Subgroups — C₂₃×#60811 #19208437

Order 5888.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3220	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3213	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3205	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3155	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#555	—	2	1	no	—
25	C₂₃×#553	—	2	1	no	—
26	C₂₃×#553	—	2	1	no	—
27	C₂₃×#551	—	2	2	no	—
28	C₂₃×#547	—	2	1	no	—
29	C₂₃×#546	—	2	2	no	—
30	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#542	C₂²	1	2	yes	complemented
32	C₂₃×#540	C₂²	1	2	yes	complemented
33	C₂₃×#535	—	2	2	no	—
34	C₂₃×#535	—	2	1	no	—
35	C₂₃×#535	—	2	1	no	—
36	C₂₃×#535	C₂²	1	2	yes	—
37	C₂₃×#535	C₂²	1	2	yes	—
38	C₂₃×#535	C₂²	1	4	yes	complemented
39	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₂₃×#127	C₂²	1	2	yes	complemented
42	C₂₃×#529	C₂²	1	2	yes	complemented
43	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#121	—	2	1	no	—
46	C₂×C₂₃×#121	—	2	1	no	—
47	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×#120	—	2	2	no	—
49	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
52	C₂₃×#496	C₂²	1	4	yes	complemented
53	C₂₃×#496	C₂²	1	4	yes	complemented
54	C₂₃×#495	C₂²	1	4	yes	complemented
55	C₂₃×#493	C₂²	1	4	yes	complemented
56	C₂₃×#490	C₂²	1	4	yes	complemented
57	C₂₃×#489	C₂²	1	4	yes	complemented
58	C₂₃×#488	C₂²	1	4	yes	complemented
59	C₂₃×#486	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#463	C₂²	1	4	yes	complemented
62	C₂₃×#463	C₂²	1	4	yes	complemented
63	C₂₃×#463	C₂²	1	4	yes	complemented
64	C₂₃×#460	C₂²	1	4	yes	complemented
65	C₂₃×#459	C₂²	1	4	yes	complemented
66	C₂₃×#459	C₂²	1	4	yes	complemented
67	C₂₃×#459	C₂²	1	4	yes	complemented
68	C₂₃×#452	C₂²	1	2	yes	complemented
69	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#450	C₂²	1	2	yes	complemented
71	C₂₃×#450	C₂²	1	2	yes	complemented
72	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#449	C₂²	1	2	yes	complemented
74	C₂₃×#449	C₂²	1	4	yes	complemented
75	C₂₃×#448	C₂²	1	2	yes	complemented
76	C₂₃×#448	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#447	C₂²	1	2	yes	—
78	C₂₃×#447	C₂²	1	2	yes	—
79	C₂₃×#447	C₂²	1	2	yes	complemented
80	C₂₃×#447	C₂²	1	2	yes	complemented
81	C₂₃×#447	C₂²	1	4	yes	complemented
82	C₂₃×#447	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#447	C₂²	1	2	yes	complemented
84	C₂₃×#433	C₂²	1	4	yes	complemented
85	C₂₃×#432	C₂²	1	2	yes	complemented
86	C₂₃×#431	C₂²	1	2	yes	complemented
87	C₂₃×#424	C₂²	1	2	yes	complemented
88	C₂₃×#418	C₂²	1	2	yes	complemented
89	C₂₃×#417	C₂²	1	2	yes	complemented
90	C₂₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
92	C₂₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	1	no	—
97	C₂×#41×C₂₃	—	2	1	no	—
98	C₂×#41×C₂₃	—	2	2	no	—
99	C₂×#41×C₂₃	—	4	4	no	—
100	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂×#41×C₂₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	—	2	1	no	—
106	C₂²×D₄×C₂₃	—	2	1	no	—
107	C₂²×D₄×C₂₃	—	2	1	no	—
108	C₂²×D₄×C₂₃	—	2	1	no	—
109	C₂²×D₄×C₂₃	—	2	2	no	—
110	C₂²×D₄×C₂₃	—	2	2	no	—
111	C₂²×D₄×C₂₃	—	4	4	no	—
112	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	—	2	1	no	—
118	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
120	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
121	C₂₃×#135	—	4	4	no	—
122	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	complemented
123	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
125	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
126	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
127	C₂×D₈×C₂₃	—	4	4	no	—
128	C₂×D₈×C₂₃	C₂³	1	4	yes	—
129	C₂×D₈×C₂₃	C₂³	1	4	yes	—
130	C₂×D₈×C₂₃	C₂³	1	4	yes	—
131	C₂×D₈×C₂₃	C₂³	1	2	yes	complemented
132	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
135	C₂₃×C₄⋊Q₈	—	2	1	no	—
136	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
137	C₂₃×#127	—	2	2	no	—
138	C₂₃×#127	—	2	2	no	—
139	C₂₃×#127	C₂³	1	4	yes	—
140	C₂₃×#127	C₂³	1	4	yes	—
141	C₂₃×#127	C₂³	1	2	yes	complemented
142	C₂₃×#126	—	2	2	no	—
143	C₂₃×#126	—	2	2	no	—
144	C₂₃×#125	—	2	1	no	—
145	C₂₃×#125	C₂³	1	2	yes	complemented
146	C₂₃×#124	—	2	2	no	—
147	C₂₃×#124	—	2	2	no	—
148	C₂₃×#124	—	2	2	no	—
149	C₂₃×#124	—	2	2	no	—
150	C₂₃×#124	C₂³	1	4	yes	—
151	C₂₃×#124	C₂³	1	4	yes	—
152	C₂₃×#124	C₂³	1	2	yes	complemented
153	C₂₃×#123	—	2	2	no	—
154	C₂₃×#123	—	2	1	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×#123	—	2	2	no	—
158	C₂₃×C₂²⋊Q₈	—	2	2	no	—
159	C₂₃×C₂²⋊Q₈	—	2	2	no	—
160	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×#121	—	2	1	no	—
163	C₂₃×#121	—	2	1	no	—
164	C₂₃×#121	—	2	2	no	—
165	C₂₃×#121	—	2	1	no	—
166	C₂₃×#121	—	2	1	no	—
167	C₂₃×#121	—	2	2	no	—
168	C₂₃×#121	—	2	2	no	—
169	C₂₃×#121	—	2	2	no	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	4	no	—
172	C₂₃×#121	—	2	4	no	—
173	C₂₃×#121	—	2	2	no	—
174	C₂₃×#121	—	2	2	no	—
175	C₂₃×#121	C₂³	1	2	yes	—
176	C₂₃×#121	C₂³	1	1	yes	characteristic
177	C₂₃×#121	C₂³	1	2	yes	—
178	C₂₃×#121	C₂³	1	1	yes	characteristic
179	C₂₃×#120	—	2	1	no	—
180	C₂₃×#120	—	2	2	no	—
181	C₂₃×#120	—	2	4	no	—
182	C₂₃×#120	—	2	4	no	—
183	C₂₃×#120	—	2	4	no	—
184	C₂₃×#120	—	2	4	no	—
185	C₄×Q₈×C₂₃	C₂³	1	2	yes	complemented
186	C₄×D₄×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	—	2	2	no	—
189	C₄×D₄×C₂₃	—	2	1	no	—
190	C₄×D₄×C₂₃	—	2	1	no	—
191	C₄×D₄×C₂₃	—	2	2	no	—
192	C₄×D₄×C₂₃	—	2	2	no	—
193	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
194	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
195	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
196	C₂₃×#117	—	2	1	no	—
197	C₂₃×#117	—	2	2	no	—
198	C₂₃×#117	D₄	1	2	yes	—
199	C₂₃×#117	D₄	1	1	yes	characteristic
200	C₂₃×#117	D₄	1	1	yes	characteristic
201	C₂₃×#117	C₂³	1	1	yes	characteristic
202	C₂₃×#117	C₂³	1	1	yes	characteristic
203	C₂₃×#117	C₂³	1	1	yes	characteristic
204	C₂₃×#117	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
206	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
210	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
211	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
213	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
214	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
215	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
216	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
217	C₂₃×#103	C₂³	1	2	yes	complemented
218	C₂₃×#103	C₂³	1	2	yes	complemented
219	C₂₃×#103	C₂³	1	4	yes	complemented
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	complemented
225	C₂₃×#102	C₂³	1	2	yes	complemented
226	C₂₃×#102	C₂³	1	4	yes	complemented
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₂₃×#97	C₂³	1	4	yes	complemented
233	C₄×C₈×C₂₃	C₂³	1	4	yes	complemented
234	C₂⁴×C₂₃	—	2	2	no	—
235	C₂⁴×C₂₃	—	2	1	no	—
236	C₂⁴×C₂₃	—	2	1	no	—
237	C₂⁴×C₂₃	—	2	2	no	—
238	C₂⁴×C₂₃	—	2	2	no	—
239	C₂⁴×C₂₃	—	4	4	no	—
240	C₂⁴×C₂₃	—	8	2	no	—
241	C₂⁴×C₂₃	—	8	2	no	—
242	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
243	#41×C₂₃	—	2	4	no	—
244	#41×C₂₃	—	2	4	no	—
245	#41×C₂₃	—	2	4	no	—
246	#41×C₂₃	—	4	2	no	—
247	#41×C₂₃	—	4	2	no	—
248	#41×C₂₃	—	4	4	no	—
249	#41×C₂₃	—	4	4	no	—
250	#41×C₂₃	—	8	4	no	—
251	C₂×Q₈×C₂₃	—	2	1	no	—
252	C₂×Q₈×C₂₃	—	2	2	no	—
253	C₂×Q₈×C₂₃	—	4	2	no	—
254	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₂₃	—	2	1	no	—
257	C₂×D₄×C₂₃	—	2	1	no	—
258	C₂×D₄×C₂₃	—	2	2	no	—
259	C₂×D₄×C₂₃	—	2	2	no	—
260	C₂×D₄×C₂₃	—	2	2	no	—
261	C₂×D₄×C₂₃	—	2	1	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	1	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	2	no	—
267	C₂×D₄×C₂₃	—	2	1	no	—
268	C₂×D₄×C₂₃	—	2	2	no	—
269	C₂×D₄×C₂₃	—	2	4	no	—
270	C₂×D₄×C₂₃	—	2	4	no	—
271	C₂×D₄×C₂₃	—	2	4	no	—
272	C₂×D₄×C₂₃	—	2	4	no	—
273	C₂×D₄×C₂₃	—	2	2	no	—
274	C₂×D₄×C₂₃	—	2	4	no	—
275	C₂×D₄×C₂₃	—	2	4	no	—
276	C₂×D₄×C₂₃	—	2	4	no	—
277	C₂×D₄×C₂₃	—	4	4	no	—
278	C₂×D₄×C₂₃	—	4	4	no	—
279	C₂×D₄×C₂₃	—	4	2	no	—
280	C₂×D₄×C₂₃	—	4	4	no	—
281	C₂×D₄×C₂₃	—	4	4	no	—
282	C₂×D₄×C₂₃	—	4	4	no	—
283	C₂×D₄×C₂₃	—	4	4	no	—
284	C₂×D₄×C₂₃	—	8	4	no	—
285	C₂×D₄×C₂₃	—	8	4	no	—
286	C₂×D₄×C₂₃	—	8	2	no	—
287	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
288	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	—	2	4	no	—
292	C₂²×C₄×C₂₃	—	2	1	no	—
293	C₂²×C₄×C₂₃	—	2	1	no	—
294	C₂²×C₄×C₂₃	—	2	1	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	2	no	—
297	C₂²×C₄×C₂₃	—	2	2	no	—
298	C₂²×C₄×C₂₃	—	2	2	no	—
299	C₂²×C₄×C₂₃	—	2	2	no	—
300	C₂²×C₄×C₂₃	—	4	4	no	—
301	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	Q₁₆×C₂₃	—	4	2	no	—
310	SD₁₆×C₂₃	—	4	4	no	—
311	SD₁₆×C₂₃	—	4	2	no	—
312	SD₁₆×C₂₃	—	4	2	no	—
313	SD₁₆×C₂₃	—	4	4	no	—
314	D₈×C₂₃	—	4	4	no	—
315	D₈×C₂₃	—	4	4	no	—
316	D₈×C₂₃	—	4	4	no	—
317	D₈×C₂₃	—	4	2	no	—
318	D₈×C₂₃	—	4	4	no	—
319	M₁₆×C₂₃	—	2	4	no	—
320	C₂×C₈×C₂₃	—	2	4	no	—
321	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
324	C₄⋊C₄×C₂₃	—	2	1	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
326	C₄⋊C₄×C₂₃	—	2	1	no	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	1	no	—
331	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
335	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂²⋊C₄×C₂₃	—	2	1	no	—
341	C₂²⋊C₄×C₂₃	—	2	1	no	—
342	C₂²⋊C₄×C₂₃	—	2	1	no	—
343	C₂²⋊C₄×C₂₃	—	2	2	no	—
344	C₂²⋊C₄×C₂₃	—	2	2	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	4	no	—
347	C₂²⋊C₄×C₂₃	—	2	4	no	—
348	C₂²⋊C₄×C₂₃	—	2	4	no	—
349	C₂²⋊C₄×C₂₃	—	2	4	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	1	no	—
354	C₂²⋊C₄×C₂₃	—	2	2	no	—
355	C₂²⋊C₄×C₂₃	—	2	1	no	—
356	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
358	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
359	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₄²×C₂₃	—	2	2	no	—
361	C₄²×C₂₃	—	2	1	no	—
362	C₄²×C₂₃	C₂×D₄	1	2	yes	—
363	C₄²×C₂₃	C₂×D₄	1	2	yes	—
364	C₄²×C₂₃	C₂⁴	1	2	yes	—
365	C₄²×C₂₃	C₂⁴	1	2	yes	—
366	#60811	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂³×C₂₃	—	2	2	no	—
368	C₂³×C₂₃	—	2	2	no	—
369	C₂³×C₂₃	—	2	2	no	—
370	C₂³×C₂₃	—	2	1	no	—
371	C₂³×C₂₃	—	2	4	no	—
372	C₂³×C₂₃	—	2	2	no	—
373	C₂³×C₂₃	—	4	1	no	—
374	C₂³×C₂₃	—	4	2	no	—
375	C₂³×C₂₃	—	4	4	no	—
376	C₂³×C₂₃	—	4	4	no	—
377	C₂³×C₂₃	—	4	2	no	—
378	C₂³×C₂₃	—	4	4	no	—
379	C₂³×C₂₃	—	4	4	no	—
380	C₂³×C₂₃	—	4	2	no	—
381	C₂³×C₂₃	—	4	4	no	—
382	C₂³×C₂₃	—	4	2	no	—
383	C₂³×C₂₃	—	8	2	no	—
384	C₂³×C₂₃	—	8	2	no	—
385	C₂³×C₂₃	—	8	2	no	—
386	C₂³×C₂₃	—	8	2	no	—
387	C₂³×C₂₃	—	8	1	no	—
388	C₂³×C₂₃	—	8	1	no	—
389	C₂³×C₂₃	—	8	16	no	—
390	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	Q₈×C₂₃	—	2	2	no	—
394	Q₈×C₂₃	—	2	2	no	—
395	Q₈×C₂₃	—	2	2	no	—
396	Q₈×C₂₃	—	4	2	no	—
397	Q₈×C₂₃	—	8	2	no	—
398	D₄×C₂₃	—	2	4	no	—
399	D₄×C₂₃	—	2	2	no	—
400	D₄×C₂₃	—	2	4	no	—
401	D₄×C₂₃	—	2	2	no	—
402	D₄×C₂₃	—	2	4	no	—
403	D₄×C₂₃	—	2	2	no	—
404	D₄×C₂₃	—	4	4	no	—
405	D₄×C₂₃	—	4	4	no	—
406	D₄×C₂₃	—	4	2	no	—
407	D₄×C₂₃	—	4	4	no	—
408	D₄×C₂₃	—	4	4	no	—
409	D₄×C₂₃	—	4	2	no	—
410	D₄×C₂₃	—	4	4	no	—
411	D₄×C₂₃	—	4	2	no	—
412	D₄×C₂₃	—	4	2	no	—
413	D₄×C₂₃	—	4	4	no	—
414	D₄×C₂₃	—	8	2	no	—
415	D₄×C₂₃	—	8	4	no	—
416	D₄×C₂₃	—	8	4	no	—
417	D₄×C₂₃	—	8	4	no	—
418	D₄×C₂₃	—	8	4	no	—
419	D₄×C₂₃	—	8	2	no	—
420	D₄×C₂₃	—	8	1	no	—
421	D₄×C₂₃	—	8	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	4	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	2	1	no	—
430	C₂×C₄×C₂₃	—	2	1	no	—
431	C₂×C₄×C₂₃	—	2	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	4	2	no	—
434	C₂×C₄×C₂₃	—	4	4	no	—
435	C₂×C₄×C₂₃	—	4	2	no	—
436	C₂×C₄×C₂₃	—	4	4	no	—
437	C₂×C₄×C₂₃	—	4	2	no	—
438	C₂×C₄×C₂₃	—	8	2	no	—
439	C₂×C₄×C₂₃	—	8	2	no	—
440	C₂×C₄×C₂₃	—	8	2	no	—
441	C₂×C₄×C₂₃	—	8	1	no	—
442	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
450	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
451	C₈×C₂₃	—	2	2	no	—
452	C₈×C₂₃	—	2	2	no	—
453	C₈×C₂₃	—	2	4	no	—
454	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
455	C₂×#535	C₂×C₂₃	1	1	yes	characteristic, complemented
456	#3224	C₂×C₂₃	1	4	yes	complemented
457	#3220	C₂×C₂₃	1	4	yes	complemented
458	#3217	C₂×C₂₃	1	2	yes	complemented
459	#3213	C₂×C₂₃	1	2	yes	complemented
460	#3211	C₂×C₂₃	1	2	yes	complemented
461	#3205	C₂×C₂₃	1	2	yes	complemented
462	#3155	C₂×C₂₃	1	2	yes	complemented
463	#3136	C₂×C₂₃	1	2	yes	complemented
464	#3045	C₂×C₂₃	1	2	yes	complemented
465	#3041	C₂×C₂₃	1	2	yes	complemented
466	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
467	#3003	C₂×C₂₃	1	1	yes	characteristic, complemented
468	#3002	C₂×C₂₃	1	1	yes	characteristic, complemented
469	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
470	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
471	C₂²×C₂₃	—	2	1	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	2	1	no	—
474	C₂²×C₂₃	—	2	1	no	—
475	C₂²×C₂₃	—	2	1	no	—
476	C₂²×C₂₃	—	2	1	no	—
477	C₂²×C₂₃	—	2	1	no	—
478	C₂²×C₂₃	—	4	4	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	1	no	—
482	C₂²×C₂₃	—	4	4	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	4	1	no	—
485	C₂²×C₂₃	—	4	4	no	—
486	C₂²×C₂₃	—	4	2	no	—
487	C₂²×C₂₃	—	4	1	no	—
488	C₂²×C₂₃	—	4	2	no	—
489	C₂²×C₂₃	—	4	2	no	—
490	C₂²×C₂₃	—	4	4	no	—
491	C₂²×C₂₃	—	8	4	no	—
492	C₂²×C₂₃	—	8	8	no	—
493	C₂²×C₂₃	—	8	8	no	—
494	C₂²×C₂₃	—	8	8	no	—
495	C₂²×C₂₃	—	16	2	no	—
496	C₂²×C₂₃	#535	1	2	yes	—
497	C₂²×C₂₃	#576	1	2	yes	—
498	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
499	C₄×C₂₃	—	2	2	no	—
500	C₄×C₂₃	—	2	2	no	—
501	C₄×C₂₃	—	2	1	no	—
502	C₄×C₂₃	—	2	1	no	—
503	C₄×C₂₃	—	2	2	no	—
504	C₄×C₂₃	—	2	2	no	—
505	C₄×C₂₃	—	4	1	no	—
506	C₄×C₂₃	—	4	2	no	—
507	C₄×C₂₃	—	4	1	no	—
508	C₄×C₂₃	—	4	2	no	—
509	C₄×C₂₃	—	4	1	no	—
510	C₄×C₂₃	#535	1	2	yes	—
511	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
512	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
513	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
514	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
515	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
516	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
517	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
518	#555	—	2	1	no	—
519	#553	—	2	1	no	—
520	#553	—	2	1	no	—
521	#551	—	2	2	no	—
522	#547	—	2	1	no	—
523	#546	—	2	2	no	—
524	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	#542	C₂²×C₂₃	1	2	yes	complemented
526	#540	C₂²×C₂₃	1	2	yes	complemented
527	#535	—	2	2	no	—
528	#535	—	2	1	no	—
529	#535	—	2	1	no	—
530	#535	C₂²×C₂₃	1	2	yes	—
531	#535	C₂²×C₂₃	1	2	yes	—
532	#535	C₂²×C₂₃	1	4	yes	complemented
533	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
534	#532	C₂²×C₂₃	1	2	yes	complemented
535	C₂×#127	C₂²×C₂₃	1	2	yes	complemented
536	#529	C₂²×C₂₃	1	2	yes	complemented
537	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
538	#525	C₂²×C₂₃	1	1	yes	characteristic
539	C₂×#121	—	2	1	no	—
540	C₂×#121	—	2	1	no	—
541	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
542	C₂×#120	—	2	2	no	—
543	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
544	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
545	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
546	#496	C₂²×C₂₃	1	4	yes	complemented
547	#496	C₂²×C₂₃	1	4	yes	complemented
548	#495	C₂²×C₂₃	1	4	yes	complemented
549	#493	C₂²×C₂₃	1	4	yes	complemented
550	#490	C₂²×C₂₃	1	4	yes	complemented
551	#489	C₂²×C₂₃	1	4	yes	complemented
552	#488	C₂²×C₂₃	1	4	yes	complemented
553	#486	C₂²×C₂₃	1	4	yes	complemented
554	#464	C₂²×C₂₃	1	4	yes	complemented
555	#463	C₂²×C₂₃	1	4	yes	complemented
556	#463	C₂²×C₂₃	1	4	yes	complemented
557	#463	C₂²×C₂₃	1	4	yes	complemented
558	#460	C₂²×C₂₃	1	4	yes	complemented
559	#459	C₂²×C₂₃	1	4	yes	complemented
560	#459	C₂²×C₂₃	1	4	yes	complemented
561	#459	C₂²×C₂₃	1	4	yes	complemented
562	#452	C₂²×C₂₃	1	2	yes	complemented
563	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	#450	C₂²×C₂₃	1	2	yes	complemented
565	#450	C₂²×C₂₃	1	2	yes	complemented
566	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
567	#449	C₂²×C₂₃	1	2	yes	complemented
568	#449	C₂²×C₂₃	1	4	yes	complemented
569	#448	C₂²×C₂₃	1	2	yes	complemented
570	#448	C₂²×C₂₃	1	1	yes	characteristic, complemented
571	#447	C₂²×C₂₃	1	2	yes	—
572	#447	C₂²×C₂₃	1	2	yes	—
573	#447	C₂²×C₂₃	1	2	yes	complemented
574	#447	C₂²×C₂₃	1	2	yes	complemented
575	#447	C₂²×C₂₃	1	4	yes	complemented
576	#447	C₂²×C₂₃	1	1	yes	characteristic, complemented
577	#447	C₂²×C₂₃	1	2	yes	complemented
578	#433	C₂²×C₂₃	1	4	yes	complemented
579	#432	C₂²×C₂₃	1	2	yes	complemented
580	#431	C₂²×C₂₃	1	2	yes	complemented
581	#424	C₂²×C₂₃	1	2	yes	complemented
582	#418	C₂²×C₂₃	1	2	yes	complemented
583	#417	C₂²×C₂₃	1	2	yes	complemented
584	#416	C₂²×C₂₃	1	2	yes	complemented
585	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
586	#407	C₂²×C₂₃	1	1	yes	characteristic
587	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
588	#405	C₂²×C₂₃	1	2	yes	complemented
589	C₂×C₂₃	—	2	2	no	—
590	C₂×C₂₃	—	2	2	no	—
591	C₂×C₂₃	—	4	1	no	—
592	C₂×C₂₃	—	8	1	no	—
593	C₂×C₂₃	—	8	2	no	—
594	C₂×C₂₃	—	8	4	no	—
595	C₂×C₂₃	—	8	2	no	—
596	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
597	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
598	C₂×C₂₃	#3585	1	1	yes	characteristic
599	C₂⁵	—	2	1	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	2	no	—
603	C₂×#41	—	4	4	no	—
604	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
605	C₂×#41	C₂³×C₂₃	1	2	yes	—
606	C₂×#41	C₂³×C₂₃	1	2	yes	—
607	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₂²×D₄	—	2	1	no	—
609	C₂²×D₄	—	2	1	no	—
610	C₂²×D₄	—	2	1	no	—
611	C₂²×D₄	—	2	1	no	—
612	C₂²×D₄	—	2	1	no	—
613	C₂²×D₄	—	2	2	no	—
614	C₂²×D₄	—	2	2	no	—
615	C₂²×D₄	—	4	4	no	—
616	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
618	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
619	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
621	C₂³×C₄	—	2	1	no	—
622	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
623	AGL(1,ℤ/8)	—	4	4	no	—
624	AGL(1,ℤ/8)	—	4	4	no	—
625	#135	—	4	4	no	—
626	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	complemented
627	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
628	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
629	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
630	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
631	C₂×D₈	—	4	4	no	—
632	C₂×D₈	C₂³×C₂₃	1	4	yes	—
633	C₂×D₈	C₂³×C₂₃	1	4	yes	—
634	C₂×D₈	C₂³×C₂₃	1	4	yes	—
635	C₂×D₈	C₂³×C₂₃	1	2	yes	complemented
636	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
637	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
638	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
641	#127	—	2	2	no	—
642	#127	—	2	2	no	—
643	#127	C₂³×C₂₃	1	4	yes	—
644	#127	C₂³×C₂₃	1	4	yes	—
645	#127	C₂³×C₂₃	1	2	yes	complemented
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#125	—	2	1	no	—
649	#125	C₂³×C₂₃	1	2	yes	complemented
650	#124	—	2	2	no	—
651	#124	—	2	2	no	—
652	#124	—	2	2	no	—
653	#124	—	2	2	no	—
654	#124	C₂³×C₂₃	1	4	yes	—
655	#124	C₂³×C₂₃	1	4	yes	—
656	#124	C₂³×C₂₃	1	2	yes	complemented
657	#123	—	2	1	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
665	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
666	#121	—	2	1	no	—
667	#121	—	2	1	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	2	no	—
672	#121	—	2	2	no	—
673	#121	—	2	4	no	—
674	#121	—	2	4	no	—
675	#121	—	2	1	no	—
676	#121	—	2	1	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	C₂³×C₂₃	1	2	yes	—
680	#121	C₂³×C₂₃	1	2	yes	—
681	#121	C₂³×C₂₃	1	1	yes	characteristic
682	#121	C₂³×C₂₃	1	1	yes	characteristic
683	#120	—	2	1	no	—
684	#120	—	2	4	no	—
685	#120	—	2	4	no	—
686	#120	—	2	4	no	—
687	#120	—	2	4	no	—
688	#120	—	2	2	no	—
689	C₄×Q₈	C₂³×C₂₃	1	2	yes	complemented
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
698	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
699	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
700	#117	—	2	1	no	—
701	#117	—	2	2	no	—
702	#117	D₄×C₂₃	1	2	yes	—
703	#117	D₄×C₂₃	1	1	yes	characteristic
704	#117	D₄×C₂₃	1	1	yes	characteristic
705	#117	C₂³×C₂₃	1	1	yes	characteristic
706	#117	C₂³×C₂₃	1	1	yes	characteristic
707	#117	C₂³×C₂₃	1	1	yes	characteristic
708	#117	C₂³×C₂₃	1	2	yes	—
709	C₂×C₄⋊C₄	—	2	1	no	—
710	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
711	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	—	2	2	no	—
714	C₂×C₂²⋊C₄	—	2	2	no	—
715	C₂×C₂²⋊C₄	—	2	1	no	—
716	C₂×C₂²⋊C₄	—	2	2	no	—
717	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
718	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
719	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
720	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
721	#103	C₂³×C₂₃	1	2	yes	complemented
722	#103	C₂³×C₂₃	1	2	yes	complemented
723	#103	C₂³×C₂₃	1	4	yes	complemented
724	#102	C₂³×C₂₃	1	4	yes	—
725	#102	C₂³×C₂₃	1	4	yes	—
726	#102	C₂³×C₂₃	1	4	yes	—
727	#102	C₂³×C₂₃	1	4	yes	—
728	#102	C₂³×C₂₃	1	2	yes	complemented
729	#102	C₂³×C₂₃	1	2	yes	complemented
730	#102	C₂³×C₂₃	1	4	yes	complemented
731	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
733	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
736	#97	C₂³×C₂₃	1	4	yes	complemented
737	C₄×C₈	C₂³×C₂₃	1	4	yes	complemented
738	C₂₃	#60811	1	1	yes	characteristic, direct product factor, Sylow
739	C₂⁴	—	2	2	no	—
740	C₂⁴	—	2	1	no	—
741	C₂⁴	—	2	1	no	—
742	C₂⁴	—	2	2	no	—
743	C₂⁴	—	2	2	no	—
744	C₂⁴	—	4	4	no	—
745	C₂⁴	—	8	2	no	—
746	C₂⁴	—	8	2	no	—
747	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
748	#41	—	2	4	no	—
749	#41	—	2	4	no	—
750	#41	—	2	4	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	#41	—	4	4	no	—
754	#41	—	4	4	no	—
755	#41	—	8	4	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
760	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	4	4	no	—
783	C₂×D₄	—	4	4	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	4	4	no	—
788	C₂×D₄	—	4	4	no	—
789	C₂×D₄	—	8	4	no	—
790	C₂×D₄	—	8	4	no	—
791	C₂×D₄	—	8	2	no	—
792	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
793	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
794	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
795	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	4	4	no	—
806	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
807	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
808	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
814	Q₁₆	—	4	2	no	—
815	SD₁₆	—	4	4	no	—
816	SD₁₆	—	4	2	no	—
817	SD₁₆	—	4	2	no	—
818	SD₁₆	—	4	4	no	—
819	D₈	—	4	4	no	—
820	D₈	—	4	4	no	—
821	D₈	—	4	4	no	—
822	D₈	—	4	2	no	—
823	D₈	—	4	4	no	—
824	M₁₆	—	2	4	no	—
825	C₂×C₈	—	2	4	no	—
826	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
828	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
838	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
839	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
841	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
863	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
864	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	1	no	—
867	C₄²	C₂×D₄×C₂₃	1	2	yes	—
868	C₄²	C₂×D₄×C₂₃	1	2	yes	—
869	C₄²	C₂⁴×C₂₃	1	2	yes	—
870	C₄²	C₂⁴×C₂₃	1	2	yes	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	4	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	1	no	—
878	C₂³	—	4	2	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	4	no	—
881	C₂³	—	4	2	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	4	2	no	—
884	C₂³	—	4	4	no	—
885	C₂³	—	4	4	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	8	2	no	—
888	C₂³	—	8	2	no	—
889	C₂³	—	8	2	no	—
890	C₂³	—	8	2	no	—
891	C₂³	—	8	1	no	—
892	C₂³	—	8	1	no	—
893	C₂³	—	8	16	no	—
894	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
895	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
896	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	8	2	no	—
902	D₄	—	2	4	no	—
903	D₄	—	2	2	no	—
904	D₄	—	2	4	no	—
905	D₄	—	2	2	no	—
906	D₄	—	2	4	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	2	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	4	no	—
913	D₄	—	4	2	no	—
914	D₄	—	4	4	no	—
915	D₄	—	4	2	no	—
916	D₄	—	4	4	no	—
917	D₄	—	4	2	no	—
918	D₄	—	8	4	no	—
919	D₄	—	8	4	no	—
920	D₄	—	8	4	no	—
921	D₄	—	8	4	no	—
922	D₄	—	8	2	no	—
923	D₄	—	8	2	no	—
924	D₄	—	8	2	no	—
925	D₄	—	8	1	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	1	no	—
946	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
949	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
950	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
953	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
954	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	4	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	4	4	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	4	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	4	no	—
978	C₂²	—	8	8	no	—
979	C₂²	—	8	4	no	—
980	C₂²	—	8	8	no	—
981	C₂²	—	8	8	no	—
982	C₂²	—	16	2	no	—
983	C₂²	C₂₃×#535	1	2	yes	—
984	C₂²	C₂₃×#576	1	2	yes	—
985	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	C₂₃×#535	1	2	yes	—
998	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
999	C₂	—	2	2	no	—
1000	C₂	—	2	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	8	4	no	—
1003	C₂	—	8	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
1007	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
1008	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 ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂×C₂₃×#535	C₂	semidirect
3. C₂₃×#3224	C₂	semidirect
4. C₂₃×#3220	C₂	semidirect
5. C₂₃×#3217	C₂	semidirect
6. C₂₃×#3213	C₂	semidirect
7. C₂₃×#3211	C₂	semidirect
8. C₂₃×#3205	C₂	semidirect
9. C₂₃×#3155	C₂	semidirect
10. C₂₃×#3136	C₂	semidirect
11. C₂₃×#3045	C₂	semidirect
12. C₂₃×#3041	C₂	semidirect
13. C₂₃×#3006	C₂	semidirect
14. C₂₃×#3003	C₂	semidirect
15. C₂₃×#3002	C₂	semidirect
16. C₂×C₂₃×#447	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
20. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₂₃×#135	C₂²	semidirect
23. C₂²×D₈×C₂₃	C₂²	semidirect
30. C₂₃×#544	C₂²	semidirect
31. C₂₃×#542	C₂²	semidirect
32. C₂₃×#540	C₂²	semidirect
38. C₂₃×#535	C₂²	semidirect
39. C₂₃×#535	C₂²	semidirect
40. C₂₃×#532	C₂²	semidirect
41. C₂×C₂₃×#127	C₂²	semidirect
42. C₂₃×#529	C₂²	semidirect
43. C₂×C₂₃×#124	C₂²	semidirect
49. C₂₃×#520	C₂²	semidirect
50. C₂₃×#518	C₂²	semidirect
52. C₂₃×#496	C₂²	semidirect
53. C₂₃×#496	C₂²	semidirect
54. C₂₃×#495	C₂²	semidirect
55. C₂₃×#493	C₂²	semidirect
56. C₂₃×#490	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
58. C₂₃×#488	C₂²	semidirect
59. C₂₃×#486	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#463	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#460	C₂²	semidirect
65. C₂₃×#459	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
67. C₂₃×#459	C₂²	semidirect
68. C₂₃×#452	C₂²	semidirect
69. C₂₃×#451	C₂²	semidirect
70. C₂₃×#450	C₂²	semidirect
71. C₂₃×#450	C₂²	semidirect
72. C₂₃×#450	C₂²	semidirect
73. C₂₃×#449	C₂²	semidirect
74. C₂₃×#449	C₂²	semidirect
75. C₂₃×#448	C₂²	semidirect
76. C₂₃×#448	C₂²	semidirect
79. C₂₃×#447	C₂²	semidirect
80. C₂₃×#447	C₂²	semidirect
81. C₂₃×#447	C₂²	semidirect
82. C₂₃×#447	C₂²	semidirect
83. C₂₃×#447	C₂²	semidirect
84. C₂₃×#433	C₂²	semidirect
85. C₂₃×#432	C₂²	semidirect
86. C₂₃×#431	C₂²	semidirect
87. C₂₃×#424	C₂²	semidirect
88. C₂₃×#418	C₂²	semidirect
89. C₂₃×#417	C₂²	semidirect
90. C₂₃×#416	C₂²	semidirect
91. C₂×C₂₃×#102	C₂²	semidirect
94. C₂₃×#405	C₂²	semidirect
122. C₂×Q₁₆×C₂₃	C₂³	semidirect
124. C₂×SD₁₆×C₂₃	C₂³	semidirect
125. C₂×SD₁₆×C₂₃	C₂³	semidirect
126. C₂×SD₁₆×C₂₃	C₂³	semidirect
131. C₂×D₈×C₂₃	C₂³	semidirect
132. C₂×D₈×C₂₃	C₂³	semidirect
136. C₂₃×C₄⋊Q₈	C₂³	semidirect
141. C₂₃×#127	C₂³	semidirect
145. C₂₃×#125	C₂³	semidirect
152. C₂₃×#124	C₂³	semidirect
185. C₄×Q₈×C₂₃	C₂³	semidirect
193. C₄×D₄×C₂₃	C₂³	semidirect
194. C₄×D₄×C₂₃	C₂³	semidirect
195. C₄×D₄×C₂₃	C₂³	semidirect
215. C₂₃×C₄⋊C₈	C₂³	semidirect
216. C₂₃×C₄⋊C₈	C₂³	semidirect
217. C₂₃×#103	C₂³	semidirect
218. C₂₃×#103	C₂³	semidirect
219. C₂₃×#103	C₂³	semidirect
224. C₂₃×#102	C₂³	semidirect
225. C₂₃×#102	C₂³	semidirect
226. C₂₃×#102	C₂³	semidirect
232. C₂₃×#97	C₂³	semidirect
233. C₄×C₈×C₂₃	C₂³	semidirect
366. #60811	C₂₃	direct (N × H)
454. #3494	C₂×C₂₃	semidirect
455. C₂×#535	C₂×C₂₃	semidirect
456. #3224	C₂×C₂₃	semidirect
457. #3220	C₂×C₂₃	semidirect
458. #3217	C₂×C₂₃	semidirect
459. #3213	C₂×C₂₃	semidirect
460. #3211	C₂×C₂₃	semidirect
461. #3205	C₂×C₂₃	semidirect
462. #3155	C₂×C₂₃	semidirect
463. #3136	C₂×C₂₃	semidirect
464. #3045	C₂×C₂₃	semidirect
465. #3041	C₂×C₂₃	semidirect
466. #3006	C₂×C₂₃	semidirect
467. #3003	C₂×C₂₃	semidirect
468. #3002	C₂×C₂₃	semidirect
469. C₂×#447	C₂×C₂₃	semidirect
470. #2924	C₂×C₂₃	semidirect
514. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
515. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
516. C₂×#135	C₂²×C₂₃	semidirect
517. C₂²×D₈	C₂²×C₂₃	semidirect
524. #544	C₂²×C₂₃	semidirect
525. #542	C₂²×C₂₃	semidirect
526. #540	C₂²×C₂₃	semidirect
532. #535	C₂²×C₂₃	semidirect
533. #535	C₂²×C₂₃	semidirect
534. #532	C₂²×C₂₃	semidirect
535. C₂×#127	C₂²×C₂₃	semidirect
536. #529	C₂²×C₂₃	semidirect
537. C₂×#124	C₂²×C₂₃	semidirect
543. #520	C₂²×C₂₃	semidirect
544. #518	C₂²×C₂₃	semidirect
546. #496	C₂²×C₂₃	semidirect
547. #496	C₂²×C₂₃	semidirect
548. #495	C₂²×C₂₃	semidirect
549. #493	C₂²×C₂₃	semidirect
550. #490	C₂²×C₂₃	semidirect
551. #489	C₂²×C₂₃	semidirect
552. #488	C₂²×C₂₃	semidirect
553. #486	C₂²×C₂₃	semidirect
554. #464	C₂²×C₂₃	semidirect
555. #463	C₂²×C₂₃	semidirect
556. #463	C₂²×C₂₃	semidirect
557. #463	C₂²×C₂₃	semidirect
558. #460	C₂²×C₂₃	semidirect
559. #459	C₂²×C₂₃	semidirect
560. #459	C₂²×C₂₃	semidirect
561. #459	C₂²×C₂₃	semidirect
562. #452	C₂²×C₂₃	semidirect
563. #451	C₂²×C₂₃	semidirect
564. #450	C₂²×C₂₃	semidirect
565. #450	C₂²×C₂₃	semidirect
566. #450	C₂²×C₂₃	semidirect
567. #449	C₂²×C₂₃	semidirect
568. #449	C₂²×C₂₃	semidirect
569. #448	C₂²×C₂₃	semidirect
570. #448	C₂²×C₂₃	semidirect
573. #447	C₂²×C₂₃	semidirect
574. #447	C₂²×C₂₃	semidirect
575. #447	C₂²×C₂₃	semidirect
576. #447	C₂²×C₂₃	semidirect
577. #447	C₂²×C₂₃	semidirect
578. #433	C₂²×C₂₃	semidirect
579. #432	C₂²×C₂₃	semidirect
580. #431	C₂²×C₂₃	semidirect
581. #424	C₂²×C₂₃	semidirect
582. #418	C₂²×C₂₃	semidirect
583. #417	C₂²×C₂₃	semidirect
584. #416	C₂²×C₂₃	semidirect
585. C₂×#102	C₂²×C₂₃	semidirect
588. #405	C₂²×C₂₃	semidirect
626. C₂×Q₁₆	C₂³×C₂₃	semidirect
628. C₂×SD₁₆	C₂³×C₂₃	semidirect
629. C₂×SD₁₆	C₂³×C₂₃	semidirect
630. C₂×SD₁₆	C₂³×C₂₃	semidirect
635. C₂×D₈	C₂³×C₂₃	semidirect
636. C₂×D₈	C₂³×C₂₃	semidirect
640. C₄⋊Q₈	C₂³×C₂₃	semidirect
645. #127	C₂³×C₂₃	semidirect
649. #125	C₂³×C₂₃	semidirect
656. #124	C₂³×C₂₃	semidirect
689. C₄×Q₈	C₂³×C₂₃	semidirect
697. C₄×D₄	C₂³×C₂₃	semidirect
698. C₄×D₄	C₂³×C₂₃	semidirect
699. C₄×D₄	C₂³×C₂₃	semidirect
719. C₄⋊C₈	C₂³×C₂₃	semidirect
720. C₄⋊C₈	C₂³×C₂₃	semidirect
721. #103	C₂³×C₂₃	semidirect
722. #103	C₂³×C₂₃	semidirect
723. #103	C₂³×C₂₃	semidirect
728. #102	C₂³×C₂₃	semidirect
729. #102	C₂³×C₂₃	semidirect
730. #102	C₂³×C₂₃	semidirect
736. #97	C₂³×C₂₃	semidirect
737. C₄×C₈	C₂³×C₂₃	semidirect
738. C₂₃	#60811	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×#3494	2
C₂×C₂₃×#535	2
C₂₃×#3224	2
C₂₃×#3220	2
C₂₃×#3217	2
C₂₃×#3213	2
C₂₃×#3211	2
C₂₃×#3205	2
C₂₃×#3155	2
C₂₃×#3136	2
C₂₃×#3045	2
C₂₃×#3041	2
C₂₃×#3006	2
C₂₃×#3003	2
C₂₃×#3002	2
C₂×C₂₃×#447	2
C₂₃×#2924	2
#60811	23

Subgroups — C23×#60811 #19208437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60811 #19208437