Subgroups — C₂₃×#61021 #19208647

Order 5888.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3258	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3257	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3204	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3203	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3180	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3124	C₂	1	2	yes	maximal, complemented
21	C₂₃×#3120	C₂	1	2	yes	maximal, complemented
22	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	—	2	1	no	—
25	C₂₃×#555	—	2	1	no	—
26	C₂₃×#554	—	2	1	no	—
27	C₂₃×#553	—	2	1	no	—
28	C₂₃×#553	—	2	1	no	—
29	C₂₃×#553	—	2	1	no	—
30	C₂₃×#553	—	2	1	no	—
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#553	—	2	1	no	—
35	C₂₃×#552	—	2	1	no	—
36	C₂₃×#552	—	2	1	no	—
37	C₂₃×#548	—	2	1	no	—
38	C₂₃×#548	—	2	1	no	—
39	C₂₃×#547	—	2	1	no	—
40	C₂₃×#542	C₂²	1	2	yes	—
41	C₂₃×#542	C₂²	1	2	yes	—
42	C₂₃×#541	C₂²	1	1	yes	characteristic
43	C₂₃×#541	C₂²	1	1	yes	characteristic
44	C₂₃×#540	C₂²	1	1	yes	characteristic
45	C₂₃×#540	C₂²	1	1	yes	characteristic
46	C₂₃×#537	C₂²	1	1	yes	characteristic
47	C₂₃×#537	C₂²	1	2	yes	—
48	C₂₃×#537	C₂²	1	1	yes	characteristic
49	C₂₃×#533	C₂²	1	1	yes	characteristic
50	C₂₃×#533	C₂²	1	1	yes	characteristic
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂₃×#532	C₂²	1	1	yes	characteristic
53	C₂₃×#532	C₂²	1	1	yes	characteristic
54	C₂₃×#532	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂₃×#529	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	C₂₃×#520	C₂²	1	2	yes	—
62	C₂₃×#520	C₂²	1	1	yes	characteristic
63	C₂₃×#520	C₂²	1	1	yes	characteristic
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×#501	C₂²	1	1	yes	characteristic
69	C₂₃×#497	C₂²	1	1	yes	characteristic
70	C₂₃×#497	C₂²	1	1	yes	characteristic
71	C₂₃×#496	C₂²	1	1	yes	characteristic
72	C₂₃×#496	C₂²	1	1	yes	characteristic
73	C₂₃×#491	C₂²	1	1	yes	characteristic
74	C₂₃×#491	C₂²	1	1	yes	characteristic
75	C₂₃×#490	C₂²	1	1	yes	characteristic
76	C₂₃×#490	C₂²	1	1	yes	characteristic
77	C₂₃×#489	C₂²	1	1	yes	characteristic
78	C₂₃×#489	C₂²	1	1	yes	characteristic
79	C₂₃×#489	C₂²	1	1	yes	characteristic
80	C₂₃×#489	C₂²	1	1	yes	characteristic
81	C₂₃×#484	C₂²	1	2	yes	—
82	C₂₃×#484	C₂²	1	2	yes	—
83	C₂₃×#483	C₂²	1	2	yes	—
84	C₂₃×#483	C₂²	1	2	yes	—
85	C₂₃×#481	C₂²	1	2	yes	—
86	C₂₃×#481	C₂²	1	2	yes	—
87	C₂₃×#480	C₂²	1	2	yes	—
88	C₂₃×#480	C₂²	1	2	yes	—
89	C₂₃×#479	C₂²	1	2	yes	—
90	C₂₃×#479	C₂²	1	2	yes	—
91	C₂₃×#478	C₂²	1	2	yes	—
92	C₂₃×#478	C₂²	1	2	yes	—
93	C₂₃×#477	C₂²	1	2	yes	—
94	C₂₃×#476	C₂²	1	2	yes	—
95	C₂₃×#475	C₂²	1	2	yes	—
96	C₂₃×#474	C₂²	1	2	yes	—
97	C₂₃×#470	C₂²	1	2	yes	—
98	C₂₃×#469	C₂²	1	2	yes	—
99	C₂₃×#468	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×#460	C₂²	1	2	yes	—
112	C₂₃×#459	C₂²	1	2	yes	—
113	C₂₃×#452	C₂²	1	2	yes	—
114	C₂₃×#452	C₂²	1	2	yes	—
115	C₂₃×#452	C₂²	1	2	yes	—
116	C₂₃×#452	C₂²	1	2	yes	—
117	C₂₃×#449	C₂²	1	2	yes	—
118	C₂₃×#449	C₂²	1	2	yes	—
119	C₂₃×#449	C₂²	1	2	yes	—
120	C₂₃×#449	C₂²	1	2	yes	—
121	C₂₃×#442	C₂²	1	2	yes	—
122	C₂₃×#441	C₂²	1	2	yes	—
123	C₂₃×#440	C₂²	1	2	yes	—
124	C₂₃×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
128	C₄×D₈×C₂₃	C₂²	1	2	yes	—
129	C₂₃×#433	C₂²	1	2	yes	—
130	C₂₃×#433	C₂²	1	2	yes	—
131	C₂₃×#432	C₂²	1	1	yes	characteristic
132	C₂₃×#432	C₂²	1	1	yes	characteristic
133	C₂₃×#432	C₂²	1	1	yes	characteristic
134	C₂₃×#432	C₂²	1	1	yes	characteristic
135	C₂₃×#424	C₂²	1	2	yes	—
136	C₂₃×#408	C₂²	1	2	yes	—
137	C₄×M₁₆×C₂₃	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	C₂³	1	1	yes	characteristic
142	C₂×#41×C₂₃	C₂³	1	2	yes	—
143	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₂₃	—	2	1	no	—
146	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×D₈×C₂₃	C₂³	1	2	yes	—
153	C₂×D₈×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
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×#127	C₂³	1	1	yes	characteristic
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	1	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×#126	—	2	1	no	—
174	C₂₃×#126	—	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	C₂³	1	1	yes	characteristic
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×#124	—	2	2	no	—
188	C₂₃×#124	—	2	2	no	—
189	C₂₃×#124	—	2	1	no	—
190	C₂₃×#124	—	2	1	no	—
191	C₂₃×#124	C₂³	1	2	yes	—
192	C₂₃×#124	C₂³	1	1	yes	characteristic
193	C₂₃×#124	C₂³	1	1	yes	characteristic
194	C₂₃×#123	—	2	1	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	1	no	—
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	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂₃×#121	—	2	2	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	1	no	—
223	C₂₃×#121	—	2	1	no	—
224	C₂₃×#121	—	2	1	no	—
225	C₂₃×#121	—	2	1	no	—
226	C₂₃×#121	—	2	1	no	—
227	C₂₃×#121	—	2	1	no	—
228	C₂₃×#121	—	2	1	no	—
229	C₂₃×#121	—	2	1	no	—
230	C₂₃×#121	—	2	1	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	2	yes	—
238	C₂₃×#121	C₂³	1	1	yes	characteristic
239	C₂₃×#121	C₂³	1	1	yes	characteristic
240	C₂₃×#121	C₂³	1	2	yes	—
241	C₂₃×#121	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₂₃	—	2	1	no	—
243	C₄×Q₈×C₂₃	—	2	1	no	—
244	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
245	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
246	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
248	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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	—	2	1	no	—
266	C₄×D₄×C₂₃	—	2	1	no	—
267	C₄×D₄×C₂₃	—	2	1	no	—
268	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
269	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
270	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
271	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
272	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
273	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
274	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
275	C₄×D₄×C₂₃	C₂³	1	2	yes	—
276	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₂₃	C₂³	1	2	yes	—
278	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
280	C₂₃×#117	—	2	1	no	—
281	C₂₃×#117	—	2	1	no	—
282	C₂₃×#117	—	2	1	no	—
283	C₂₃×#117	—	2	1	no	—
284	C₂₃×#117	—	2	2	no	—
285	C₂₃×#117	—	2	1	no	—
286	C₂₃×#117	—	2	1	no	—
287	C₂₃×#117	—	2	1	no	—
288	C₂₃×#117	—	2	1	no	—
289	C₂₃×#117	C₂³	1	1	yes	characteristic
290	C₂₃×#117	C₂³	1	1	yes	characteristic
291	C₂₃×#117	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
300	C₂×C₄⋊C₄×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	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
304	C₂₃×#107	C₂³	1	2	yes	—
305	C₂₃×#107	C₂³	1	2	yes	—
306	C₂₃×#107	C₂³	1	2	yes	—
307	C₂₃×#107	C₂³	1	2	yes	—
308	C₂₃×#106	C₂³	1	2	yes	—
309	C₂₃×#106	C₂³	1	2	yes	—
310	C₂₃×#106	C₂³	1	2	yes	—
311	C₂₃×#106	C₂³	1	2	yes	—
312	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
314	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
315	C₂₃×C₄⋊C₈	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×#102	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×C₂²⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	no	—
344	#41×C₂₃	—	4	2	no	—
345	#41×C₂₃	—	4	2	no	—
346	#41×C₂₃	—	4	2	no	—
347	#41×C₂₃	—	8	2	no	—
348	#41×C₂₃	—	8	2	no	—
349	C₂×Q₈×C₂₃	—	2	1	no	—
350	C₂×Q₈×C₂₃	—	2	1	no	—
351	C₂×Q₈×C₂₃	—	2	2	no	—
352	C₂×Q₈×C₂₃	—	8	2	no	—
353	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₂₃	—	2	2	no	—
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	1	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	1	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	2	1	no	—
367	C₂×D₄×C₂₃	—	2	1	no	—
368	C₂×D₄×C₂₃	—	2	1	no	—
369	C₂×D₄×C₂₃	—	2	1	no	—
370	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₂₃	—	2	1	no	—
377	C₂²×C₄×C₂₃	—	2	1	no	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	1	no	—
385	C₂²×C₄×C₂₃	—	2	1	no	—
386	C₂²×C₄×C₂₃	—	2	2	no	—
387	C₂²×C₄×C₂₃	—	2	2	no	—
388	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	Q₁₆×C₂₃	—	4	2	no	—
398	Q₁₆×C₂₃	—	4	2	no	—
399	SD₁₆×C₂₃	—	4	2	no	—
400	SD₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	SD₁₆×C₂₃	—	4	2	no	—
403	D₈×C₂₃	—	4	2	no	—
404	D₈×C₂₃	—	4	2	no	—
405	M₁₆×C₂₃	—	4	2	no	—
406	C₂×C₈×C₂₃	—	4	2	no	—
407	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₃	—	2	1	no	—
412	C₄⋊C₄×C₂₃	—	2	1	no	—
413	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
418	C₄⋊C₄×C₂₃	—	2	1	no	—
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	—	2	1	no	—
435	C₄⋊C₄×C₂₃	—	2	1	no	—
436	C₄⋊C₄×C₂₃	—	2	1	no	—
437	C₄⋊C₄×C₂₃	—	2	1	no	—
438	C₄⋊C₄×C₂₃	—	2	1	no	—
439	C₄⋊C₄×C₂₃	—	2	2	no	—
440	C₄⋊C₄×C₂₃	—	2	2	no	—
441	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
450	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₂²⋊C₄×C₂₃	—	2	2	no	—
454	C₂²⋊C₄×C₂₃	—	2	2	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	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	1	no	—
464	C₂²⋊C₄×C₂₃	—	2	1	no	—
465	C₂²⋊C₄×C₂₃	—	2	2	no	—
466	C₂²⋊C₄×C₂₃	—	2	2	no	—
467	C₂²⋊C₄×C₂₃	—	2	1	no	—
468	C₂²⋊C₄×C₂₃	—	2	1	no	—
469	C₂²⋊C₄×C₂₃	—	2	1	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	2	no	—
474	C₂²⋊C₄×C₂₃	—	2	2	no	—
475	C₂²⋊C₄×C₂₃	—	2	2	no	—
476	C₂²⋊C₄×C₂₃	—	2	2	no	—
477	C₂²⋊C₄×C₂₃	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	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₂₃	—	2	1	no	—
484	C₄²×C₂₃	—	2	1	no	—
485	C₄²×C₂₃	—	2	1	no	—
486	C₄²×C₂₃	—	2	1	no	—
487	C₄²×C₂₃	—	2	2	no	—
488	C₄²×C₂₃	—	2	2	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	#61021	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂³×C₂₃	—	2	2	no	—
501	C₂³×C₂₃	—	2	1	no	—
502	C₂³×C₂₃	—	2	1	no	—
503	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
505	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	2	no	—
514	D₄×C₂₃	—	2	2	no	—
515	D₄×C₂₃	—	2	2	no	—
516	D₄×C₂₃	—	2	2	no	—
517	D₄×C₂₃	—	2	2	no	—
518	D₄×C₂₃	—	4	1	no	—
519	D₄×C₂₃	—	4	1	no	—
520	D₄×C₂₃	—	4	1	no	—
521	D₄×C₂₃	—	4	2	no	—
522	D₄×C₂₃	—	4	2	no	—
523	D₄×C₂₃	—	4	4	no	—
524	D₄×C₂₃	—	4	2	no	—
525	D₄×C₂₃	—	4	2	no	—
526	D₄×C₂₃	—	8	1	no	—
527	D₄×C₂₃	—	8	1	no	—
528	D₄×C₂₃	—	8	1	no	—
529	D₄×C₂₃	—	8	1	no	—
530	D₄×C₂₃	—	8	1	no	—
531	D₄×C₂₃	—	8	1	no	—
532	D₄×C₂₃	—	8	2	no	—
533	D₄×C₂₃	—	8	2	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	2	no	—
536	C₂×C₄×C₂₃	—	2	2	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	1	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	2	no	—
545	C₂×C₄×C₂₃	—	2	2	no	—
546	C₂×C₄×C₂₃	—	4	1	no	—
547	C₂×C₄×C₂₃	—	4	1	no	—
548	C₂×C₄×C₂₃	—	4	1	no	—
549	C₂×C₄×C₂₃	—	4	1	no	—
550	C₂×C₄×C₂₃	—	4	1	no	—
551	C₂×C₄×C₂₃	—	4	1	no	—
552	C₂×C₄×C₂₃	—	4	4	no	—
553	C₂×C₄×C₂₃	—	4	2	no	—
554	C₂×C₄×C₂₃	—	4	2	no	—
555	C₂×C₄×C₂₃	—	8	1	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	—	8	1	no	—
558	C₂×C₄×C₂₃	—	8	1	no	—
559	C₂×C₄×C₂₃	—	8	2	no	—
560	C₂×C₄×C₂₃	—	8	2	no	—
561	C₂×C₄×C₂₃	—	8	1	no	—
562	C₂×C₄×C₂₃	—	8	1	no	—
563	C₂×C₄×C₂₃	—	8	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
576	C₈×C₂₃	—	2	2	no	—
577	C₈×C₂₃	—	2	2	no	—
578	C₈×C₂₃	—	2	2	no	—
579	C₈×C₂₃	—	2	2	no	—
580	#3512	C₂×C₂₃	1	1	yes	characteristic, complemented
581	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
582	#3258	C₂×C₂₃	1	2	yes	complemented
583	#3257	C₂×C₂₃	1	2	yes	complemented
584	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3238	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	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
591	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#3204	C₂×C₂₃	1	2	yes	complemented
593	#3203	C₂×C₂₃	1	2	yes	complemented
594	#3181	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3180	C₂×C₂₃	1	1	yes	characteristic, complemented
596	#3172	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#3171	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3125	C₂×C₂₃	1	2	yes	complemented
599	#3124	C₂×C₂₃	1	2	yes	complemented
600	#3120	C₂×C₂₃	1	2	yes	complemented
601	#3119	C₂×C₂₃	1	2	yes	complemented
602	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
603	C₂²×C₂₃	—	2	1	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	2	1	no	—
607	C₂²×C₂₃	—	2	1	no	—
608	C₂²×C₂₃	—	2	1	no	—
609	C₂²×C₂₃	—	2	1	no	—
610	C₂²×C₂₃	—	2	1	no	—
611	C₂²×C₂₃	—	2	1	no	—
612	C₂²×C₂₃	—	4	2	no	—
613	C₂²×C₂₃	—	4	1	no	—
614	C₂²×C₂₃	—	4	1	no	—
615	C₂²×C₂₃	—	4	1	no	—
616	C₂²×C₂₃	—	4	2	no	—
617	C₂²×C₂₃	—	4	1	no	—
618	C₂²×C₂₃	—	4	2	no	—
619	C₂²×C₂₃	—	4	1	no	—
620	C₂²×C₂₃	—	4	1	no	—
621	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
622	C₄×C₂₃	—	2	1	no	—
623	C₄×C₂₃	—	2	1	no	—
624	C₄×C₂₃	—	2	1	no	—
625	C₄×C₂₃	—	2	1	no	—
626	C₄×C₂₃	—	2	1	no	—
627	C₄×C₂₃	—	2	1	no	—
628	C₄×C₂₃	—	2	1	no	—
629	C₄×C₂₃	—	2	1	no	—
630	C₄×C₂₃	—	2	1	no	—
631	C₄×C₂₃	—	2	1	no	—
632	C₄×C₂₃	—	2	1	no	—
633	C₄×C₂₃	—	4	1	no	—
634	C₄×C₂₃	—	4	1	no	—
635	C₄×C₂₃	—	4	2	no	—
636	C₄×C₂₃	—	4	2	no	—
637	C₄×C₂₃	—	4	1	no	—
638	C₄×C₂₃	—	4	1	no	—
639	C₄×C₂₃	—	4	2	no	—
640	C₄×C₂₃	—	4	1	no	—
641	C₄×C₂₃	—	4	1	no	—
642	C₄×C₂₃	#585	1	2	yes	—
643	#556	—	2	1	no	—
644	#555	—	2	1	no	—
645	#554	—	2	1	no	—
646	#553	—	2	1	no	—
647	#553	—	2	1	no	—
648	#553	—	2	1	no	—
649	#553	—	2	1	no	—
650	#553	—	2	1	no	—
651	#553	—	2	1	no	—
652	#553	—	2	1	no	—
653	#553	—	2	1	no	—
654	#552	—	2	1	no	—
655	#552	—	2	1	no	—
656	#548	—	2	1	no	—
657	#548	—	2	1	no	—
658	#547	—	2	1	no	—
659	#542	C₂²×C₂₃	1	2	yes	—
660	#542	C₂²×C₂₃	1	2	yes	—
661	#541	C₂²×C₂₃	1	1	yes	characteristic
662	#541	C₂²×C₂₃	1	1	yes	characteristic
663	#540	C₂²×C₂₃	1	1	yes	characteristic
664	#540	C₂²×C₂₃	1	1	yes	characteristic
665	#537	C₂²×C₂₃	1	1	yes	characteristic
666	#537	C₂²×C₂₃	1	2	yes	—
667	#537	C₂²×C₂₃	1	1	yes	characteristic
668	#533	C₂²×C₂₃	1	1	yes	characteristic
669	#533	C₂²×C₂₃	1	1	yes	characteristic
670	#532	C₂²×C₂₃	1	1	yes	characteristic
671	#532	C₂²×C₂₃	1	1	yes	characteristic
672	#532	C₂²×C₂₃	1	1	yes	characteristic
673	#532	C₂²×C₂₃	1	1	yes	characteristic
674	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
675	#529	C₂²×C₂₃	1	1	yes	characteristic
676	#529	C₂²×C₂₃	1	1	yes	characteristic
677	#529	C₂²×C₂₃	1	1	yes	characteristic
678	#529	C₂²×C₂₃	1	1	yes	characteristic
679	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
680	#520	C₂²×C₂₃	1	2	yes	—
681	#520	C₂²×C₂₃	1	1	yes	characteristic
682	#520	C₂²×C₂₃	1	1	yes	characteristic
683	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
684	#501	C₂²×C₂₃	1	1	yes	characteristic
685	#501	C₂²×C₂₃	1	1	yes	characteristic
686	#501	C₂²×C₂₃	1	1	yes	characteristic
687	#501	C₂²×C₂₃	1	1	yes	characteristic
688	#497	C₂²×C₂₃	1	1	yes	characteristic
689	#497	C₂²×C₂₃	1	1	yes	characteristic
690	#496	C₂²×C₂₃	1	1	yes	characteristic
691	#496	C₂²×C₂₃	1	1	yes	characteristic
692	#491	C₂²×C₂₃	1	1	yes	characteristic
693	#491	C₂²×C₂₃	1	1	yes	characteristic
694	#490	C₂²×C₂₃	1	1	yes	characteristic
695	#490	C₂²×C₂₃	1	1	yes	characteristic
696	#489	C₂²×C₂₃	1	1	yes	characteristic
697	#489	C₂²×C₂₃	1	1	yes	characteristic
698	#489	C₂²×C₂₃	1	1	yes	characteristic
699	#489	C₂²×C₂₃	1	1	yes	characteristic
700	#484	C₂²×C₂₃	1	2	yes	—
701	#484	C₂²×C₂₃	1	2	yes	—
702	#483	C₂²×C₂₃	1	2	yes	—
703	#483	C₂²×C₂₃	1	2	yes	—
704	#481	C₂²×C₂₃	1	2	yes	—
705	#481	C₂²×C₂₃	1	2	yes	—
706	#480	C₂²×C₂₃	1	2	yes	—
707	#480	C₂²×C₂₃	1	2	yes	—
708	#479	C₂²×C₂₃	1	2	yes	—
709	#479	C₂²×C₂₃	1	2	yes	—
710	#478	C₂²×C₂₃	1	2	yes	—
711	#478	C₂²×C₂₃	1	2	yes	—
712	#477	C₂²×C₂₃	1	2	yes	—
713	#476	C₂²×C₂₃	1	2	yes	—
714	#475	C₂²×C₂₃	1	2	yes	—
715	#474	C₂²×C₂₃	1	2	yes	—
716	#470	C₂²×C₂₃	1	2	yes	—
717	#469	C₂²×C₂₃	1	2	yes	—
718	#468	C₂²×C₂₃	1	2	yes	—
719	#468	C₂²×C₂₃	1	2	yes	—
720	#467	C₂²×C₂₃	1	2	yes	—
721	#466	C₂²×C₂₃	1	2	yes	—
722	#465	C₂²×C₂₃	1	2	yes	—
723	#465	C₂²×C₂₃	1	2	yes	—
724	#464	C₂²×C₂₃	1	2	yes	—
725	#464	C₂²×C₂₃	1	2	yes	—
726	#463	C₂²×C₂₃	1	2	yes	—
727	#463	C₂²×C₂₃	1	2	yes	—
728	#462	C₂²×C₂₃	1	2	yes	—
729	#461	C₂²×C₂₃	1	2	yes	—
730	#460	C₂²×C₂₃	1	2	yes	—
731	#459	C₂²×C₂₃	1	2	yes	—
732	#452	C₂²×C₂₃	1	2	yes	—
733	#452	C₂²×C₂₃	1	2	yes	—
734	#452	C₂²×C₂₃	1	2	yes	—
735	#452	C₂²×C₂₃	1	2	yes	—
736	#449	C₂²×C₂₃	1	2	yes	—
737	#449	C₂²×C₂₃	1	2	yes	—
738	#449	C₂²×C₂₃	1	2	yes	—
739	#449	C₂²×C₂₃	1	2	yes	—
740	#442	C₂²×C₂₃	1	2	yes	—
741	#441	C₂²×C₂₃	1	2	yes	—
742	#440	C₂²×C₂₃	1	2	yes	—
743	#440	C₂²×C₂₃	1	2	yes	—
744	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
745	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
746	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
747	C₄×D₈	C₂²×C₂₃	1	2	yes	—
748	#433	C₂²×C₂₃	1	2	yes	—
749	#433	C₂²×C₂₃	1	2	yes	—
750	#432	C₂²×C₂₃	1	1	yes	characteristic
751	#432	C₂²×C₂₃	1	1	yes	characteristic
752	#432	C₂²×C₂₃	1	1	yes	characteristic
753	#432	C₂²×C₂₃	1	1	yes	characteristic
754	#424	C₂²×C₂₃	1	2	yes	—
755	#408	C₂²×C₂₃	1	2	yes	—
756	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
757	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
758	C₂×C₂₃	—	4	1	no	—
759	C₂×C₂₃	—	4	1	no	—
760	C₂×C₂₃	—	4	1	no	—
761	C₂×C₂₃	—	8	2	no	—
762	C₂×C₂₃	—	8	1	no	—
763	C₂×C₂₃	—	8	1	no	—
764	C₂×C₂₃	#3449	1	1	yes	characteristic
765	C₂×C₂₃	#3585	1	1	yes	characteristic
766	C₂×C₂₃	#3586	1	1	yes	characteristic
767	C₂×#41	—	2	1	no	—
768	C₂×#41	—	2	1	no	—
769	C₂×#41	C₂³×C₂₃	1	2	yes	—
770	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
771	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
773	C₂²×Q₈	—	2	1	no	—
774	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
775	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
780	C₂×D₈	C₂³×C₂₃	1	2	yes	—
781	C₂×D₈	C₂³×C₂₃	1	2	yes	—
782	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
783	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
784	C₄⋊Q₈	—	2	1	no	—
785	C₄⋊Q₈	—	2	1	no	—
786	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
787	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
791	#127	C₂³×C₂₃	1	1	yes	characteristic
792	#127	C₂³×C₂₃	1	1	yes	characteristic
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#126	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	—	2	1	no	—
810	#125	—	2	1	no	—
811	#125	C₂³×C₂₃	1	1	yes	characteristic
812	#125	C₂³×C₂₃	1	1	yes	characteristic
813	#125	C₂³×C₂₃	1	1	yes	characteristic
814	#125	C₂³×C₂₃	1	1	yes	characteristic
815	#124	—	2	2	no	—
816	#124	—	2	2	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	C₂³×C₂₃	1	1	yes	characteristic
820	#124	C₂³×C₂₃	1	1	yes	characteristic
821	#124	C₂³×C₂₃	1	2	yes	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	#123	—	2	1	no	—
828	#123	—	2	1	no	—
829	#123	—	2	1	no	—
830	#123	—	2	2	no	—
831	#123	—	2	2	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	2	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	C₂³×C₂₃	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	1	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	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	C₂³×C₂₃	1	1	yes	characteristic
865	#121	C₂³×C₂₃	1	1	yes	characteristic
866	#121	C₂³×C₂₃	1	1	yes	characteristic
867	#121	C₂³×C₂₃	1	1	yes	characteristic
868	#121	C₂³×C₂₃	1	2	yes	—
869	#121	C₂³×C₂₃	1	2	yes	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
873	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
874	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
879	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
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	2	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
897	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
898	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
899	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
900	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
901	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
902	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
903	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
904	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₂₃	1	2	yes	—
907	C₄×D₄	C₂³×C₂₃	1	2	yes	—
908	#117	—	2	1	no	—
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	2	no	—
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	C₂³×C₂₃	1	1	yes	characteristic
918	#117	C₂³×C₂₃	1	1	yes	characteristic
919	#117	C₂³×C₂₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	—	2	1	no	—
921	C₂×C₄⋊C₄	—	2	1	no	—
922	C₂×C₄⋊C₄	—	2	1	no	—
923	C₂×C₄⋊C₄	—	2	2	no	—
924	C₂×C₄⋊C₄	—	2	1	no	—
925	C₂×C₄⋊C₄	—	2	1	no	—
926	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
927	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
929	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
930	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
931	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
932	#107	C₂³×C₂₃	1	2	yes	—
933	#107	C₂³×C₂₃	1	2	yes	—
934	#107	C₂³×C₂₃	1	2	yes	—
935	#107	C₂³×C₂₃	1	2	yes	—
936	#106	C₂³×C₂₃	1	2	yes	—
937	#106	C₂³×C₂₃	1	2	yes	—
938	#106	C₂³×C₂₃	1	2	yes	—
939	#106	C₂³×C₂₃	1	2	yes	—
940	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
941	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
942	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
943	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
944	#103	C₂³×C₂₃	1	2	yes	—
945	#103	C₂³×C₂₃	1	2	yes	—
946	#103	C₂³×C₂₃	1	2	yes	—
947	#103	C₂³×C₂₃	1	2	yes	—
948	#103	C₂³×C₂₃	1	2	yes	—
949	#103	C₂³×C₂₃	1	2	yes	—
950	#103	C₂³×C₂₃	1	2	yes	—
951	#103	C₂³×C₂₃	1	2	yes	—
952	#102	C₂³×C₂₃	1	2	yes	—
953	#102	C₂³×C₂₃	1	2	yes	—
954	#102	C₂³×C₂₃	1	2	yes	—
955	#102	C₂³×C₂₃	1	2	yes	—
956	#102	C₂³×C₂₃	1	2	yes	—
957	#102	C₂³×C₂₃	1	2	yes	—
958	#102	C₂³×C₂₃	1	2	yes	—
959	#102	C₂³×C₂₃	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
964	#97	C₂³×C₂₃	1	1	yes	characteristic
965	#97	C₂³×C₂₃	1	1	yes	characteristic
966	#97	C₂³×C₂₃	1	2	yes	—
967	#97	C₂³×C₂₃	1	1	yes	characteristic
968	#97	C₂³×C₂₃	1	1	yes	characteristic
969	C₄×C₈	C₂³×C₂₃	1	2	yes	—
970	C₂₃	#61021	1	1	yes	characteristic, direct product factor, Sylow
971	#41	—	4	2	no	—
972	#41	—	4	2	no	—
973	#41	—	4	2	no	—
974	#41	—	4	2	no	—
975	#41	—	4	2	no	—
976	#41	—	8	2	no	—
977	#41	—	8	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	2	1	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	8	2	no	—
982	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
984	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1001	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1002	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1003	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1004	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1026	Q₁₆	—	4	2	no	—
1027	Q₁₆	—	4	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	D₈	—	4	2	no	—
1033	D₈	—	4	2	no	—
1034	M₁₆	—	4	2	no	—
1035	C₂×C₈	—	4	2	no	—
1036	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1038	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1039	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	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	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	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	1	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	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1071	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1075	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1080	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	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	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	—	2	2	no	—
1118	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1119	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1120	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1121	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1122	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1123	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1124	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1125	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1126	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1127	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	1	no	—
1130	C₂³	—	2	1	no	—
1131	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1132	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1133	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	4	1	no	—
1139	Q₈	—	4	2	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	8	2	no	—
1142	D₄	—	2	2	no	—
1143	D₄	—	2	2	no	—
1144	D₄	—	2	2	no	—
1145	D₄	—	2	2	no	—
1146	D₄	—	4	1	no	—
1147	D₄	—	4	1	no	—
1148	D₄	—	4	1	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	4	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	8	1	no	—
1155	D₄	—	8	1	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	8	2	no	—
1158	D₄	—	8	1	no	—
1159	D₄	—	8	1	no	—
1160	D₄	—	8	1	no	—
1161	D₄	—	8	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	4	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	1	no	—
1187	C₂×C₄	—	8	1	no	—
1188	C₂×C₄	—	8	1	no	—
1189	C₂×C₄	—	8	2	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1197	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1198	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1199	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1200	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1203	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1204	C₈	—	2	2	no	—
1205	C₈	—	2	2	no	—
1206	C₈	—	2	2	no	—
1207	C₈	—	2	2	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	C₂₃×#585	1	2	yes	—
1248	C₂	—	4	1	no	—
1249	C₂	—	4	1	no	—
1250	C₂	—	4	1	no	—
1251	C₂	—	8	2	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₂₃×#3449	1	1	yes	characteristic
1255	C₂	C₂₃×#3585	1	1	yes	characteristic
1256	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×#3512	C₂	semidirect
2. C₂₃×#3511	C₂	semidirect
3. C₂₃×#3258	C₂	semidirect
4. C₂₃×#3257	C₂	semidirect
5. C₂₃×#3239	C₂	semidirect
6. C₂₃×#3238	C₂	semidirect
7. C₂₃×#3236	C₂	semidirect
8. C₂₃×#3234	C₂	semidirect
9. C₂₃×#3219	C₂	semidirect
10. C₂₃×#3219	C₂	semidirect
11. C₂₃×#3216	C₂	semidirect
12. C₂₃×#3214	C₂	semidirect
13. C₂₃×#3204	C₂	semidirect
14. C₂₃×#3203	C₂	semidirect
15. C₂₃×#3181	C₂	semidirect
16. C₂₃×#3180	C₂	semidirect
17. C₂₃×#3172	C₂	semidirect
18. C₂₃×#3171	C₂	semidirect
19. C₂₃×#3125	C₂	semidirect
20. C₂₃×#3124	C₂	semidirect
21. C₂₃×#3120	C₂	semidirect
22. C₂₃×#3119	C₂	semidirect
23. C₂₃×#2923	C₂	semidirect
499. #61021	C₂₃	direct (N × H)
580. #3512	C₂×C₂₃	semidirect
581. #3511	C₂×C₂₃	semidirect
582. #3258	C₂×C₂₃	semidirect
583. #3257	C₂×C₂₃	semidirect
584. #3239	C₂×C₂₃	semidirect
585. #3238	C₂×C₂₃	semidirect
586. #3236	C₂×C₂₃	semidirect
587. #3234	C₂×C₂₃	semidirect
588. #3219	C₂×C₂₃	semidirect
589. #3219	C₂×C₂₃	semidirect
590. #3216	C₂×C₂₃	semidirect
591. #3214	C₂×C₂₃	semidirect
592. #3204	C₂×C₂₃	semidirect
593. #3203	C₂×C₂₃	semidirect
594. #3181	C₂×C₂₃	semidirect
595. #3180	C₂×C₂₃	semidirect
596. #3172	C₂×C₂₃	semidirect
597. #3171	C₂×C₂₃	semidirect
598. #3125	C₂×C₂₃	semidirect
599. #3124	C₂×C₂₃	semidirect
600. #3120	C₂×C₂₃	semidirect
601. #3119	C₂×C₂₃	semidirect
602. #2923	C₂×C₂₃	semidirect
970. C₂₃	#61021	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×#3512	2
C₂₃×#3511	2
C₂₃×#3258	2
C₂₃×#3257	2
C₂₃×#3239	2
C₂₃×#3238	2
C₂₃×#3236	2
C₂₃×#3234	2
C₂₃×#3219	2
C₂₃×#3216	2
C₂₃×#3214	2
C₂₃×#3204	2
C₂₃×#3203	2
C₂₃×#3181	2
C₂₃×#3180	2
C₂₃×#3172	2
C₂₃×#3171	2
C₂₃×#3125	2
C₂₃×#3124	2
C₂₃×#3120	2
C₂₃×#3119	2
C₂₃×#2923	2
#61021	23

Subgroups — C23×#61021 #19208647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61021 #19208647