Subgroups — C₂₃×#62579 #19210205

Order 5888.

1728 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3316	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3301	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3180	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#557	C₂²	1	1	yes	characteristic
25	C₂₃×#556	C₂²	1	2	yes	—
26	C₂₃×#555	—	2	1	no	—
27	C₂₃×#554	—	2	1	no	—
28	C₂₃×#554	C₂²	1	1	yes	characteristic
29	C₂₃×#554	C₂²	1	1	yes	characteristic
30	C₂₃×#553	—	2	1	no	—
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	C₂²	1	1	yes	characteristic
33	C₂₃×#553	C₂²	1	1	yes	characteristic
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	—	2	1	no	—
36	C₂₃×#552	—	2	1	no	—
37	C₂₃×#552	C₂²	1	1	yes	characteristic
38	C₂₃×#552	C₂²	1	1	yes	characteristic
39	C₂₃×#548	C₂²	1	2	yes	—
40	C₂₃×#548	C₂²	1	2	yes	—
41	C₂₃×#547	—	2	1	no	—
42	C₂₃×#547	C₂²	1	2	yes	—
43	C₂₃×#547	C₂²	1	1	yes	characteristic
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#542	—	2	1	no	—
46	C₂₃×#541	—	2	1	no	—
47	C₂₃×#539	—	2	1	no	—
48	C₂₃×#539	—	2	1	no	—
49	C₂₃×#537	—	2	1	no	—
50	C₂₃×#533	C₂²	1	1	yes	characteristic
51	C₂₃×#533	C₂²	1	1	yes	characteristic
52	C₂₃×#533	C₂²	1	1	yes	characteristic
53	C₂₃×#532	C₂²	1	1	yes	characteristic
54	C₂₃×#532	C₂²	1	1	yes	characteristic
55	C₂₃×#532	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂₃×#529	C₂²	1	1	yes	characteristic
58	C₂₃×#529	C₂²	1	1	yes	characteristic
59	C₂₃×#529	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
62	C₂₃×#520	—	2	1	no	—
63	C₂₃×#520	—	2	1	no	—
64	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
65	C₂₃×#501	C₂²	1	1	yes	characteristic
66	C₂₃×#501	C₂²	1	1	yes	characteristic
67	C₂₃×#501	C₂²	1	1	yes	characteristic
68	C₂₃×#497	C₂²	1	1	yes	characteristic
69	C₂₃×#497	C₂²	1	1	yes	characteristic
70	C₂₃×#496	C₂²	1	1	yes	characteristic
71	C₂₃×#491	C₂²	1	1	yes	characteristic
72	C₂₃×#491	C₂²	1	1	yes	characteristic
73	C₂₃×#491	C₂²	1	1	yes	characteristic
74	C₂₃×#491	C₂²	1	1	yes	characteristic
75	C₂₃×#491	C₂²	1	1	yes	characteristic
76	C₂₃×#491	C₂²	1	1	yes	characteristic
77	C₂₃×#491	C₂²	1	2	yes	—
78	C₂₃×#491	C₂²	1	2	yes	—
79	C₂₃×#490	C₂²	1	1	yes	characteristic
80	C₂₃×#490	C₂²	1	1	yes	characteristic
81	C₂₃×#490	C₂²	1	1	yes	characteristic
82	C₂₃×#489	C₂²	1	1	yes	characteristic
83	C₂₃×#489	C₂²	1	2	yes	—
84	C₂₃×#489	C₂²	1	2	yes	—
85	C₂₃×#488	C₂²	1	2	yes	—
86	C₂₃×#488	C₂²	1	2	yes	—
87	C₂₃×#485	C₂²	1	2	yes	—
88	C₂₃×#485	C₂²	1	2	yes	—
89	C₂₃×#484	C₂²	1	2	yes	—
90	C₂₃×#483	C₂²	1	2	yes	—
91	C₂₃×#481	C₂²	1	2	yes	—
92	C₂₃×#480	C₂²	1	2	yes	—
93	C₂₃×#479	C₂²	1	2	yes	—
94	C₂₃×#479	C₂²	1	2	yes	—
95	C₂₃×#478	C₂²	1	2	yes	—
96	C₂₃×#478	C₂²	1	2	yes	—
97	C₂₃×#477	C₂²	1	2	yes	—
98	C₂₃×#475	C₂²	1	2	yes	—
99	C₂₃×#470	C₂²	1	2	yes	—
100	C₂₃×#468	C₂²	1	2	yes	—
101	C₂₃×#467	C₂²	1	2	yes	—
102	C₂₃×#466	C₂²	1	2	yes	—
103	C₂₃×#465	C₂²	1	2	yes	—
104	C₂₃×#465	C₂²	1	2	yes	—
105	C₂₃×#464	C₂²	1	2	yes	—
106	C₂₃×#464	C₂²	1	2	yes	—
107	C₂₃×#463	C₂²	1	2	yes	—
108	C₂₃×#463	C₂²	1	2	yes	—
109	C₂₃×#462	C₂²	1	2	yes	—
110	C₂₃×#461	C₂²	1	2	yes	—
111	C₂₃×#452	C₂²	1	2	yes	—
112	C₂₃×#452	C₂²	1	2	yes	—
113	C₂₃×#451	C₂²	1	2	yes	—
114	C₂₃×#449	C₂²	1	2	yes	—
115	C₂₃×#449	C₂²	1	2	yes	—
116	C₂₃×#448	C₂²	1	2	yes	—
117	C₂₃×#446	C₂²	1	2	yes	—
118	C₂₃×#442	C₂²	1	2	yes	—
119	C₂₃×#441	C₂²	1	2	yes	—
120	C₂₃×#440	C₂²	1	2	yes	—
121	C₂₃×#440	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
124	C₂₃×#435	C₂²	1	2	yes	—
125	C₂₃×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₂₃	C₂²	1	2	yes	—
127	C₂₃×#432	C₂²	1	1	yes	characteristic
128	C₂₃×#432	C₂²	1	1	yes	characteristic
129	C₂₃×#432	C₂²	1	1	yes	characteristic
130	C₂₃×#417	C₂²	1	2	yes	—
131	C₂₃×#417	C₂²	1	2	yes	—
132	C₂₃×#416	C₂²	1	2	yes	—
133	C₂₃×#416	C₂²	1	2	yes	—
134	C₂×C₂₃×#103	C₂²	1	2	yes	—
135	C₂×C₂₃×#103	C₂²	1	2	yes	—
136	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
137	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
138	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
142	C₂×#41×C₂₃	C₂³	1	2	yes	—
143	C₂×#41×C₂₃	C₂³	1	2	yes	—
144	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×D₈×C₂₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×#127	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	1	no	—
169	C₂₃×#126	—	2	1	no	—
170	C₂₃×#126	—	2	1	no	—
171	C₂₃×#126	—	2	1	no	—
172	C₂₃×#126	—	2	1	no	—
173	C₂₃×#125	—	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	—	2	1	no	—
180	C₂₃×#125	—	2	1	no	—
181	C₂₃×#125	—	2	1	no	—
182	C₂₃×#125	—	2	1	no	—
183	C₂₃×#125	—	2	1	no	—
184	C₂₃×#125	C₂³	1	1	yes	characteristic
185	C₂₃×#125	C₂³	1	1	yes	characteristic
186	C₂₃×#125	C₂³	1	1	yes	characteristic
187	C₂₃×#125	C₂³	1	1	yes	characteristic
188	C₂₃×#125	C₂³	1	1	yes	characteristic
189	C₂₃×#125	C₂³	1	1	yes	characteristic
190	C₂₃×#125	C₂³	1	1	yes	characteristic
191	C₂₃×#124	—	2	2	no	—
192	C₂₃×#124	—	2	2	no	—
193	C₂₃×#124	—	2	1	no	—
194	C₂₃×#124	C₂³	1	2	yes	—
195	C₂₃×#124	C₂³	1	2	yes	—
196	C₂₃×#124	C₂³	1	1	yes	characteristic
197	C₂₃×#123	—	2	1	no	—
198	C₂₃×#123	—	2	1	no	—
199	C₂₃×#123	—	2	1	no	—
200	C₂₃×#123	—	2	1	no	—
201	C₂₃×#123	—	2	1	no	—
202	C₂₃×#123	—	2	1	no	—
203	C₂₃×#123	—	2	1	no	—
204	C₂₃×#123	—	2	2	no	—
205	C₂₃×#123	—	2	2	no	—
206	C₂₃×#123	—	2	1	no	—
207	C₂₃×#123	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	1	no	—
212	C₂₃×C₂²⋊Q₈	—	2	1	no	—
213	C₂₃×C₂²⋊Q₈	—	2	1	no	—
214	C₂₃×C₂²⋊Q₈	—	2	1	no	—
215	C₂₃×C₂²⋊Q₈	—	2	2	no	—
216	C₂₃×C₂²⋊Q₈	—	2	2	no	—
217	C₂₃×C₂²⋊Q₈	—	2	1	no	—
218	C₂₃×C₂²⋊Q₈	—	2	1	no	—
219	C₂₃×C₂²⋊Q₈	—	2	1	no	—
220	C₂₃×C₂²⋊Q₈	—	2	1	no	—
221	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂₃×#121	—	2	1	no	—
227	C₂₃×#121	—	2	1	no	—
228	C₂₃×#121	—	2	2	no	—
229	C₂₃×#121	—	2	2	no	—
230	C₂₃×#121	—	2	2	no	—
231	C₂₃×#121	—	2	1	no	—
232	C₂₃×#121	—	2	1	no	—
233	C₂₃×#121	—	2	1	no	—
234	C₂₃×#121	—	2	1	no	—
235	C₂₃×#121	—	2	1	no	—
236	C₂₃×#121	C₂³	1	1	yes	characteristic
237	C₂₃×#121	C₂³	1	1	yes	characteristic
238	C₂₃×#121	C₂³	1	2	yes	—
239	C₂₃×#121	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₂₃	—	2	1	no	—
241	C₄×Q₈×C₂₃	—	2	1	no	—
242	C₄×Q₈×C₂₃	—	2	1	no	—
243	C₄×Q₈×C₂₃	—	2	1	no	—
244	C₄×Q₈×C₂₃	—	2	1	no	—
245	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
246	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
247	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
248	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₂₃	—	2	1	no	—
253	C₄×D₄×C₂₃	—	2	1	no	—
254	C₄×D₄×C₂₃	—	2	1	no	—
255	C₄×D₄×C₂₃	—	2	1	no	—
256	C₄×D₄×C₂₃	—	2	2	no	—
257	C₄×D₄×C₂₃	—	2	2	no	—
258	C₄×D₄×C₂₃	—	2	1	no	—
259	C₄×D₄×C₂₃	—	2	1	no	—
260	C₄×D₄×C₂₃	—	2	1	no	—
261	C₄×D₄×C₂₃	—	2	1	no	—
262	C₄×D₄×C₂₃	—	2	1	no	—
263	C₄×D₄×C₂₃	—	2	1	no	—
264	C₄×D₄×C₂₃	—	2	1	no	—
265	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
266	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
267	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
268	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₂₃	C₂³	1	2	yes	—
270	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
275	C₂₃×#117	—	2	1	no	—
276	C₂₃×#117	—	2	1	no	—
277	C₂₃×#117	—	2	2	no	—
278	C₂₃×#117	—	2	1	no	—
279	C₂₃×#117	—	2	1	no	—
280	C₂₃×#117	—	2	1	no	—
281	C₂₃×#117	—	2	1	no	—
282	C₂₃×#117	—	2	1	no	—
283	C₂₃×#117	D₄	1	1	yes	characteristic
284	C₂₃×#117	D₄	1	1	yes	characteristic
285	C₂₃×#117	D₄	1	1	yes	characteristic
286	C₂₃×#117	C₂³	1	1	yes	characteristic
287	C₂₃×#117	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
303	C₂₃×#107	C₂³	1	2	yes	—
304	C₂₃×#107	C₂³	1	2	yes	—
305	C₂₃×#107	C₂³	1	2	yes	—
306	C₂₃×#106	C₂³	1	2	yes	—
307	C₂₃×#106	C₂³	1	2	yes	—
308	C₂₃×#106	C₂³	1	2	yes	—
309	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
312	C₂₃×#103	C₂³	1	2	yes	—
313	C₂₃×#103	C₂³	1	2	yes	—
314	C₂₃×#103	C₂³	1	2	yes	—
315	C₂₃×#103	C₂³	1	2	yes	—
316	C₂₃×#103	C₂³	1	2	yes	—
317	C₂₃×#103	C₂³	1	2	yes	—
318	C₂₃×#103	C₂³	1	2	yes	—
319	C₂₃×#103	C₂³	1	2	yes	—
320	C₂₃×#103	C₂³	1	2	yes	—
321	C₂₃×#103	C₂³	1	2	yes	—
322	C₂₃×#103	C₂³	1	2	yes	—
323	C₂₃×#103	C₂³	1	2	yes	—
324	C₂₃×#103	C₂³	1	2	yes	—
325	C₂₃×#102	C₂³	1	2	yes	—
326	C₂₃×#102	C₂³	1	2	yes	—
327	C₂₃×#102	C₂³	1	2	yes	—
328	C₂₃×#102	C₂³	1	2	yes	—
329	C₂₃×#102	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	2	yes	—
331	C₂₃×#102	C₂³	1	2	yes	—
332	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
333	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
334	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂₃×#97	C₂³	1	1	yes	characteristic
336	C₂₃×#97	C₂³	1	1	yes	characteristic
337	C₂₃×#97	C₂³	1	1	yes	characteristic
338	C₂₃×#97	C₂³	1	2	yes	—
339	C₂₃×#97	C₂³	1	2	yes	—
340	C₂₃×#97	C₂³	1	1	yes	characteristic
341	C₄×C₈×C₂₃	C₂³	1	2	yes	—
342	#41×C₂₃	—	4	2	no	—
343	#41×C₂₃	—	4	4	no	—
344	#41×C₂₃	—	4	2	no	—
345	#41×C₂₃	—	4	2	no	—
346	#41×C₂₃	—	4	2	no	—
347	#41×C₂₃	—	4	2	no	—
348	#41×C₂₃	—	4	4	no	—
349	C₂×Q₈×C₂₃	—	2	1	no	—
350	C₂×Q₈×C₂₃	—	2	1	no	—
351	C₂×Q₈×C₂₃	—	2	1	no	—
352	C₂×Q₈×C₂₃	—	2	2	no	—
353	C₂×Q₈×C₂₃	—	4	2	no	—
354	C₂×Q₈×C₂₃	—	4	2	no	—
355	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
356	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
358	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₂₃	—	2	2	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	2	1	no	—
363	C₂×D₄×C₂₃	—	2	2	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	1	no	—
366	C₂×D₄×C₂₃	—	2	1	no	—
367	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
371	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	1	no	—
374	C₂²×C₄×C₂₃	—	2	1	no	—
375	C₂²×C₄×C₂₃	—	2	1	no	—
376	C₂²×C₄×C₂₃	—	2	2	no	—
377	C₂²×C₄×C₂₃	—	2	2	no	—
378	C₂²×C₄×C₂₃	—	2	1	no	—
379	C₂²×C₄×C₂₃	—	2	1	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	2	no	—
382	C₂²×C₄×C₂₃	—	2	2	no	—
383	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
392	Q₁₆×C₂₃	—	4	2	no	—
393	Q₁₆×C₂₃	—	4	2	no	—
394	SD₁₆×C₂₃	—	4	2	no	—
395	SD₁₆×C₂₃	—	4	2	no	—
396	SD₁₆×C₂₃	—	4	2	no	—
397	D₈×C₂₃	—	4	2	no	—
398	M₁₆×C₂₃	—	4	2	no	—
399	C₂×C₈×C₂₃	—	4	2	no	—
400	C₂×C₈×C₂₃	—	4	2	no	—
401	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
402	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
403	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
404	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	—	2	1	no	—
407	C₄⋊C₄×C₂₃	—	2	1	no	—
408	C₄⋊C₄×C₂₃	—	2	1	no	—
409	C₄⋊C₄×C₂₃	—	2	1	no	—
410	C₄⋊C₄×C₂₃	—	2	1	no	—
411	C₄⋊C₄×C₂₃	—	2	1	no	—
412	C₄⋊C₄×C₂₃	—	2	1	no	—
413	C₄⋊C₄×C₂₃	—	2	1	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	1	no	—
416	C₄⋊C₄×C₂₃	—	2	1	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	—	2	2	no	—
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	1	no	—
421	C₄⋊C₄×C₂₃	—	2	1	no	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	1	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
438	C₄⋊C₄×C₂₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂⁴	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	2	yes	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	2	no	—
470	C₂²⋊C₄×C₂₃	—	2	2	no	—
471	C₂²⋊C₄×C₂₃	—	2	2	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	1	no	—
474	C₂²⋊C₄×C₂₃	—	2	2	no	—
475	C₂²⋊C₄×C₂₃	—	2	1	no	—
476	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₂₃	—	2	2	no	—
483	C₄²×C₂₃	—	2	2	no	—
484	C₄²×C₂₃	—	2	1	no	—
485	C₄²×C₂₃	—	2	1	no	—
486	C₄²×C₂₃	—	2	1	no	—
487	C₄²×C₂₃	—	2	1	no	—
488	C₄²×C₂₃	—	2	1	no	—
489	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
496	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
497	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
498	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
499	#62579	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂³×C₂₃	—	2	1	no	—
501	C₂³×C₂₃	—	2	2	no	—
502	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
505	Q₈×C₂₃	—	2	2	no	—
506	Q₈×C₂₃	—	2	2	no	—
507	Q₈×C₂₃	—	2	2	no	—
508	Q₈×C₂₃	—	2	2	no	—
509	Q₈×C₂₃	—	2	2	no	—
510	Q₈×C₂₃	—	4	1	no	—
511	Q₈×C₂₃	—	4	2	no	—
512	Q₈×C₂₃	—	4	2	no	—
513	Q₈×C₂₃	—	8	1	no	—
514	Q₈×C₂₃	—	8	2	no	—
515	D₄×C₂₃	—	2	2	no	—
516	D₄×C₂₃	—	2	2	no	—
517	D₄×C₂₃	—	2	2	no	—
518	D₄×C₂₃	—	2	2	no	—
519	D₄×C₂₃	—	2	2	no	—
520	D₄×C₂₃	—	4	1	no	—
521	D₄×C₂₃	—	4	2	no	—
522	D₄×C₂₃	—	4	2	no	—
523	D₄×C₂₃	—	4	2	no	—
524	D₄×C₂₃	—	4	4	no	—
525	D₄×C₂₃	—	4	2	no	—
526	D₄×C₂₃	—	8	1	no	—
527	D₄×C₂₃	—	8	2	no	—
528	D₄×C₂₃	—	8	2	no	—
529	C₂×C₄×C₂₃	—	2	2	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	2	no	—
532	C₂×C₄×C₂₃	—	2	2	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	1	no	—
536	C₂×C₄×C₂₃	—	2	1	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	4	1	no	—
544	C₂×C₄×C₂₃	—	4	1	no	—
545	C₂×C₄×C₂₃	—	4	1	no	—
546	C₂×C₄×C₂₃	—	4	1	no	—
547	C₂×C₄×C₂₃	—	4	1	no	—
548	C₂×C₄×C₂₃	—	4	4	no	—
549	C₂×C₄×C₂₃	—	4	2	no	—
550	C₂×C₄×C₂₃	—	4	2	no	—
551	C₂×C₄×C₂₃	—	4	2	no	—
552	C₂×C₄×C₂₃	—	8	1	no	—
553	C₂×C₄×C₂₃	—	8	1	no	—
554	C₂×C₄×C₂₃	—	8	2	no	—
555	C₂×C₄×C₂₃	—	8	2	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	—	8	1	no	—
558	C₂×C₄×C₂₃	—	8	2	no	—
559	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
571	C₈×C₂₃	—	2	2	no	—
572	C₈×C₂₃	—	2	2	no	—
573	C₈×C₂₃	—	2	2	no	—
574	C₈×C₂₃	—	2	2	no	—
575	#3515	C₂×C₂₃	1	1	yes	characteristic, complemented
576	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
577	#3377	C₂×C₂₃	1	2	yes	complemented
578	#3376	C₂×C₂₃	1	2	yes	complemented
579	#3316	C₂×C₂₃	1	2	yes	complemented
580	#3315	C₂×C₂₃	1	2	yes	complemented
581	#3308	C₂×C₂₃	1	2	yes	complemented
582	#3307	C₂×C₂₃	1	2	yes	complemented
583	#3301	C₂×C₂₃	1	2	yes	complemented
584	#3300	C₂×C₂₃	1	2	yes	complemented
585	#3237	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3236	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3234	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3219	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3219	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
591	#3181	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#3180	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3172	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3142	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3135	C₂×C₂₃	1	1	yes	characteristic, complemented
596	C₂×#491	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
598	C₂²×C₂₃	—	2	1	no	—
599	C₂²×C₂₃	—	2	1	no	—
600	C₂²×C₂₃	—	2	1	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	1	no	—
603	C₂²×C₂₃	—	2	1	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	4	1	no	—
607	C₂²×C₂₃	—	4	2	no	—
608	C₂²×C₂₃	—	4	2	no	—
609	C₂²×C₂₃	—	4	1	no	—
610	C₂²×C₂₃	—	4	2	no	—
611	C₂²×C₂₃	—	4	1	no	—
612	C₂²×C₂₃	#575	1	2	yes	—
613	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
614	C₄×C₂₃	—	2	1	no	—
615	C₄×C₂₃	—	2	1	no	—
616	C₄×C₂₃	—	2	1	no	—
617	C₄×C₂₃	—	2	1	no	—
618	C₄×C₂₃	—	2	1	no	—
619	C₄×C₂₃	—	2	1	no	—
620	C₄×C₂₃	—	2	1	no	—
621	C₄×C₂₃	—	2	1	no	—
622	C₄×C₂₃	—	2	1	no	—
623	C₄×C₂₃	—	2	1	no	—
624	C₄×C₂₃	—	2	1	no	—
625	C₄×C₂₃	—	4	1	no	—
626	C₄×C₂₃	—	4	1	no	—
627	C₄×C₂₃	—	4	1	no	—
628	C₄×C₂₃	—	4	2	no	—
629	C₄×C₂₃	—	4	2	no	—
630	C₄×C₂₃	—	4	1	no	—
631	C₄×C₂₃	—	4	1	no	—
632	C₄×C₂₃	—	4	2	no	—
633	C₄×C₂₃	—	4	1	no	—
634	C₄×C₂₃	—	4	1	no	—
635	C₄×C₂₃	#585	1	2	yes	—
636	#557	C₂²×C₂₃	1	1	yes	characteristic
637	#556	C₂²×C₂₃	1	2	yes	—
638	#555	—	2	1	no	—
639	#554	—	2	1	no	—
640	#554	C₂²×C₂₃	1	1	yes	characteristic
641	#554	C₂²×C₂₃	1	1	yes	characteristic
642	#553	—	2	1	no	—
643	#553	—	2	1	no	—
644	#553	C₂²×C₂₃	1	1	yes	characteristic
645	#553	C₂²×C₂₃	1	1	yes	characteristic
646	#552	—	2	1	no	—
647	#552	—	2	1	no	—
648	#552	—	2	1	no	—
649	#552	C₂²×C₂₃	1	1	yes	characteristic
650	#552	C₂²×C₂₃	1	1	yes	characteristic
651	#548	C₂²×C₂₃	1	2	yes	—
652	#548	C₂²×C₂₃	1	2	yes	—
653	#547	—	2	1	no	—
654	#547	C₂²×C₂₃	1	2	yes	—
655	#547	C₂²×C₂₃	1	1	yes	characteristic
656	#542	—	2	1	no	—
657	#542	—	2	1	no	—
658	#541	—	2	1	no	—
659	#539	—	2	1	no	—
660	#539	—	2	1	no	—
661	#537	—	2	1	no	—
662	#533	C₂²×C₂₃	1	1	yes	characteristic
663	#533	C₂²×C₂₃	1	1	yes	characteristic
664	#533	C₂²×C₂₃	1	1	yes	characteristic
665	#532	C₂²×C₂₃	1	1	yes	characteristic
666	#532	C₂²×C₂₃	1	1	yes	characteristic
667	#532	C₂²×C₂₃	1	1	yes	characteristic
668	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
669	#529	C₂²×C₂₃	1	1	yes	characteristic
670	#529	C₂²×C₂₃	1	1	yes	characteristic
671	#529	C₂²×C₂₃	1	1	yes	characteristic
672	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
673	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
674	#520	—	2	1	no	—
675	#520	—	2	1	no	—
676	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
677	#501	C₂²×C₂₃	1	1	yes	characteristic
678	#501	C₂²×C₂₃	1	1	yes	characteristic
679	#501	C₂²×C₂₃	1	1	yes	characteristic
680	#497	C₂²×C₂₃	1	1	yes	characteristic
681	#497	C₂²×C₂₃	1	1	yes	characteristic
682	#496	C₂²×C₂₃	1	1	yes	characteristic
683	#491	C₂²×C₂₃	1	2	yes	—
684	#491	C₂²×C₂₃	1	2	yes	—
685	#491	C₂²×C₂₃	1	1	yes	characteristic
686	#491	C₂²×C₂₃	1	1	yes	characteristic
687	#491	C₂²×C₂₃	1	1	yes	characteristic
688	#491	C₂²×C₂₃	1	1	yes	characteristic
689	#491	C₂²×C₂₃	1	1	yes	characteristic
690	#491	C₂²×C₂₃	1	1	yes	characteristic
691	#490	C₂²×C₂₃	1	1	yes	characteristic
692	#490	C₂²×C₂₃	1	1	yes	characteristic
693	#490	C₂²×C₂₃	1	1	yes	characteristic
694	#489	C₂²×C₂₃	1	2	yes	—
695	#489	C₂²×C₂₃	1	2	yes	—
696	#489	C₂²×C₂₃	1	1	yes	characteristic
697	#488	C₂²×C₂₃	1	2	yes	—
698	#488	C₂²×C₂₃	1	2	yes	—
699	#485	C₂²×C₂₃	1	2	yes	—
700	#485	C₂²×C₂₃	1	2	yes	—
701	#484	C₂²×C₂₃	1	2	yes	—
702	#483	C₂²×C₂₃	1	2	yes	—
703	#481	C₂²×C₂₃	1	2	yes	—
704	#480	C₂²×C₂₃	1	2	yes	—
705	#479	C₂²×C₂₃	1	2	yes	—
706	#479	C₂²×C₂₃	1	2	yes	—
707	#478	C₂²×C₂₃	1	2	yes	—
708	#478	C₂²×C₂₃	1	2	yes	—
709	#477	C₂²×C₂₃	1	2	yes	—
710	#475	C₂²×C₂₃	1	2	yes	—
711	#470	C₂²×C₂₃	1	2	yes	—
712	#468	C₂²×C₂₃	1	2	yes	—
713	#467	C₂²×C₂₃	1	2	yes	—
714	#466	C₂²×C₂₃	1	2	yes	—
715	#465	C₂²×C₂₃	1	2	yes	—
716	#465	C₂²×C₂₃	1	2	yes	—
717	#464	C₂²×C₂₃	1	2	yes	—
718	#464	C₂²×C₂₃	1	2	yes	—
719	#463	C₂²×C₂₃	1	2	yes	—
720	#463	C₂²×C₂₃	1	2	yes	—
721	#462	C₂²×C₂₃	1	2	yes	—
722	#461	C₂²×C₂₃	1	2	yes	—
723	#452	C₂²×C₂₃	1	2	yes	—
724	#452	C₂²×C₂₃	1	2	yes	—
725	#451	C₂²×C₂₃	1	2	yes	—
726	#449	C₂²×C₂₃	1	2	yes	—
727	#449	C₂²×C₂₃	1	2	yes	—
728	#448	C₂²×C₂₃	1	2	yes	—
729	#446	C₂²×C₂₃	1	2	yes	—
730	#442	C₂²×C₂₃	1	2	yes	—
731	#441	C₂²×C₂₃	1	2	yes	—
732	#440	C₂²×C₂₃	1	2	yes	—
733	#440	C₂²×C₂₃	1	2	yes	—
734	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
735	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
736	#435	C₂²×C₂₃	1	2	yes	—
737	#435	C₂²×C₂₃	1	2	yes	—
738	C₈×D₄	C₂²×C₂₃	1	2	yes	—
739	#432	C₂²×C₂₃	1	1	yes	characteristic
740	#432	C₂²×C₂₃	1	1	yes	characteristic
741	#432	C₂²×C₂₃	1	1	yes	characteristic
742	#417	C₂²×C₂₃	1	2	yes	—
743	#417	C₂²×C₂₃	1	2	yes	—
744	#416	C₂²×C₂₃	1	2	yes	—
745	#416	C₂²×C₂₃	1	2	yes	—
746	C₂×#103	C₂²×C₂₃	1	2	yes	—
747	C₂×#103	C₂²×C₂₃	1	2	yes	—
748	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
749	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
750	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
751	C₂×C₂₃	—	2	2	no	—
752	C₂×C₂₃	—	4	1	no	—
753	C₂×C₂₃	—	4	1	no	—
754	C₂×C₂₃	—	8	1	no	—
755	C₂×C₂₃	—	8	2	no	—
756	C₂×C₂₃	#3500	1	1	yes	characteristic
757	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
758	C₂×C₂₃	#3586	1	1	yes	characteristic
759	C₂×#41	—	2	1	no	—
760	C₂×#41	—	2	1	no	—
761	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
762	C₂×#41	C₂³×C₂₃	1	2	yes	—
763	C₂×#41	C₂³×C₂₃	1	2	yes	—
764	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
765	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
766	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
768	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
769	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
770	C₂×D₈	C₂³×C₂₃	1	2	yes	—
771	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
772	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
773	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	—	2	1	no	—
776	C₄⋊Q₈	—	2	1	no	—
777	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
778	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
780	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
781	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	#127	C₂³×C₂₃	1	1	yes	characteristic
784	#126	—	2	1	no	—
785	#126	—	2	1	no	—
786	#126	—	2	2	no	—
787	#126	—	2	2	no	—
788	#126	—	2	1	no	—
789	#126	—	2	1	no	—
790	#126	—	2	1	no	—
791	#126	—	2	1	no	—
792	#126	—	2	1	no	—
793	#125	—	2	1	no	—
794	#125	—	2	1	no	—
795	#125	—	2	1	no	—
796	#125	—	2	1	no	—
797	#125	—	2	1	no	—
798	#125	—	2	1	no	—
799	#125	—	2	1	no	—
800	#125	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	C₂³×C₂₃	1	1	yes	characteristic
805	#125	C₂³×C₂₃	1	1	yes	characteristic
806	#125	C₂³×C₂₃	1	1	yes	characteristic
807	#125	C₂³×C₂₃	1	1	yes	characteristic
808	#125	C₂³×C₂₃	1	1	yes	characteristic
809	#125	C₂³×C₂₃	1	1	yes	characteristic
810	#125	C₂³×C₂₃	1	1	yes	characteristic
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	—	2	1	no	—
814	#124	C₂³×C₂₃	1	1	yes	characteristic
815	#124	C₂³×C₂₃	1	2	yes	—
816	#124	C₂³×C₂₃	1	2	yes	—
817	#123	—	2	1	no	—
818	#123	—	2	1	no	—
819	#123	—	2	1	no	—
820	#123	—	2	1	no	—
821	#123	—	2	1	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	2	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	1	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	1	no	—
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	C₂³×C₂₃	1	1	yes	characteristic
857	#121	C₂³×C₂₃	1	1	yes	characteristic
858	#121	C₂³×C₂₃	1	1	yes	characteristic
859	#121	C₂³×C₂₃	1	2	yes	—
860	C₄×Q₈	—	2	1	no	—
861	C₄×Q₈	—	2	1	no	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
866	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
867	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
868	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
869	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
870	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
871	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
886	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
887	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₂₃	1	2	yes	—
892	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
893	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
894	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	2	no	—
898	#117	—	2	1	no	—
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	—	2	1	no	—
902	#117	—	2	1	no	—
903	#117	D₄×C₂₃	1	1	yes	characteristic
904	#117	D₄×C₂₃	1	1	yes	characteristic
905	#117	D₄×C₂₃	1	1	yes	characteristic
906	#117	C₂³×C₂₃	1	1	yes	characteristic
907	#117	C₂³×C₂₃	1	1	yes	characteristic
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	—	2	1	no	—
911	C₂×C₄⋊C₄	—	2	1	no	—
912	C₂×C₄⋊C₄	—	2	1	no	—
913	C₂×C₄⋊C₄	—	2	1	no	—
914	C₂×C₄⋊C₄	—	2	2	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
920	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
921	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
922	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
923	#107	C₂³×C₂₃	1	2	yes	—
924	#107	C₂³×C₂₃	1	2	yes	—
925	#107	C₂³×C₂₃	1	2	yes	—
926	#106	C₂³×C₂₃	1	2	yes	—
927	#106	C₂³×C₂₃	1	2	yes	—
928	#106	C₂³×C₂₃	1	2	yes	—
929	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
930	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
931	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
932	#103	C₂³×C₂₃	1	2	yes	—
933	#103	C₂³×C₂₃	1	2	yes	—
934	#103	C₂³×C₂₃	1	2	yes	—
935	#103	C₂³×C₂₃	1	2	yes	—
936	#103	C₂³×C₂₃	1	2	yes	—
937	#103	C₂³×C₂₃	1	2	yes	—
938	#103	C₂³×C₂₃	1	2	yes	—
939	#103	C₂³×C₂₃	1	2	yes	—
940	#103	C₂³×C₂₃	1	2	yes	—
941	#103	C₂³×C₂₃	1	2	yes	—
942	#103	C₂³×C₂₃	1	2	yes	—
943	#103	C₂³×C₂₃	1	2	yes	—
944	#103	C₂³×C₂₃	1	2	yes	—
945	#102	C₂³×C₂₃	1	2	yes	—
946	#102	C₂³×C₂₃	1	2	yes	—
947	#102	C₂³×C₂₃	1	2	yes	—
948	#102	C₂³×C₂₃	1	2	yes	—
949	#102	C₂³×C₂₃	1	2	yes	—
950	#102	C₂³×C₂₃	1	2	yes	—
951	#102	C₂³×C₂₃	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
954	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
955	#97	C₂³×C₂₃	1	1	yes	characteristic
956	#97	C₂³×C₂₃	1	1	yes	characteristic
957	#97	C₂³×C₂₃	1	1	yes	characteristic
958	#97	C₂³×C₂₃	1	2	yes	—
959	#97	C₂³×C₂₃	1	2	yes	—
960	#97	C₂³×C₂₃	1	1	yes	characteristic
961	C₄×C₈	C₂³×C₂₃	1	2	yes	—
962	C₂₃	#62579	1	1	yes	characteristic, direct product factor, Sylow
963	#41	—	4	2	no	—
964	#41	—	4	4	no	—
965	#41	—	4	2	no	—
966	#41	—	4	2	no	—
967	#41	—	4	2	no	—
968	#41	—	4	2	no	—
969	#41	—	4	4	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	2	no	—
974	C₂×Q₈	—	4	2	no	—
975	C₂×Q₈	—	4	2	no	—
976	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
977	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
978	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
979	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
989	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
990	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
991	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
992	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1005	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1006	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1013	Q₁₆	—	4	2	no	—
1014	Q₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	SD₁₆	—	4	2	no	—
1018	D₈	—	4	2	no	—
1019	M₁₆	—	4	2	no	—
1020	C₂×C₈	—	4	2	no	—
1021	C₂×C₈	—	4	2	no	—
1022	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1023	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1024	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1073	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1075	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1098	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1099	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1102	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1103	C₄²	—	2	2	no	—
1104	C₄²	—	2	2	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	1	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1111	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1112	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1113	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1114	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1115	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1116	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1117	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1118	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1119	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	2	no	—
1122	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1123	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1124	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1125	Q₈	—	2	2	no	—
1126	Q₈	—	2	2	no	—
1127	Q₈	—	2	2	no	—
1128	Q₈	—	2	2	no	—
1129	Q₈	—	2	2	no	—
1130	Q₈	—	4	1	no	—
1131	Q₈	—	4	2	no	—
1132	Q₈	—	4	2	no	—
1133	Q₈	—	8	2	no	—
1134	Q₈	—	8	1	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	2	2	no	—
1138	D₄	—	2	2	no	—
1139	D₄	—	2	2	no	—
1140	D₄	—	4	1	no	—
1141	D₄	—	4	2	no	—
1142	D₄	—	4	2	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	4	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	2	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	—	8	1	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	1	no	—
1178	C₂×C₄	—	8	1	no	—
1179	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1183	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1184	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1185	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1190	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	2	2	no	—
1194	C₈	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	4	2	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	C₂₃×#575	1	2	yes	—
1210	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	2	1	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	2	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	C₂₃×#585	1	2	yes	—
1233	C₂	—	2	2	no	—
1234	C₂	—	4	1	no	—
1235	C₂	—	4	1	no	—
1236	C₂	—	8	2	no	—
1237	C₂	—	8	1	no	—
1238	C₂	C₂₃×#3500	1	1	yes	characteristic
1239	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1240	C₂	C₂₃×#3586	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3515	C₂	semidirect
2. C₂₃×#3511	C₂	semidirect
3. C₂₃×#3377	C₂	semidirect
4. C₂₃×#3376	C₂	semidirect
5. C₂₃×#3316	C₂	semidirect
6. C₂₃×#3315	C₂	semidirect
7. C₂₃×#3308	C₂	semidirect
8. C₂₃×#3307	C₂	semidirect
9. C₂₃×#3301	C₂	semidirect
10. C₂₃×#3300	C₂	semidirect
11. C₂₃×#3237	C₂	semidirect
12. C₂₃×#3236	C₂	semidirect
13. C₂₃×#3234	C₂	semidirect
14. C₂₃×#3219	C₂	semidirect
15. C₂₃×#3219	C₂	semidirect
16. C₂₃×#3218	C₂	semidirect
17. C₂₃×#3181	C₂	semidirect
18. C₂₃×#3180	C₂	semidirect
19. C₂₃×#3172	C₂	semidirect
20. C₂₃×#3142	C₂	semidirect
21. C₂₃×#3135	C₂	semidirect
22. C₂×C₂₃×#491	C₂	semidirect
23. C₂₃×#2970	C₂	semidirect
499. #62579	C₂₃	direct (N × H)
575. #3515	C₂×C₂₃	semidirect
576. #3511	C₂×C₂₃	semidirect
577. #3377	C₂×C₂₃	semidirect
578. #3376	C₂×C₂₃	semidirect
579. #3316	C₂×C₂₃	semidirect
580. #3315	C₂×C₂₃	semidirect
581. #3308	C₂×C₂₃	semidirect
582. #3307	C₂×C₂₃	semidirect
583. #3301	C₂×C₂₃	semidirect
584. #3300	C₂×C₂₃	semidirect
585. #3237	C₂×C₂₃	semidirect
586. #3236	C₂×C₂₃	semidirect
587. #3234	C₂×C₂₃	semidirect
588. #3219	C₂×C₂₃	semidirect
589. #3219	C₂×C₂₃	semidirect
590. #3218	C₂×C₂₃	semidirect
591. #3181	C₂×C₂₃	semidirect
592. #3180	C₂×C₂₃	semidirect
593. #3172	C₂×C₂₃	semidirect
594. #3142	C₂×C₂₃	semidirect
595. #3135	C₂×C₂₃	semidirect
596. C₂×#491	C₂×C₂₃	semidirect
597. #2970	C₂×C₂₃	semidirect
962. C₂₃	#62579	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3515	2
C₂₃×#3511	2
C₂₃×#3377	2
C₂₃×#3376	2
C₂₃×#3316	2
C₂₃×#3315	2
C₂₃×#3308	2
C₂₃×#3307	2
C₂₃×#3301	2
C₂₃×#3300	2
C₂₃×#3237	2
C₂₃×#3236	2
C₂₃×#3234	2
C₂₃×#3219	2
C₂₃×#3218	2
C₂₃×#3181	2
C₂₃×#3180	2
C₂₃×#3172	2
C₂₃×#3142	2
C₂₃×#3135	2
C₂×C₂₃×#491	2
C₂₃×#2970	2
#62579	23

Subgroups — C23×#62579 #19210205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62579 #19210205