Subgroups — C₂₃×#62573 #19210199

Order 5888.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3332	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3309	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3220	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3179	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#563	—	2	1	no	—
21	C₂₃×#562	—	2	1	no	—
22	C₂₃×#560	—	2	2	no	—
23	C₂₃×#556	C₂²	1	1	yes	characteristic
24	C₂₃×#554	C₂²	1	2	yes	complemented
25	C₂₃×#553	—	2	1	no	—
26	C₂₃×#553	C₂²	1	2	yes	—
27	C₂₃×#553	C₂²	1	2	yes	complemented
28	C₂₃×#550	C₂²	1	2	yes	—
29	C₂₃×#550	C₂²	1	1	yes	characteristic
30	C₂₃×#547	—	2	2	no	—
31	C₂₃×#547	C₂²	1	1	yes	characteristic
32	C₂₃×#547	C₂²	1	2	yes	complemented
33	C₂₃×#546	—	2	1	no	—
34	C₂₃×#546	C₂²	1	2	yes	—
35	D₄²×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#544	C₂²	1	2	yes	complemented
37	C₂₃×#542	C₂²	1	2	yes	—
38	C₂₃×#540	C₂²	1	2	yes	complemented
39	C₂₃×#539	—	2	2	no	—
40	C₂₃×#539	—	2	1	no	—
41	C₂₃×#538	—	2	2	no	—
42	C₂₃×#537	—	2	1	no	—
43	C₂₃×#537	—	2	1	no	—
44	C₂₃×#535	—	2	1	no	—
45	C₂₃×#535	C₂²	1	2	yes	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	1	yes	characteristic
48	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#501	C₂²	1	2	yes	complemented
52	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#496	C₂²	1	2	yes	complemented
54	C₂₃×#493	C₂²	1	1	yes	characteristic
55	C₂₃×#491	C₂²	1	2	yes	complemented
56	C₂₃×#490	C₂²	1	2	yes	—
57	C₂₃×#490	C₂²	1	2	yes	—
58	C₂₃×#490	C₂²	1	2	yes	complemented
59	C₂₃×#489	C₂²	1	2	yes	—
60	C₂₃×#489	C₂²	1	2	yes	complemented
61	C₂₃×#488	C₂²	1	2	yes	—
62	C₂₃×#488	C₂²	1	2	yes	complemented
63	C₂₃×#488	C₂²	1	2	yes	complemented
64	C₂₃×#486	C₂²	1	1	yes	characteristic
65	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#483	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	—
70	C₂₃×#481	C₂²	1	1	yes	characteristic
71	C₂₃×#481	C₂²	1	2	yes	—
72	C₂₃×#481	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#480	C₂²	1	1	yes	characteristic
74	C₂₃×#480	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#479	C₂²	1	2	yes	complemented
76	C₂₃×#478	C₂²	1	2	yes	—
77	C₂₃×#478	C₂²	1	2	yes	complemented
78	C₂₃×#478	C₂²	1	2	yes	complemented
79	C₂₃×#476	C₂²	1	2	yes	complemented
80	C₂₃×#475	C₂²	1	2	yes	complemented
81	C₂₃×#469	C₂²	1	2	yes	—
82	C₂₃×#469	C₂²	1	2	yes	—
83	C₂₃×#469	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#466	C₂²	1	2	yes	—
86	C₂₃×#465	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	—
89	C₂₃×#461	C₂²	1	2	yes	complemented
90	C₂₃×#459	C₂²	1	2	yes	—
91	C₂₃×#459	C₂²	1	2	yes	complemented
92	C₂₃×#459	C₂²	1	2	yes	complemented
93	C₂₃×#449	C₂²	1	2	yes	complemented
94	C₂₃×#449	C₂²	1	2	yes	complemented
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#449	C₂²	1	2	yes	complemented
97	C₂₃×#447	C₂²	1	2	yes	—
98	C₂₃×#447	C₂²	1	2	yes	—
99	C₂₃×#446	C₂²	1	2	yes	complemented
100	C₂₃×#442	C₂²	1	2	yes	—
101	C₂₃×#442	C₂²	1	2	yes	complemented
102	C₂₃×#442	C₂²	1	2	yes	complemented
103	C₂₃×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#436	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	—
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₂₃×#433	C₂²	1	2	yes	complemented
110	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#418	C₂²	1	2	yes	—
112	C₂₃×#417	C₂²	1	2	yes	complemented
113	C₂₃×#417	C₂²	1	2	yes	complemented
114	C₂₃×#417	C₂²	1	2	yes	complemented
115	C₂₃×#416	C₂²	1	2	yes	complemented
116	C₂×C₂₃×#102	C₂²	1	2	yes	—
117	C₂₃×#405	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₂₃	—	2	1	no	—
120	C₂×#41×C₂₃	—	2	2	no	—
121	C₂×#41×C₂₃	—	2	1	no	—
122	C₂×#41×C₂₃	—	2	1	no	—
123	C₂×#41×C₂₃	C₂³	1	2	yes	—
124	C₂×#41×C₂₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₂₃	—	2	1	no	—
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	2	yes	—
131	C₂×D₈×C₂₃	C₂³	1	2	yes	—
132	C₂×D₈×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
136	C₂₃×C₄⋊Q₈	—	2	2	no	—
137	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₂₃×#127	—	2	2	no	—
142	C₂₃×#127	C₂³	1	2	yes	—
143	C₂₃×#127	C₂³	1	1	yes	characteristic
144	C₂₃×#127	C₂³	1	1	yes	characteristic
145	C₂₃×#127	C₂³	1	1	yes	characteristic
146	C₂₃×#126	—	2	2	no	—
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	—	2	2	no	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#126	D₄	1	2	yes	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	1	no	—
153	C₂₃×#125	—	2	1	no	—
154	C₂₃×#125	D₄	1	1	yes	characteristic
155	C₂₃×#125	C₂³	1	2	yes	—
156	C₂₃×#125	C₂³	1	2	yes	—
157	C₂₃×#125	C₂³	1	2	yes	—
158	C₂₃×#124	—	2	2	no	—
159	C₂₃×#124	—	2	1	no	—
160	C₂₃×#124	—	2	1	no	—
161	C₂₃×#124	D₄	1	1	yes	characteristic
162	C₂₃×#124	C₂³	1	2	yes	—
163	C₂₃×#124	C₂³	1	2	yes	—
164	C₂₃×#123	—	2	2	no	—
165	C₂₃×#123	—	2	2	no	—
166	C₂₃×#123	—	2	2	no	—
167	C₂₃×#123	—	2	2	no	—
168	C₂₃×#123	—	2	2	no	—
169	C₂₃×#123	—	2	2	no	—
170	C₂₃×#123	—	2	2	no	—
171	C₂₃×#123	—	2	2	no	—
172	C₂₃×#123	—	2	2	no	—
173	C₂₃×#123	D₄	1	2	yes	—
174	C₂₃×C₂²⋊Q₈	—	2	2	no	—
175	C₂₃×C₂²⋊Q₈	—	2	1	no	—
176	C₂₃×C₂²⋊Q₈	—	2	2	no	—
177	C₂₃×C₂²⋊Q₈	—	2	2	no	—
178	C₂₃×C₂²⋊Q₈	—	2	2	no	—
179	C₂₃×C₂²⋊Q₈	—	2	2	no	—
180	C₂₃×C₂²⋊Q₈	—	2	2	no	—
181	C₂₃×C₂²⋊Q₈	—	2	2	no	—
182	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
183	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
184	C₂₃×#121	—	2	2	no	—
185	C₂₃×#121	—	2	1	no	—
186	C₂₃×#121	—	2	2	no	—
187	C₂₃×#121	—	2	1	no	—
188	C₂₃×#121	—	2	1	no	—
189	C₂₃×#121	—	2	1	no	—
190	C₂₃×#121	—	2	1	no	—
191	C₂₃×#121	—	2	1	no	—
192	C₂₃×#121	—	2	2	no	—
193	C₂₃×#121	—	2	2	no	—
194	C₂₃×#121	—	2	1	no	—
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	2	no	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	D₄	1	1	yes	characteristic
202	C₂₃×#121	C₂³	1	2	yes	—
203	C₂₃×#121	C₂³	1	2	yes	—
204	C₂₃×#121	C₂³	1	1	yes	characteristic
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	1	yes	characteristic
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₂₃×#120	—	2	2	no	—
211	C₂₃×#120	—	2	2	no	—
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₂₃	—	2	2	no	—
215	C₄×D₄×C₂₃	—	2	2	no	—
216	C₄×D₄×C₂₃	—	2	2	no	—
217	C₄×D₄×C₂₃	—	2	1	no	—
218	C₄×D₄×C₂₃	—	2	1	no	—
219	C₄×D₄×C₂₃	—	2	1	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₂₃	C₂³	1	2	yes	—
223	C₄×D₄×C₂₃	C₂³	1	2	yes	—
224	C₄×D₄×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	C₂³	1	2	yes	—
226	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₂₃	C₂³	1	2	yes	—
229	C₂₃×#117	—	2	1	no	—
230	C₂₃×#117	C₂³	1	2	yes	—
231	C₂₃×#117	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
238	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
240	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#107	C₂³	1	2	yes	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#106	C₂³	1	2	yes	—
244	C₂₃×#106	C₂³	1	2	yes	—
245	C₂₃×#106	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×#103	C₂³	1	2	yes	—
251	C₂₃×#103	C₂³	1	2	yes	—
252	C₂₃×#103	C₂³	1	2	yes	—
253	C₂₃×#103	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	C₂³	1	2	yes	—
256	C₂₃×#102	C₂³	1	2	yes	—
257	C₂₃×#102	C₂³	1	2	yes	—
258	C₂₃×#102	C₂³	1	2	yes	—
259	C₂₃×#102	C₂³	1	2	yes	—
260	C₂₃×#102	C₂³	1	2	yes	—
261	C₂₃×#102	C₂³	1	2	yes	—
262	C₂₃×#102	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₂₃×#97	C₂³	1	2	yes	—
275	C₂₃×#97	C₂³	1	2	yes	—
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	—	2	2	no	—
281	#41×C₂₃	—	4	2	no	—
282	#41×C₂₃	—	4	2	no	—
283	#41×C₂₃	—	4	2	no	—
284	#41×C₂₃	—	4	2	no	—
285	#41×C₂₃	—	8	2	no	—
286	#41×C₂₃	—	8	2	no	—
287	#41×C₂₃	—	8	4	no	—
288	#41×C₂₃	—	8	2	no	—
289	C₂×Q₈×C₂₃	—	2	2	no	—
290	C₂×Q₈×C₂₃	—	2	1	no	—
291	C₂×Q₈×C₂₃	—	2	1	no	—
292	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	2	2	no	—
296	C₂×D₄×C₂₃	—	2	1	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	2	no	—
299	C₂×D₄×C₂₃	—	2	2	no	—
300	C₂×D₄×C₂₃	—	2	2	no	—
301	C₂×D₄×C₂₃	—	2	1	no	—
302	C₂×D₄×C₂₃	—	2	1	no	—
303	C₂×D₄×C₂₃	—	2	1	no	—
304	C₂×D₄×C₂₃	—	2	1	no	—
305	C₂×D₄×C₂₃	—	2	2	no	—
306	C₂×D₄×C₂₃	—	2	1	no	—
307	C₂×D₄×C₂₃	—	2	1	no	—
308	C₂×D₄×C₂₃	—	2	2	no	—
309	C₂×D₄×C₂₃	—	2	2	no	—
310	C₂×D₄×C₂₃	—	2	1	no	—
311	C₂×D₄×C₂₃	—	4	2	no	—
312	C₂×D₄×C₂₃	—	4	2	no	—
313	C₂×D₄×C₂₃	—	8	2	no	—
314	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₂₃	—	2	1	no	—
321	C₂²×C₄×C₂₃	—	2	1	no	—
322	C₂²×C₄×C₂₃	—	2	2	no	—
323	C₂²×C₄×C₂₃	—	2	1	no	—
324	C₂²×C₄×C₂₃	—	2	1	no	—
325	C₂²×C₄×C₂₃	—	2	2	no	—
326	C₂²×C₄×C₂₃	—	2	2	no	—
327	C₂²×C₄×C₂₃	—	2	2	no	—
328	C₂²×C₄×C₂₃	—	2	2	no	—
329	C₂²×C₄×C₂₃	—	2	2	no	—
330	C₂²×C₄×C₂₃	—	2	2	no	—
331	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
335	SD₁₆×C₂₃	—	4	2	no	—
336	SD₁₆×C₂₃	—	4	2	no	—
337	D₈×C₂₃	—	4	2	no	—
338	D₈×C₂₃	—	4	2	no	—
339	D₈×C₂₃	—	4	2	no	—
340	D₈×C₂₃	—	4	2	no	—
341	M₁₆×C₂₃	—	4	2	no	—
342	M₁₆×C₂₃	—	4	2	no	—
343	C₂×C₈×C₂₃	—	4	2	no	—
344	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
345	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
346	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
347	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
349	C₄⋊C₄×C₂₃	—	2	1	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	2	no	—
353	C₄⋊C₄×C₂₃	—	2	2	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	1	no	—
357	C₄⋊C₄×C₂₃	—	2	2	no	—
358	C₄⋊C₄×C₂₃	—	2	1	no	—
359	C₄⋊C₄×C₂₃	—	2	1	no	—
360	C₄⋊C₄×C₂₃	—	2	1	no	—
361	C₄⋊C₄×C₂₃	—	2	1	no	—
362	C₄⋊C₄×C₂₃	—	2	2	no	—
363	C₄⋊C₄×C₂₃	—	2	2	no	—
364	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	—	2	2	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	2	no	—
382	C₂²⋊C₄×C₂₃	—	2	2	no	—
383	C₂²⋊C₄×C₂₃	—	2	2	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	2	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	—	2	1	no	—
388	C₂²⋊C₄×C₂₃	—	2	2	no	—
389	C₂²⋊C₄×C₂₃	—	2	1	no	—
390	C₂²⋊C₄×C₂₃	—	2	2	no	—
391	C₂²⋊C₄×C₂₃	—	2	2	no	—
392	C₂²⋊C₄×C₂₃	—	2	2	no	—
393	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
398	C₄²×C₂₃	—	2	2	no	—
399	C₄²×C₂₃	—	2	2	no	—
400	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄²×C₂₃	C₂⁴	1	2	yes	—
404	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
405	#62573	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂³×C₂₃	—	2	2	no	—
407	C₂³×C₂₃	—	2	1	no	—
408	C₂³×C₂₃	—	2	2	no	—
409	C₂³×C₂₃	—	2	1	no	—
410	C₂³×C₂₃	—	8	2	no	—
411	C₂³×C₂₃	—	8	2	no	—
412	C₂³×C₂₃	—	8	2	no	—
413	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
414	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
415	Q₈×C₂₃	—	2	2	no	—
416	Q₈×C₂₃	—	2	2	no	—
417	Q₈×C₂₃	—	4	1	no	—
418	Q₈×C₂₃	—	8	1	no	—
419	Q₈×C₂₃	—	8	1	no	—
420	Q₈×C₂₃	—	8	2	no	—
421	D₄×C₂₃	—	2	2	no	—
422	D₄×C₂₃	—	2	2	no	—
423	D₄×C₂₃	—	2	2	no	—
424	D₄×C₂₃	—	2	2	no	—
425	D₄×C₂₃	—	2	2	no	—
426	D₄×C₂₃	—	2	2	no	—
427	D₄×C₂₃	—	4	1	no	—
428	D₄×C₂₃	—	4	2	no	—
429	D₄×C₂₃	—	4	2	no	—
430	D₄×C₂₃	—	4	4	no	—
431	D₄×C₂₃	—	8	1	no	—
432	D₄×C₂₃	—	8	1	no	—
433	D₄×C₂₃	—	8	1	no	—
434	D₄×C₂₃	—	8	2	no	—
435	D₄×C₂₃	—	8	2	no	—
436	D₄×C₂₃	—	8	1	no	—
437	D₄×C₂₃	—	8	1	no	—
438	D₄×C₂₃	—	8	2	no	—
439	D₄×C₂₃	—	8	2	no	—
440	D₄×C₂₃	—	8	2	no	—
441	D₄×C₂₃	—	8	2	no	—
442	D₄×C₂₃	—	8	2	no	—
443	D₄×C₂₃	—	8	1	no	—
444	D₄×C₂₃	—	8	2	no	—
445	D₄×C₂₃	—	8	1	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	1	no	—
450	C₂×C₄×C₂₃	—	2	2	no	—
451	C₂×C₄×C₂₃	—	2	2	no	—
452	C₂×C₄×C₂₃	—	2	2	no	—
453	C₂×C₄×C₂₃	—	2	1	no	—
454	C₂×C₄×C₂₃	—	2	2	no	—
455	C₂×C₄×C₂₃	—	4	1	no	—
456	C₂×C₄×C₂₃	—	4	1	no	—
457	C₂×C₄×C₂₃	—	4	2	no	—
458	C₂×C₄×C₂₃	—	4	2	no	—
459	C₂×C₄×C₂₃	—	4	2	no	—
460	C₂×C₄×C₂₃	—	8	2	no	—
461	C₂×C₄×C₂₃	—	8	2	no	—
462	C₂×C₄×C₂₃	—	8	2	no	—
463	C₂×C₄×C₂₃	—	8	2	no	—
464	C₂×C₄×C₂₃	—	8	2	no	—
465	C₂×C₄×C₂₃	—	8	2	no	—
466	C₂×C₄×C₂₃	—	8	1	no	—
467	C₂×C₄×C₂₃	—	8	2	no	—
468	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
477	C₈×C₂₃	—	2	2	no	—
478	C₈×C₂₃	—	2	2	no	—
479	C₈×C₂₃	—	2	2	no	—
480	C₈×C₂₃	—	2	2	no	—
481	#3559	C₂×C₂₃	1	1	yes	characteristic, complemented
482	#3546	C₂×C₂₃	1	1	yes	characteristic, complemented
483	#3376	C₂×C₂₃	1	2	yes	complemented
484	#3366	C₂×C₂₃	1	2	yes	complemented
485	#3332	C₂×C₂₃	1	2	yes	complemented
486	#3322	C₂×C₂₃	1	2	yes	complemented
487	#3318	C₂×C₂₃	1	2	yes	complemented
488	#3309	C₂×C₂₃	1	2	yes	complemented
489	#3307	C₂×C₂₃	1	2	yes	complemented
490	#3306	C₂×C₂₃	1	2	yes	complemented
491	#3244	C₂×C₂₃	1	2	yes	complemented
492	#3234	C₂×C₂₃	1	1	yes	characteristic, complemented
493	#3220	C₂×C₂₃	1	2	yes	complemented
494	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
495	#3184	C₂×C₂₃	1	1	yes	characteristic, complemented
496	#3179	C₂×C₂₃	1	2	yes	complemented
497	#3142	C₂×C₂₃	1	1	yes	characteristic, complemented
498	#3136	C₂×C₂₃	1	2	yes	complemented
499	#2967	C₂×C₂₃	1	1	yes	characteristic, complemented
500	C₂²×C₂₃	—	2	1	no	—
501	C₂²×C₂₃	—	2	1	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	2	no	—
504	C₂²×C₂₃	—	2	1	no	—
505	C₂²×C₂₃	—	2	2	no	—
506	C₂²×C₂₃	—	4	1	no	—
507	C₂²×C₂₃	—	4	1	no	—
508	C₂²×C₂₃	—	4	2	no	—
509	C₂²×C₂₃	—	4	2	no	—
510	C₂²×C₂₃	—	4	2	no	—
511	C₂²×C₂₃	—	4	1	no	—
512	C₂²×C₂₃	—	4	2	no	—
513	C₂²×C₂₃	—	4	1	no	—
514	C₂²×C₂₃	—	4	1	no	—
515	C₂²×C₂₃	—	4	2	no	—
516	C₂²×C₂₃	—	4	1	no	—
517	C₂²×C₂₃	—	4	2	no	—
518	C₂²×C₂₃	—	16	4	no	—
519	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
520	C₄×C₂₃	—	2	1	no	—
521	C₄×C₂₃	—	2	1	no	—
522	C₄×C₂₃	—	2	1	no	—
523	C₄×C₂₃	—	2	1	no	—
524	C₄×C₂₃	—	2	2	no	—
525	C₄×C₂₃	—	2	2	no	—
526	C₄×C₂₃	—	2	1	no	—
527	C₄×C₂₃	—	2	2	no	—
528	C₄×C₂₃	—	4	1	no	—
529	C₄×C₂₃	—	4	2	no	—
530	C₄×C₂₃	—	4	1	no	—
531	C₄×C₂₃	—	4	2	no	—
532	C₄×C₂₃	—	4	2	no	—
533	C₄×C₂₃	—	4	2	no	—
534	C₄×C₂₃	#585	1	2	yes	—
535	#563	—	2	1	no	—
536	#562	—	2	1	no	—
537	#560	—	2	2	no	—
538	#556	C₂²×C₂₃	1	1	yes	characteristic
539	#554	C₂²×C₂₃	1	2	yes	complemented
540	#553	—	2	1	no	—
541	#553	C₂²×C₂₃	1	2	yes	—
542	#553	C₂²×C₂₃	1	2	yes	complemented
543	#550	C₂²×C₂₃	1	2	yes	—
544	#550	C₂²×C₂₃	1	1	yes	characteristic
545	#547	—	2	2	no	—
546	#547	C₂²×C₂₃	1	1	yes	characteristic
547	#547	C₂²×C₂₃	1	2	yes	complemented
548	#546	—	2	1	no	—
549	#546	C₂²×C₂₃	1	2	yes	—
550	D₄²	C₂²×C₂₃	1	1	yes	characteristic
551	#544	C₂²×C₂₃	1	2	yes	complemented
552	#542	C₂²×C₂₃	1	2	yes	—
553	#540	C₂²×C₂₃	1	2	yes	complemented
554	#539	—	2	2	no	—
555	#539	—	2	1	no	—
556	#538	—	2	2	no	—
557	#537	—	2	1	no	—
558	#537	—	2	1	no	—
559	#535	—	2	1	no	—
560	#535	C₂²×C₂₃	1	2	yes	—
561	#532	C₂²×C₂₃	1	1	yes	characteristic
562	#532	C₂²×C₂₃	1	1	yes	characteristic
563	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	#529	C₂²×C₂₃	1	1	yes	characteristic
565	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
566	#501	C₂²×C₂₃	1	2	yes	complemented
567	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
568	#496	C₂²×C₂₃	1	2	yes	complemented
569	#493	C₂²×C₂₃	1	1	yes	characteristic
570	#491	C₂²×C₂₃	1	2	yes	complemented
571	#490	C₂²×C₂₃	1	2	yes	—
572	#490	C₂²×C₂₃	1	2	yes	—
573	#490	C₂²×C₂₃	1	2	yes	complemented
574	#489	C₂²×C₂₃	1	2	yes	—
575	#489	C₂²×C₂₃	1	2	yes	complemented
576	#488	C₂²×C₂₃	1	2	yes	—
577	#488	C₂²×C₂₃	1	2	yes	complemented
578	#488	C₂²×C₂₃	1	2	yes	complemented
579	#486	C₂²×C₂₃	1	1	yes	characteristic
580	#486	C₂²×C₂₃	1	2	yes	complemented
581	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
582	#485	C₂²×C₂₃	1	2	yes	complemented
583	#483	C₂²×C₂₃	1	2	yes	complemented
584	#482	C₂²×C₂₃	1	2	yes	—
585	#481	C₂²×C₂₃	1	2	yes	—
586	#481	C₂²×C₂₃	1	1	yes	characteristic
587	#481	C₂²×C₂₃	1	1	yes	characteristic, complemented
588	#480	C₂²×C₂₃	1	1	yes	characteristic
589	#480	C₂²×C₂₃	1	1	yes	characteristic, complemented
590	#479	C₂²×C₂₃	1	2	yes	complemented
591	#478	C₂²×C₂₃	1	2	yes	—
592	#478	C₂²×C₂₃	1	2	yes	complemented
593	#478	C₂²×C₂₃	1	2	yes	complemented
594	#476	C₂²×C₂₃	1	2	yes	complemented
595	#475	C₂²×C₂₃	1	2	yes	complemented
596	#469	C₂²×C₂₃	1	2	yes	—
597	#469	C₂²×C₂₃	1	2	yes	—
598	#469	C₂²×C₂₃	1	2	yes	complemented
599	#468	C₂²×C₂₃	1	2	yes	complemented
600	#466	C₂²×C₂₃	1	2	yes	—
601	#465	C₂²×C₂₃	1	2	yes	complemented
602	#463	C₂²×C₂₃	1	2	yes	—
603	#463	C₂²×C₂₃	1	2	yes	—
604	#461	C₂²×C₂₃	1	2	yes	complemented
605	#459	C₂²×C₂₃	1	2	yes	—
606	#459	C₂²×C₂₃	1	2	yes	complemented
607	#459	C₂²×C₂₃	1	2	yes	complemented
608	#449	C₂²×C₂₃	1	2	yes	complemented
609	#449	C₂²×C₂₃	1	2	yes	complemented
610	#449	C₂²×C₂₃	1	2	yes	complemented
611	#449	C₂²×C₂₃	1	2	yes	complemented
612	#447	C₂²×C₂₃	1	2	yes	—
613	#447	C₂²×C₂₃	1	2	yes	—
614	#446	C₂²×C₂₃	1	2	yes	complemented
615	#442	C₂²×C₂₃	1	2	yes	—
616	#442	C₂²×C₂₃	1	2	yes	complemented
617	#442	C₂²×C₂₃	1	2	yes	complemented
618	#440	C₂²×C₂₃	1	2	yes	complemented
619	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
620	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
621	#436	C₂²×C₂₃	1	2	yes	complemented
622	#435	C₂²×C₂₃	1	2	yes	—
623	#435	C₂²×C₂₃	1	2	yes	complemented
624	#433	C₂²×C₂₃	1	2	yes	complemented
625	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	#418	C₂²×C₂₃	1	2	yes	—
627	#417	C₂²×C₂₃	1	2	yes	complemented
628	#417	C₂²×C₂₃	1	2	yes	complemented
629	#417	C₂²×C₂₃	1	2	yes	complemented
630	#416	C₂²×C₂₃	1	2	yes	complemented
631	C₂×#102	C₂²×C₂₃	1	2	yes	—
632	#405	C₂²×C₂₃	1	2	yes	complemented
633	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
634	C₂×C₂₃	—	4	1	no	—
635	C₂×C₂₃	—	4	2	no	—
636	C₂×C₂₃	—	8	1	no	—
637	C₂×C₂₃	—	8	2	no	—
638	C₂×C₂₃	—	8	2	no	—
639	C₂×C₂₃	—	8	1	no	—
640	C₂×C₂₃	#3500	1	1	yes	characteristic
641	C₂×C₂₃	#3585	1	1	yes	characteristic
642	C₂×C₂₃	#3585	1	1	yes	characteristic
643	C₂×#41	—	2	1	no	—
644	C₂×#41	—	2	2	no	—
645	C₂×#41	—	2	1	no	—
646	C₂×#41	—	2	1	no	—
647	C₂×#41	C₂³×C₂₃	1	2	yes	—
648	C₂×#41	C₂³×C₂₃	1	2	yes	—
649	C₂²×D₄	—	2	1	no	—
650	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
651	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
652	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
653	C₂×D₈	C₂³×C₂₃	1	2	yes	—
654	C₂×D₈	C₂³×C₂₃	1	2	yes	—
655	C₂×D₈	C₂³×C₂₃	1	2	yes	—
656	C₂×D₈	C₂³×C₂₃	1	2	yes	—
657	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
658	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
659	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
660	C₄⋊Q₈	—	2	2	no	—
661	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
662	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
663	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
664	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
665	#127	—	2	2	no	—
666	#127	C₂³×C₂₃	1	1	yes	characteristic
667	#127	C₂³×C₂₃	1	1	yes	characteristic
668	#127	C₂³×C₂₃	1	1	yes	characteristic
669	#127	C₂³×C₂₃	1	2	yes	—
670	#126	—	2	2	no	—
671	#126	—	2	2	no	—
672	#126	—	2	2	no	—
673	#126	—	2	2	no	—
674	#126	D₄×C₂₃	1	2	yes	—
675	#125	—	2	2	no	—
676	#125	—	2	1	no	—
677	#125	—	2	1	no	—
678	#125	D₄×C₂₃	1	1	yes	characteristic
679	#125	C₂³×C₂₃	1	2	yes	—
680	#125	C₂³×C₂₃	1	2	yes	—
681	#125	C₂³×C₂₃	1	2	yes	—
682	#124	—	2	2	no	—
683	#124	—	2	1	no	—
684	#124	—	2	1	no	—
685	#124	D₄×C₂₃	1	1	yes	characteristic
686	#124	C₂³×C₂₃	1	2	yes	—
687	#124	C₂³×C₂₃	1	2	yes	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	D₄×C₂₃	1	2	yes	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
707	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	1	no	—
712	#121	—	2	1	no	—
713	#121	—	2	1	no	—
714	#121	—	2	1	no	—
715	#121	—	2	1	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	1	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	D₄×C₂₃	1	1	yes	characteristic
726	#121	C₂³×C₂₃	1	1	yes	characteristic
727	#121	C₂³×C₂₃	1	1	yes	characteristic
728	#121	C₂³×C₂₃	1	2	yes	—
729	#121	C₂³×C₂₃	1	2	yes	—
730	#121	C₂³×C₂₃	1	2	yes	—
731	#121	C₂³×C₂₃	1	2	yes	—
732	#120	—	2	2	no	—
733	#120	—	2	2	no	—
734	#120	—	2	2	no	—
735	#120	—	2	2	no	—
736	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
737	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	2	no	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	1	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	1	no	—
745	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
746	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
747	C₄×D₄	C₂³×C₂₃	1	2	yes	—
748	C₄×D₄	C₂³×C₂₃	1	2	yes	—
749	C₄×D₄	C₂³×C₂₃	1	2	yes	—
750	C₄×D₄	C₂³×C₂₃	1	2	yes	—
751	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
752	C₄×D₄	C₂³×C₂₃	1	2	yes	—
753	#117	—	2	1	no	—
754	#117	C₂³×C₂₃	1	2	yes	—
755	#117	C₂³×C₂₃	1	2	yes	—
756	C₂×C₄⋊C₄	—	2	1	no	—
757	C₂×C₄⋊C₄	—	2	1	no	—
758	C₂×C₄⋊C₄	—	2	1	no	—
759	C₂×C₄⋊C₄	—	2	2	no	—
760	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
763	C₂×C₂²⋊C₄	—	2	2	no	—
764	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
765	#107	C₂³×C₂₃	1	2	yes	—
766	#107	C₂³×C₂₃	1	2	yes	—
767	#106	C₂³×C₂₃	1	2	yes	—
768	#106	C₂³×C₂₃	1	2	yes	—
769	#106	C₂³×C₂₃	1	2	yes	—
770	#106	C₂³×C₂₃	1	2	yes	—
771	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
772	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
773	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
774	#103	C₂³×C₂₃	1	2	yes	—
775	#103	C₂³×C₂₃	1	2	yes	—
776	#103	C₂³×C₂₃	1	2	yes	—
777	#103	C₂³×C₂₃	1	2	yes	—
778	#103	C₂³×C₂₃	1	2	yes	—
779	#103	C₂³×C₂₃	1	2	yes	—
780	#102	C₂³×C₂₃	1	2	yes	—
781	#102	C₂³×C₂₃	1	2	yes	—
782	#102	C₂³×C₂₃	1	2	yes	—
783	#102	C₂³×C₂₃	1	2	yes	—
784	#102	C₂³×C₂₃	1	2	yes	—
785	#102	C₂³×C₂₃	1	2	yes	—
786	#102	C₂³×C₂₃	1	2	yes	—
787	#102	C₂³×C₂₃	1	2	yes	—
788	#102	C₂³×C₂₃	1	2	yes	—
789	#102	C₂³×C₂₃	1	2	yes	—
790	#102	C₂³×C₂₃	1	2	yes	—
791	#102	C₂³×C₂₃	1	2	yes	—
792	#102	C₂³×C₂₃	1	2	yes	—
793	#102	C₂³×C₂₃	1	2	yes	—
794	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
795	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
798	#97	C₂³×C₂₃	1	2	yes	—
799	#97	C₂³×C₂₃	1	2	yes	—
800	#97	C₂³×C₂₃	1	2	yes	—
801	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
802	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
803	C₄×C₈	C₂³×C₂₃	1	2	yes	—
804	C₂₃	#62573	1	1	yes	characteristic, direct product factor, Sylow
805	C₂⁴	—	2	2	no	—
806	#41	—	4	2	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	8	2	no	—
811	#41	—	8	2	no	—
812	#41	—	8	4	no	—
813	#41	—	8	2	no	—
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
818	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	8	2	no	—
839	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
840	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
841	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
842	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
843	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
857	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
860	SD₁₆	—	4	2	no	—
861	SD₁₆	—	4	2	no	—
862	D₈	—	4	2	no	—
863	D₈	—	4	2	no	—
864	D₈	—	4	2	no	—
865	D₈	—	4	2	no	—
866	M₁₆	—	4	2	no	—
867	M₁₆	—	4	2	no	—
868	C₂×C₈	—	4	2	no	—
869	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
870	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
871	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
872	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
890	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
891	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
892	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
895	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
897	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	1	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	1	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
919	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
926	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
927	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
928	C₄²	C₂⁴×C₂₃	1	2	yes	—
929	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	8	2	no	—
935	C₂³	—	8	2	no	—
936	C₂³	—	8	2	no	—
937	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
938	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
939	Q₈	—	2	2	no	—
940	Q₈	—	2	2	no	—
941	Q₈	—	4	1	no	—
942	Q₈	—	8	1	no	—
943	Q₈	—	8	1	no	—
944	Q₈	—	8	2	no	—
945	D₄	—	2	2	no	—
946	D₄	—	2	2	no	—
947	D₄	—	2	2	no	—
948	D₄	—	2	2	no	—
949	D₄	—	2	2	no	—
950	D₄	—	2	2	no	—
951	D₄	—	4	1	no	—
952	D₄	—	4	2	no	—
953	D₄	—	4	2	no	—
954	D₄	—	4	4	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	1	no	—
957	D₄	—	8	1	no	—
958	D₄	—	8	2	no	—
959	D₄	—	8	1	no	—
960	D₄	—	8	1	no	—
961	D₄	—	8	1	no	—
962	D₄	—	8	2	no	—
963	D₄	—	8	2	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	1	no	—
967	D₄	—	8	2	no	—
968	D₄	—	8	1	no	—
969	D₄	—	8	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	—	8	2	no	—
989	C₂×C₄	—	8	2	no	—
990	C₂×C₄	—	8	2	no	—
991	C₂×C₄	—	8	1	no	—
992	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
993	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
995	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
996	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
997	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
999	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1000	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1001	C₈	—	2	2	no	—
1002	C₈	—	2	2	no	—
1003	C₈	—	2	2	no	—
1004	C₈	—	2	2	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	2	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	16	4	no	—
1024	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1025	C₄	—	2	1	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	C₂₃×#585	1	2	yes	—
1040	C₂	—	4	2	no	—
1041	C₂	—	4	1	no	—
1042	C₂	—	8	1	no	—
1043	C₂	—	8	2	no	—
1044	C₂	—	8	1	no	—
1045	C₂	—	8	2	no	—
1046	C₂	C₂₃×#3500	1	1	yes	characteristic
1047	C₂	C₂₃×#3585	1	1	yes	characteristic
1048	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3559	C₂	semidirect
2. C₂₃×#3546	C₂	semidirect
3. C₂₃×#3376	C₂	semidirect
4. C₂₃×#3366	C₂	semidirect
5. C₂₃×#3332	C₂	semidirect
6. C₂₃×#3322	C₂	semidirect
7. C₂₃×#3318	C₂	semidirect
8. C₂₃×#3309	C₂	semidirect
9. C₂₃×#3307	C₂	semidirect
10. C₂₃×#3306	C₂	semidirect
11. C₂₃×#3244	C₂	semidirect
12. C₂₃×#3234	C₂	semidirect
13. C₂₃×#3220	C₂	semidirect
14. C₂₃×#3214	C₂	semidirect
15. C₂₃×#3184	C₂	semidirect
16. C₂₃×#3179	C₂	semidirect
17. C₂₃×#3142	C₂	semidirect
18. C₂₃×#3136	C₂	semidirect
19. C₂₃×#2967	C₂	semidirect
24. C₂₃×#554	C₂²	semidirect
27. C₂₃×#553	C₂²	semidirect
32. C₂₃×#547	C₂²	semidirect
36. C₂₃×#544	C₂²	semidirect
38. C₂₃×#540	C₂²	semidirect
48. C₂₃×#532	C₂²	semidirect
50. C₂×C₂₃×#125	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#498	C₂²	semidirect
53. C₂₃×#496	C₂²	semidirect
55. C₂₃×#491	C₂²	semidirect
58. C₂₃×#490	C₂²	semidirect
60. C₂₃×#489	C₂²	semidirect
62. C₂₃×#488	C₂²	semidirect
63. C₂₃×#488	C₂²	semidirect
65. C₂₃×#486	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#483	C₂²	semidirect
72. C₂₃×#481	C₂²	semidirect
74. C₂₃×#480	C₂²	semidirect
75. C₂₃×#479	C₂²	semidirect
77. C₂₃×#478	C₂²	semidirect
78. C₂₃×#478	C₂²	semidirect
79. C₂₃×#476	C₂²	semidirect
80. C₂₃×#475	C₂²	semidirect
83. C₂₃×#469	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
86. C₂₃×#465	C₂²	semidirect
89. C₂₃×#461	C₂²	semidirect
91. C₂₃×#459	C₂²	semidirect
92. C₂₃×#459	C₂²	semidirect
93. C₂₃×#449	C₂²	semidirect
94. C₂₃×#449	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
96. C₂₃×#449	C₂²	semidirect
99. C₂₃×#446	C₂²	semidirect
101. C₂₃×#442	C₂²	semidirect
102. C₂₃×#442	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₄×SD₁₆×C₂₃	C₂²	semidirect
105. C₄×D₈×C₂₃	C₂²	semidirect
106. C₂₃×#436	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₂₃×#433	C₂²	semidirect
110. C₂₃×#432	C₂²	semidirect
112. C₂₃×#417	C₂²	semidirect
113. C₂₃×#417	C₂²	semidirect
114. C₂₃×#417	C₂²	semidirect
115. C₂₃×#416	C₂²	semidirect
117. C₂₃×#405	C₂²	semidirect
118. C₄×M₁₆×C₂₃	C₂²	semidirect
405. #62573	C₂₃	direct (N × H)
481. #3559	C₂×C₂₃	semidirect
482. #3546	C₂×C₂₃	semidirect
483. #3376	C₂×C₂₃	semidirect
484. #3366	C₂×C₂₃	semidirect
485. #3332	C₂×C₂₃	semidirect
486. #3322	C₂×C₂₃	semidirect
487. #3318	C₂×C₂₃	semidirect
488. #3309	C₂×C₂₃	semidirect
489. #3307	C₂×C₂₃	semidirect
490. #3306	C₂×C₂₃	semidirect
491. #3244	C₂×C₂₃	semidirect
492. #3234	C₂×C₂₃	semidirect
493. #3220	C₂×C₂₃	semidirect
494. #3214	C₂×C₂₃	semidirect
495. #3184	C₂×C₂₃	semidirect
496. #3179	C₂×C₂₃	semidirect
497. #3142	C₂×C₂₃	semidirect
498. #3136	C₂×C₂₃	semidirect
499. #2967	C₂×C₂₃	semidirect
539. #554	C₂²×C₂₃	semidirect
542. #553	C₂²×C₂₃	semidirect
547. #547	C₂²×C₂₃	semidirect
551. #544	C₂²×C₂₃	semidirect
553. #540	C₂²×C₂₃	semidirect
563. #532	C₂²×C₂₃	semidirect
565. C₂×#125	C₂²×C₂₃	semidirect
566. #501	C₂²×C₂₃	semidirect
567. #498	C₂²×C₂₃	semidirect
568. #496	C₂²×C₂₃	semidirect
570. #491	C₂²×C₂₃	semidirect
573. #490	C₂²×C₂₃	semidirect
575. #489	C₂²×C₂₃	semidirect
577. #488	C₂²×C₂₃	semidirect
578. #488	C₂²×C₂₃	semidirect
580. #486	C₂²×C₂₃	semidirect
581. #486	C₂²×C₂₃	semidirect
582. #485	C₂²×C₂₃	semidirect
583. #483	C₂²×C₂₃	semidirect
587. #481	C₂²×C₂₃	semidirect
589. #480	C₂²×C₂₃	semidirect
590. #479	C₂²×C₂₃	semidirect
592. #478	C₂²×C₂₃	semidirect
593. #478	C₂²×C₂₃	semidirect
594. #476	C₂²×C₂₃	semidirect
595. #475	C₂²×C₂₃	semidirect
598. #469	C₂²×C₂₃	semidirect
599. #468	C₂²×C₂₃	semidirect
601. #465	C₂²×C₂₃	semidirect
604. #461	C₂²×C₂₃	semidirect
606. #459	C₂²×C₂₃	semidirect
607. #459	C₂²×C₂₃	semidirect
608. #449	C₂²×C₂₃	semidirect
609. #449	C₂²×C₂₃	semidirect
610. #449	C₂²×C₂₃	semidirect
611. #449	C₂²×C₂₃	semidirect
614. #446	C₂²×C₂₃	semidirect
616. #442	C₂²×C₂₃	semidirect
617. #442	C₂²×C₂₃	semidirect
618. #440	C₂²×C₂₃	semidirect
619. C₄×SD₁₆	C₂²×C₂₃	semidirect
620. C₄×D₈	C₂²×C₂₃	semidirect
621. #436	C₂²×C₂₃	semidirect
623. #435	C₂²×C₂₃	semidirect
624. #433	C₂²×C₂₃	semidirect
625. #432	C₂²×C₂₃	semidirect
627. #417	C₂²×C₂₃	semidirect
628. #417	C₂²×C₂₃	semidirect
629. #417	C₂²×C₂₃	semidirect
630. #416	C₂²×C₂₃	semidirect
632. #405	C₂²×C₂₃	semidirect
633. C₄×M₁₆	C₂²×C₂₃	semidirect
804. C₂₃	#62573	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×#3559	2
C₂₃×#3546	2
C₂₃×#3376	2
C₂₃×#3366	2
C₂₃×#3332	2
C₂₃×#3322	2
C₂₃×#3318	2
C₂₃×#3309	2
C₂₃×#3307	2
C₂₃×#3306	2
C₂₃×#3244	2
C₂₃×#3234	2
C₂₃×#3220	2
C₂₃×#3214	2
C₂₃×#3184	2
C₂₃×#3179	2
C₂₃×#3142	2
C₂₃×#3136	2
C₂₃×#2967	2
#62573	23

Subgroups — C23×#62573 #19210199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62573 #19210199