Subgroups — C₂₃×#61574 #19209200

Order 5888.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3505	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3320	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3312	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3270	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3218	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3004	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
19	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
21	C₂₃×#553	—	2	2	no	—
22	C₂₃×#553	C₂²	1	2	yes	—
23	C₂₃×#552	C₂²	1	2	yes	—
24	C₂₃×#551	—	2	2	no	—
25	D₄×Q₈×C₂₃	—	2	2	no	—
26	D₄×Q₈×C₂₃	—	2	2	no	—
27	D₄×Q₈×C₂₃	C₂²	1	4	yes	—
28	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
29	C₂₃×#548	C₂²	1	2	yes	—
30	C₂₃×#546	C₂²	1	2	yes	—
31	C₂₃×#539	—	2	1	no	—
32	C₂₃×#538	—	2	1	no	—
33	C₂₃×#534	—	2	1	no	—
34	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
35	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#525	C₂²	1	2	yes	—
38	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
40	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
44	C₂₃×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₂₃	—	2	1	no	—
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#497	C₂²	1	4	yes	complemented
49	C₂₃×#491	C₂²	1	4	yes	complemented
50	C₂₃×#485	C₂²	1	4	yes	complemented
51	C₂₃×#484	C₂²	1	2	yes	complemented
52	C₂₃×#484	C₂²	1	2	yes	complemented
53	C₂₃×#483	C₂²	1	2	yes	complemented
54	C₂₃×#481	C₂²	1	2	yes	—
55	C₂₃×#479	C₂²	1	4	yes	complemented
56	C₂₃×#470	C₂²	1	4	yes	complemented
57	C₂₃×#468	C₂²	1	4	yes	complemented
58	C₂₃×#467	C₂²	1	4	yes	complemented
59	C₂₃×#465	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#462	C₂²	1	4	yes	complemented
62	C₂₃×#461	C₂²	1	4	yes	complemented
63	C₂₃×#452	C₂²	1	4	yes	complemented
64	C₂₃×#451	C₂²	1	2	yes	complemented
65	C₂₃×#451	C₂²	1	2	yes	complemented
66	C₂₃×#451	C₂²	1	2	yes	complemented
67	C₂₃×#451	C₂²	1	2	yes	complemented
68	C₂₃×#451	C₂²	1	4	yes	complemented
69	C₂₃×#451	C₂²	1	4	yes	complemented
70	C₂₃×#450	C₂²	1	2	yes	complemented
71	C₂₃×#448	C₂²	1	2	yes	—
72	C₂₃×#448	C₂²	1	2	yes	—
73	C₂₃×#448	C₂²	1	2	yes	—
74	C₂₃×#448	C₂²	1	4	yes	complemented
75	C₂₃×#448	C₂²	1	4	yes	complemented
76	C₂₃×#441	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	4	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	—
79	C₂₃×#435	C₂²	1	4	yes	complemented
80	C₂₃×#432	C₂²	1	2	yes	complemented
81	C₂₃×#419	C₂²	1	4	yes	complemented
82	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
84	C₂₃×#407	C₂²	1	2	yes	complemented
85	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
87	C₂×#41×C₂₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₂₃	—	2	1	no	—
89	C₂²×Q₈×C₂₃	—	2	1	no	—
90	C₂²×Q₈×C₂₃	—	2	2	no	—
91	C₂²×Q₈×C₂₃	—	2	1	no	—
92	C₂²×Q₈×C₂₃	—	2	1	no	—
93	C₂²×Q₈×C₂₃	—	4	4	no	—
94	C₂²×Q₈×C₂₃	—	4	4	no	—
95	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
98	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	—	2	1	no	—
103	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₂₃	—	2	1	no	—
106	C₂³×C₄×C₂₃	—	2	1	no	—
107	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂₃×#137	—	4	8	no	—
110	C₂×Q₁₆×C₂₃	—	4	4	no	—
111	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₂₃	—	4	4	no	—
115	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
121	C₂₃×C₄⋊Q₈	—	2	4	no	—
122	C₂₃×C₄⋊Q₈	—	2	4	no	—
123	C₂₃×C₄⋊Q₈	—	2	2	no	—
124	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×#126	—	2	2	no	—
126	C₂₃×#126	—	2	2	no	—
127	C₂₃×#126	—	2	2	no	—
128	C₂₃×#125	—	2	2	no	—
129	C₂₃×#125	C₂³	1	2	yes	—
130	C₂₃×#124	—	2	2	no	—
131	C₂₃×#124	C₂³	1	2	yes	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	2	no	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×#123	—	2	2	no	—
136	C₂₃×#123	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	1	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	1	no	—
141	C₂₃×C₂²⋊Q₈	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	—	2	2	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	—	2	4	no	—
145	C₂₃×C₂²⋊Q₈	—	2	4	no	—
146	C₂₃×C₂²⋊Q₈	—	2	4	no	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	1	no	—
156	C₂₃×#121	—	2	1	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	C₂³	1	2	yes	—
159	C₂₃×#121	C₂³	1	2	yes	—
160	C₂₃×#121	C₂³	1	2	yes	—
161	C₂₃×#120	—	2	2	no	—
162	C₂₃×#120	—	2	2	no	—
163	C₄×Q₈×C₂₃	—	2	2	no	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
166	C₄×D₄×C₂₃	—	2	4	no	—
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	D₄	1	2	yes	—
174	C₄×D₄×C₂₃	D₄	1	2	yes	—
175	C₄×D₄×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₂₃×#117	—	2	2	no	—
179	C₂₃×#117	—	2	2	no	—
180	C₂₃×#117	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
182	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
183	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
184	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	—	2	1	no	—
199	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂₃×#107	C₂³	1	4	yes	—
201	C₂₃×#106	C₂³	1	4	yes	—
202	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₂₃×#103	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	4	yes	—
206	C₂₃×#103	C₂³	1	4	yes	—
207	C₂₃×#103	C₂³	1	4	yes	—
208	C₂₃×#103	C₂³	1	4	yes	—
209	C₂₃×#103	C₂³	1	4	yes	—
210	C₂₃×#102	C₂³	1	4	yes	—
211	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₂₃×#97	C₂³	1	4	yes	—
217	C₂⁴×C₂₃	—	2	1	no	—
218	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
220	#41×C₂₃	—	4	4	no	—
221	C₂×Q₈×C₂₃	—	2	4	no	—
222	C₂×Q₈×C₂₃	—	2	1	no	—
223	C₂×Q₈×C₂₃	—	2	4	no	—
224	C₂×Q₈×C₂₃	—	2	2	no	—
225	C₂×Q₈×C₂₃	—	2	2	no	—
226	C₂×Q₈×C₂₃	—	2	1	no	—
227	C₂×Q₈×C₂₃	—	2	1	no	—
228	C₂×Q₈×C₂₃	—	2	1	no	—
229	C₂×Q₈×C₂₃	—	2	4	no	—
230	C₂×Q₈×C₂₃	—	2	4	no	—
231	C₂×Q₈×C₂₃	—	2	8	no	—
232	C₂×Q₈×C₂₃	—	4	2	no	—
233	C₂×Q₈×C₂₃	—	4	2	no	—
234	C₂×Q₈×C₂₃	—	4	4	no	—
235	C₂×Q₈×C₂₃	—	4	2	no	—
236	C₂×Q₈×C₂₃	—	4	2	no	—
237	C₂×Q₈×C₂₃	—	4	4	no	—
238	C₂×Q₈×C₂₃	—	4	4	no	—
239	C₂×Q₈×C₂₃	—	4	2	no	—
240	C₂×Q₈×C₂₃	—	4	4	no	—
241	C₂×Q₈×C₂₃	—	4	4	no	—
242	C₂×Q₈×C₂₃	—	4	8	no	—
243	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂×D₄×C₂₃	—	2	1	no	—
253	C₂×D₄×C₂₃	—	4	2	no	—
254	C₂×D₄×C₂₃	—	4	4	no	—
255	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	1	no	—
261	C₂²×C₄×C₂₃	—	2	1	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	1	no	—
267	C₂²×C₄×C₂₃	—	2	1	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	4	2	no	—
271	C₂²×C₄×C₂₃	—	4	2	no	—
272	C₂²×C₄×C₂₃	—	4	4	no	—
273	C₂²×C₄×C₂₃	—	4	4	no	—
274	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	Q₁₆×C₂₃	—	2	8	no	—
286	Q₁₆×C₂₃	—	4	4	no	—
287	Q₁₆×C₂₃	—	4	4	no	—
288	SD₁₆×C₂₃	—	2	8	no	—
289	SD₁₆×C₂₃	—	4	4	no	—
290	SD₁₆×C₂₃	—	4	4	no	—
291	M₁₆×C₂₃	—	4	4	no	—
292	C₂×C₈×C₂₃	—	4	2	no	—
293	C₂×C₈×C₂₃	—	4	2	no	—
294	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
295	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	4	no	—
298	C₄⋊C₄×C₂₃	—	2	4	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	4	no	—
301	C₄⋊C₄×C₂₃	—	2	4	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	1	no	—
305	C₄⋊C₄×C₂₃	—	2	1	no	—
306	C₄⋊C₄×C₂₃	—	2	1	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	2	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	2	no	—
311	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	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	—	2	2	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	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₄²×C₂₃	—	2	4	no	—
334	C₄²×C₂₃	—	2	2	no	—
335	C₄²×C₂₃	—	2	2	no	—
336	C₄²×C₂₃	C₂×D₄	1	2	yes	—
337	C₄²×C₂₃	C₂⁴	1	2	yes	—
338	#61574	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	4	1	no	—
342	C₂³×C₂₃	—	4	1	no	—
343	C₂³×C₂₃	—	4	1	no	—
344	C₂³×C₂₃	—	4	1	no	—
345	C₂³×C₂₃	—	4	2	no	—
346	C₂³×C₂₃	—	8	1	no	—
347	C₂³×C₂₃	—	8	1	no	—
348	C₂³×C₂₃	#137	1	4	yes	complemented
349	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
350	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
352	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
353	Q₈×C₂₃	—	2	4	no	—
354	Q₈×C₂₃	—	2	2	no	—
355	Q₈×C₂₃	—	2	2	no	—
356	Q₈×C₂₃	—	2	4	no	—
357	Q₈×C₂₃	—	2	4	no	—
358	Q₈×C₂₃	—	2	2	no	—
359	Q₈×C₂₃	—	4	8	no	—
360	Q₈×C₂₃	—	4	4	no	—
361	Q₈×C₂₃	—	4	4	no	—
362	Q₈×C₂₃	—	4	2	no	—
363	Q₈×C₂₃	—	4	2	no	—
364	Q₈×C₂₃	—	8	1	no	—
365	Q₈×C₂₃	H(5,𝔽₂)	1	4	yes	—
366	D₄×C₂₃	—	2	4	no	—
367	D₄×C₂₃	—	2	4	no	—
368	D₄×C₂₃	—	2	4	no	—
369	D₄×C₂₃	—	4	4	no	—
370	D₄×C₂₃	—	4	4	no	—
371	D₄×C₂₃	—	8	1	no	—
372	D₄×C₂₃	—	8	2	no	—
373	D₄×C₂₃	—	8	2	no	—
374	C₂×C₄×C₂₃	—	2	4	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	4	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	4	2	no	—
388	C₂×C₄×C₂₃	—	4	1	no	—
389	C₂×C₄×C₂₃	—	4	1	no	—
390	C₂×C₄×C₂₃	—	4	1	no	—
391	C₂×C₄×C₂₃	—	4	1	no	—
392	C₂×C₄×C₂₃	—	4	1	no	—
393	C₂×C₄×C₂₃	—	4	4	no	—
394	C₂×C₄×C₂₃	—	4	4	no	—
395	C₂×C₄×C₂₃	—	4	8	no	—
396	C₂×C₄×C₂₃	—	4	2	no	—
397	C₂×C₄×C₂₃	—	4	2	no	—
398	C₂×C₄×C₂₃	—	4	2	no	—
399	C₂×C₄×C₂₃	—	4	2	no	—
400	C₂×C₄×C₂₃	—	8	2	no	—
401	C₂×C₄×C₂₃	—	8	2	no	—
402	C₂×C₄×C₂₃	—	8	1	no	—
403	C₂×C₄×C₂₃	—	8	1	no	—
404	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
411	C₈×C₂₃	—	2	4	no	—
412	C₈×C₂₃	—	2	4	no	—
413	#3505	C₂×C₂₃	1	1	yes	characteristic
414	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#3320	C₂×C₂₃	1	4	yes	complemented
416	#3312	C₂×C₂₃	1	4	yes	complemented
417	#3270	C₂×C₂₃	1	4	yes	complemented
418	#3266	C₂×C₂₃	1	4	yes	complemented
419	#3218	C₂×C₂₃	1	2	yes	complemented
420	#3196	C₂×C₂₃	1	2	yes	complemented
421	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#3117	C₂×C₂₃	1	2	yes	complemented
424	#3004	C₂×C₂₃	1	2	yes	complemented
425	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
426	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
427	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
428	C₂²×C₂₃	—	2	1	no	—
429	C₂²×C₂₃	—	2	1	no	—
430	C₂²×C₂₃	—	2	1	no	—
431	C₂²×C₂₃	—	2	1	no	—
432	C₂²×C₂₃	—	2	1	no	—
433	C₂²×C₂₃	—	2	1	no	—
434	C₂²×C₂₃	—	2	2	no	—
435	C₂²×C₂₃	—	2	2	no	—
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	4	4	no	—
438	C₂²×C₂₃	—	4	4	no	—
439	C₂²×C₂₃	—	4	2	no	—
440	C₂²×C₂₃	—	4	2	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	16	2	no	—
443	C₂²×C₂₃	C₂×#137	1	2	yes	—
444	C₂²×C₂₃	C₂×#137	1	2	yes	—
445	C₂²×C₂₃	C₂×#137	1	2	yes	—
446	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
447	C₄×C₂₃	—	2	2	no	—
448	C₄×C₂₃	—	2	4	no	—
449	C₄×C₂₃	—	2	1	no	—
450	C₄×C₂₃	—	2	2	no	—
451	C₄×C₂₃	—	2	1	no	—
452	C₄×C₂₃	—	2	1	no	—
453	C₄×C₂₃	—	2	2	no	—
454	C₄×C₂₃	—	4	2	no	—
455	C₄×C₂₃	—	4	2	no	—
456	C₄×C₂₃	—	4	2	no	—
457	C₄×C₂₃	—	4	2	no	—
458	C₄×C₂₃	—	4	2	no	—
459	C₄×C₂₃	—	4	2	no	—
460	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
461	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
462	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
464	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
465	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
466	#553	—	2	2	no	—
467	#553	C₂²×C₂₃	1	2	yes	—
468	#552	C₂²×C₂₃	1	2	yes	—
469	#551	—	2	2	no	—
470	D₄×Q₈	—	2	2	no	—
471	D₄×Q₈	—	2	2	no	—
472	D₄×Q₈	C₂²×C₂₃	1	4	yes	—
473	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
474	#548	C₂²×C₂₃	1	2	yes	—
475	#546	C₂²×C₂₃	1	2	yes	—
476	#539	—	2	1	no	—
477	#538	—	2	1	no	—
478	#534	—	2	1	no	—
479	C₂×C₄⋊Q₈	—	2	1	no	—
480	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#529	C₂²×C₂₃	1	2	yes	—
482	#525	C₂²×C₂₃	1	2	yes	—
483	C₂×C₂²⋊Q₈	—	2	1	no	—
484	C₂×C₂²⋊Q₈	—	2	1	no	—
485	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
486	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
489	#518	—	2	1	no	—
490	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	C₂×C₄×D₄	—	2	1	no	—
492	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
493	#497	C₂²×C₂₃	1	4	yes	complemented
494	#491	C₂²×C₂₃	1	4	yes	complemented
495	#485	C₂²×C₂₃	1	4	yes	complemented
496	#484	C₂²×C₂₃	1	2	yes	complemented
497	#484	C₂²×C₂₃	1	2	yes	complemented
498	#483	C₂²×C₂₃	1	2	yes	complemented
499	#481	C₂²×C₂₃	1	2	yes	—
500	#479	C₂²×C₂₃	1	4	yes	complemented
501	#470	C₂²×C₂₃	1	4	yes	complemented
502	#468	C₂²×C₂₃	1	4	yes	complemented
503	#467	C₂²×C₂₃	1	4	yes	complemented
504	#465	C₂²×C₂₃	1	4	yes	complemented
505	#464	C₂²×C₂₃	1	4	yes	complemented
506	#462	C₂²×C₂₃	1	4	yes	complemented
507	#461	C₂²×C₂₃	1	4	yes	complemented
508	#452	C₂²×C₂₃	1	4	yes	complemented
509	#451	C₂²×C₂₃	1	2	yes	complemented
510	#451	C₂²×C₂₃	1	2	yes	complemented
511	#451	C₂²×C₂₃	1	2	yes	complemented
512	#451	C₂²×C₂₃	1	2	yes	complemented
513	#451	C₂²×C₂₃	1	4	yes	complemented
514	#451	C₂²×C₂₃	1	4	yes	complemented
515	#450	C₂²×C₂₃	1	2	yes	complemented
516	#448	C₂²×C₂₃	1	2	yes	—
517	#448	C₂²×C₂₃	1	2	yes	—
518	#448	C₂²×C₂₃	1	2	yes	—
519	#448	C₂²×C₂₃	1	4	yes	complemented
520	#448	C₂²×C₂₃	1	4	yes	complemented
521	#441	C₂²×C₂₃	1	4	yes	complemented
522	#440	C₂²×C₂₃	1	4	yes	complemented
523	#435	C₂²×C₂₃	1	4	yes	—
524	#435	C₂²×C₂₃	1	4	yes	complemented
525	#432	C₂²×C₂₃	1	2	yes	complemented
526	#419	C₂²×C₂₃	1	4	yes	complemented
527	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
528	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
529	#407	C₂²×C₂₃	1	2	yes	complemented
530	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
532	C₂×C₂₃	—	2	2	no	—
533	C₂×C₂₃	—	2	2	no	—
534	C₂×C₂₃	—	2	2	no	—
535	C₂×C₂₃	—	4	2	no	—
536	C₂×C₂₃	—	8	2	no	—
537	C₂×C₂₃	#3484	1	1	yes	characteristic
538	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
539	C₂×C₂₃	#3586	1	1	yes	characteristic
540	C₂×#41	C₂³×C₂₃	1	2	yes	—
541	C₂²×Q₈	—	2	1	no	—
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×Q₈	—	2	1	no	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×Q₈	—	2	2	no	—
546	C₂²×Q₈	—	4	4	no	—
547	C₂²×Q₈	—	4	4	no	—
548	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
551	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
552	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
553	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
562	#137	—	4	8	no	—
563	C₂×Q₁₆	—	4	4	no	—
564	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
565	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
566	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
567	C₂×SD₁₆	—	4	4	no	—
568	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
569	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
571	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
572	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
573	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
574	C₄⋊Q₈	—	2	4	no	—
575	C₄⋊Q₈	—	2	4	no	—
576	C₄⋊Q₈	—	2	2	no	—
577	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#125	—	2	2	no	—
582	#125	C₂³×C₂₃	1	2	yes	—
583	#124	—	2	2	no	—
584	#124	C₂³×C₂₃	1	2	yes	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	4	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	C₂³×C₂₃	1	2	yes	—
612	#121	C₂³×C₂₃	1	2	yes	—
613	#121	C₂³×C₂₃	1	2	yes	—
614	#120	—	2	2	no	—
615	#120	—	2	2	no	—
616	C₄×Q₈	—	2	2	no	—
617	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
618	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
619	C₄×D₄	—	2	4	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	D₄×C₂₃	1	2	yes	—
627	C₄×D₄	D₄×C₂₃	1	2	yes	—
628	C₄×D₄	C₂³×C₂₃	1	2	yes	—
629	C₄×D₄	C₂³×C₂₃	1	2	yes	—
630	C₄×D₄	C₂³×C₂₃	1	2	yes	—
631	#117	—	2	2	no	—
632	#117	—	2	2	no	—
633	#117	C₂³×C₂₃	1	2	yes	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
653	#107	C₂³×C₂₃	1	4	yes	—
654	#106	C₂³×C₂₃	1	4	yes	—
655	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
656	#103	C₂³×C₂₃	1	4	yes	—
657	#103	C₂³×C₂₃	1	4	yes	—
658	#103	C₂³×C₂₃	1	4	yes	—
659	#103	C₂³×C₂₃	1	4	yes	—
660	#103	C₂³×C₂₃	1	4	yes	—
661	#103	C₂³×C₂₃	1	4	yes	—
662	#103	C₂³×C₂₃	1	4	yes	—
663	#102	C₂³×C₂₃	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
669	#97	C₂³×C₂₃	1	4	yes	—
670	C₂₃	#61574	1	1	yes	characteristic, direct product factor, Sylow
671	C₂⁴	—	2	1	no	—
672	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
674	#41	—	4	4	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	2	8	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	4	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	—	4	4	no	—
695	C₂×Q₈	—	4	4	no	—
696	C₂×Q₈	—	4	8	no	—
697	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
698	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
699	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
710	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
711	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	4	no	—
727	C₂²×C₄	—	4	4	no	—
728	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
739	Q₁₆	—	2	8	no	—
740	Q₁₆	—	4	4	no	—
741	Q₁₆	—	4	4	no	—
742	SD₁₆	—	2	8	no	—
743	SD₁₆	—	4	4	no	—
744	SD₁₆	—	4	4	no	—
745	M₁₆	—	4	4	no	—
746	C₂×C₈	—	4	2	no	—
747	C₂×C₈	—	4	2	no	—
748	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
749	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
766	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
784	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	C₂×D₄×C₂₃	1	2	yes	—
791	C₄²	C₂⁴×C₂₃	1	2	yes	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	8	1	no	—
800	C₂³	—	8	1	no	—
801	C₂³	C₂₃×#137	1	4	yes	complemented
802	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
803	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
804	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
806	Q₈	—	2	4	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	4	no	—
810	Q₈	—	2	4	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	4	8	no	—
813	Q₈	—	4	4	no	—
814	Q₈	—	4	4	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	4	2	no	—
817	Q₈	—	8	1	no	—
818	Q₈	C₂₃×H(5,𝔽₂)	1	4	yes	—
819	D₄	—	2	4	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	1	no	—
825	D₄	—	8	2	no	—
826	D₄	—	8	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	—	8	1	no	—
856	C₂×C₄	—	8	1	no	—
857	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
863	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
864	C₈	—	2	4	no	—
865	C₈	—	2	4	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	16	2	no	—
881	C₂²	C₂×C₂₃×#137	1	2	yes	—
882	C₂²	C₂×C₂₃×#137	1	2	yes	—
883	C₂²	C₂×C₂₃×#137	1	2	yes	—
884	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
885	C₄	—	2	4	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
899	C₂	—	2	2	no	—
900	C₂	—	2	2	no	—
901	C₂	—	2	2	no	—
902	C₂	—	4	2	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂₃×#3484	1	1	yes	characteristic
905	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
906	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₂₃	C₂	semidirect
3. C₂₃×#3320	C₂	semidirect
4. C₂₃×#3312	C₂	semidirect
5. C₂₃×#3270	C₂	semidirect
6. C₂₃×#3266	C₂	semidirect
7. C₂₃×#3218	C₂	semidirect
8. C₂₃×#3196	C₂	semidirect
9. C₂₃×#3189	C₂	semidirect
10. C₂₃×#3187	C₂	semidirect
11. C₂₃×#3117	C₂	semidirect
12. C₂₃×#3004	C₂	semidirect
13. C₂×C₂₃×#451	C₂	semidirect
14. C₂×C₂₃×#448	C₂	semidirect
15. C₂₃×#2973	C₂	semidirect
17. C₂³×Q₈×C₂₃	C₂²	semidirect
18. C₂×C₂₃×#137	C₂²	semidirect
19. C₂²×Q₁₆×C₂₃	C₂²	semidirect
20. C₂²×SD₁₆×C₂₃	C₂²	semidirect
28. D₄×Q₈×C₂₃	C₂²	semidirect
35. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
48. C₂₃×#497	C₂²	semidirect
49. C₂₃×#491	C₂²	semidirect
50. C₂₃×#485	C₂²	semidirect
51. C₂₃×#484	C₂²	semidirect
52. C₂₃×#484	C₂²	semidirect
53. C₂₃×#483	C₂²	semidirect
55. C₂₃×#479	C₂²	semidirect
56. C₂₃×#470	C₂²	semidirect
57. C₂₃×#468	C₂²	semidirect
58. C₂₃×#467	C₂²	semidirect
59. C₂₃×#465	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#462	C₂²	semidirect
62. C₂₃×#461	C₂²	semidirect
63. C₂₃×#452	C₂²	semidirect
64. C₂₃×#451	C₂²	semidirect
65. C₂₃×#451	C₂²	semidirect
66. C₂₃×#451	C₂²	semidirect
67. C₂₃×#451	C₂²	semidirect
68. C₂₃×#451	C₂²	semidirect
69. C₂₃×#451	C₂²	semidirect
70. C₂₃×#450	C₂²	semidirect
74. C₂₃×#448	C₂²	semidirect
75. C₂₃×#448	C₂²	semidirect
76. C₂₃×#441	C₂²	semidirect
77. C₂₃×#440	C₂²	semidirect
79. C₂₃×#435	C₂²	semidirect
80. C₂₃×#432	C₂²	semidirect
81. C₂₃×#419	C₂²	semidirect
82. C₂×C₂₃×#103	C₂²	semidirect
83. C₂×C₂₃×#103	C₂²	semidirect
84. C₂₃×#407	C₂²	semidirect
338. #61574	C₂₃	direct (N × H)
348. C₂³×C₂₃	#137	semidirect
414. C₂×D₄×Q₈	C₂×C₂₃	semidirect
415. #3320	C₂×C₂₃	semidirect
416. #3312	C₂×C₂₃	semidirect
417. #3270	C₂×C₂₃	semidirect
418. #3266	C₂×C₂₃	semidirect
419. #3218	C₂×C₂₃	semidirect
420. #3196	C₂×C₂₃	semidirect
421. #3189	C₂×C₂₃	semidirect
422. #3187	C₂×C₂₃	semidirect
423. #3117	C₂×C₂₃	semidirect
424. #3004	C₂×C₂₃	semidirect
425. C₂×#451	C₂×C₂₃	semidirect
426. C₂×#448	C₂×C₂₃	semidirect
427. #2973	C₂×C₂₃	semidirect
462. C₂³×Q₈	C₂²×C₂₃	semidirect
463. C₂×#137	C₂²×C₂₃	semidirect
464. C₂²×Q₁₆	C₂²×C₂₃	semidirect
465. C₂²×SD₁₆	C₂²×C₂₃	semidirect
473. D₄×Q₈	C₂²×C₂₃	semidirect
480. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
487. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
490. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
493. #497	C₂²×C₂₃	semidirect
494. #491	C₂²×C₂₃	semidirect
495. #485	C₂²×C₂₃	semidirect
496. #484	C₂²×C₂₃	semidirect
497. #484	C₂²×C₂₃	semidirect
498. #483	C₂²×C₂₃	semidirect
500. #479	C₂²×C₂₃	semidirect
501. #470	C₂²×C₂₃	semidirect
502. #468	C₂²×C₂₃	semidirect
503. #467	C₂²×C₂₃	semidirect
504. #465	C₂²×C₂₃	semidirect
505. #464	C₂²×C₂₃	semidirect
506. #462	C₂²×C₂₃	semidirect
507. #461	C₂²×C₂₃	semidirect
508. #452	C₂²×C₂₃	semidirect
509. #451	C₂²×C₂₃	semidirect
510. #451	C₂²×C₂₃	semidirect
511. #451	C₂²×C₂₃	semidirect
512. #451	C₂²×C₂₃	semidirect
513. #451	C₂²×C₂₃	semidirect
514. #451	C₂²×C₂₃	semidirect
515. #450	C₂²×C₂₃	semidirect
519. #448	C₂²×C₂₃	semidirect
520. #448	C₂²×C₂₃	semidirect
521. #441	C₂²×C₂₃	semidirect
522. #440	C₂²×C₂₃	semidirect
524. #435	C₂²×C₂₃	semidirect
525. #432	C₂²×C₂₃	semidirect
526. #419	C₂²×C₂₃	semidirect
527. C₂×#103	C₂²×C₂₃	semidirect
528. C₂×#103	C₂²×C₂₃	semidirect
529. #407	C₂²×C₂₃	semidirect
670. C₂₃	#61574	direct (N × H)
801. C₂³	C₂₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3505	2
C₂×D₄×Q₈×C₂₃	2
C₂₃×#3320	2
C₂₃×#3312	2
C₂₃×#3270	2
C₂₃×#3266	2
C₂₃×#3218	2
C₂₃×#3196	2
C₂₃×#3189	2
C₂₃×#3187	2
C₂₃×#3117	2
C₂₃×#3004	2
C₂×C₂₃×#451	2
C₂×C₂₃×#448	2
C₂₃×#2973	2
#61574	23

Subgroups — C23×#61574 #19209200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61574 #19209200