Subgroups — C₂₃×#61938 #19209564

Order 5888.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3403	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3401	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3399	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3399	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3376	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3373	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3366	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3224	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3220	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#562	—	2	2	no	—
21	C₂₃×#559	C₂²	1	2	yes	—
22	C₂₃×#559	C₂²	1	2	yes	—
23	C₂₃×#559	C₂²	1	2	yes	complemented
24	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#556	C₂²	1	2	yes	—
27	C₂₃×#555	—	2	1	no	—
28	C₂₃×#554	C₂²	1	2	yes	complemented
29	C₂₃×#553	—	2	2	no	—
30	C₂₃×#550	C₂²	1	2	yes	—
31	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
32	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#548	—	2	1	no	—
34	C₂₃×#547	—	2	1	no	—
35	C₂₃×#547	—	2	1	no	—
36	C₂₃×#542	—	2	1	no	—
37	C₂₃×#542	C₂²	1	2	yes	—
38	C₂₃×#540	C₂²	1	2	yes	—
39	C₂₃×#539	—	2	2	no	—
40	C₂₃×#538	—	2	1	no	—
41	C₂₃×#538	—	2	1	no	—
42	C₂₃×#536	—	2	1	no	—
43	C₂₃×#535	C₂²	1	2	yes	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#532	C₂²	1	1	yes	characteristic
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#529	C₂²	1	1	yes	characteristic
48	C₂₃×#525	—	2	2	no	—
49	C₂₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#496	C₂²	1	2	yes	—
53	C₂₃×#496	C₂²	1	2	yes	—
54	C₂₃×#496	C₂²	1	2	yes	complemented
55	C₂₃×#496	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#495	C₂²	1	2	yes	—
57	C₂₃×#493	C₂²	1	2	yes	—
58	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#490	C₂²	1	2	yes	—
60	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#489	C₂²	1	2	yes	—
62	C₂₃×#489	C₂²	1	2	yes	complemented
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#486	C₂²	1	2	yes	—
65	C₂₃×#483	C₂²	1	1	yes	characteristic
66	C₂₃×#481	C₂²	1	2	yes	—
67	C₂₃×#480	C₂²	1	1	yes	characteristic
68	C₂₃×#479	C₂²	1	2	yes	complemented
69	C₂₃×#478	C₂²	1	2	yes	—
70	C₂₃×#478	C₂²	1	2	yes	complemented
71	C₂₃×#476	C₂²	1	2	yes	—
72	C₂₃×#476	C₂²	1	2	yes	complemented
73	C₂₃×#475	C₂²	1	2	yes	complemented
74	C₂₃×#464	C₂²	1	2	yes	—
75	C₂₃×#464	C₂²	1	2	yes	complemented
76	C₂₃×#464	C₂²	1	2	yes	complemented
77	C₂₃×#463	C₂²	1	2	yes	—
78	C₂₃×#463	C₂²	1	2	yes	—
79	C₂₃×#463	C₂²	1	2	yes	—
80	C₂₃×#463	C₂²	1	2	yes	—
81	C₂₃×#463	C₂²	1	2	yes	complemented
82	C₂₃×#463	C₂²	1	2	yes	complemented
83	C₂₃×#461	C₂²	1	2	yes	complemented
84	C₂₃×#460	C₂²	1	2	yes	—
85	C₂₃×#460	C₂²	1	2	yes	complemented
86	C₂₃×#459	C₂²	1	2	yes	—
87	C₂₃×#459	C₂²	1	2	yes	—
88	C₂₃×#459	C₂²	1	2	yes	—
89	C₂₃×#459	C₂²	1	2	yes	—
90	C₂₃×#459	C₂²	1	2	yes	complemented
91	C₂₃×#459	C₂²	1	2	yes	complemented
92	C₂₃×#452	C₂²	1	2	yes	—
93	C₂₃×#450	C₂²	1	1	yes	characteristic
94	C₂₃×#449	C₂²	1	2	yes	—
95	C₂₃×#449	C₂²	1	2	yes	—
96	C₂₃×#449	C₂²	1	2	yes	—
97	C₂₃×#447	C₂²	1	1	yes	characteristic
98	C₂₃×#447	C₂²	1	2	yes	—
99	C₂₃×#446	C₂²	1	2	yes	complemented
100	C₂₃×#446	C₂²	1	2	yes	complemented
101	C₂₃×#446	C₂²	1	2	yes	complemented
102	C₂₃×#446	C₂²	1	2	yes	complemented
103	C₂₃×#442	C₂²	1	2	yes	—
104	C₂₃×#442	C₂²	1	2	yes	—
105	C₂₃×#442	C₂²	1	2	yes	—
106	C₂₃×#442	C₂²	1	2	yes	complemented
107	C₂₃×#442	C₂²	1	2	yes	complemented
108	C₂₃×#441	C₂²	1	2	yes	complemented
109	C₂₃×#440	C₂²	1	2	yes	—
110	C₂₃×#440	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
114	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
115	C₂₃×#433	C₂²	1	2	yes	—
116	C₂₃×#433	C₂²	1	2	yes	—
117	C₂₃×#432	C₂²	1	1	yes	characteristic
118	C₂₃×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₃	—	2	2	no	—
120	C₂×#41×C₂₃	—	2	1	no	—
121	C₂×#41×C₂₃	—	2	1	no	—
122	C₂×#41×C₂₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₂₃	—	2	1	no	—
124	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₃	—	2	1	no	—
126	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂×D₈×C₂₃	C₂³	1	2	yes	—
133	C₂×D₈×C₂₃	C₂³	1	2	yes	—
134	C₂×D₈×C₂₃	C₂³	1	2	yes	—
135	C₂×D₈×C₂₃	C₂³	1	2	yes	—
136	C₂×D₈×C₂₃	C₂³	1	2	yes	—
137	C₂×D₈×C₂₃	C₂³	1	2	yes	—
138	C₂₃×C₄⋊Q₈	—	2	1	no	—
139	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
140	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
141	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₂₃×#127	C₂³	1	1	yes	characteristic
145	C₂₃×#127	C₂³	1	2	yes	—
146	C₂₃×#127	C₂³	1	2	yes	—
147	C₂₃×#127	C₂³	1	1	yes	characteristic
148	C₂₃×#127	C₂³	1	2	yes	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#126	—	2	2	no	—
151	C₂₃×#126	—	2	2	no	—
152	C₂₃×#126	—	2	1	no	—
153	C₂₃×#125	—	2	2	no	—
154	C₂₃×#125	D₄	1	2	yes	—
155	C₂₃×#125	C₂³	1	1	yes	characteristic
156	C₂₃×#125	C₂³	1	2	yes	—
157	C₂₃×#124	—	2	1	no	—
158	C₂₃×#124	—	2	2	no	—
159	C₂₃×#124	—	2	2	no	—
160	C₂₃×#124	—	2	2	no	—
161	C₂₃×#124	—	2	2	no	—
162	C₂₃×#124	—	2	1	no	—
163	C₂₃×#124	C₂³	1	2	yes	—
164	C₂₃×#124	C₂³	1	2	yes	—
165	C₂₃×#124	C₂³	1	2	yes	—
166	C₂₃×#124	C₂³	1	1	yes	characteristic
167	C₂₃×#124	C₂³	1	2	yes	—
168	C₂₃×#123	—	2	1	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	—	2	2	no	—
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×C₂²⋊Q₈	—	2	2	no	—
180	C₂₃×C₂²⋊Q₈	—	2	2	no	—
181	C₂₃×C₂²⋊Q₈	—	2	1	no	—
182	C₂₃×C₂²⋊Q₈	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
187	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₂₃×#121	—	2	1	no	—
191	C₂₃×#121	—	2	1	no	—
192	C₂₃×#121	—	2	1	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	—	2	2	no	—
202	C₂₃×#121	C₂³	1	1	yes	characteristic
203	C₂₃×#121	C₂³	1	2	yes	—
204	C₂₃×#120	—	2	2	no	—
205	C₂₃×#120	—	2	2	no	—
206	C₄×Q₈×C₂₃	—	2	1	no	—
207	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₂₃	—	2	1	no	—
215	C₄×D₄×C₂₃	—	2	1	no	—
216	C₄×D₄×C₂₃	—	2	2	no	—
217	C₄×D₄×C₂₃	—	2	2	no	—
218	C₄×D₄×C₂₃	—	2	2	no	—
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	2	no	—
221	C₄×D₄×C₂₃	—	2	1	no	—
222	C₄×D₄×C₂₃	—	2	1	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	1	no	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₂₃	C₂³	1	2	yes	—
228	C₄×D₄×C₂₃	C₂³	1	2	yes	—
229	C₄×D₄×C₂₃	C₂³	1	2	yes	—
230	C₄×D₄×C₂₃	C₂³	1	2	yes	—
231	C₄×D₄×C₂₃	C₂³	1	2	yes	—
232	C₄×D₄×C₂₃	C₂³	1	2	yes	—
233	C₄×D₄×C₂₃	C₂³	1	2	yes	—
234	C₄×D₄×C₂₃	C₂³	1	2	yes	—
235	C₂₃×#117	—	2	2	no	—
236	C₂₃×#117	—	2	2	no	—
237	C₂₃×#117	—	2	1	no	—
238	C₂₃×#117	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
240	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
241	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
243	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#106	C₂³	1	2	yes	—
246	C₂₃×#106	C₂³	1	2	yes	—
247	C₂₃×#106	C₂³	1	2	yes	—
248	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₂₃×#103	C₂³	1	2	yes	—
255	C₂₃×#103	C₂³	1	2	yes	—
256	C₂₃×#103	C₂³	1	2	yes	—
257	C₂₃×#103	C₂³	1	2	yes	—
258	C₂₃×#103	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	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×#97	C₂³	1	2	yes	—
274	C₂₃×#97	C₂³	1	1	yes	characteristic
275	C₂₃×#97	C₂³	1	1	yes	characteristic
276	C₂₃×#97	C₂³	1	2	yes	—
277	C₂₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₂₃	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	—	2	1	no	—
281	#41×C₂₃	—	4	2	no	—
282	#41×C₂₃	—	4	2	no	—
283	#41×C₂₃	—	8	2	no	—
284	#41×C₂₃	—	8	4	no	—
285	#41×C₂₃	—	8	2	no	—
286	C₂×Q₈×C₂₃	—	2	1	no	—
287	C₂×Q₈×C₂₃	—	2	2	no	—
288	C₂×Q₈×C₂₃	—	8	2	no	—
289	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
290	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	2	1	no	—
296	C₂×D₄×C₂₃	—	2	2	no	—
297	C₂×D₄×C₂₃	—	2	1	no	—
298	C₂×D₄×C₂₃	—	2	1	no	—
299	C₂×D₄×C₂₃	—	2	1	no	—
300	C₂×D₄×C₂₃	—	2	2	no	—
301	C₂×D₄×C₂₃	—	2	2	no	—
302	C₂×D₄×C₂₃	—	2	1	no	—
303	C₂×D₄×C₂₃	—	2	1	no	—
304	C₂×D₄×C₂₃	—	2	2	no	—
305	C₂×D₄×C₂₃	—	2	2	no	—
306	C₂×D₄×C₂₃	—	2	2	no	—
307	C₂×D₄×C₂₃	—	2	2	no	—
308	C₂×D₄×C₂₃	—	4	2	no	—
309	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
311	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
312	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	—	2	1	no	—
314	C₂²×C₄×C₂₃	—	2	2	no	—
315	C₂²×C₄×C₂₃	—	2	2	no	—
316	C₂²×C₄×C₂₃	—	2	1	no	—
317	C₂²×C₄×C₂₃	—	2	2	no	—
318	C₂²×C₄×C₂₃	—	2	2	no	—
319	C₂²×C₄×C₂₃	—	2	2	no	—
320	C₂²×C₄×C₂₃	—	2	2	no	—
321	C₂²×C₄×C₂₃	—	2	2	no	—
322	C₂²×C₄×C₂₃	—	2	2	no	—
323	C₂²×C₄×C₂₃	—	2	2	no	—
324	C₂²×C₄×C₂₃	—	8	2	no	—
325	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	Q₁₆×C₂₃	—	4	2	no	—
329	SD₁₆×C₂₃	—	4	2	no	—
330	SD₁₆×C₂₃	—	4	2	no	—
331	SD₁₆×C₂₃	—	4	2	no	—
332	SD₁₆×C₂₃	—	4	2	no	—
333	SD₁₆×C₂₃	—	4	2	no	—
334	D₈×C₂₃	—	4	2	no	—
335	D₈×C₂₃	—	4	2	no	—
336	D₈×C₂₃	—	4	2	no	—
337	D₈×C₂₃	—	4	2	no	—
338	D₈×C₂₃	—	4	2	no	—
339	D₈×C₂₃	—	4	2	no	—
340	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
342	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
343	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₂₃	—	2	1	no	—
345	C₄⋊C₄×C₂₃	—	2	1	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	2	no	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	1	no	—
351	C₄⋊C₄×C₂₃	—	2	1	no	—
352	C₄⋊C₄×C₂₃	—	2	1	no	—
353	C₄⋊C₄×C₂₃	—	2	1	no	—
354	C₄⋊C₄×C₂₃	—	2	1	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	—	2	1	no	—
358	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
371	C₂²⋊C₄×C₂₃	—	2	1	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	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	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
388	C₂²⋊C₄×C₂₃	—	2	1	no	—
389	C₂²⋊C₄×C₂₃	—	2	2	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	C₄²×C₂₃	—	2	2	no	—
396	C₄²×C₂₃	—	2	2	no	—
397	C₄²×C₂₃	—	2	1	no	—
398	C₄²×C₂₃	—	2	2	no	—
399	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄²×C₂₃	C₂⁴	1	2	yes	—
404	C₄²×C₂₃	C₂⁴	1	2	yes	—
405	#61938	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂³×C₂₃	—	2	1	no	—
407	C₂³×C₂₃	—	2	2	no	—
408	C₂³×C₂₃	—	2	2	no	—
409	C₂³×C₂₃	—	2	2	no	—
410	C₂³×C₂₃	—	4	2	no	—
411	C₂³×C₂₃	—	8	1	no	—
412	C₂³×C₂₃	—	8	1	no	—
413	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
414	Q₈×C₂₃	—	2	2	no	—
415	Q₈×C₂₃	—	2	2	no	—
416	Q₈×C₂₃	—	2	2	no	—
417	Q₈×C₂₃	—	4	1	no	—
418	Q₈×C₂₃	—	4	2	no	—
419	Q₈×C₂₃	—	4	1	no	—
420	Q₈×C₂₃	—	4	2	no	—
421	Q₈×C₂₃	—	8	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	—	2	2	no	—
428	D₄×C₂₃	—	2	2	no	—
429	D₄×C₂₃	—	4	2	no	—
430	D₄×C₂₃	—	4	2	no	—
431	D₄×C₂₃	—	4	2	no	—
432	D₄×C₂₃	—	4	4	no	—
433	D₄×C₂₃	—	8	1	no	—
434	D₄×C₂₃	—	8	1	no	—
435	D₄×C₂₃	—	8	2	no	—
436	D₄×C₂₃	—	8	2	no	—
437	D₄×C₂₃	—	8	2	no	—
438	D₄×C₂₃	—	8	2	no	—
439	D₄×C₂₃	—	8	2	no	—
440	D₄×C₂₃	—	8	2	no	—
441	D₄×C₂₃	—	8	1	no	—
442	D₄×C₂₃	—	8	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	1	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	1	no	—
450	C₂×C₄×C₂₃	—	4	1	no	—
451	C₂×C₄×C₂₃	—	4	1	no	—
452	C₂×C₄×C₂₃	—	4	4	no	—
453	C₂×C₄×C₂₃	—	4	2	no	—
454	C₂×C₄×C₂₃	—	4	4	no	—
455	C₂×C₄×C₂₃	—	8	2	no	—
456	C₂×C₄×C₂₃	—	8	2	no	—
457	C₂×C₄×C₂₃	—	8	2	no	—
458	C₂×C₄×C₂₃	—	8	2	no	—
459	C₂×C₄×C₂₃	—	8	2	no	—
460	C₂×C₄×C₂₃	—	8	2	no	—
461	C₂×C₄×C₂₃	—	8	2	no	—
462	C₂×C₄×C₂₃	—	8	1	no	—
463	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
473	C₈×C₂₃	—	2	2	no	—
474	C₈×C₂₃	—	2	2	no	—
475	C₈×C₂₃	—	2	2	no	—
476	C₈×C₂₃	—	2	2	no	—
477	#3554	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#3403	C₂×C₂₃	1	2	yes	complemented
480	#3401	C₂×C₂₃	1	2	yes	complemented
481	#3399	C₂×C₂₃	1	2	yes	complemented
482	#3399	C₂×C₂₃	1	2	yes	complemented
483	#3376	C₂×C₂₃	1	2	yes	complemented
484	#3373	C₂×C₂₃	1	2	yes	complemented
485	#3371	C₂×C₂₃	1	2	yes	complemented
486	#3366	C₂×C₂₃	1	2	yes	complemented
487	#3224	C₂×C₂₃	1	2	yes	complemented
488	#3220	C₂×C₂₃	1	2	yes	complemented
489	#3219	C₂×C₂₃	1	1	yes	characteristic, complemented
490	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#3125	C₂×C₂₃	1	2	yes	complemented
492	#3119	C₂×C₂₃	1	2	yes	complemented
493	#3114	C₂×C₂₃	1	1	yes	characteristic, complemented
494	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
495	#2987	C₂×C₂₃	1	1	yes	characteristic, complemented
496	C₂²×C₂₃	—	2	1	no	—
497	C₂²×C₂₃	—	2	1	no	—
498	C₂²×C₂₃	—	2	1	no	—
499	C₂²×C₂₃	—	4	1	no	—
500	C₂²×C₂₃	—	4	2	no	—
501	C₂²×C₂₃	—	4	2	no	—
502	C₂²×C₂₃	—	4	2	no	—
503	C₂²×C₂₃	—	4	2	no	—
504	C₂²×C₂₃	—	4	2	no	—
505	C₂²×C₂₃	—	4	1	no	—
506	C₂²×C₂₃	—	4	2	no	—
507	C₂²×C₂₃	—	4	2	no	—
508	C₂²×C₂₃	—	4	2	no	—
509	C₂²×C₂₃	—	4	2	no	—
510	C₂²×C₂₃	—	4	1	no	—
511	C₂²×C₂₃	—	8	4	no	—
512	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₂₃	—	2	1	no	—
514	C₄×C₂₃	—	2	1	no	—
515	C₄×C₂₃	—	2	1	no	—
516	C₄×C₂₃	—	2	1	no	—
517	C₄×C₂₃	—	2	2	no	—
518	C₄×C₂₃	—	2	2	no	—
519	C₄×C₂₃	—	2	2	no	—
520	C₄×C₂₃	—	2	2	no	—
521	C₄×C₂₃	—	2	1	no	—
522	C₄×C₂₃	—	4	2	no	—
523	C₄×C₂₃	—	4	1	no	—
524	C₄×C₂₃	—	4	1	no	—
525	C₄×C₂₃	—	4	2	no	—
526	C₄×C₂₃	—	4	2	no	—
527	C₄×C₂₃	—	4	1	no	—
528	C₄×C₂₃	#585	1	2	yes	—
529	#562	—	2	2	no	—
530	#559	C₂²×C₂₃	1	2	yes	—
531	#559	C₂²×C₂₃	1	2	yes	—
532	#559	C₂²×C₂₃	1	2	yes	complemented
533	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
534	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
535	#556	C₂²×C₂₃	1	2	yes	—
536	#555	—	2	1	no	—
537	#554	C₂²×C₂₃	1	2	yes	complemented
538	#553	—	2	2	no	—
539	#550	C₂²×C₂₃	1	2	yes	—
540	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
541	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
542	#548	—	2	1	no	—
543	#547	—	2	1	no	—
544	#547	—	2	1	no	—
545	#542	—	2	1	no	—
546	#542	C₂²×C₂₃	1	2	yes	—
547	#540	C₂²×C₂₃	1	2	yes	—
548	#539	—	2	2	no	—
549	#538	—	2	1	no	—
550	#538	—	2	1	no	—
551	#536	—	2	1	no	—
552	#535	C₂²×C₂₃	1	2	yes	—
553	#533	C₂²×C₂₃	1	1	yes	characteristic
554	#532	C₂²×C₂₃	1	1	yes	characteristic
555	#532	C₂²×C₂₃	1	1	yes	characteristic
556	#529	C₂²×C₂₃	1	1	yes	characteristic
557	#525	—	2	2	no	—
558	#520	C₂²×C₂₃	1	2	yes	—
559	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
560	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
561	#496	C₂²×C₂₃	1	2	yes	—
562	#496	C₂²×C₂₃	1	2	yes	—
563	#496	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	#496	C₂²×C₂₃	1	2	yes	complemented
565	#495	C₂²×C₂₃	1	2	yes	—
566	#493	C₂²×C₂₃	1	2	yes	—
567	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
568	#490	C₂²×C₂₃	1	2	yes	—
569	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	#489	C₂²×C₂₃	1	2	yes	—
571	#489	C₂²×C₂₃	1	2	yes	complemented
572	#488	C₂²×C₂₃	1	2	yes	—
573	#486	C₂²×C₂₃	1	2	yes	—
574	#483	C₂²×C₂₃	1	1	yes	characteristic
575	#481	C₂²×C₂₃	1	2	yes	—
576	#480	C₂²×C₂₃	1	1	yes	characteristic
577	#479	C₂²×C₂₃	1	2	yes	complemented
578	#478	C₂²×C₂₃	1	2	yes	—
579	#478	C₂²×C₂₃	1	2	yes	complemented
580	#476	C₂²×C₂₃	1	2	yes	—
581	#476	C₂²×C₂₃	1	2	yes	complemented
582	#475	C₂²×C₂₃	1	2	yes	complemented
583	#464	C₂²×C₂₃	1	2	yes	—
584	#464	C₂²×C₂₃	1	2	yes	complemented
585	#464	C₂²×C₂₃	1	2	yes	complemented
586	#463	C₂²×C₂₃	1	2	yes	—
587	#463	C₂²×C₂₃	1	2	yes	—
588	#463	C₂²×C₂₃	1	2	yes	—
589	#463	C₂²×C₂₃	1	2	yes	—
590	#463	C₂²×C₂₃	1	2	yes	complemented
591	#463	C₂²×C₂₃	1	2	yes	complemented
592	#461	C₂²×C₂₃	1	2	yes	complemented
593	#460	C₂²×C₂₃	1	2	yes	—
594	#460	C₂²×C₂₃	1	2	yes	complemented
595	#459	C₂²×C₂₃	1	2	yes	—
596	#459	C₂²×C₂₃	1	2	yes	—
597	#459	C₂²×C₂₃	1	2	yes	—
598	#459	C₂²×C₂₃	1	2	yes	—
599	#459	C₂²×C₂₃	1	2	yes	complemented
600	#459	C₂²×C₂₃	1	2	yes	complemented
601	#452	C₂²×C₂₃	1	2	yes	—
602	#450	C₂²×C₂₃	1	1	yes	characteristic
603	#449	C₂²×C₂₃	1	2	yes	—
604	#449	C₂²×C₂₃	1	2	yes	—
605	#449	C₂²×C₂₃	1	2	yes	—
606	#447	C₂²×C₂₃	1	2	yes	—
607	#447	C₂²×C₂₃	1	1	yes	characteristic
608	#446	C₂²×C₂₃	1	2	yes	complemented
609	#446	C₂²×C₂₃	1	2	yes	complemented
610	#446	C₂²×C₂₃	1	2	yes	complemented
611	#446	C₂²×C₂₃	1	2	yes	complemented
612	#442	C₂²×C₂₃	1	2	yes	—
613	#442	C₂²×C₂₃	1	2	yes	—
614	#442	C₂²×C₂₃	1	2	yes	—
615	#442	C₂²×C₂₃	1	2	yes	complemented
616	#442	C₂²×C₂₃	1	2	yes	complemented
617	#441	C₂²×C₂₃	1	2	yes	complemented
618	#440	C₂²×C₂₃	1	2	yes	—
619	#440	C₂²×C₂₃	1	2	yes	complemented
620	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
621	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
622	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
623	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
624	#433	C₂²×C₂₃	1	2	yes	—
625	#433	C₂²×C₂₃	1	2	yes	—
626	#432	C₂²×C₂₃	1	1	yes	characteristic
627	#432	C₂²×C₂₃	1	1	yes	characteristic
628	C₂×C₂₃	—	4	1	no	—
629	C₂×C₂₃	—	8	1	no	—
630	C₂×C₂₃	—	8	2	no	—
631	C₂×C₂₃	—	8	2	no	—
632	C₂×C₂₃	—	8	2	no	—
633	C₂×C₂₃	#3487	1	1	yes	characteristic
634	C₂×C₂₃	#3585	1	1	yes	characteristic
635	C₂×C₂₃	#3585	1	1	yes	characteristic
636	C₂×#41	—	2	2	no	—
637	C₂×#41	—	2	1	no	—
638	C₂×#41	—	2	1	no	—
639	C₂×#41	C₂³×C₂₃	1	2	yes	—
640	C₂²×Q₈	—	2	1	no	—
641	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
642	C₂³×C₄	—	2	1	no	—
643	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
644	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
645	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
646	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
647	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
649	C₂×D₈	C₂³×C₂₃	1	2	yes	—
650	C₂×D₈	C₂³×C₂₃	1	2	yes	—
651	C₂×D₈	C₂³×C₂₃	1	2	yes	—
652	C₂×D₈	C₂³×C₂₃	1	2	yes	—
653	C₂×D₈	C₂³×C₂₃	1	2	yes	—
654	C₂×D₈	C₂³×C₂₃	1	2	yes	—
655	C₄⋊Q₈	—	2	1	no	—
656	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
657	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
658	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
659	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
660	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
661	#127	C₂³×C₂₃	1	1	yes	characteristic
662	#127	C₂³×C₂₃	1	1	yes	characteristic
663	#127	C₂³×C₂₃	1	2	yes	—
664	#127	C₂³×C₂₃	1	2	yes	—
665	#127	C₂³×C₂₃	1	2	yes	—
666	#126	—	2	2	no	—
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	—	2	1	no	—
670	#125	—	2	2	no	—
671	#125	D₄×C₂₃	1	2	yes	—
672	#125	C₂³×C₂₃	1	1	yes	characteristic
673	#125	C₂³×C₂₃	1	2	yes	—
674	#124	—	2	1	no	—
675	#124	—	2	2	no	—
676	#124	—	2	2	no	—
677	#124	—	2	2	no	—
678	#124	—	2	2	no	—
679	#124	—	2	1	no	—
680	#124	C₂³×C₂₃	1	1	yes	characteristic
681	#124	C₂³×C₂₃	1	2	yes	—
682	#124	C₂³×C₂₃	1	2	yes	—
683	#124	C₂³×C₂₃	1	2	yes	—
684	#124	C₂³×C₂₃	1	2	yes	—
685	#123	—	2	1	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
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	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	1	no	—
703	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
704	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
705	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
706	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
707	#121	—	2	1	no	—
708	#121	—	2	1	no	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	1	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	C₂³×C₂₃	1	1	yes	characteristic
720	#121	C₂³×C₂₃	1	2	yes	—
721	#120	—	2	2	no	—
722	#120	—	2	2	no	—
723	C₄×Q₈	—	2	1	no	—
724	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
725	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
726	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
727	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
728	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
729	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
730	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	1	no	—
739	C₄×D₄	—	2	1	no	—
740	C₄×D₄	—	2	1	no	—
741	C₄×D₄	—	2	1	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	C₂³×C₂₃	1	2	yes	—
744	C₄×D₄	C₂³×C₂₃	1	2	yes	—
745	C₄×D₄	C₂³×C₂₃	1	2	yes	—
746	C₄×D₄	C₂³×C₂₃	1	2	yes	—
747	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
752	#117	—	2	2	no	—
753	#117	—	2	2	no	—
754	#117	—	2	1	no	—
755	#117	C₂³×C₂₃	1	2	yes	—
756	C₂×C₄⋊C₄	—	2	2	no	—
757	C₂×C₄⋊C₄	—	2	2	no	—
758	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	—	2	1	no	—
760	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
761	#107	C₂³×C₂₃	1	2	yes	—
762	#106	C₂³×C₂₃	1	2	yes	—
763	#106	C₂³×C₂₃	1	2	yes	—
764	#106	C₂³×C₂₃	1	2	yes	—
765	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
766	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
767	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
768	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
769	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
770	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
771	#103	C₂³×C₂₃	1	2	yes	—
772	#103	C₂³×C₂₃	1	2	yes	—
773	#103	C₂³×C₂₃	1	2	yes	—
774	#103	C₂³×C₂₃	1	2	yes	—
775	#103	C₂³×C₂₃	1	2	yes	—
776	#102	C₂³×C₂₃	1	2	yes	—
777	#102	C₂³×C₂₃	1	2	yes	—
778	#102	C₂³×C₂₃	1	2	yes	—
779	#102	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	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
790	#97	C₂³×C₂₃	1	2	yes	—
791	#97	C₂³×C₂₃	1	1	yes	characteristic
792	#97	C₂³×C₂₃	1	1	yes	characteristic
793	#97	C₂³×C₂₃	1	2	yes	—
794	#97	C₂³×C₂₃	1	2	yes	—
795	C₄×C₈	C₂³×C₂₃	1	2	yes	—
796	C₄×C₈	C₂³×C₂₃	1	2	yes	—
797	C₂₃	#61938	1	1	yes	characteristic, direct product factor, Sylow
798	C₂⁴	—	2	1	no	—
799	#41	—	4	2	no	—
800	#41	—	4	2	no	—
801	#41	—	8	2	no	—
802	#41	—	8	4	no	—
803	#41	—	8	2	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	8	2	no	—
807	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
808	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
809	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
810	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
811	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	1	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	—	4	2	no	—
827	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
828	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
829	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
830	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	8	2	no	—
843	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
844	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
846	Q₁₆	—	4	2	no	—
847	SD₁₆	—	4	2	no	—
848	SD₁₆	—	4	2	no	—
849	SD₁₆	—	4	2	no	—
850	SD₁₆	—	4	2	no	—
851	SD₁₆	—	4	2	no	—
852	D₈	—	4	2	no	—
853	D₈	—	4	2	no	—
854	D₈	—	4	2	no	—
855	D₈	—	4	2	no	—
856	D₈	—	4	2	no	—
857	D₈	—	4	2	no	—
858	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
859	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
860	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
861	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
878	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
881	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
882	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
883	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
887	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
888	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	1	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₂₃	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	1	no	—
916	C₄²	—	2	2	no	—
917	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
918	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
919	C₄²	C₂⁴×C₂₃	1	2	yes	—
920	C₄²	C₂⁴×C₂₃	1	2	yes	—
921	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
922	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	8	1	no	—
929	C₂³	—	8	1	no	—
930	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	4	1	no	—
935	Q₈	—	4	2	no	—
936	Q₈	—	4	1	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	8	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	2	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	4	no	—
950	D₄	—	8	2	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	1	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	D₄	—	8	2	no	—
959	D₄	—	8	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	2	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	1	no	—
980	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
983	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
984	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
989	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
990	C₈	—	2	2	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	8	4	no	—
1010	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	C₂₃×#585	1	2	yes	—
1027	C₂	—	4	1	no	—
1028	C₂	—	8	2	no	—
1029	C₂	—	8	2	no	—
1030	C₂	—	8	1	no	—
1031	C₂	—	8	2	no	—
1032	C₂	C₂₃×#3487	1	1	yes	characteristic
1033	C₂	C₂₃×#3585	1	1	yes	characteristic
1034	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3554	C₂	semidirect
2. C₂₃×#3506	C₂	semidirect
3. C₂₃×#3403	C₂	semidirect
4. C₂₃×#3401	C₂	semidirect
5. C₂₃×#3399	C₂	semidirect
6. C₂₃×#3399	C₂	semidirect
7. C₂₃×#3376	C₂	semidirect
8. C₂₃×#3373	C₂	semidirect
9. C₂₃×#3371	C₂	semidirect
10. C₂₃×#3366	C₂	semidirect
11. C₂₃×#3224	C₂	semidirect
12. C₂₃×#3220	C₂	semidirect
13. C₂₃×#3219	C₂	semidirect
14. C₂₃×#3214	C₂	semidirect
15. C₂₃×#3125	C₂	semidirect
16. C₂₃×#3119	C₂	semidirect
17. C₂₃×#3114	C₂	semidirect
18. C₂₃×#3109	C₂	semidirect
19. C₂₃×#2987	C₂	semidirect
23. C₂₃×#559	C₂²	semidirect
24. C₂₃×#559	C₂²	semidirect
25. C₂₃×#557	C₂²	semidirect
28. C₂₃×#554	C₂²	semidirect
31. C₂₃×#550	C₂²	semidirect
32. D₄×Q₈×C₂₃	C₂²	semidirect
51. C₂₃×#497	C₂²	semidirect
54. C₂₃×#496	C₂²	semidirect
55. C₂₃×#496	C₂²	semidirect
58. C₂₃×#491	C₂²	semidirect
60. C₂₃×#490	C₂²	semidirect
62. C₂₃×#489	C₂²	semidirect
68. C₂₃×#479	C₂²	semidirect
70. C₂₃×#478	C₂²	semidirect
72. C₂₃×#476	C₂²	semidirect
73. C₂₃×#475	C₂²	semidirect
75. C₂₃×#464	C₂²	semidirect
76. C₂₃×#464	C₂²	semidirect
81. C₂₃×#463	C₂²	semidirect
82. C₂₃×#463	C₂²	semidirect
83. C₂₃×#461	C₂²	semidirect
85. C₂₃×#460	C₂²	semidirect
90. C₂₃×#459	C₂²	semidirect
91. C₂₃×#459	C₂²	semidirect
99. C₂₃×#446	C₂²	semidirect
100. C₂₃×#446	C₂²	semidirect
101. C₂₃×#446	C₂²	semidirect
102. C₂₃×#446	C₂²	semidirect
106. C₂₃×#442	C₂²	semidirect
107. C₂₃×#442	C₂²	semidirect
108. C₂₃×#441	C₂²	semidirect
110. C₂₃×#440	C₂²	semidirect
111. C₄×SD₁₆×C₂₃	C₂²	semidirect
112. C₄×SD₁₆×C₂₃	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×D₈×C₂₃	C₂²	semidirect
405. #61938	C₂₃	direct (N × H)
477. #3554	C₂×C₂₃	semidirect
478. #3506	C₂×C₂₃	semidirect
479. #3403	C₂×C₂₃	semidirect
480. #3401	C₂×C₂₃	semidirect
481. #3399	C₂×C₂₃	semidirect
482. #3399	C₂×C₂₃	semidirect
483. #3376	C₂×C₂₃	semidirect
484. #3373	C₂×C₂₃	semidirect
485. #3371	C₂×C₂₃	semidirect
486. #3366	C₂×C₂₃	semidirect
487. #3224	C₂×C₂₃	semidirect
488. #3220	C₂×C₂₃	semidirect
489. #3219	C₂×C₂₃	semidirect
490. #3214	C₂×C₂₃	semidirect
491. #3125	C₂×C₂₃	semidirect
492. #3119	C₂×C₂₃	semidirect
493. #3114	C₂×C₂₃	semidirect
494. #3109	C₂×C₂₃	semidirect
495. #2987	C₂×C₂₃	semidirect
532. #559	C₂²×C₂₃	semidirect
533. #559	C₂²×C₂₃	semidirect
534. #557	C₂²×C₂₃	semidirect
537. #554	C₂²×C₂₃	semidirect
540. #550	C₂²×C₂₃	semidirect
541. D₄×Q₈	C₂²×C₂₃	semidirect
560. #497	C₂²×C₂₃	semidirect
563. #496	C₂²×C₂₃	semidirect
564. #496	C₂²×C₂₃	semidirect
567. #491	C₂²×C₂₃	semidirect
569. #490	C₂²×C₂₃	semidirect
571. #489	C₂²×C₂₃	semidirect
577. #479	C₂²×C₂₃	semidirect
579. #478	C₂²×C₂₃	semidirect
581. #476	C₂²×C₂₃	semidirect
582. #475	C₂²×C₂₃	semidirect
584. #464	C₂²×C₂₃	semidirect
585. #464	C₂²×C₂₃	semidirect
590. #463	C₂²×C₂₃	semidirect
591. #463	C₂²×C₂₃	semidirect
592. #461	C₂²×C₂₃	semidirect
594. #460	C₂²×C₂₃	semidirect
599. #459	C₂²×C₂₃	semidirect
600. #459	C₂²×C₂₃	semidirect
608. #446	C₂²×C₂₃	semidirect
609. #446	C₂²×C₂₃	semidirect
610. #446	C₂²×C₂₃	semidirect
611. #446	C₂²×C₂₃	semidirect
615. #442	C₂²×C₂₃	semidirect
616. #442	C₂²×C₂₃	semidirect
617. #441	C₂²×C₂₃	semidirect
619. #440	C₂²×C₂₃	semidirect
620. C₄×SD₁₆	C₂²×C₂₃	semidirect
621. C₄×SD₁₆	C₂²×C₂₃	semidirect
622. C₄×SD₁₆	C₂²×C₂₃	semidirect
623. C₄×D₈	C₂²×C₂₃	semidirect
797. C₂₃	#61938	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×#3554	2
C₂₃×#3506	2
C₂₃×#3403	2
C₂₃×#3401	2
C₂₃×#3399	2
C₂₃×#3376	2
C₂₃×#3373	2
C₂₃×#3371	2
C₂₃×#3366	2
C₂₃×#3224	2
C₂₃×#3220	2
C₂₃×#3219	2
C₂₃×#3214	2
C₂₃×#3125	2
C₂₃×#3119	2
C₂₃×#3114	2
C₂₃×#3109	2
C₂₃×#2987	2
#61938	23

Subgroups — C23×#61938 #19209564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61938 #19209564