Subgroups — C₂₃×#61437 #19209063

Order 5888.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1214 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	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3306	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, 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	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	—	2	1	no	—
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×D₈×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×#552	—	2	1	no	—
32	C₂₃×#552	C₂²	1	2	yes	complemented
33	C₂₃×#551	—	2	2	no	—
34	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#548	—	2	1	no	—
37	C₂₃×#547	C₂²	1	2	yes	—
38	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#546	—	2	2	no	—
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₂₃	C₂²	1	2	yes	—
44	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	2	yes	complemented
48	C₂₃×#529	—	2	2	no	—
49	C₂₃×#529	C₂²	1	2	yes	complemented
50	C₂₃×#525	—	2	1	no	—
51	C₂₃×#525	—	2	1	no	—
52	C₂₃×#525	—	2	2	no	—
53	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
58	C₂×C₂₃×#117	—	2	1	no	—
59	C₂₃×#501	C₂²	1	2	yes	complemented
60	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#496	C₂²	1	2	yes	complemented
62	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#490	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#484	C₂²	1	2	yes	complemented
68	C₂₃×#483	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	complemented
70	C₂₃×#482	C₂²	1	2	yes	complemented
71	C₂₃×#481	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#478	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#477	C₂²	1	2	yes	complemented
76	C₂₃×#476	C₂²	1	2	yes	complemented
77	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#469	C₂²	1	2	yes	complemented
82	C₂₃×#469	C₂²	1	2	yes	complemented
83	C₂₃×#468	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#465	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#460	C₂²	1	2	yes	complemented
92	C₂₃×#459	C₂²	1	2	yes	complemented
93	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#450	C₂²	1	2	yes	—
96	C₂₃×#450	C₂²	1	2	yes	complemented
97	C₂₃×#449	C₂²	1	2	yes	complemented
98	C₂₃×#449	C₂²	1	2	yes	complemented
99	C₂₃×#447	C₂²	1	2	yes	—
100	C₂₃×#447	C₂²	1	2	yes	complemented
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	complemented
106	C₂₃×#440	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
111	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
117	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
126	C₂₃×#431	C₂²	1	2	yes	complemented
127	C₂₃×#428	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#418	C₂²	1	2	yes	complemented
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂×C₂₃×#102	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	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	1	no	—
139	C₂×#41×C₂₃	—	2	2	no	—
140	C₂×#41×C₂₃	—	4	8	no	—
141	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
142	C₂×#41×C₂₃	C₂³	1	2	yes	—
143	C₂²×Q₈×C₂₃	—	2	1	no	—
144	C₂²×D₄×C₂₃	—	2	2	no	—
145	C₂²×D₄×C₂₃	—	2	1	no	—
146	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₂₃	—	2	1	no	—
150	C₂³×C₄×C₂₃	—	2	2	no	—
151	C₂³×C₄×C₂₃	—	2	1	no	—
152	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×D₈×C₂₃	—	2	4	no	—
158	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₂₃	C₂³	1	2	yes	—
162	C₂×D₈×C₂₃	C₂³	1	2	yes	—
163	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₂₃×#127	C₂³	1	1	yes	characteristic
173	C₂₃×#127	C₂³	1	2	yes	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	C₂³	1	2	yes	—
180	C₂₃×#124	—	2	2	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×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	1	no	—
192	C₂₃×C₂²⋊Q₈	—	2	1	no	—
193	C₂₃×C₂²⋊Q₈	—	2	1	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	1	no	—
196	C₂₃×C₂²⋊Q₈	—	2	1	no	—
197	C₂₃×C₂²⋊Q₈	—	2	2	no	—
198	C₂₃×C₂²⋊Q₈	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂₃×#121	—	2	1	no	—
202	C₂₃×#121	—	2	1	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	—	2	1	no	—
207	C₂₃×#121	—	2	1	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	2	no	—
210	C₂₃×#121	C₂³	1	2	yes	—
211	C₂₃×#121	C₂³	1	2	yes	—
212	C₂₃×#121	C₂³	1	2	yes	—
213	C₂₃×#121	C₂³	1	2	yes	—
214	C₂₃×#120	—	2	2	no	—
215	C₂₃×#120	—	2	2	no	—
216	C₂₃×#120	—	2	2	no	—
217	C₂₃×#120	—	2	2	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
220	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	1	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	1	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	2	no	—
234	C₄×D₄×C₂₃	D₄	1	2	yes	—
235	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	2	yes	—
248	C₄×D₄×C₂₃	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₂₃×#117	—	2	1	no	—
251	C₂₃×#117	—	2	1	no	—
252	C₂₃×#117	—	2	1	no	—
253	C₂₃×#117	—	2	2	no	—
254	C₂₃×#117	—	2	2	no	—
255	C₂₃×#117	—	2	2	no	—
256	C₂₃×#117	D₄	1	1	yes	characteristic
257	C₂₃×#117	D₄	1	2	yes	—
258	C₂₃×#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
268	C₂×C₄²×C₂₃	—	2	2	no	—
269	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	1	yes	characteristic
273	C₂₃×#107	C₂³	1	1	yes	characteristic
274	C₂₃×#107	C₂³	1	1	yes	characteristic
275	C₂₃×#107	C₂³	1	2	yes	—
276	C₂₃×#107	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×#106	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
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	1	yes	characteristic
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₂⁴×C₂₃	—	2	1	no	—
316	C₂⁴×C₂₃	—	2	2	no	—
317	C₂⁴×C₂₃	—	2	1	no	—
318	#41×C₂₃	—	2	4	no	—
319	#41×C₂₃	—	2	4	no	—
320	#41×C₂₃	—	4	2	no	—
321	#41×C₂₃	—	4	8	no	—
322	#41×C₂₃	—	4	8	no	—
323	#41×C₂₃	—	4	4	no	—
324	#41×C₂₃	—	4	4	no	—
325	#41×C₂₃	—	4	4	no	—
326	C₂×Q₈×C₂₃	—	2	2	no	—
327	C₂×Q₈×C₂₃	—	2	1	no	—
328	C₂×Q₈×C₂₃	—	2	1	no	—
329	C₂×Q₈×C₂₃	—	4	4	no	—
330	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	4	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	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	1	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	2	no	—
346	C₂×D₄×C₂₃	—	2	1	no	—
347	C₂×D₄×C₂₃	—	4	1	no	—
348	C₂×D₄×C₂₃	—	4	1	no	—
349	C₂×D₄×C₂₃	—	4	2	no	—
350	C₂×D₄×C₂₃	—	4	8	no	—
351	C₂×D₄×C₂₃	—	4	4	no	—
352	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
357	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	2	no	—
361	C₂²×C₄×C₂₃	—	2	1	no	—
362	C₂²×C₄×C₂₃	—	2	2	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	1	no	—
367	C₂²×C₄×C₂₃	—	2	2	no	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	2	1	no	—
371	C₂²×C₄×C₂₃	—	2	1	no	—
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	2	no	—
374	C₂²×C₄×C₂₃	—	2	2	no	—
375	C₂²×C₄×C₂₃	—	4	8	no	—
376	C₂²×C₄×C₂₃	—	4	4	no	—
377	C₂²×C₄×C₂₃	—	4	4	no	—
378	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
384	SD₁₆×C₂₃	—	2	4	no	—
385	SD₁₆×C₂₃	—	2	4	no	—
386	SD₁₆×C₂₃	—	4	2	no	—
387	SD₁₆×C₂₃	—	4	2	no	—
388	D₈×C₂₃	—	2	2	no	—
389	D₈×C₂₃	—	2	2	no	—
390	D₈×C₂₃	—	2	4	no	—
391	D₈×C₂₃	—	2	2	no	—
392	D₈×C₂₃	—	4	2	no	—
393	D₈×C₂₃	#41	1	4	yes	complemented
394	M₁₆×C₂₃	—	2	4	no	—
395	M₁₆×C₂₃	—	4	2	no	—
396	C₂×C₈×C₂₃	—	2	2	no	—
397	C₂×C₈×C₂₃	—	4	1	no	—
398	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
401	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
402	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
409	C₄⋊C₄×C₂₃	—	2	1	no	—
410	C₄⋊C₄×C₂₃	—	2	1	no	—
411	C₄⋊C₄×C₂₃	—	2	2	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	2	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	1	no	—
418	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	1	no	—
437	C₂²⋊C₄×C₂₃	—	2	2	no	—
438	C₂²⋊C₄×C₂₃	—	2	1	no	—
439	C₂²⋊C₄×C₂₃	—	2	1	no	—
440	C₂²⋊C₄×C₂₃	—	2	2	no	—
441	C₂²⋊C₄×C₂₃	—	2	1	no	—
442	C₂²⋊C₄×C₂₃	—	2	1	no	—
443	C₂²⋊C₄×C₂₃	—	2	1	no	—
444	C₂²⋊C₄×C₂₃	—	2	2	no	—
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	—	2	2	no	—
447	C₂²⋊C₄×C₂₃	—	2	2	no	—
448	C₂²⋊C₄×C₂₃	—	2	2	no	—
449	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
452	C₄²×C₂₃	—	2	2	no	—
453	C₄²×C₂₃	—	2	2	no	—
454	C₄²×C₂₃	—	2	2	no	—
455	C₄²×C₂₃	C₂×D₄	1	2	yes	—
456	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₂₃	C₂×D₄	1	2	yes	—
458	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
460	C₄²×C₂₃	C₂⁴	1	2	yes	—
461	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
462	#61437	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂³×C₂₃	—	2	1	no	—
464	C₂³×C₂₃	—	2	1	no	—
465	C₂³×C₂₃	—	2	1	no	—
466	C₂³×C₂₃	—	2	1	no	—
467	C₂³×C₂₃	—	2	2	no	—
468	C₂³×C₂₃	—	4	2	no	—
469	C₂³×C₂₃	—	4	2	no	—
470	C₂³×C₂₃	—	4	4	no	—
471	C₂³×C₂₃	—	4	4	no	—
472	C₂³×C₂₃	—	4	2	no	—
473	C₂³×C₂₃	—	4	2	no	—
474	C₂³×C₂₃	—	8	1	no	—
475	C₂³×C₂₃	—	8	1	no	—
476	C₂³×C₂₃	—	8	2	no	—
477	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
478	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
479	Q₈×C₂₃	—	2	2	no	—
480	Q₈×C₂₃	—	2	2	no	—
481	Q₈×C₂₃	—	2	2	no	—
482	Q₈×C₂₃	—	4	4	no	—
483	Q₈×C₂₃	—	4	2	no	—
484	Q₈×C₂₃	—	8	1	no	—
485	D₄×C₂₃	—	2	4	no	—
486	D₄×C₂₃	—	2	2	no	—
487	D₄×C₂₃	—	2	1	no	—
488	D₄×C₂₃	—	2	1	no	—
489	D₄×C₂₃	—	2	2	no	—
490	D₄×C₂₃	—	2	1	no	—
491	D₄×C₂₃	—	2	1	no	—
492	D₄×C₂₃	—	2	1	no	—
493	D₄×C₂₃	—	2	2	no	—
494	D₄×C₂₃	—	2	1	no	—
495	D₄×C₂₃	—	4	4	no	—
496	D₄×C₂₃	—	4	2	no	—
497	D₄×C₂₃	—	4	2	no	—
498	D₄×C₂₃	—	4	4	no	—
499	D₄×C₂₃	—	4	4	no	—
500	D₄×C₂₃	—	4	4	no	—
501	D₄×C₂₃	—	4	4	no	—
502	D₄×C₂₃	—	4	4	no	—
503	D₄×C₂₃	—	4	2	no	—
504	D₄×C₂₃	—	8	2	no	—
505	D₄×C₂₃	—	8	1	no	—
506	D₄×C₂₃	—	8	2	no	—
507	D₄×C₂₃	C₂×#41	1	2	yes	—
508	D₄×C₂₃	C₂×#41	1	2	yes	complemented
509	C₂×C₄×C₂₃	—	2	4	no	—
510	C₂×C₄×C₂₃	—	2	1	no	—
511	C₂×C₄×C₂₃	—	2	2	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	2	1	no	—
515	C₂×C₄×C₂₃	—	2	2	no	—
516	C₂×C₄×C₂₃	—	2	2	no	—
517	C₂×C₄×C₂₃	—	2	1	no	—
518	C₂×C₄×C₂₃	—	2	1	no	—
519	C₂×C₄×C₂₃	—	2	2	no	—
520	C₂×C₄×C₂₃	—	2	1	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	1	no	—
523	C₂×C₄×C₂₃	—	4	4	no	—
524	C₂×C₄×C₂₃	—	4	4	no	—
525	C₂×C₄×C₂₃	—	4	4	no	—
526	C₂×C₄×C₂₃	—	4	4	no	—
527	C₂×C₄×C₂₃	—	4	2	no	—
528	C₂×C₄×C₂₃	—	4	2	no	—
529	C₂×C₄×C₂₃	—	4	2	no	—
530	C₂×C₄×C₂₃	—	4	2	no	—
531	C₂×C₄×C₂₃	—	4	2	no	—
532	C₂×C₄×C₂₃	—	4	2	no	—
533	C₂×C₄×C₂₃	—	4	2	no	—
534	C₂×C₄×C₂₃	—	4	2	no	—
535	C₂×C₄×C₂₃	—	4	2	no	—
536	C₂×C₄×C₂₃	—	4	4	no	—
537	C₂×C₄×C₂₃	—	4	2	no	—
538	C₂×C₄×C₂₃	—	8	2	no	—
539	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
540	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
549	C₈×C₂₃	—	2	1	no	—
550	C₈×C₂₃	—	2	2	no	—
551	C₈×C₂₃	—	2	1	no	—
552	C₈×C₂₃	—	2	1	no	—
553	C₈×C₂₃	—	2	2	no	—
554	C₈×C₂₃	C₂×#41	1	2	yes	complemented
555	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
556	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#3397	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#3384	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3367	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#3366	C₂×C₂₃	1	1	yes	characteristic, complemented
561	#3354	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#3343	C₂×C₂₃	1	2	yes	complemented
563	#3330	C₂×C₂₃	1	1	yes	characteristic, complemented
564	#3325	C₂×C₂₃	1	1	yes	characteristic, complemented
565	#3310	C₂×C₂₃	1	2	yes	complemented
566	#3306	C₂×C₂₃	1	2	yes	complemented
567	#3272	C₂×C₂₃	1	1	yes	characteristic, complemented
568	#3264	C₂×C₂₃	1	2	yes	complemented
569	#3171	C₂×C₂₃	1	2	yes	complemented
570	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
571	#3106	C₂×C₂₃	1	2	yes	complemented
572	#3105	C₂×C₂₃	1	2	yes	complemented
573	#3101	C₂×C₂₃	1	1	yes	characteristic, complemented
574	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
575	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
576	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
577	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
578	C₂²×C₂₃	—	2	1	no	—
579	C₂²×C₂₃	—	2	1	no	—
580	C₂²×C₂₃	—	2	2	no	—
581	C₂²×C₂₃	—	2	2	no	—
582	C₂²×C₂₃	—	2	2	no	—
583	C₂²×C₂₃	—	2	2	no	—
584	C₂²×C₂₃	—	2	2	no	—
585	C₂²×C₂₃	—	4	1	no	—
586	C₂²×C₂₃	—	4	1	no	—
587	C₂²×C₂₃	—	4	1	no	—
588	C₂²×C₂₃	—	4	1	no	—
589	C₂²×C₂₃	—	4	1	no	—
590	C₂²×C₂₃	—	4	2	no	—
591	C₂²×C₂₃	—	4	1	no	—
592	C₂²×C₂₃	—	4	1	no	—
593	C₂²×C₂₃	—	4	1	no	—
594	C₂²×C₂₃	—	4	2	no	—
595	C₂²×C₂₃	—	4	2	no	—
596	C₂²×C₂₃	—	4	1	no	—
597	C₂²×C₂₃	—	4	1	no	—
598	C₂²×C₂₃	—	8	4	no	—
599	C₂²×C₂₃	—	8	4	no	—
600	C₂²×C₂₃	—	8	8	no	—
601	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
602	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
603	C₄×C₂₃	—	2	1	no	—
604	C₄×C₂₃	—	2	2	no	—
605	C₄×C₂₃	—	2	1	no	—
606	C₄×C₂₃	—	2	2	no	—
607	C₄×C₂₃	—	2	1	no	—
608	C₄×C₂₃	—	2	2	no	—
609	C₄×C₂₃	—	4	2	no	—
610	C₄×C₂₃	—	4	2	no	—
611	C₄×C₂₃	—	4	1	no	—
612	C₄×C₂₃	—	4	1	no	—
613	C₄×C₂₃	—	4	1	no	—
614	C₄×C₂₃	—	4	2	no	—
615	C₄×C₂₃	—	4	1	no	—
616	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
617	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
618	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
619	C₄×C₂₃	#585	1	1	yes	characteristic
620	C₂²×#41	—	2	1	no	—
621	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
622	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
623	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#553	—	2	1	no	—
627	#552	—	2	1	no	—
628	#552	C₂²×C₂₃	1	2	yes	complemented
629	#551	—	2	2	no	—
630	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
631	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#548	—	2	1	no	—
633	#547	C₂²×C₂₃	1	2	yes	—
634	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
636	#546	—	2	2	no	—
637	#546	—	2	1	no	—
638	#546	C₂²×C₂₃	1	2	yes	complemented
639	D₄²	C₂²×C₂₃	1	2	yes	—
640	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#532	C₂²×C₂₃	1	1	yes	characteristic
643	#532	C₂²×C₂₃	1	2	yes	complemented
644	#529	—	2	2	no	—
645	#529	C₂²×C₂₃	1	2	yes	complemented
646	#525	—	2	1	no	—
647	#525	—	2	1	no	—
648	#525	—	2	2	no	—
649	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
650	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
651	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
652	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
654	C₂×#117	—	2	1	no	—
655	#501	C₂²×C₂₃	1	2	yes	complemented
656	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	#496	C₂²×C₂₃	1	2	yes	complemented
658	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#490	C₂²×C₂₃	1	2	yes	complemented
660	#489	C₂²×C₂₃	1	2	yes	complemented
661	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#484	C₂²×C₂₃	1	2	yes	complemented
664	#483	C₂²×C₂₃	1	2	yes	complemented
665	#482	C₂²×C₂₃	1	2	yes	complemented
666	#482	C₂²×C₂₃	1	2	yes	complemented
667	#481	C₂²×C₂₃	1	2	yes	complemented
668	#480	C₂²×C₂₃	1	2	yes	complemented
669	#478	C₂²×C₂₃	1	2	yes	complemented
670	#478	C₂²×C₂₃	1	2	yes	complemented
671	#477	C₂²×C₂₃	1	2	yes	complemented
672	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	#476	C₂²×C₂₃	1	2	yes	complemented
675	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#469	C₂²×C₂₃	1	2	yes	complemented
678	#469	C₂²×C₂₃	1	2	yes	complemented
679	#468	C₂²×C₂₃	1	2	yes	complemented
680	#468	C₂²×C₂₃	1	2	yes	complemented
681	#465	C₂²×C₂₃	1	2	yes	complemented
682	#465	C₂²×C₂₃	1	2	yes	complemented
683	#463	C₂²×C₂₃	1	2	yes	—
684	#463	C₂²×C₂₃	1	2	yes	complemented
685	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#460	C₂²×C₂₃	1	2	yes	complemented
688	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#459	C₂²×C₂₃	1	2	yes	complemented
691	#450	C₂²×C₂₃	1	2	yes	—
692	#450	C₂²×C₂₃	1	2	yes	complemented
693	#449	C₂²×C₂₃	1	2	yes	complemented
694	#449	C₂²×C₂₃	1	2	yes	complemented
695	#447	C₂²×C₂₃	1	2	yes	—
696	#447	C₂²×C₂₃	1	2	yes	complemented
697	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#442	C₂²×C₂₃	1	2	yes	—
700	#442	C₂²×C₂₃	1	2	yes	complemented
701	#440	C₂²×C₂₃	1	2	yes	complemented
702	#440	C₂²×C₂₃	1	2	yes	complemented
703	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
704	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
707	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
708	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
709	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
710	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
711	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
714	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
715	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
716	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
717	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
718	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	#435	C₂²×C₂₃	1	2	yes	complemented
720	#435	C₂²×C₂₃	1	2	yes	complemented
721	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	#431	C₂²×C₂₃	1	2	yes	complemented
723	#428	C₂²×C₂₃	1	2	yes	complemented
724	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
725	#418	C₂²×C₂₃	1	2	yes	complemented
726	#417	C₂²×C₂₃	1	2	yes	complemented
727	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
728	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
729	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
730	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	C₂×C₂₃	—	2	2	no	—
732	C₂×C₂₃	—	4	2	no	—
733	C₂×C₂₃	—	4	2	no	—
734	C₂×C₂₃	—	4	2	no	—
735	C₂×C₂₃	—	8	1	no	—
736	C₂×C₂₃	—	8	2	no	—
737	C₂×C₂₃	—	8	1	no	—
738	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
739	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
740	C₂×C₂₃	#3584	1	1	yes	characteristic
741	C₂×#41	—	2	1	no	—
742	C₂×#41	—	2	2	no	—
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	1	no	—
745	C₂×#41	—	2	2	no	—
746	C₂×#41	—	4	8	no	—
747	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
748	C₂×#41	C₂³×C₂₃	1	2	yes	—
749	C₂²×Q₈	—	2	1	no	—
750	C₂²×D₄	—	2	2	no	—
751	C₂²×D₄	—	2	1	no	—
752	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
753	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
754	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
755	C₂³×C₄	—	2	1	no	—
756	C₂³×C₄	—	2	1	no	—
757	C₂³×C₄	—	2	2	no	—
758	AGL(1,ℤ/8)	—	2	8	no	—
759	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
763	C₂×D₈	—	2	4	no	—
764	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
765	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
766	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
767	C₂×D₈	C₂³×C₂₃	1	2	yes	—
768	C₂×D₈	C₂³×C₂₃	1	2	yes	—
769	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
771	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
772	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
774	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
775	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
777	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
778	#127	C₂³×C₂₃	1	1	yes	characteristic
779	#127	C₂³×C₂₃	1	2	yes	—
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#125	—	2	2	no	—
784	#125	—	2	1	no	—
785	#125	C₂³×C₂₃	1	2	yes	—
786	#124	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	—	2	2	no	—
789	#124	C₂³×C₂₃	1	2	yes	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	1	no	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	1	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	C₂³×C₂₃	1	2	yes	—
817	#121	C₂³×C₂₃	1	2	yes	—
818	#121	C₂³×C₂₃	1	2	yes	—
819	#121	C₂³×C₂₃	1	2	yes	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
827	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
828	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	D₄×C₂₃	1	2	yes	—
841	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₂₃	1	2	yes	—
849	C₄×D₄	C₂³×C₂₃	1	2	yes	—
850	C₄×D₄	C₂³×C₂₃	1	2	yes	—
851	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₂₃	1	2	yes	—
854	C₄×D₄	C₂³×C₂₃	1	2	yes	—
855	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	2	no	—
860	#117	—	2	2	no	—
861	#117	—	2	2	no	—
862	#117	D₄×C₂₃	1	1	yes	characteristic
863	#117	D₄×C₂₃	1	2	yes	—
864	#117	C₂³×C₂₃	1	2	yes	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	—	2	1	no	—
867	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
869	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₂²⋊C₄	—	2	2	no	—
872	C₂×C₂²⋊C₄	—	2	1	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₄²	—	2	2	no	—
875	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
876	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
877	#107	C₂³×C₂₃	1	1	yes	characteristic
878	#107	C₂³×C₂₃	1	1	yes	characteristic
879	#107	C₂³×C₂₃	1	1	yes	characteristic
880	#107	C₂³×C₂₃	1	1	yes	characteristic
881	#107	C₂³×C₂₃	1	2	yes	—
882	#107	C₂³×C₂₃	1	2	yes	—
883	#106	C₂³×C₂₃	1	2	yes	—
884	#106	C₂³×C₂₃	1	2	yes	—
885	#106	C₂³×C₂₃	1	2	yes	—
886	#106	C₂³×C₂₃	1	2	yes	—
887	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
888	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
889	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
890	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
891	#103	C₂³×C₂₃	1	2	yes	—
892	#103	C₂³×C₂₃	1	2	yes	—
893	#103	C₂³×C₂₃	1	2	yes	—
894	#103	C₂³×C₂₃	1	2	yes	—
895	#102	C₂³×C₂₃	1	1	yes	characteristic
896	#102	C₂³×C₂₃	1	1	yes	characteristic
897	#102	C₂³×C₂₃	1	1	yes	characteristic
898	#102	C₂³×C₂₃	1	1	yes	characteristic
899	#102	C₂³×C₂₃	1	1	yes	characteristic
900	#102	C₂³×C₂₃	1	1	yes	characteristic
901	#102	C₂³×C₂₃	1	1	yes	characteristic
902	#102	C₂³×C₂₃	1	1	yes	characteristic
903	#102	C₂³×C₂₃	1	2	yes	—
904	#102	C₂³×C₂₃	1	2	yes	—
905	#102	C₂³×C₂₃	1	2	yes	—
906	#102	C₂³×C₂₃	1	2	yes	—
907	#102	C₂³×C₂₃	1	2	yes	—
908	#102	C₂³×C₂₃	1	2	yes	—
909	#102	C₂³×C₂₃	1	2	yes	—
910	#102	C₂³×C₂₃	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
914	#97	C₂³×C₂₃	1	2	yes	—
915	#97	C₂³×C₂₃	1	2	yes	—
916	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
917	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
918	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
919	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
920	C₄×C₈	C₂³×C₂₃	1	2	yes	—
921	C₂₃	#61437	1	1	yes	characteristic, direct product factor, Sylow
922	C₂⁴	—	2	1	no	—
923	C₂⁴	—	2	2	no	—
924	C₂⁴	—	2	1	no	—
925	#41	—	2	4	no	—
926	#41	—	2	4	no	—
927	#41	—	4	2	no	—
928	#41	—	4	8	no	—
929	#41	—	4	8	no	—
930	#41	—	4	4	no	—
931	#41	—	4	4	no	—
932	#41	—	4	4	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	1	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	4	4	no	—
937	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
938	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	4	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	4	1	no	—
955	C₂×D₄	—	4	1	no	—
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	4	8	no	—
958	C₂×D₄	—	4	4	no	—
959	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
960	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
961	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
964	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	4	8	no	—
983	C₂²×C₄	—	4	4	no	—
984	C₂²×C₄	—	4	4	no	—
985	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
986	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
988	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
991	SD₁₆	—	2	4	no	—
992	SD₁₆	—	2	4	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	D₈	—	2	2	no	—
996	D₈	—	2	2	no	—
997	D₈	—	2	4	no	—
998	D₈	—	2	2	no	—
999	D₈	—	4	2	no	—
1000	D₈	#41×C₂₃	1	4	yes	complemented
1001	M₁₆	—	2	4	no	—
1002	M₁₆	—	4	2	no	—
1003	C₂×C₈	—	2	2	no	—
1004	C₂×C₈	—	4	1	no	—
1005	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1006	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1009	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1010	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1026	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1028	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1029	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1030	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
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	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1063	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1064	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1065	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1066	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1067	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₂₃	1	2	yes	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	4	2	no	—
1075	C₂³	—	4	2	no	—
1076	C₂³	—	4	4	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	4	2	no	—
1079	C₂³	—	4	2	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1084	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	4	4	no	—
1089	Q₈	—	4	2	no	—
1090	Q₈	—	8	1	no	—
1091	D₄	—	2	4	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	4	4	no	—
1102	D₄	—	4	2	no	—
1103	D₄	—	4	2	no	—
1104	D₄	—	4	4	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	4	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	1	no	—
1112	D₄	—	8	2	no	—
1113	D₄	C₂×#41×C₂₃	1	2	yes	—
1114	D₄	C₂×#41×C₂₃	1	2	yes	complemented
1115	C₂×C₄	—	2	4	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
1146	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1147	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1150	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1152	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1153	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1154	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1155	C₈	—	2	1	no	—
1156	C₈	—	2	2	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	2	no	—
1160	C₈	C₂×#41×C₂₃	1	2	yes	complemented
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	8	4	no	—
1182	C₂²	—	8	4	no	—
1183	C₂²	—	8	8	no	—
1184	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1185	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1186	C₄	—	2	2	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	1	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	2	no	—
1199	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1200	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1201	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1202	C₄	C₂₃×#585	1	1	yes	characteristic
1203	C₂	—	2	2	no	—
1204	C₂	—	4	2	no	—
1205	C₂	—	4	2	no	—
1206	C₂	—	4	2	no	—
1207	C₂	—	8	1	no	—
1208	C₂	—	8	2	no	—
1209	C₂	—	8	1	no	—
1210	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1211	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1212	C₂	C₂₃×#3584	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×#3475	C₂	semidirect
2. D₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3397	C₂	semidirect
4. C₂₃×#3384	C₂	semidirect
5. C₂₃×#3367	C₂	semidirect
6. C₂₃×#3366	C₂	semidirect
7. C₂₃×#3354	C₂	semidirect
8. C₂₃×#3343	C₂	semidirect
9. C₂₃×#3330	C₂	semidirect
10. C₂₃×#3325	C₂	semidirect
11. C₂₃×#3310	C₂	semidirect
12. C₂₃×#3306	C₂	semidirect
13. C₂₃×#3272	C₂	semidirect
14. C₂₃×#3264	C₂	semidirect
15. C₂₃×#3171	C₂	semidirect
16. C₂₃×#3167	C₂	semidirect
17. C₂₃×#3106	C₂	semidirect
18. C₂₃×#3105	C₂	semidirect
19. C₂₃×#3101	C₂	semidirect
20. C₂₃×#3100	C₂	semidirect
21. C₂₃×#2965	C₂	semidirect
22. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₄×D₈×C₂₃	C₂	semidirect
27. C₂₃×#556	C₂²	semidirect
28. C₂₃×#555	C₂²	semidirect
29. C₂₃×#554	C₂²	semidirect
32. C₂₃×#552	C₂²	semidirect
34. C₂₃×#550	C₂²	semidirect
35. D₄×Q₈×C₂₃	C₂²	semidirect
38. C₂₃×#547	C₂²	semidirect
39. C₂₃×#547	C₂²	semidirect
42. C₂₃×#546	C₂²	semidirect
44. D₄²×C₂₃	C₂²	semidirect
45. C₂₃×#533	C₂²	semidirect
47. C₂₃×#532	C₂²	semidirect
49. C₂₃×#529	C₂²	semidirect
54. C₄×#41×C₂₃	C₂²	semidirect
56. C₂×C₄×D₄×C₂₃	C₂²	semidirect
57. C₂×C₄×D₄×C₂₃	C₂²	semidirect
59. C₂₃×#501	C₂²	semidirect
60. C₂₃×#498	C₂²	semidirect
61. C₂₃×#496	C₂²	semidirect
62. C₂₃×#492	C₂²	semidirect
63. C₂₃×#490	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#484	C₂²	semidirect
68. C₂₃×#483	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#481	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
73. C₂₃×#478	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#476	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#476	C₂²	semidirect
79. C₂₃×#474	C₂²	semidirect
80. C₂₃×#474	C₂²	semidirect
81. C₂₃×#469	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
83. C₂₃×#468	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#465	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
89. C₂₃×#461	C₂²	semidirect
90. C₂₃×#461	C₂²	semidirect
91. C₂₃×#460	C₂²	semidirect
92. C₂₃×#459	C₂²	semidirect
93. C₂₃×#459	C₂²	semidirect
94. C₂₃×#459	C₂²	semidirect
96. C₂₃×#450	C₂²	semidirect
97. C₂₃×#449	C₂²	semidirect
98. C₂₃×#449	C₂²	semidirect
100. C₂₃×#447	C₂²	semidirect
101. C₂₃×#446	C₂²	semidirect
102. C₂₃×#446	C₂²	semidirect
104. C₂₃×#442	C₂²	semidirect
105. C₂₃×#440	C₂²	semidirect
106. C₂₃×#440	C₂²	semidirect
107. C₄×SD₁₆×C₂₃	C₂²	semidirect
108. C₄×SD₁₆×C₂₃	C₂²	semidirect
109. C₄×SD₁₆×C₂₃	C₂²	semidirect
110. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×D₈×C₂₃	C₂²	semidirect
116. C₄×D₈×C₂₃	C₂²	semidirect
117. C₄×D₈×C₂₃	C₂²	semidirect
118. C₄×D₈×C₂₃	C₂²	semidirect
119. C₄×D₈×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#436	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. C₂×C₂₃×#107	C₂²	semidirect
129. C₂₃×#418	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
132. C₂×C₂₃×#102	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
393. D₈×C₂₃	#41	semidirect
462. #61437	C₂₃	direct (N × H)
508. D₄×C₂₃	C₂×#41	semidirect
539. C₂×C₄×C₂₃	AGL(1,ℤ/8)	semidirect
554. C₈×C₂₃	C₂×#41	semidirect
555. #3475	C₂×C₂₃	semidirect
556. D₄×#41	C₂×C₂₃	semidirect
557. #3397	C₂×C₂₃	semidirect
558. #3384	C₂×C₂₃	semidirect
559. #3367	C₂×C₂₃	semidirect
560. #3366	C₂×C₂₃	semidirect
561. #3354	C₂×C₂₃	semidirect
562. #3343	C₂×C₂₃	semidirect
563. #3330	C₂×C₂₃	semidirect
564. #3325	C₂×C₂₃	semidirect
565. #3310	C₂×C₂₃	semidirect
566. #3306	C₂×C₂₃	semidirect
567. #3272	C₂×C₂₃	semidirect
568. #3264	C₂×C₂₃	semidirect
569. #3171	C₂×C₂₃	semidirect
570. #3167	C₂×C₂₃	semidirect
571. #3106	C₂×C₂₃	semidirect
572. #3105	C₂×C₂₃	semidirect
573. #3101	C₂×C₂₃	semidirect
574. #3100	C₂×C₂₃	semidirect
575. #2965	C₂×C₂₃	semidirect
576. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
577. C₂×C₄×D₈	C₂×C₂₃	semidirect
623. #556	C₂²×C₂₃	semidirect
624. #555	C₂²×C₂₃	semidirect
625. #554	C₂²×C₂₃	semidirect
628. #552	C₂²×C₂₃	semidirect
630. #550	C₂²×C₂₃	semidirect
631. D₄×Q₈	C₂²×C₂₃	semidirect
634. #547	C₂²×C₂₃	semidirect
635. #547	C₂²×C₂₃	semidirect
638. #546	C₂²×C₂₃	semidirect
640. D₄²	C₂²×C₂₃	semidirect
641. #533	C₂²×C₂₃	semidirect
643. #532	C₂²×C₂₃	semidirect
645. #529	C₂²×C₂₃	semidirect
650. C₄×#41	C₂²×C₂₃	semidirect
652. C₂×C₄×D₄	C₂²×C₂₃	semidirect
653. C₂×C₄×D₄	C₂²×C₂₃	semidirect
655. #501	C₂²×C₂₃	semidirect
656. #498	C₂²×C₂₃	semidirect
657. #496	C₂²×C₂₃	semidirect
658. #492	C₂²×C₂₃	semidirect
659. #490	C₂²×C₂₃	semidirect
660. #489	C₂²×C₂₃	semidirect
661. #487	C₂²×C₂₃	semidirect
662. #486	C₂²×C₂₃	semidirect
663. #484	C₂²×C₂₃	semidirect
664. #483	C₂²×C₂₃	semidirect
665. #482	C₂²×C₂₃	semidirect
666. #482	C₂²×C₂₃	semidirect
667. #481	C₂²×C₂₃	semidirect
668. #480	C₂²×C₂₃	semidirect
669. #478	C₂²×C₂₃	semidirect
670. #478	C₂²×C₂₃	semidirect
671. #477	C₂²×C₂₃	semidirect
672. #476	C₂²×C₂₃	semidirect
673. #476	C₂²×C₂₃	semidirect
674. #476	C₂²×C₂₃	semidirect
675. #474	C₂²×C₂₃	semidirect
676. #474	C₂²×C₂₃	semidirect
677. #469	C₂²×C₂₃	semidirect
678. #469	C₂²×C₂₃	semidirect
679. #468	C₂²×C₂₃	semidirect
680. #468	C₂²×C₂₃	semidirect
681. #465	C₂²×C₂₃	semidirect
682. #465	C₂²×C₂₃	semidirect
684. #463	C₂²×C₂₃	semidirect
685. #461	C₂²×C₂₃	semidirect
686. #461	C₂²×C₂₃	semidirect
687. #460	C₂²×C₂₃	semidirect
688. #459	C₂²×C₂₃	semidirect
689. #459	C₂²×C₂₃	semidirect
690. #459	C₂²×C₂₃	semidirect
692. #450	C₂²×C₂₃	semidirect
693. #449	C₂²×C₂₃	semidirect
694. #449	C₂²×C₂₃	semidirect
696. #447	C₂²×C₂₃	semidirect
697. #446	C₂²×C₂₃	semidirect
698. #446	C₂²×C₂₃	semidirect
700. #442	C₂²×C₂₃	semidirect
701. #440	C₂²×C₂₃	semidirect
702. #440	C₂²×C₂₃	semidirect
703. C₄×SD₁₆	C₂²×C₂₃	semidirect
704. C₄×SD₁₆	C₂²×C₂₃	semidirect
705. C₄×SD₁₆	C₂²×C₂₃	semidirect
706. C₄×SD₁₆	C₂²×C₂₃	semidirect
711. C₄×D₈	C₂²×C₂₃	semidirect
712. C₄×D₈	C₂²×C₂₃	semidirect
713. C₄×D₈	C₂²×C₂₃	semidirect
714. C₄×D₈	C₂²×C₂₃	semidirect
715. C₄×D₈	C₂²×C₂₃	semidirect
716. C₄×D₈	C₂²×C₂₃	semidirect
717. #436	C₂²×C₂₃	semidirect
718. #436	C₂²×C₂₃	semidirect
719. #435	C₂²×C₂₃	semidirect
720. #435	C₂²×C₂₃	semidirect
721. #431	C₂²×C₂₃	semidirect
722. #431	C₂²×C₂₃	semidirect
723. #428	C₂²×C₂₃	semidirect
724. C₂×#107	C₂²×C₂₃	semidirect
725. #418	C₂²×C₂₃	semidirect
726. #417	C₂²×C₂₃	semidirect
728. C₂×#102	C₂²×C₂₃	semidirect
729. C₄×M₁₆	C₂²×C₂₃	semidirect
730. C₂×C₄×C₈	C₂²×C₂₃	semidirect
921. C₂₃	#61437	direct (N × H)
1000. D₈	#41×C₂₃	semidirect
1114. D₄	C₂×#41×C₂₃	semidirect
1145. C₂×C₄	C₂₃×AGL(1,ℤ/8)	semidirect
1160. C₈	C₂×#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
D₄×#41×C₂₃	2
C₂₃×#3397	2
C₂₃×#3384	2
C₂₃×#3367	2
C₂₃×#3366	2
C₂₃×#3354	2
C₂₃×#3343	2
C₂₃×#3330	2
C₂₃×#3325	2
C₂₃×#3310	2
C₂₃×#3306	2
C₂₃×#3272	2
C₂₃×#3264	2
C₂₃×#3171	2
C₂₃×#3167	2
C₂₃×#3106	2
C₂₃×#3105	2
C₂₃×#3101	2
C₂₃×#3100	2
C₂₃×#2965	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂×C₄×D₈×C₂₃	2
#61437	23

Subgroups — C23×#61437 #19209063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61437 #19209063