Subgroups — C₂₃×#33347 #19180973

Order 5888.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#413	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#410	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2123	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2122	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2121	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2120	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₂₃	C₄	1	1	yes	characteristic, complemented
9	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	—	2	1	no	—
11	C₂₃×#537	—	2	1	no	—
12	C₂₃×#537	—	2	1	no	—
13	C₂₃×#536	—	2	1	no	—
14	C₂₃×#536	C₄	1	1	yes	characteristic, complemented
15	C₂₃×#536	C₂²	1	1	yes	characteristic
16	C₂₃×#535	—	2	1	no	—
17	C₂₃×#535	C₄	1	1	yes	characteristic, complemented
18	C₂₃×#535	C₂²	1	1	yes	characteristic
19	C₂₃×#534	C₄	1	2	yes	complemented
20	C₂₃×#534	C₂²	1	2	yes	—
21	C₂₃×#532	—	2	1	no	—
22	C₂₃×#532	—	2	1	no	—
23	C₂₃×#525	—	2	1	no	—
24	C₂₃×#525	—	2	1	no	—
25	C₂₃×#525	C₄	1	2	yes	complemented
26	C₂₃×#525	C₂²	1	2	yes	—
27	C₂×C₂₃×#117	—	2	1	no	—
28	C₂×C₂₃×#117	C₄	1	1	yes	characteristic, complemented
29	C₂₃×#413	—	2	1	no	—
30	C₂₃×#413	—	2	1	no	—
31	C₂₃×#413	C₂²	1	2	yes	—
32	C₂₃×#413	C₂²	1	2	yes	—
33	C₂×C₂₃×#101	—	2	1	no	—
34	C₂×C₂₃×#100	C₂²	1	2	yes	—
35	C₂₃×#410	—	2	1	no	—
36	C₂₃×#410	—	2	1	no	—
37	C₂₃×#410	C₂²	1	2	yes	—
38	C₂₃×#410	C₂²	1	2	yes	—
39	C₂×C₂₃×#99	—	2	1	no	—
40	C₂×C₂₃×#99	C₂²	1	2	yes	—
41	C₂₃×#352	C₂²	1	8	yes	complemented
42	C₂₃×AΣL(1,𝔽₁₆)	C₂²	1	8	yes	complemented
43	C₂×#41×C₂₃	—	2	1	no	—
44	C₂×#41×C₂₃	—	2	1	no	—
45	C₂×#41×C₂₃	—	2	1	no	—
46	C₂×#41×C₂₃	—	2	1	no	—
47	C₂×#41×C₂₃	—	4	1	no	—
48	C₂×#41×C₂₃	—	4	1	no	—
49	C₂×#41×C₂₃	—	4	1	no	—
50	C₂×#41×C₂₃	—	4	1	no	—
51	C₂×#41×C₂₃	—	4	1	no	—
52	C₂×#41×C₂₃	—	4	1	no	—
53	C₂×#41×C₂₃	—	4	1	no	—
54	C₂×#41×C₂₃	—	4	1	no	—
55	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
56	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
57	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
58	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
59	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
60	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
61	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
62	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
67	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	complemented
72	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₂₃	—	2	2	no	—
75	C₂×M₁₆×C₂₃	—	2	2	no	—
76	C₂×M₁₆×C₂₃	—	2	2	no	—
77	C₂×M₁₆×C₂₃	—	4	1	no	—
78	C₂×M₁₆×C₂₃	—	4	1	no	—
79	C₂×M₁₆×C₂₃	—	4	1	no	—
80	C₂²×C₈×C₂₃	—	4	1	no	—
81	C₂₃×C₄⋊Q₈	—	2	1	no	—
82	C₂₃×C₄⋊Q₈	—	2	1	no	—
83	C₂₃×#127	—	2	1	no	—
84	C₂₃×#127	—	2	1	no	—
85	C₂₃×#124	—	2	1	no	—
86	C₂₃×#124	—	2	1	no	—
87	C₂₃×#124	—	2	1	no	—
88	C₂₃×#124	—	2	1	no	—
89	C₂₃×#123	—	2	2	no	—
90	C₂₃×#123	—	2	2	no	—
91	C₂₃×#123	C₂×C₄	1	2	yes	—
92	C₂₃×#123	C₂×C₄	1	2	yes	complemented
93	C₂₃×#123	C₂×C₄	1	2	yes	complemented
94	C₂₃×#123	C₂³	1	2	yes	—
95	C₂₃×C₂²⋊Q₈	—	2	2	no	—
96	C₂₃×C₂²⋊Q₈	—	2	2	no	—
97	C₂₃×C₂²⋊Q₈	—	2	1	no	—
98	C₂₃×C₂²⋊Q₈	—	2	1	no	—
99	C₂₃×C₂²⋊Q₈	—	2	1	no	—
100	C₂₃×C₂²⋊Q₈	—	2	1	no	—
101	C₂₃×#121	—	2	2	no	—
102	C₂₃×#121	—	2	2	no	—
103	C₂₃×#121	—	2	2	no	—
104	C₂₃×#121	—	2	2	no	—
105	C₂₃×#121	—	2	2	no	—
106	C₂₃×#121	—	2	2	no	—
107	C₂₃×#121	—	2	1	no	—
108	C₂₃×#121	—	2	1	no	—
109	C₂₃×#121	—	2	1	no	—
110	C₂₃×#121	—	2	1	no	—
111	C₂₃×#120	—	2	2	no	—
112	C₂₃×#120	—	2	2	no	—
113	C₂₃×#120	C₂×C₄	1	2	yes	—
114	C₂₃×#120	C₂×C₄	1	2	yes	complemented
115	C₂₃×#120	C₂×C₄	1	2	yes	complemented
116	C₂₃×#120	C₂³	1	2	yes	—
117	C₄×D₄×C₂₃	—	2	2	no	—
118	C₄×D₄×C₂₃	—	2	2	no	—
119	C₄×D₄×C₂₃	—	2	2	no	—
120	C₄×D₄×C₂₃	—	2	2	no	—
121	C₂₃×#117	—	2	1	no	—
122	C₂₃×#117	—	2	1	no	—
123	C₂₃×#117	—	2	2	no	—
124	C₂₃×#117	—	2	2	no	—
125	C₂₃×#117	—	4	1	no	—
126	C₂₃×#117	—	4	1	no	—
127	C₂₃×#117	C₂×C₄	1	2	yes	complemented
128	C₂₃×#117	C₂×C₄	1	1	yes	characteristic, complemented
129	C₂₃×#117	C₂×C₄	1	1	yes	characteristic, complemented
130	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
134	C₂×C₄²×C₂₃	—	2	1	no	—
135	C₂×C₄²×C₂₃	—	4	1	no	—
136	C₂₃×#101	—	2	2	no	—
137	C₂₃×#101	—	2	2	no	—
138	C₂₃×#100	—	2	2	no	—
139	C₂₃×#100	C₂³	1	4	yes	—
140	C₂₃×#99	—	2	2	no	—
141	C₂₃×#99	—	2	2	no	—
142	C₂₃×#99	—	2	2	no	—
143	C₂₃×#99	C₂³	1	4	yes	—
144	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
147	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
148	#41×C₂₃	—	4	1	no	—
149	#41×C₂₃	—	4	1	no	—
150	#41×C₂₃	—	4	1	no	—
151	#41×C₂₃	—	4	1	no	—
152	#41×C₂₃	—	4	1	no	—
153	#41×C₂₃	—	4	1	no	—
154	#41×C₂₃	—	4	1	no	—
155	#41×C₂₃	—	4	1	no	—
156	#41×C₂₃	—	4	1	no	—
157	#41×C₂₃	—	4	1	no	—
158	#41×C₂₃	—	4	1	no	—
159	#41×C₂₃	—	4	1	no	—
160	#41×C₂₃	—	4	1	no	—
161	#41×C₂₃	—	4	1	no	—
162	#41×C₂₃	—	4	1	no	—
163	#41×C₂₃	—	4	1	no	—
164	#41×C₂₃	—	4	2	no	—
165	#41×C₂₃	—	4	2	no	—
166	#41×C₂₃	—	4	2	no	—
167	#41×C₂₃	—	4	2	no	—
168	#41×C₂₃	—	4	2	no	—
169	#41×C₂₃	—	4	2	no	—
170	#41×C₂₃	—	4	1	no	—
171	#41×C₂₃	—	4	1	no	—
172	#41×C₂₃	—	4	1	no	—
173	#41×C₂₃	—	4	1	no	—
174	C₂×Q₈×C₂₃	—	2	1	no	—
175	C₂×Q₈×C₂₃	—	2	1	no	—
176	C₂×Q₈×C₂₃	—	4	1	no	—
177	C₂×Q₈×C₂₃	—	4	1	no	—
178	C₂×Q₈×C₂₃	—	4	1	no	—
179	C₂×Q₈×C₂₃	—	4	1	no	—
180	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₂×D₄×C₂₃	—	2	2	no	—
185	C₂×D₄×C₂₃	—	2	2	no	—
186	C₂×D₄×C₂₃	—	2	2	no	—
187	C₂×D₄×C₂₃	—	2	2	no	—
188	C₂×D₄×C₂₃	—	2	2	no	—
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	4	1	no	—
193	C₂×D₄×C₂₃	—	4	1	no	—
194	C₂×D₄×C₂₃	—	4	1	no	—
195	C₂×D₄×C₂₃	—	4	1	no	—
196	C₂×D₄×C₂₃	—	4	1	no	—
197	C₂×D₄×C₂₃	—	4	1	no	—
198	C₂×D₄×C₂₃	—	4	1	no	—
199	C₂×D₄×C₂₃	—	4	1	no	—
200	C₂×D₄×C₂₃	—	4	2	no	—
201	C₂×D₄×C₂₃	—	4	2	no	—
202	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
203	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
204	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
205	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
206	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
209	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	1	no	—
222	C₂²×C₄×C₂₃	—	2	1	no	—
223	C₂²×C₄×C₂₃	—	2	1	no	—
224	C₂²×C₄×C₂₃	—	2	1	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	2	2	no	—
228	C₂²×C₄×C₂₃	—	2	2	no	—
229	C₂²×C₄×C₂₃	—	4	2	no	—
230	C₂²×C₄×C₂₃	—	4	2	no	—
231	C₂²×C₄×C₂₃	—	4	2	no	—
232	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	M₁₆×C₂₃	—	2	4	no	—
250	M₁₆×C₂₃	—	4	2	no	—
251	M₁₆×C₂₃	—	4	2	no	—
252	M₁₆×C₂₃	—	4	2	no	—
253	C₂×C₈×C₂₃	—	4	2	no	—
254	C₂×C₈×C₂₃	—	4	2	no	—
255	C₂×C₈×C₂₃	—	4	2	no	—
256	C₄⋊C₄×C₂₃	—	2	2	no	—
257	C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	2	no	—
260	C₄⋊C₄×C₂₃	—	2	2	no	—
261	C₄⋊C₄×C₂₃	—	2	2	no	—
262	C₄⋊C₄×C₂₃	—	2	2	no	—
263	C₄⋊C₄×C₂₃	—	4	2	no	—
264	C₄⋊C₄×C₂₃	—	4	2	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	2	no	—
268	C₂²⋊C₄×C₂₃	—	2	2	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	2	no	—
271	C₂²⋊C₄×C₂₃	—	2	2	no	—
272	C₂²⋊C₄×C₂₃	—	2	2	no	—
273	C₂²⋊C₄×C₂₃	—	2	2	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	—	4	2	no	—
276	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
277	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
278	C₄²×C₂₃	—	2	2	no	—
279	C₄²×C₂₃	—	2	1	no	—
280	C₄²×C₂₃	—	2	1	no	—
281	C₄²×C₂₃	—	4	2	no	—
282	C₄²×C₂₃	—	4	2	no	—
283	#33347	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	1	no	—
286	C₂³×C₂₃	—	2	1	no	—
287	C₂³×C₂₃	—	2	1	no	—
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	1	no	—
290	C₂³×C₂₃	—	2	2	no	—
291	C₂³×C₂₃	—	4	2	no	—
292	C₂³×C₂₃	—	8	1	no	—
293	C₂³×C₂₃	—	8	1	no	—
294	C₂³×C₂₃	—	8	1	no	—
295	C₂³×C₂₃	—	8	2	no	—
296	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
302	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₂₃	—	4	1	no	—
304	Q₈×C₂₃	—	4	1	no	—
305	Q₈×C₂₃	—	4	1	no	—
306	Q₈×C₂₃	—	4	1	no	—
307	Q₈×C₂₃	—	4	2	no	—
308	Q₈×C₂₃	—	4	1	no	—
309	Q₈×C₂₃	—	4	1	no	—
310	D₄×C₂₃	—	4	1	no	—
311	D₄×C₂₃	—	4	1	no	—
312	D₄×C₂₃	—	4	1	no	—
313	D₄×C₂₃	—	4	1	no	—
314	D₄×C₂₃	—	4	1	no	—
315	D₄×C₂₃	—	4	1	no	—
316	D₄×C₂₃	—	4	1	no	—
317	D₄×C₂₃	—	4	1	no	—
318	D₄×C₂₃	—	4	1	no	—
319	D₄×C₂₃	—	4	1	no	—
320	D₄×C₂₃	—	4	1	no	—
321	D₄×C₂₃	—	4	1	no	—
322	D₄×C₂₃	—	4	2	no	—
323	D₄×C₂₃	—	4	4	no	—
324	D₄×C₂₃	—	4	2	no	—
325	D₄×C₂₃	—	4	2	no	—
326	D₄×C₂₃	—	4	1	no	—
327	D₄×C₂₃	—	4	1	no	—
328	D₄×C₂₃	—	8	2	no	—
329	D₄×C₂₃	—	8	2	no	—
330	D₄×C₂₃	—	8	2	no	—
331	D₄×C₂₃	—	8	2	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	1	no	—
337	C₂×C₄×C₂₃	—	2	1	no	—
338	C₂×C₄×C₂₃	—	2	1	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	1	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	2	1	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	1	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	1	no	—
351	C₂×C₄×C₂₃	—	2	1	no	—
352	C₂×C₄×C₂₃	—	2	1	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	1	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	4	4	no	—
366	C₂×C₄×C₂₃	—	4	2	no	—
367	C₂×C₄×C₂₃	—	4	2	no	—
368	C₂×C₄×C₂₃	—	4	2	no	—
369	C₂×C₄×C₂₃	—	4	4	no	—
370	C₂×C₄×C₂₃	—	8	2	no	—
371	C₂×C₄×C₂₃	—	8	4	no	—
372	C₂×C₄×C₂₃	#99	1	1	yes	characteristic
373	C₂×C₄×C₂₃	#99	1	1	yes	characteristic
374	C₂×C₄×C₂₃	#99	1	1	yes	characteristic
375	C₂×C₄×C₂₃	#99	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₈×C₂₃	—	4	4	no	—
385	#3449	C₂×C₂₃	1	1	yes	characteristic
386	C₂×#413	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂×#410	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#2123	C₂×C₂₃	1	2	yes	complemented
389	#2122	C₂×C₂₃	1	2	yes	complemented
390	#2121	C₂×C₂₃	1	4	yes	complemented
391	#2120	C₂×C₂₃	1	4	yes	complemented
392	C₂²×C₂₃	—	2	1	no	—
393	C₂²×C₂₃	—	2	1	no	—
394	C₂²×C₂₃	—	2	1	no	—
395	C₂²×C₂₃	—	2	1	no	—
396	C₂²×C₂₃	—	2	1	no	—
397	C₂²×C₂₃	—	2	1	no	—
398	C₂²×C₂₃	—	4	1	no	—
399	C₂²×C₂₃	—	4	1	no	—
400	C₂²×C₂₃	—	4	1	no	—
401	C₂²×C₂₃	—	4	1	no	—
402	C₂²×C₂₃	—	4	1	no	—
403	C₂²×C₂₃	—	4	1	no	—
404	C₂²×C₂₃	—	4	1	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	2	no	—
410	C₂²×C₂₃	—	8	1	no	—
411	C₂²×C₂₃	—	8	1	no	—
412	C₂²×C₂₃	—	8	1	no	—
413	C₂²×C₂₃	—	8	1	no	—
414	C₂²×C₂₃	—	8	4	no	—
415	C₂²×C₂₃	C₂×#99	1	1	yes	characteristic
416	C₂²×C₂₃	C₂×#99	1	1	yes	characteristic
417	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	1	no	—
420	C₄×C₂₃	—	2	1	no	—
421	C₄×C₂₃	—	2	1	no	—
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	1	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	8	4	no	—
428	C₄×C₂₃	C₂×#99	1	1	yes	characteristic
429	C₄×C₂₃	C₂×#99	1	1	yes	characteristic
430	C₄×C₂₃	C₂×#99	1	1	yes	characteristic
431	C₄×C₂₃	C₂×#99	1	1	yes	characteristic
432	C₂²×#41	C₄×C₂₃	1	1	yes	characteristic, complemented
433	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
434	C₂²×M₁₆	—	2	1	no	—
435	#537	—	2	1	no	—
436	#537	—	2	1	no	—
437	#536	—	2	1	no	—
438	#536	C₄×C₂₃	1	1	yes	characteristic, complemented
439	#536	C₂²×C₂₃	1	1	yes	characteristic
440	#535	—	2	1	no	—
441	#535	C₄×C₂₃	1	1	yes	characteristic, complemented
442	#535	C₂²×C₂₃	1	1	yes	characteristic
443	#534	C₄×C₂₃	1	2	yes	complemented
444	#534	C₂²×C₂₃	1	2	yes	—
445	#532	—	2	1	no	—
446	#532	—	2	1	no	—
447	#525	—	2	1	no	—
448	#525	—	2	1	no	—
449	#525	C₄×C₂₃	1	2	yes	complemented
450	#525	C₂²×C₂₃	1	2	yes	—
451	C₂×#117	—	2	1	no	—
452	C₂×#117	C₄×C₂₃	1	1	yes	characteristic, complemented
453	#413	—	2	1	no	—
454	#413	—	2	1	no	—
455	#413	C₂²×C₂₃	1	2	yes	—
456	#413	C₂²×C₂₃	1	2	yes	—
457	C₂×#101	—	2	1	no	—
458	C₂×#100	C₂²×C₂₃	1	2	yes	—
459	#410	—	2	1	no	—
460	#410	—	2	1	no	—
461	#410	C₂²×C₂₃	1	2	yes	—
462	#410	C₂²×C₂₃	1	2	yes	—
463	C₂×#99	—	2	1	no	—
464	C₂×#99	C₂²×C₂₃	1	2	yes	—
465	#352	C₂²×C₂₃	1	8	yes	complemented
466	AΣL(1,𝔽₁₆)	C₂²×C₂₃	1	8	yes	complemented
467	C₂×C₂₃	—	2	1	no	—
468	C₂×C₂₃	—	2	1	no	—
469	C₂×C₂₃	—	2	1	no	—
470	C₂×C₂₃	—	4	1	no	—
471	C₂×C₂₃	—	4	1	no	—
472	C₂×C₂₃	—	4	1	no	—
473	C₂×C₂₃	—	4	1	no	—
474	C₂×C₂₃	—	4	1	no	—
475	C₂×C₂₃	—	4	1	no	—
476	C₂×C₂₃	—	8	2	no	—
477	C₂×C₂₃	C₂²×#99	1	1	yes	characteristic
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	—	4	1	no	—
483	C₂×#41	—	4	1	no	—
484	C₂×#41	—	4	1	no	—
485	C₂×#41	—	4	1	no	—
486	C₂×#41	—	4	1	no	—
487	C₂×#41	—	4	1	no	—
488	C₂×#41	—	4	1	no	—
489	C₂×#41	—	4	1	no	—
490	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
491	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
492	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
493	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
494	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
495	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
496	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
498	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
499	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
500	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
501	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
502	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
503	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
506	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	complemented
507	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
508	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
509	C₂×M₁₆	—	2	2	no	—
510	C₂×M₁₆	—	2	2	no	—
511	C₂×M₁₆	—	2	2	no	—
512	C₂×M₁₆	—	4	1	no	—
513	C₂×M₁₆	—	4	1	no	—
514	C₂×M₁₆	—	4	1	no	—
515	C₂²×C₈	—	4	1	no	—
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	—	2	1	no	—
518	#127	—	2	1	no	—
519	#127	—	2	1	no	—
520	#124	—	2	1	no	—
521	#124	—	2	1	no	—
522	#124	—	2	1	no	—
523	#124	—	2	1	no	—
524	#123	—	2	2	no	—
525	#123	—	2	2	no	—
526	#123	C₂×C₄×C₂₃	1	2	yes	—
527	#123	C₂×C₄×C₂₃	1	2	yes	complemented
528	#123	C₂×C₄×C₂₃	1	2	yes	complemented
529	#123	C₂³×C₂₃	1	2	yes	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	2	no	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#120	—	2	2	no	—
547	#120	—	2	2	no	—
548	#120	C₂×C₄×C₂₃	1	2	yes	—
549	#120	C₂×C₄×C₂₃	1	2	yes	complemented
550	#120	C₂×C₄×C₂₃	1	2	yes	complemented
551	#120	C₂³×C₂₃	1	2	yes	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	#117	—	2	1	no	—
557	#117	—	2	1	no	—
558	#117	—	2	2	no	—
559	#117	—	2	2	no	—
560	#117	—	4	1	no	—
561	#117	—	4	1	no	—
562	#117	C₂×C₄×C₂₃	1	2	yes	complemented
563	#117	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
564	#117	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	4	1	no	—
567	C₂×C₂²⋊C₄	—	2	2	no	—
568	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	4	1	no	—
571	#101	—	2	2	no	—
572	#101	—	2	2	no	—
573	#100	—	2	2	no	—
574	#100	C₂³×C₂₃	1	4	yes	—
575	#99	—	2	2	no	—
576	#99	—	2	2	no	—
577	#99	—	2	2	no	—
578	#99	C₂³×C₂₃	1	4	yes	—
579	C₂₃	#33347	1	1	yes	characteristic, direct product factor, Sylow
580	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
581	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
582	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
583	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
584	#41	—	4	1	no	—
585	#41	—	4	1	no	—
586	#41	—	4	1	no	—
587	#41	—	4	1	no	—
588	#41	—	4	1	no	—
589	#41	—	4	1	no	—
590	#41	—	4	1	no	—
591	#41	—	4	1	no	—
592	#41	—	4	1	no	—
593	#41	—	4	1	no	—
594	#41	—	4	1	no	—
595	#41	—	4	1	no	—
596	#41	—	4	1	no	—
597	#41	—	4	1	no	—
598	#41	—	4	1	no	—
599	#41	—	4	1	no	—
600	#41	—	4	2	no	—
601	#41	—	4	2	no	—
602	#41	—	4	2	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	2	no	—
606	#41	—	4	1	no	—
607	#41	—	4	1	no	—
608	#41	—	4	1	no	—
609	#41	—	4	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	4	1	no	—
613	C₂×Q₈	—	4	1	no	—
614	C₂×Q₈	—	4	1	no	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
617	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
618	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
619	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
639	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
640	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
641	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
642	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
643	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
644	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
645	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
646	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
647	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
669	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
670	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
671	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
672	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
680	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
685	M₁₆	—	2	4	no	—
686	M₁₆	—	4	2	no	—
687	M₁₆	—	4	2	no	—
688	M₁₆	—	4	2	no	—
689	C₂×C₈	—	4	2	no	—
690	C₂×C₈	—	4	2	no	—
691	C₂×C₈	—	4	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
713	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
714	C₄²	—	2	2	no	—
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	4	2	no	—
718	C₄²	—	4	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	1	no	—
729	C₂³	—	8	1	no	—
730	C₂³	—	8	2	no	—
731	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
732	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
733	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
734	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
735	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
736	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
737	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
738	Q₈	—	4	1	no	—
739	Q₈	—	4	1	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	4	1	no	—
755	D₄	—	4	1	no	—
756	D₄	—	4	1	no	—
757	D₄	—	4	2	no	—
758	D₄	—	4	4	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	1	no	—
763	D₄	—	8	2	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	2	no	—
766	D₄	—	8	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	C₂₃×#99	1	1	yes	characteristic
808	C₂×C₄	C₂₃×#99	1	1	yes	characteristic
809	C₂×C₄	C₂₃×#99	1	1	yes	characteristic
810	C₂×C₄	C₂₃×#99	1	1	yes	characteristic
811	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
812	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
813	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
814	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
815	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
816	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
817	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₈	—	4	4	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	8	1	no	—
839	C₂²	—	8	1	no	—
840	C₂²	—	8	1	no	—
841	C₂²	—	8	1	no	—
842	C₂²	—	8	4	no	—
843	C₂²	C₂×C₂₃×#99	1	1	yes	characteristic
844	C₂²	C₂×C₂₃×#99	1	1	yes	characteristic
845	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	8	4	no	—
856	C₄	C₂×C₂₃×#99	1	1	yes	characteristic
857	C₄	C₂×C₂₃×#99	1	1	yes	characteristic
858	C₄	C₂×C₂₃×#99	1	1	yes	characteristic
859	C₄	C₂×C₂₃×#99	1	1	yes	characteristic
860	C₂	—	2	1	no	—
861	C₂	—	2	1	no	—
862	C₂	—	2	1	no	—
863	C₂	—	4	1	no	—
864	C₂	—	4	1	no	—
865	C₂	—	4	1	no	—
866	C₂	—	4	1	no	—
867	C₂	—	4	1	no	—
868	C₂	—	4	1	no	—
869	C₂	—	8	2	no	—
870	C₂	C₂²×C₂₃×#99	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	C₂×#99
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×D₄	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂²×#99
prime radical	C₂₃×#3449	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#413	C₂	semidirect
3. C₂×C₂₃×#410	C₂	semidirect
4. C₂₃×#2123	C₂	semidirect
5. C₂₃×#2122	C₂	semidirect
6. C₂₃×#2121	C₂	semidirect
7. C₂₃×#2120	C₂	semidirect
8. C₂²×#41×C₂₃	C₄	semidirect
14. C₂₃×#536	C₄	semidirect
17. C₂₃×#535	C₄	semidirect
19. C₂₃×#534	C₄	semidirect
25. C₂₃×#525	C₄	semidirect
28. C₂×C₂₃×#117	C₄	semidirect
41. C₂₃×#352	C₂²	semidirect
42. C₂₃×AΣL(1,𝔽₁₆)	C₂²	semidirect
63. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
67. C₂²×D₄×C₂₃	C₂×C₄	semidirect
71. C₂³×C₄×C₂₃	C₂×C₄	semidirect
92. C₂₃×#123	C₂×C₄	semidirect
93. C₂₃×#123	C₂×C₄	semidirect
114. C₂₃×#120	C₂×C₄	semidirect
115. C₂₃×#120	C₂×C₄	semidirect
127. C₂₃×#117	C₂×C₄	semidirect
128. C₂₃×#117	C₂×C₄	semidirect
129. C₂₃×#117	C₂×C₄	semidirect
283. #33347	C₂₃	direct (N × H)
386. C₂×#413	C₂×C₂₃	semidirect
387. C₂×#410	C₂×C₂₃	semidirect
388. #2123	C₂×C₂₃	semidirect
389. #2122	C₂×C₂₃	semidirect
390. #2121	C₂×C₂₃	semidirect
391. #2120	C₂×C₂₃	semidirect
432. C₂²×#41	C₄×C₂₃	semidirect
438. #536	C₄×C₂₃	semidirect
441. #535	C₄×C₂₃	semidirect
443. #534	C₄×C₂₃	semidirect
449. #525	C₄×C₂₃	semidirect
452. C₂×#117	C₄×C₂₃	semidirect
465. #352	C₂²×C₂₃	semidirect
466. AΣL(1,𝔽₁₆)	C₂²×C₂₃	semidirect
498. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
502. C₂²×D₄	C₂×C₄×C₂₃	semidirect
506. C₂³×C₄	C₂×C₄×C₂₃	semidirect
527. #123	C₂×C₄×C₂₃	semidirect
528. #123	C₂×C₄×C₂₃	semidirect
549. #120	C₂×C₄×C₂₃	semidirect
550. #120	C₂×C₄×C₂₃	semidirect
562. #117	C₂×C₄×C₂₃	semidirect
563. #117	C₂×C₄×C₂₃	semidirect
564. #117	C₂×C₄×C₂₃	semidirect
579. C₂₃	#33347	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×#3449	2
C₂×C₂₃×#413	2
C₂×C₂₃×#410	2
C₂₃×#2123	2
C₂₃×#2122	2
C₂₃×#2121	2
C₂₃×#2120	2
#33347	23

Subgroups — C23×#33347 #19180973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33347 #19180973