₃	—	4	2	no	—
717	C₂×C₂₃	—	4	2	no	—
718	C₂×C₂₃	—	8	2	no	—
719	C₂×C₂₃	—	8	1	no	—
720	C₂×C₂₃	—	8	2	no	—
721	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
722	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
723	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	2	2	no	—
727	C₂×#41	—	2	1	no	—
728	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
729	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×#41	C₂³×C₂₃	1	2	yes	—
731	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
732	C₂²×D₄	—	2	1	no	—
733	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
734	C₂³×C₄	—	2	2	no	—
735	AGL(1,ℤ/8)	—	2	8	no	—
736	#135	—	2	4	no	—
737	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×D₈	C₂³×C₂₃	1	2	yes	—
744	C₂×D₈	C₂³×C₂₃	1	2	yes	—
745	C₂×D₈	C₂³×C₂₃	1	2	yes	—
746	C₂×D₈	C₂³×C₂₃	1	2	yes	—
747	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
748	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
749	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
751	C₄⋊Q₈	—	2	1	no	—
752	C₄⋊Q₈	—	2	2	no	—
753	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
756	#127	—	2	1	no	—
757	#127	—	2	2	no	—
758	#127	C₂³×C₂₃	1	1	yes	characteristic
759	#127	C₂³×C₂₃	1	1	yes	characteristic
760	#127	C₂³×C₂₃	1	2	yes	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	C₂³×C₂₃	1	2	yes	—
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	C₂³×C₂₃	1	2	yes	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	C₂³×C₂₃	1	2	yes	—
795	#121	C₂³×C₂₃	1	2	yes	—
796	#121	C₂³×C₂₃	1	2	yes	—
797	#121	C₂³×C₂₃	1	2	yes	—
798	#121	C₂³×C₂₃	1	2	yes	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
808	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
827	C₄×D₄	D₄×C₂₃	1	2	yes	—
828	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₂₃	1	2	yes	—
830	C₄×D₄	C₂³×C₂₃	1	2	yes	—
831	C₄×D₄	C₂³×C₂₃	1	2	yes	—
832	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₂₃	1	2	yes	—
834	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₂₃	1	2	yes	—
837	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₂₃	1	2	yes	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	D₄×C₂₃	1	2	yes	—
846	#117	D₄×C₂₃	1	1	yes	characteristic
847	#117	C₂³×C₂₃	1	1	yes	characteristic
848	#117	C₂³×C₂₃	1	2	yes	—
849	#117	C₂³×C₂₃	1	1	yes	characteristic
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	—	2	2	no	—
857	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
858	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
859	#107	C₂³×C₂₃	1	1	yes	characteristic
860	#107	C₂³×C₂₃	1	1	yes	characteristic
861	#107	C₂³×C₂₃	1	2	yes	—
862	#107	C₂³×C₂₃	1	2	yes	—
863	#107	C₂³×C₂₃	1	2	yes	—
864	#107	C₂³×C₂₃	1	2	yes	—
865	#106	C₂³×C₂₃	1	1	yes	characteristic
866	#106	C₂³×C₂₃	1	1	yes	characteristic
867	#106	C₂³×C₂₃	1	2	yes	—
868	#106	C₂³×C₂₃	1	2	yes	—
869	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
870	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
871	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
873	#103	C₂³×C₂₃	1	1	yes	characteristic
874	#103	C₂³×C₂₃	1	1	yes	characteristic
875	#103	C₂³×C₂₃	1	1	yes	characteristic
876	#103	C₂³×C₂₃	1	1	yes	characteristic
877	#103	C₂³×C₂₃	1	2	yes	—
878	#103	C₂³×C₂₃	1	2	yes	—
879	#102	C₂³×C₂₃	1	1	yes	characteristic
880	#102	C₂³×C₂₃	1	1	yes	characteristic
881	#102	C₂³×C₂₃	1	1	yes	characteristic
882	#102	C₂³×C₂₃	1	1	yes	characteristic
883	#102	C₂³×C₂₃	1	2	yes	—
884	#102	C₂³×C₂₃	1	2	yes	—
885	#102	C₂³×C₂₃	1	2	yes	—
886	#102	C₂³×C₂₃	1	2	yes	—
887	#102	C₂³×C₂₃	1	2	yes	—
888	#102	C₂³×C₂₃	1	2	yes	—
889	#102	C₂³×C₂₃	1	2	yes	—
890	#102	C₂³×C₂₃	1	2	yes	—
891	#102	C₂³×C₂₃	1	2	yes	—
892	#102	C₂³×C₂₃	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
896	#97	C₂³×C₂₃	1	2	yes	—
897	#97	C₂³×C₂₃	1	2	yes	—
898	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₂₃	1	2	yes	—
903	C₂₃	#61449	1	1	yes	characteristic, direct product factor, Sylow
904	C₂⁴	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	4	no	—
907	#41	—	2	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	1	no	—
910	#41	—	4	1	no	—
911	#41	—	4	2	no	—
912	#41	—	4	4	no	—
913	#41	—	8	4	no	—
914	#41	—	8	2	no	—
915	#41	—	8	2	no	—
916	C₂×Q₈	—	2	1	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
920	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
921	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
922	C₂×D₄	—	2	4	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
941	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
942	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
943	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
944	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	8	4	no	—
960	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
961	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
962	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
964	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	Q₁₆	—	2	2	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	2	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	#41×C₂₃	1	4	yes	complemented
971	D₈	—	2	2	no	—
972	D₈	—	2	4	no	—
973	D₈	—	2	4	no	—
974	D₈	—	4	2	no	—
975	D₈	—	4	2	no	—
976	M₁₆	—	2	4	no	—
977	M₁₆	—	4	2	no	—
978	C₂×C₈	—	2	2	no	—
979	C₂×C₈	—	4	1	no	—
980	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
984	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
985	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1040	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1041	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1043	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₂₃	1	2	yes	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	4	no	—
1051	C₂³	—	4	4	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1054	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	—	8	1	no	—
1061	Q₈	—	8	1	no	—
1062	Q₈	C₂×#41×C₂₃	1	2	yes	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	4	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	1	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	C₂×#41×C₂₃	1	2	yes	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	4	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1122	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1125	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1126	C₈	—	2	1	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₈	—	2	2	no	—
1131	C₈	C₂×#41×C₂₃	1	2	yes	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	8	8	no	—
1151	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	2	no	—
1166	C₄	C₂₃×#575	1	2	yes	—
1167	C₄	C₂₃×#576	1	2	yes	—
1168	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1169	C₄	C₂₃×#585	1	1	yes	characteristic
1170	C₂	—	4	2	no	—
1171	C₂	—	4	1	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	8	2	no	—
1174	C₂	—	8	2	no	—
1175	C₂	—	8	1	no	—
1176	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1177	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1178	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3483	C₂	semidirect
2. C₂₃×#3481	C₂	semidirect
3. C₂₃×#3399	C₂	semidirect
4. C₂₃×#3385	C₂	semidirect
5. C₂₃×#3375	C₂	semidirect
6. C₂₃×#3366	C₂	semidirect
7. C₂₃×#3357	C₂	semidirect
8. C₂₃×#3347	C₂	semidirect
9. C₂₃×#3333	C₂	semidirect
10. C₂₃×#3325	C₂	semidirect
11. C₂₃×#3319	C₂	semidirect
12. C₂₃×#3309	C₂	semidirect
13. C₂₃×#3274	C₂	semidirect
14. C₂₃×#3268	C₂	semidirect
15. C₂₃×#3171	C₂	semidirect
16. C₂₃×#3169	C₂	semidirect
17. C₂₃×#3106	C₂	semidirect
18. C₂₃×#3106	C₂	semidirect
19. C₂₃×#3102	C₂	semidirect
20. C₂₃×#3100	C₂	semidirect
21. C₂₃×#2965	C₂	semidirect
22. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₄×C₂₃×#135	C₂	semidirect
27. Q₈²×C₂₃	C₂²	semidirect
31. C₂₃×#555	C₂²	semidirect
39. C₂₃×#550	C₂²	semidirect
40. C₂₃×#550	C₂²	semidirect
47. C₂₃×#532	C₂²	semidirect
48. C₂₃×#532	C₂²	semidirect
55. C₄×#41×C₂₃	C₂²	semidirect
56. C₄×#41×C₂₃	C₂²	semidirect
59. C₂₃×#501	C₂²	semidirect
60. C₂₃×#500	C₂²	semidirect
61. C₂₃×#496	C₂²	semidirect
63. C₂₃×#490	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#480	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
78. C₂₃×#476	C₂²	semidirect
80. C₂₃×#474	C₂²	semidirect
83. C₂₃×#468	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#466	C₂²	semidirect
86. C₂₃×#466	C₂²	semidirect
87. C₂₃×#464	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
90. C₂₃×#460	C₂²	semidirect
94. C₂₃×#459	C₂²	semidirect
95. C₂₃×#452	C₂²	semidirect
98. C₂₃×#449	C₂²	semidirect
101. C₂₃×#446	C₂²	semidirect
102. C₂₃×#446	C₂²	semidirect
104. C₂₃×#442	C₂²	semidirect
106. C₂₃×#440	C₂²	semidirect
107. C₄×Q₁₆×C₂₃	C₂²	semidirect
108. C₄×Q₁₆×C₂₃	C₂²	semidirect
111. C₄×SD₁₆×C₂₃	C₂²	semidirect
112. C₄×SD₁₆×C₂₃	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₄×D₈×C₂₃	C₂²	semidirect
119. C₄×D₈×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₂₃×#431	C₂²	semidirect
126. C₂₃×#431	C₂²	semidirect
127. C₂₃×#428	C₂²	semidirect
128. C₂₃×#427	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
380. SD₁₆×C₂₃	#41	semidirect
456. #61449	C₂₃	direct (N × H)
543. #3483	C₂×C₂₃	semidirect
544. #3481	C₂×C₂₃	semidirect
545. #3399	C₂×C₂₃	semidirect
546. #3385	C₂×C₂₃	semidirect
547. #3375	C₂×C₂₃	semidirect
548. #3366	C₂×C₂₃	semidirect
549. #3357	C₂×C₂₃	semidirect
550. #3347	C₂×C₂₃	semidirect
551. #3333	C₂×C₂₃	semidirect
552. #3325	C₂×C₂₃	semidirect
553. #3319	C₂×C₂₃	semidirect
554. #3309	C₂×C₂₃	semidirect
555. #3274	C₂×C₂₃	semidirect
556. #3268	C₂×C₂₃	semidirect
557. #3171	C₂×C₂₃	semidirect
558. #3169	C₂×C₂₃	semidirect
559. #3106	C₂×C₂₃	semidirect
560. #3106	C₂×C₂₃	semidirect
561. #3102	C₂×C₂₃	semidirect
562. #3100	C₂×C₂₃	semidirect
563. #2965	C₂×C₂₃	semidirect
564. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
565. C₄×#135	C₂×C₂₃	semidirect
607. Q₈²	C₂²×C₂₃	semidirect
611. #555	C₂²×C₂₃	semidirect
619. #550	C₂²×C₂₃	semidirect
620. #550	C₂²×C₂₃	semidirect
627. #532	C₂²×C₂₃	semidirect
628. #532	C₂²×C₂₃	semidirect
635. C₄×#41	C₂²×C₂₃	semidirect
636. C₄×#41	C₂²×C₂₃	semidirect
639. #501	C₂²×C₂₃	semidirect
640. #500	C₂²×C₂₃	semidirect
641. #496	C₂²×C₂₃	semidirect
643. #490	C₂²×C₂₃	semidirect
644. #489	C₂²×C₂₃	semidirect
646. #486	C₂²×C₂₃	semidirect
647. #485	C₂²×C₂₃	semidirect
649. #482	C₂²×C₂₃	semidirect
650. #482	C₂²×C₂₃	semidirect
651. #480	C₂²×C₂₃	semidirect
652. #480	C₂²×C₂₃	semidirect
653. #479	C₂²×C₂₃	semidirect
654. #478	C₂²×C₂₃	semidirect
655. #477	C₂²×C₂₃	semidirect
656. #477	C₂²×C₂₃	semidirect
658. #476	C₂²×C₂₃	semidirect
660. #474	C₂²×C₂₃	semidirect
663. #468	C₂²×C₂₃	semidirect
664. #468	C₂²×C₂₃	semidirect
665. #466	C₂²×C₂₃	semidirect
666. #466	C₂²×C₂₃	semidirect
667. #464	C₂²×C₂₃	semidirect
668. #463	C₂²×C₂₃	semidirect
670. #460	C₂²×C₂₃	semidirect
674. #459	C₂²×C₂₃	semidirect
675. #452	C₂²×C₂₃	semidirect
678. #449	C₂²×C₂₃	semidirect
681. #446	C₂²×C₂₃	semidirect
682. #446	C₂²×C₂₃	semidirect
684. #442	C₂²×C₂₃	semidirect
686. #440	C₂²×C₂₃	semidirect
687. C₄×Q₁₆	C₂²×C₂₃	semidirect
688. C₄×Q₁₆	C₂²×C₂₃	semidirect
691. C₄×SD₁₆	C₂²×C₂₃	semidirect
692. C₄×SD₁₆	C₂²×C₂₃	semidirect
693. C₄×SD₁₆	C₂²×C₂₃	semidirect
694. C₄×SD₁₆	C₂²×C₂₃	semidirect
698. C₄×D₈	C₂²×C₂₃	semidirect
699. C₄×D₈	C₂²×C₂₃	semidirect
700. C₄×D₈	C₂²×C₂₃	semidirect
703. #435	C₂²×C₂₃	semidirect
704. #435	C₂²×C₂₃	semidirect
705. #431	C₂²×C₂₃	semidirect
706. #431	C₂²×C₂₃	semidirect
707. #428	C₂²×C₂₃	semidirect
708. #427	C₂²×C₂₃	semidirect
710. #417	C₂²×C₂₃	semidirect
712. #416	C₂²×C₂₃	semidirect
713. C₄×M₁₆	C₂²×C₂₃	semidirect
714. C₂×C₄×C₈	C₂²×C₂₃	semidirect
903. C₂₃	#61449	direct (N × H)
970. SD₁₆	#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×#3483	2
C₂₃×#3481	2
C₂₃×#3399	2
C₂₃×#3385	2
C₂₃×#3375	2
C₂₃×#3366	2
C₂₃×#3357	2
C₂₃×#3347	2
C₂₃×#3333	2
C₂₃×#3325	2
C₂₃×#3319	2
C₂₃×#3309	2
C₂₃×#3274	2
C₂₃×#3268	2
C₂₃×#3171	2
C₂₃×#3169	2
C₂₃×#3106	2
C₂₃×#3102	2
C₂₃×#3100	2
C₂₃×#2965	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₄×C₂₃×#135	2
#61449	23

Subgroups — C23×#61449 #19209075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61449 #19209075