Subgroups — C₂₃×#60813 #19208439

Order 5888.

2086 conjugacy classes of subgroups.

The subgroup lattice has 968 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×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3221	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3218	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×#3206	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3042	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#448	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×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₂₃×#135	C₂²	1	2	yes	—
23	C₂²×SD₁₆×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×#536	—	2	2	no	—
34	C₂₃×#536	—	2	1	no	—
35	C₂₃×#536	—	2	1	no	—
36	C₂₃×#536	C₂²	1	2	yes	—
37	C₂₃×#536	C₂²	1	2	yes	—
38	C₂₃×#536	C₂²	1	4	yes	complemented
39	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#532	C₂²	1	2	yes	—
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂₃×#529	C₂²	1	2	yes	—
43	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#123	—	2	2	no	—
46	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
47	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
48	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
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×#497	C₂²	1	4	yes	complemented
53	C₂₃×#496	C₂²	1	4	yes	complemented
54	C₂₃×#495	C₂²	1	4	yes	complemented
55	C₂₃×#492	C₂²	1	4	yes	complemented
56	C₂₃×#491	C₂²	1	4	yes	complemented
57	C₂₃×#489	C₂²	1	4	yes	complemented
58	C₂₃×#488	C₂²	1	4	yes	complemented
59	C₂₃×#487	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×#462	C₂²	1	4	yes	complemented
65	C₂₃×#461	C₂²	1	4	yes	complemented
66	C₂₃×#461	C₂²	1	4	yes	complemented
67	C₂₃×#461	C₂²	1	4	yes	complemented
68	C₂₃×#452	C₂²	1	2	yes	complemented
69	C₂₃×#451	C₂²	1	2	yes	complemented
70	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#451	C₂²	1	2	yes	complemented
72	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#449	C₂²	1	4	yes	—
74	C₂₃×#449	C₂²	1	2	yes	complemented
75	C₂₃×#448	C₂²	1	2	yes	—
76	C₂₃×#448	C₂²	1	2	yes	—
77	C₂₃×#448	C₂²	1	2	yes	—
78	C₂₃×#448	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#448	C₂²	1	2	yes	complemented
80	C₂₃×#448	C₂²	1	2	yes	complemented
81	C₂₃×#448	C₂²	1	4	yes	complemented
82	C₂₃×#447	C₂²	1	2	yes	—
83	C₂₃×#447	C₂²	1	1	yes	characteristic, 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×#419	C₂²	1	2	yes	complemented
89	C₂₃×#417	C₂²	1	2	yes	—
90	C₂₃×#416	C₂²	1	2	yes	—
91	C₂×C₂₃×#103	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	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	1	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	4	4	no	—
99	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	—	2	1	no	—
103	C₂²×Q₈×C₂₃	—	2	1	no	—
104	C₂²×Q₈×C₂₃	—	2	1	no	—
105	C₂²×Q₈×C₂₃	—	4	4	no	—
106	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	—	2	1	no	—
111	C₂²×D₄×C₂₃	—	2	1	no	—
112	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	—	2	1	no	—
115	C₂³×C₄×C₂₃	—	2	1	no	—
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂₃×#137	—	4	4	no	—
118	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
119	C₂₃×#135	—	4	4	no	—
120	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
122	C₂×SD₁₆×C₂₃	—	4	4	no	—
123	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	4	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
133	C₂₃×C₄⋊Q₈	—	2	1	no	—
134	C₂₃×C₄⋊Q₈	—	2	2	no	—
135	C₂₃×C₄⋊Q₈	—	2	2	no	—
136	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
138	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₃×#127	C₂³	1	2	yes	—
140	C₂₃×#126	—	2	2	no	—
141	C₂₃×#126	—	2	2	no	—
142	C₂₃×#125	—	2	1	no	—
143	C₂₃×#125	C₂³	1	2	yes	—
144	C₂₃×#124	—	2	2	no	—
145	C₂₃×#124	—	2	2	no	—
146	C₂₃×#124	—	2	2	no	—
147	C₂₃×#124	—	2	2	no	—
148	C₂₃×#124	C₂³	1	4	yes	—
149	C₂₃×#124	C₂³	1	4	yes	—
150	C₂₃×#124	C₂³	1	2	yes	—
151	C₂₃×#123	—	2	2	no	—
152	C₂₃×#123	—	2	1	no	—
153	C₂₃×#123	—	2	2	no	—
154	C₂₃×#123	—	2	2	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	4	no	—
157	C₂₃×#123	—	2	4	no	—
158	C₂₃×#123	—	2	4	no	—
159	C₂₃×#123	—	2	4	no	—
160	C₂₃×C₂²⋊Q₈	—	2	2	no	—
161	C₂₃×C₂²⋊Q₈	—	2	2	no	—
162	C₂₃×C₂²⋊Q₈	—	2	2	no	—
163	C₂₃×C₂²⋊Q₈	—	2	2	no	—
164	C₂₃×C₂²⋊Q₈	—	2	2	no	—
165	C₂₃×C₂²⋊Q₈	—	2	4	no	—
166	C₂₃×C₂²⋊Q₈	—	2	4	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
169	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
170	C₂₃×#121	—	2	1	no	—
171	C₂₃×#121	—	2	1	no	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	—	2	1	no	—
174	C₂₃×#121	—	2	1	no	—
175	C₂₃×#121	—	2	2	no	—
176	C₂₃×#121	—	2	2	no	—
177	C₂₃×#121	C₂³	1	2	yes	—
178	C₂₃×#121	C₂³	1	1	yes	characteristic
179	C₂₃×#121	C₂³	1	2	yes	—
180	C₂₃×#121	C₂³	1	1	yes	characteristic
181	C₂₃×#120	—	2	1	no	—
182	C₂₃×#120	—	2	2	no	—
183	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
184	C₄×D₄×C₂₃	—	2	1	no	—
185	C₄×D₄×C₂₃	—	2	1	no	—
186	C₄×D₄×C₂₃	—	2	2	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	—	2	1	no	—
189	C₄×D₄×C₂₃	—	2	2	no	—
190	C₄×D₄×C₂₃	—	2	2	no	—
191	C₄×D₄×C₂₃	C₂³	1	2	yes	—
192	C₄×D₄×C₂₃	C₂³	1	2	yes	—
193	C₄×D₄×C₂₃	C₂³	1	2	yes	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	—	2	2	no	—
196	C₂₃×#117	D₄	1	2	yes	—
197	C₂₃×#117	D₄	1	1	yes	characteristic
198	C₂₃×#117	D₄	1	1	yes	characteristic
199	C₂₃×#117	C₂³	1	1	yes	characteristic
200	C₂₃×#117	C₂³	1	1	yes	characteristic
201	C₂₃×#117	C₂³	1	1	yes	characteristic
202	C₂₃×#117	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
204	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
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	—
216	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#103	C₂³	1	2	yes	—
220	C₂₃×#103	C₂³	1	2	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#103	C₂³	1	4	yes	—
223	C₂₃×#103	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	—
225	C₂₃×#102	C₂³	1	2	yes	—
226	C₂₃×#102	C₂³	1	4	yes	—
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	—
233	C₄×C₈×C₂₃	C₂³	1	4	yes	—
234	C₂⁴×C₂₃	—	2	1	no	—
235	C₂⁴×C₂₃	—	2	1	no	—
236	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
237	#41×C₂₃	—	2	4	no	—
238	#41×C₂₃	—	2	4	no	—
239	#41×C₂₃	—	2	4	no	—
240	#41×C₂₃	—	4	2	no	—
241	#41×C₂₃	—	4	2	no	—
242	#41×C₂₃	—	4	4	no	—
243	#41×C₂₃	—	4	4	no	—
244	#41×C₂₃	—	8	4	no	—
245	C₂×Q₈×C₂₃	—	2	2	no	—
246	C₂×Q₈×C₂₃	—	2	2	no	—
247	C₂×Q₈×C₂₃	—	2	2	no	—
248	C₂×Q₈×C₂₃	—	2	1	no	—
249	C₂×Q₈×C₂₃	—	2	2	no	—
250	C₂×Q₈×C₂₃	—	2	4	no	—
251	C₂×Q₈×C₂₃	—	2	4	no	—
252	C₂×Q₈×C₂₃	—	4	4	no	—
253	C₂×Q₈×C₂₃	—	4	4	no	—
254	C₂×Q₈×C₂₃	—	4	2	no	—
255	C₂×Q₈×C₂₃	—	4	4	no	—
256	C₂×Q₈×C₂₃	—	4	4	no	—
257	C₂×Q₈×C₂₃	—	4	4	no	—
258	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂×D₄×C₂₃	—	2	1	no	—
262	C₂×D₄×C₂₃	—	2	1	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	1	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	1	no	—
269	C₂×D₄×C₂₃	—	2	1	no	—
270	C₂×D₄×C₂₃	—	2	2	no	—
271	C₂×D₄×C₂₃	—	2	2	no	—
272	C₂×D₄×C₂₃	—	2	4	no	—
273	C₂×D₄×C₂₃	—	4	2	no	—
274	C₂×D₄×C₂₃	—	4	4	no	—
275	C₂×D₄×C₂₃	—	8	2	no	—
276	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	—	2	4	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	1	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	2	2	no	—
284	C₂²×C₄×C₂₃	—	2	1	no	—
285	C₂²×C₄×C₂₃	—	2	1	no	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	2	2	no	—
289	C₂²×C₄×C₂₃	—	2	2	no	—
290	C₂²×C₄×C₂₃	—	2	2	no	—
291	C₂²×C₄×C₂₃	—	4	4	no	—
292	C₂²×C₄×C₂₃	—	4	4	no	—
293	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	Q₁₆×C₂₃	—	4	2	no	—
302	Q₁₆×C₂₃	—	4	4	no	—
303	SD₁₆×C₂₃	—	4	4	no	—
304	SD₁₆×C₂₃	—	4	4	no	—
305	SD₁₆×C₂₃	—	4	2	no	—
306	SD₁₆×C₂₃	—	4	2	no	—
307	SD₁₆×C₂₃	—	4	4	no	—
308	SD₁₆×C₂₃	—	4	4	no	—
309	D₈×C₂₃	—	4	2	no	—
310	D₈×C₂₃	—	4	4	no	—
311	M₁₆×C₂₃	—	2	4	no	—
312	C₂×C₈×C₂₃	—	2	4	no	—
313	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₂₃	—	2	1	no	—
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	4	no	—
319	C₄⋊C₄×C₂₃	—	2	4	no	—
320	C₄⋊C₄×C₂₃	—	2	4	no	—
321	C₄⋊C₄×C₂₃	—	2	4	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	2	no	—
324	C₄⋊C₄×C₂₃	—	2	2	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
326	C₄⋊C₄×C₂₃	—	2	1	no	—
327	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₂²⋊C₄×C₂₃	—	2	1	no	—
337	C₂²⋊C₄×C₂₃	—	2	1	no	—
338	C₂²⋊C₄×C₂₃	—	2	1	no	—
339	C₂²⋊C₄×C₂₃	—	2	2	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	—	2	2	no	—
342	C₂²⋊C₄×C₂₃	—	2	2	no	—
343	C₂²⋊C₄×C₂₃	—	2	4	no	—
344	C₂²⋊C₄×C₂₃	—	2	4	no	—
345	C₂²⋊C₄×C₂₃	—	2	4	no	—
346	C₂²⋊C₄×C₂₃	—	2	4	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	2	no	—
349	C₂²⋊C₄×C₂₃	—	2	1	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	1	no	—
352	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
355	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₄²×C₂₃	—	2	2	no	—
357	C₄²×C₂₃	—	2	1	no	—
358	C₄²×C₂₃	C₂×D₄	1	2	yes	—
359	C₄²×C₂₃	C₂×D₄	1	2	yes	—
360	C₄²×C₂₃	C₂⁴	1	2	yes	—
361	C₄²×C₂₃	C₂⁴	1	2	yes	—
362	#60813	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
363	C₂³×C₂₃	—	2	2	no	—
364	C₂³×C₂₃	—	2	2	no	—
365	C₂³×C₂₃	—	2	2	no	—
366	C₂³×C₂₃	—	2	2	no	—
367	C₂³×C₂₃	—	2	1	no	—
368	C₂³×C₂₃	—	4	1	no	—
369	C₂³×C₂₃	—	4	2	no	—
370	C₂³×C₂₃	—	4	2	no	—
371	C₂³×C₂₃	—	4	2	no	—
372	C₂³×C₂₃	—	4	2	no	—
373	C₂³×C₂₃	—	8	1	no	—
374	C₂³×C₂₃	—	8	1	no	—
375	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	Q₈×C₂₃	—	2	4	no	—
379	Q₈×C₂₃	—	2	2	no	—
380	Q₈×C₂₃	—	2	2	no	—
381	Q₈×C₂₃	—	2	4	no	—
382	Q₈×C₂₃	—	2	2	no	—
383	Q₈×C₂₃	—	4	4	no	—
384	Q₈×C₂₃	—	4	4	no	—
385	Q₈×C₂₃	—	4	2	no	—
386	Q₈×C₂₃	—	4	4	no	—
387	Q₈×C₂₃	—	8	2	no	—
388	D₄×C₂₃	—	2	2	no	—
389	D₄×C₂₃	—	2	4	no	—
390	D₄×C₂₃	—	2	2	no	—
391	D₄×C₂₃	—	2	2	no	—
392	D₄×C₂₃	—	4	2	no	—
393	D₄×C₂₃	—	4	4	no	—
394	D₄×C₂₃	—	4	4	no	—
395	D₄×C₂₃	—	4	2	no	—
396	D₄×C₂₃	—	4	4	no	—
397	D₄×C₂₃	—	4	2	no	—
398	D₄×C₂₃	—	4	2	no	—
399	D₄×C₂₃	—	8	2	no	—
400	D₄×C₂₃	—	8	2	no	—
401	D₄×C₂₃	—	8	1	no	—
402	D₄×C₂₃	—	8	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	4	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	1	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	1	no	—
412	C₂×C₄×C₂₃	—	2	2	no	—
413	C₂×C₄×C₂₃	—	2	4	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	4	2	no	—
416	C₂×C₄×C₂₃	—	4	4	no	—
417	C₂×C₄×C₂₃	—	4	2	no	—
418	C₂×C₄×C₂₃	—	4	4	no	—
419	C₂×C₄×C₂₃	—	4	4	no	—
420	C₂×C₄×C₂₃	—	4	4	no	—
421	C₂×C₄×C₂₃	—	4	4	no	—
422	C₂×C₄×C₂₃	—	4	2	no	—
423	C₂×C₄×C₂₃	—	8	2	no	—
424	C₂×C₄×C₂₃	—	8	2	no	—
425	C₂×C₄×C₂₃	—	8	2	no	—
426	C₂×C₄×C₂₃	—	8	1	no	—
427	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
435	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
436	C₈×C₂₃	—	2	2	no	—
437	C₈×C₂₃	—	2	2	no	—
438	C₈×C₂₃	—	2	4	no	—
439	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
440	C₂×#536	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#3225	C₂×C₂₃	1	4	yes	complemented
442	#3221	C₂×C₂₃	1	4	yes	complemented
443	#3218	C₂×C₂₃	1	2	yes	complemented
444	#3213	C₂×C₂₃	1	2	yes	complemented
445	#3211	C₂×C₂₃	1	2	yes	complemented
446	#3206	C₂×C₂₃	1	2	yes	complemented
447	#3154	C₂×C₂₃	1	2	yes	complemented
448	#3137	C₂×C₂₃	1	2	yes	complemented
449	#3046	C₂×C₂₃	1	2	yes	complemented
450	#3042	C₂×C₂₃	1	2	yes	complemented
451	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
452	#3004	C₂×C₂₃	1	1	yes	characteristic, complemented
453	#3002	C₂×C₂₃	1	1	yes	characteristic, complemented
454	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
456	C₂²×C₂₃	—	2	1	no	—
457	C₂²×C₂₃	—	2	1	no	—
458	C₂²×C₂₃	—	2	1	no	—
459	C₂²×C₂₃	—	2	1	no	—
460	C₂²×C₂₃	—	2	1	no	—
461	C₂²×C₂₃	—	2	1	no	—
462	C₂²×C₂₃	—	2	1	no	—
463	C₂²×C₂₃	—	4	4	no	—
464	C₂²×C₂₃	—	4	2	no	—
465	C₂²×C₂₃	—	4	1	no	—
466	C₂²×C₂₃	—	4	2	no	—
467	C₂²×C₂₃	—	4	2	no	—
468	C₂²×C₂₃	—	4	1	no	—
469	C₂²×C₂₃	—	4	2	no	—
470	C₂²×C₂₃	—	4	1	no	—
471	C₂²×C₂₃	—	4	2	no	—
472	C₂²×C₂₃	—	4	2	no	—
473	C₂²×C₂₃	—	8	4	no	—
474	C₂²×C₂₃	—	16	2	no	—
475	C₂²×C₂₃	#535	1	2	yes	—
476	C₂²×C₂₃	#577	1	2	yes	—
477	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₂₃	—	2	2	no	—
479	C₄×C₂₃	—	2	2	no	—
480	C₄×C₂₃	—	2	1	no	—
481	C₄×C₂₃	—	2	1	no	—
482	C₄×C₂₃	—	2	2	no	—
483	C₄×C₂₃	—	2	2	no	—
484	C₄×C₂₃	—	4	1	no	—
485	C₄×C₂₃	—	4	2	no	—
486	C₄×C₂₃	—	4	4	no	—
487	C₄×C₂₃	—	4	1	no	—
488	C₄×C₂₃	—	4	2	no	—
489	C₄×C₂₃	—	4	1	no	—
490	C₄×C₂₃	#535	1	2	yes	—
491	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
492	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
493	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
495	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
496	C₂×#135	C₂²×C₂₃	1	2	yes	—
497	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
498	#555	—	2	1	no	—
499	#553	—	2	1	no	—
500	#553	—	2	1	no	—
501	#551	—	2	2	no	—
502	#547	—	2	1	no	—
503	#546	—	2	2	no	—
504	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	#542	C₂²×C₂₃	1	2	yes	complemented
506	#540	C₂²×C₂₃	1	2	yes	complemented
507	#536	—	2	2	no	—
508	#536	—	2	1	no	—
509	#536	—	2	1	no	—
510	#536	C₂²×C₂₃	1	2	yes	—
511	#536	C₂²×C₂₃	1	2	yes	—
512	#536	C₂²×C₂₃	1	4	yes	complemented
513	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
514	#532	C₂²×C₂₃	1	2	yes	—
515	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
516	#529	C₂²×C₂₃	1	2	yes	—
517	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
518	#525	C₂²×C₂₃	1	1	yes	characteristic
519	C₂×#123	—	2	2	no	—
520	C₂×C₂²⋊Q₈	—	2	1	no	—
521	C₂×C₂²⋊Q₈	—	2	1	no	—
522	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
523	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
524	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
526	#497	C₂²×C₂₃	1	4	yes	complemented
527	#496	C₂²×C₂₃	1	4	yes	complemented
528	#495	C₂²×C₂₃	1	4	yes	complemented
529	#492	C₂²×C₂₃	1	4	yes	complemented
530	#491	C₂²×C₂₃	1	4	yes	complemented
531	#489	C₂²×C₂₃	1	4	yes	complemented
532	#488	C₂²×C₂₃	1	4	yes	complemented
533	#487	C₂²×C₂₃	1	4	yes	complemented
534	#464	C₂²×C₂₃	1	4	yes	complemented
535	#463	C₂²×C₂₃	1	4	yes	complemented
536	#463	C₂²×C₂₃	1	4	yes	complemented
537	#463	C₂²×C₂₃	1	4	yes	complemented
538	#462	C₂²×C₂₃	1	4	yes	complemented
539	#461	C₂²×C₂₃	1	4	yes	complemented
540	#461	C₂²×C₂₃	1	4	yes	complemented
541	#461	C₂²×C₂₃	1	4	yes	complemented
542	#452	C₂²×C₂₃	1	2	yes	complemented
543	#451	C₂²×C₂₃	1	2	yes	complemented
544	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
545	#451	C₂²×C₂₃	1	2	yes	complemented
546	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
547	#449	C₂²×C₂₃	1	4	yes	—
548	#449	C₂²×C₂₃	1	2	yes	complemented
549	#448	C₂²×C₂₃	1	2	yes	—
550	#448	C₂²×C₂₃	1	2	yes	—
551	#448	C₂²×C₂₃	1	2	yes	—
552	#448	C₂²×C₂₃	1	1	yes	characteristic, complemented
553	#448	C₂²×C₂₃	1	2	yes	complemented
554	#448	C₂²×C₂₃	1	2	yes	complemented
555	#448	C₂²×C₂₃	1	4	yes	complemented
556	#447	C₂²×C₂₃	1	2	yes	—
557	#447	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	#433	C₂²×C₂₃	1	4	yes	complemented
559	#432	C₂²×C₂₃	1	2	yes	complemented
560	#431	C₂²×C₂₃	1	2	yes	complemented
561	#424	C₂²×C₂₃	1	2	yes	complemented
562	#419	C₂²×C₂₃	1	2	yes	complemented
563	#417	C₂²×C₂₃	1	2	yes	—
564	#416	C₂²×C₂₃	1	2	yes	—
565	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
566	#407	C₂²×C₂₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
568	#405	C₂²×C₂₃	1	2	yes	complemented
569	C₂×C₂₃	—	2	2	no	—
570	C₂×C₂₃	—	2	2	no	—
571	C₂×C₂₃	—	4	1	no	—
572	C₂×C₂₃	—	8	1	no	—
573	C₂×C₂₃	—	8	2	no	—
574	C₂×C₂₃	—	8	2	no	—
575	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
576	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
577	C₂×C₂₃	#3586	1	1	yes	characteristic
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	2	no	—
581	C₂×#41	—	4	4	no	—
582	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
583	C₂×#41	C₂³×C₂₃	1	2	yes	—
584	C₂×#41	C₂³×C₂₃	1	2	yes	—
585	C₂²×Q₈	—	2	1	no	—
586	C₂²×Q₈	—	2	1	no	—
587	C₂²×Q₈	—	2	1	no	—
588	C₂²×Q₈	—	4	4	no	—
589	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
591	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₂²×D₄	—	2	1	no	—
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂³×C₄	—	2	1	no	—
598	C₂³×C₄	—	2	1	no	—
599	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
600	#137	—	4	4	no	—
601	AGL(1,ℤ/8)	—	4	4	no	—
602	#135	—	4	4	no	—
603	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
604	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
605	C₂×SD₁₆	—	4	4	no	—
606	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
607	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
608	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
611	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
612	C₂×D₈	C₂³×C₂₃	1	2	yes	—
613	C₂×D₈	C₂³×C₂₃	1	4	yes	—
614	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
615	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
616	C₄⋊Q₈	—	2	1	no	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
620	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
621	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
622	#127	C₂³×C₂₃	1	2	yes	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#125	—	2	1	no	—
626	#125	C₂³×C₂₃	1	2	yes	—
627	#124	—	2	2	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	C₂³×C₂₃	1	4	yes	—
632	#124	C₂³×C₂₃	1	4	yes	—
633	#124	C₂³×C₂₃	1	2	yes	—
634	#123	—	2	1	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	4	no	—
639	#123	—	2	4	no	—
640	#123	—	2	4	no	—
641	#123	—	2	4	no	—
642	#123	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	4	no	—
648	C₂²⋊Q₈	—	2	4	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
652	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	—	2	2	no	—
656	#121	—	2	1	no	—
657	#121	—	2	1	no	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	C₂³×C₂₃	1	2	yes	—
661	#121	C₂³×C₂₃	1	2	yes	—
662	#121	C₂³×C₂₃	1	1	yes	characteristic
663	#121	C₂³×C₂₃	1	1	yes	characteristic
664	#120	—	2	1	no	—
665	#120	—	2	2	no	—
666	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	C₂³×C₂₃	1	2	yes	—
675	C₄×D₄	C₂³×C₂₃	1	2	yes	—
676	C₄×D₄	C₂³×C₂₃	1	2	yes	—
677	#117	—	2	1	no	—
678	#117	—	2	2	no	—
679	#117	D₄×C₂₃	1	2	yes	—
680	#117	D₄×C₂₃	1	1	yes	characteristic
681	#117	D₄×C₂₃	1	1	yes	characteristic
682	#117	C₂³×C₂₃	1	1	yes	characteristic
683	#117	C₂³×C₂₃	1	1	yes	characteristic
684	#117	C₂³×C₂₃	1	1	yes	characteristic
685	#117	C₂³×C₂₃	1	2	yes	—
686	C₂×C₄⋊C₄	—	2	2	no	—
687	C₂×C₄⋊C₄	—	2	2	no	—
688	C₂×C₄⋊C₄	—	2	1	no	—
689	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
697	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
698	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
699	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
700	#103	C₂³×C₂₃	1	4	yes	—
701	#103	C₂³×C₂₃	1	4	yes	—
702	#103	C₂³×C₂₃	1	2	yes	—
703	#103	C₂³×C₂₃	1	2	yes	—
704	#103	C₂³×C₂₃	1	4	yes	—
705	#103	C₂³×C₂₃	1	4	yes	—
706	#103	C₂³×C₂₃	1	4	yes	—
707	#102	C₂³×C₂₃	1	2	yes	—
708	#102	C₂³×C₂₃	1	2	yes	—
709	#102	C₂³×C₂₃	1	4	yes	—
710	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
711	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
712	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
715	#97	C₂³×C₂₃	1	4	yes	—
716	C₄×C₈	C₂³×C₂₃	1	4	yes	—
717	C₂₃	#60813	1	1	yes	characteristic, direct product factor, Sylow
718	C₂⁴	—	2	1	no	—
719	C₂⁴	—	2	1	no	—
720	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
721	#41	—	2	4	no	—
722	#41	—	2	4	no	—
723	#41	—	2	4	no	—
724	#41	—	4	2	no	—
725	#41	—	4	2	no	—
726	#41	—	4	4	no	—
727	#41	—	4	4	no	—
728	#41	—	8	4	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	1	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	2	4	no	—
735	C₂×Q₈	—	2	4	no	—
736	C₂×Q₈	—	4	4	no	—
737	C₂×Q₈	—	4	4	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	4	4	no	—
740	C₂×Q₈	—	4	4	no	—
741	C₂×Q₈	—	4	4	no	—
742	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
743	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
744	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
745	C₂×D₄	—	2	1	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	8	2	no	—
760	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
761	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
762	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	—	4	4	no	—
777	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
778	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
785	Q₁₆	—	4	2	no	—
786	Q₁₆	—	4	4	no	—
787	SD₁₆	—	4	4	no	—
788	SD₁₆	—	4	4	no	—
789	SD₁₆	—	4	2	no	—
790	SD₁₆	—	4	2	no	—
791	SD₁₆	—	4	4	no	—
792	SD₁₆	—	4	4	no	—
793	D₈	—	4	2	no	—
794	D₈	—	4	4	no	—
795	M₁₆	—	2	4	no	—
796	C₂×C₈	—	2	4	no	—
797	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
798	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
799	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
812	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
813	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
814	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
816	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
820	C₂²⋊C₄	—	2	1	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
837	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
839	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	1	no	—
842	C₄²	C₂×D₄×C₂₃	1	2	yes	—
843	C₄²	C₂×D₄×C₂₃	1	2	yes	—
844	C₄²	C₂⁴×C₂₃	1	2	yes	—
845	C₄²	C₂⁴×C₂₃	1	2	yes	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	8	1	no	—
857	C₂³	—	8	1	no	—
858	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
859	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
860	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
861	Q₈	—	2	4	no	—
862	Q₈	—	2	2	no	—
863	Q₈	—	2	2	no	—
864	Q₈	—	2	4	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	4	4	no	—
867	Q₈	—	4	4	no	—
868	Q₈	—	4	2	no	—
869	Q₈	—	4	4	no	—
870	Q₈	—	8	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	4	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	4	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	2	no	—
881	D₄	—	4	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	1	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	1	no	—
910	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
914	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
916	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
917	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
918	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	—	2	4	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	4	4	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	8	4	no	—
940	C₂²	—	16	2	no	—
941	C₂²	C₂₃×#535	1	2	yes	—
942	C₂²	C₂₃×#577	1	2	yes	—
943	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	4	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	1	no	—
956	C₄	C₂₃×#535	1	2	yes	—
957	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
958	C₂	—	2	2	no	—
959	C₂	—	2	2	no	—
960	C₂	—	4	1	no	—
961	C₂	—	8	2	no	—
962	C₂	—	8	2	no	—
963	C₂	—	8	1	no	—
964	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
965	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
966	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ 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×#536	C₂	semidirect
3. C₂₃×#3225	C₂	semidirect
4. C₂₃×#3221	C₂	semidirect
5. C₂₃×#3218	C₂	semidirect
6. C₂₃×#3213	C₂	semidirect
7. C₂₃×#3211	C₂	semidirect
8. C₂₃×#3206	C₂	semidirect
9. C₂₃×#3154	C₂	semidirect
10. C₂₃×#3137	C₂	semidirect
11. C₂₃×#3046	C₂	semidirect
12. C₂₃×#3042	C₂	semidirect
13. C₂₃×#3006	C₂	semidirect
14. C₂₃×#3004	C₂	semidirect
15. C₂₃×#3002	C₂	semidirect
16. C₂×C₂₃×#448	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
20. C₂×C₂₃×#137	C₂²	semidirect
23. C₂²×SD₁₆×C₂₃	C₂²	semidirect
30. C₂₃×#544	C₂²	semidirect
31. C₂₃×#542	C₂²	semidirect
32. C₂₃×#540	C₂²	semidirect
38. C₂₃×#536	C₂²	semidirect
39. C₂₃×#535	C₂²	semidirect
41. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₂₃×#124	C₂²	semidirect
49. C₂₃×#520	C₂²	semidirect
50. C₂₃×#518	C₂²	semidirect
52. C₂₃×#497	C₂²	semidirect
53. C₂₃×#496	C₂²	semidirect
54. C₂₃×#495	C₂²	semidirect
55. C₂₃×#492	C₂²	semidirect
56. C₂₃×#491	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
58. C₂₃×#488	C₂²	semidirect
59. C₂₃×#487	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#463	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#461	C₂²	semidirect
66. C₂₃×#461	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
68. C₂₃×#452	C₂²	semidirect
69. C₂₃×#451	C₂²	semidirect
70. C₂₃×#451	C₂²	semidirect
71. C₂₃×#451	C₂²	semidirect
72. C₂₃×#450	C₂²	semidirect
74. C₂₃×#449	C₂²	semidirect
78. C₂₃×#448	C₂²	semidirect
79. C₂₃×#448	C₂²	semidirect
80. C₂₃×#448	C₂²	semidirect
81. C₂₃×#448	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×#419	C₂²	semidirect
91. C₂×C₂₃×#103	C₂²	semidirect
94. C₂₃×#405	C₂²	semidirect
362. #60813	C₂₃	direct (N × H)
439. #3494	C₂×C₂₃	semidirect
440. C₂×#536	C₂×C₂₃	semidirect
441. #3225	C₂×C₂₃	semidirect
442. #3221	C₂×C₂₃	semidirect
443. #3218	C₂×C₂₃	semidirect
444. #3213	C₂×C₂₃	semidirect
445. #3211	C₂×C₂₃	semidirect
446. #3206	C₂×C₂₃	semidirect
447. #3154	C₂×C₂₃	semidirect
448. #3137	C₂×C₂₃	semidirect
449. #3046	C₂×C₂₃	semidirect
450. #3042	C₂×C₂₃	semidirect
451. #3006	C₂×C₂₃	semidirect
452. #3004	C₂×C₂₃	semidirect
453. #3002	C₂×C₂₃	semidirect
454. C₂×#448	C₂×C₂₃	semidirect
455. #2924	C₂×C₂₃	semidirect
494. C₂×#137	C₂²×C₂₃	semidirect
497. C₂²×SD₁₆	C₂²×C₂₃	semidirect
504. #544	C₂²×C₂₃	semidirect
505. #542	C₂²×C₂₃	semidirect
506. #540	C₂²×C₂₃	semidirect
512. #536	C₂²×C₂₃	semidirect
513. #535	C₂²×C₂₃	semidirect
515. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
517. C₂×#124	C₂²×C₂₃	semidirect
523. #520	C₂²×C₂₃	semidirect
524. #518	C₂²×C₂₃	semidirect
526. #497	C₂²×C₂₃	semidirect
527. #496	C₂²×C₂₃	semidirect
528. #495	C₂²×C₂₃	semidirect
529. #492	C₂²×C₂₃	semidirect
530. #491	C₂²×C₂₃	semidirect
531. #489	C₂²×C₂₃	semidirect
532. #488	C₂²×C₂₃	semidirect
533. #487	C₂²×C₂₃	semidirect
534. #464	C₂²×C₂₃	semidirect
535. #463	C₂²×C₂₃	semidirect
536. #463	C₂²×C₂₃	semidirect
537. #463	C₂²×C₂₃	semidirect
538. #462	C₂²×C₂₃	semidirect
539. #461	C₂²×C₂₃	semidirect
540. #461	C₂²×C₂₃	semidirect
541. #461	C₂²×C₂₃	semidirect
542. #452	C₂²×C₂₃	semidirect
543. #451	C₂²×C₂₃	semidirect
544. #451	C₂²×C₂₃	semidirect
545. #451	C₂²×C₂₃	semidirect
546. #450	C₂²×C₂₃	semidirect
548. #449	C₂²×C₂₃	semidirect
552. #448	C₂²×C₂₃	semidirect
553. #448	C₂²×C₂₃	semidirect
554. #448	C₂²×C₂₃	semidirect
555. #448	C₂²×C₂₃	semidirect
557. #447	C₂²×C₂₃	semidirect
558. #433	C₂²×C₂₃	semidirect
559. #432	C₂²×C₂₃	semidirect
560. #431	C₂²×C₂₃	semidirect
561. #424	C₂²×C₂₃	semidirect
562. #419	C₂²×C₂₃	semidirect
565. C₂×#103	C₂²×C₂₃	semidirect
568. #405	C₂²×C₂₃	semidirect
717. C₂₃	#60813	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×#536	2
C₂₃×#3225	2
C₂₃×#3221	2
C₂₃×#3218	2
C₂₃×#3213	2
C₂₃×#3211	2
C₂₃×#3206	2
C₂₃×#3154	2
C₂₃×#3137	2
C₂₃×#3046	2
C₂₃×#3042	2
C₂₃×#3006	2
C₂₃×#3004	2
C₂₃×#3002	2
C₂×C₂₃×#448	2
C₂₃×#2924	2
#60813	23

Subgroups — C23×#60813 #19208439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60813 #19208439