Subgroups — C₂₃×#34434 #19182060

Order 5888.

1974 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#544	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2381	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2378	C₂	1	2	yes	maximal
4	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2365	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2362	C₂	1	2	yes	maximal
10	C₂₃×#2347	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#2347	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2345	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#2344	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2336	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2336	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2332	C₂	1	2	yes	maximal
17	C₂₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2323	C₂	1	2	yes	maximal
20	C₂₃×#2314	C₂	1	1	yes	maximal, characteristic
21	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2298	C₂	1	1	yes	maximal, characteristic
24	C₂₃×#544	C₄	1	16	yes	complemented
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#125	C₂²	1	2	yes	—
30	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
35	C₂×C₂₃×#117	C₂²	1	2	yes	—
36	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#391	C₂²	1	2	yes	—
40	C₂₃×#391	C₂²	1	2	yes	—
41	C₂₃×#391	C₂²	1	2	yes	—
42	C₂₃×#391	C₂²	1	2	yes	—
43	C₂₃×#391	C₂²	1	2	yes	—
44	C₂₃×#391	C₂²	1	2	yes	—
45	C₂₃×#389	C₂²	1	1	yes	characteristic
46	C₂₃×#389	C₂²	1	1	yes	characteristic
47	C₂₃×#389	C₂²	1	2	yes	—
48	C₂₃×#389	C₂²	1	1	yes	characteristic
49	C₂₃×#389	C₂²	1	1	yes	characteristic
50	C₂₃×#389	C₂²	1	2	yes	—
51	C₂₃×#389	C₂²	1	2	yes	—
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#389	C₂²	1	2	yes	—
55	C₂₃×#389	C₂²	1	1	yes	characteristic
56	C₂₃×#389	C₂²	1	1	yes	characteristic
57	C₂₃×#389	C₂²	1	2	yes	—
58	C₂₃×#389	C₂²	1	2	yes	—
59	C₂₃×#388	C₂²	1	1	yes	characteristic
60	C₂₃×#388	C₂²	1	1	yes	characteristic
61	C₂₃×#388	C₂²	1	1	yes	characteristic
62	C₂₃×#388	C₂²	1	1	yes	characteristic
63	C₂₃×#388	C₂²	1	2	yes	—
64	C₂₃×#388	C₂²	1	2	yes	—
65	C₂₃×#388	C₂²	1	2	yes	—
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#387	C₂²	1	1	yes	characteristic
70	C₂₃×#387	C₂²	1	1	yes	characteristic
71	C₂₃×#387	C₂²	1	1	yes	characteristic
72	C₂₃×#387	C₂²	1	1	yes	characteristic
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#387	C₂²	1	2	yes	—
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#387	C₂²	1	2	yes	—
88	C₂₃×#387	C₂²	1	2	yes	—
89	C₂₃×#387	C₂²	1	2	yes	—
90	C₂₃×#387	C₂²	1	2	yes	—
91	C₂₃×#384	C₂²	1	1	yes	characteristic
92	C₂₃×#383	C₂²	1	2	yes	—
93	C₂₃×#383	C₂²	1	2	yes	—
94	C₂₃×#382	C₂²	1	1	yes	characteristic
95	C₂₃×#381	C₂²	1	2	yes	—
96	C₂₃×#380	C₂²	1	1	yes	characteristic
97	C₂₃×#380	C₂²	1	1	yes	characteristic
98	C₂₃×#380	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
122	C₂₃×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₂₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
128	C₂₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
129	C₂₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
130	C₂₃×C₄⋊Q₈	C₂×C₄	1	16	yes	—
131	C₂₃×#125	C₂×C₄	1	8	yes	—
132	C₂₃×#125	C₂×C₄	1	16	yes	—
133	C₂₃×#125	C₂×C₄	1	8	yes	—
134	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
135	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
136	C₄×Q₈×C₂₃	—	4	4	no	—
137	C₄×Q₈×C₂₃	—	4	4	no	—
138	C₂₃×#117	—	4	4	no	—
139	C₂₃×#117	C₂×C₄	1	8	yes	—
140	C₂₃×#117	C₂×C₄	1	8	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	1	yes	characteristic
204	C₂₃×#95	C₂³	1	1	yes	characteristic
205	C₂₃×#95	C₂³	1	1	yes	characteristic
206	C₂₃×#95	C₂³	1	1	yes	characteristic
207	C₂₃×#95	C₂³	1	1	yes	characteristic
208	C₂₃×#95	C₂³	1	1	yes	characteristic
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂₃×#95	C₂³	1	1	yes	characteristic
211	C₂₃×#95	C₂³	1	1	yes	characteristic
212	C₂₃×#95	C₂³	1	2	yes	—
213	C₂₃×#95	C₂³	1	1	yes	characteristic
214	C₂₃×#95	C₂³	1	1	yes	characteristic
215	C₂₃×#95	C₂³	1	2	yes	—
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂₃×#95	C₂³	1	2	yes	—
218	C₂₃×#95	C₂³	1	2	yes	—
219	C₂₃×#95	C₂³	1	2	yes	—
220	C₂₃×#95	C₂³	1	2	yes	—
221	C₂₃×#95	C₂³	1	2	yes	—
222	C₂₃×#95	C₂³	1	2	yes	—
223	C₂₃×#95	C₂³	1	2	yes	—
224	C₂₃×#95	C₂³	1	2	yes	—
225	C₂₃×#95	C₂³	1	2	yes	—
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	2	yes	—
233	C₂₃×#95	C₂³	1	1	yes	characteristic
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	1	yes	characteristic
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂×Q₈×C₂₃	—	4	2	no	—
239	C₂×Q₈×C₂₃	—	4	2	no	—
240	C₂×Q₈×C₂₃	—	4	2	no	—
241	C₂×Q₈×C₂₃	—	4	2	no	—
242	C₂×Q₈×C₂₃	C₂²×C₄	1	8	yes	—
243	C₂×Q₈×C₂₃	C₂²×C₄	1	8	yes	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	4	2	no	—
247	C₂²×C₄×C₂₃	—	4	2	no	—
248	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
249	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
250	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	4	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	4	1	no	—
282	C₄⋊C₄×C₂₃	—	4	2	no	—
283	C₄⋊C₄×C₂₃	—	4	2	no	—
284	C₄⋊C₄×C₂₃	—	4	2	no	—
285	C₄⋊C₄×C₂₃	—	4	1	no	—
286	C₄⋊C₄×C₂₃	—	4	2	no	—
287	C₄⋊C₄×C₂₃	—	4	2	no	—
288	C₄⋊C₄×C₂₃	—	4	2	no	—
289	C₄⋊C₄×C₂₃	—	4	2	no	—
290	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
291	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
292	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
293	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
294	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
295	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
296	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
297	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
298	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
299	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
300	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
301	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
302	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	4	2	no	—
306	C₂²⋊C₄×C₂₃	—	4	1	no	—
307	C₂²⋊C₄×C₂₃	—	4	1	no	—
308	C₂²⋊C₄×C₂₃	—	4	2	no	—
309	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
310	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
311	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
312	C₄²×C₂₃	—	2	4	no	—
313	C₄²×C₂₃	—	2	2	no	—
314	C₄²×C₂₃	—	2	2	no	—
315	C₄²×C₂₃	—	2	2	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	—	2	2	no	—
318	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	4	2	no	—
320	C₄²×C₂₃	—	4	1	no	—
321	C₄²×C₂₃	—	4	2	no	—
322	C₄²×C₂₃	—	4	2	no	—
323	C₄²×C₂₃	—	4	2	no	—
324	C₄²×C₂₃	—	4	1	no	—
325	C₄²×C₂₃	—	4	2	no	—
326	C₄²×C₂₃	—	4	2	no	—
327	C₄²×C₂₃	—	4	2	no	—
328	C₄²×C₂₃	—	4	2	no	—
329	C₄²×C₂₃	—	4	2	no	—
330	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
331	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
332	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
333	#34434	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₂₃	—	2	1	no	—
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	—	2	1	no	—
337	C₂³×C₂₃	—	2	1	no	—
338	C₂³×C₂₃	—	2	1	no	—
339	C₂³×C₂₃	—	2	1	no	—
340	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
341	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
342	Q₈×C₂₃	—	4	8	no	—
343	Q₈×C₂₃	—	4	8	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	1	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	2	2	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	2	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	2	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	8	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	1	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	1	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	1	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	1	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	1	no	—
396	C₂×C₄×C₂₃	—	2	1	no	—
397	C₂×C₄×C₂₃	—	4	8	no	—
398	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
400	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
401	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
402	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
403	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
405	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
406	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
407	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
409	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
410	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
411	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
412	C₂×#544	C₂×C₂₃	1	1	yes	characteristic
413	#2381	C₂×C₂₃	1	2	yes	complemented
414	#2378	C₂×C₂₃	1	2	yes	—
415	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#2369	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2365	C₂×C₂₃	1	2	yes	complemented
419	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#2362	C₂×C₂₃	1	2	yes	—
421	#2347	C₂×C₂₃	1	1	yes	characteristic
422	#2347	C₂×C₂₃	1	1	yes	characteristic
423	#2345	C₂×C₂₃	1	1	yes	characteristic
424	#2344	C₂×C₂₃	1	1	yes	characteristic
425	#2336	C₂×C₂₃	1	2	yes	complemented
426	#2336	C₂×C₂₃	1	2	yes	complemented
427	#2332	C₂×C₂₃	1	2	yes	—
428	#2331	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#2330	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#2323	C₂×C₂₃	1	2	yes	—
431	#2314	C₂×C₂₃	1	1	yes	characteristic
432	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
433	C₄×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#2298	C₂×C₂₃	1	1	yes	characteristic
435	C₂²×C₂₃	—	2	2	no	—
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	4	1	no	—
439	C₂²×C₂₃	—	4	1	no	—
440	C₂²×C₂₃	—	4	1	no	—
441	C₂²×C₂₃	—	4	1	no	—
442	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
443	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂²×C₂₃	#585	1	1	yes	characteristic
448	C₂²×C₂₃	#585	1	1	yes	characteristic
449	C₄×C₂₃	—	2	2	no	—
450	C₄×C₂₃	—	2	4	no	—
451	C₄×C₂₃	—	2	4	no	—
452	C₄×C₂₃	—	2	2	no	—
453	C₄×C₂₃	—	2	4	no	—
454	C₄×C₂₃	—	2	2	no	—
455	C₄×C₂₃	—	2	2	no	—
456	C₄×C₂₃	—	2	4	no	—
457	C₄×C₂₃	—	2	2	no	—
458	C₄×C₂₃	—	2	2	no	—
459	C₄×C₂₃	—	2	2	no	—
460	C₄×C₂₃	—	4	2	no	—
461	C₄×C₂₃	—	4	1	no	—
462	C₄×C₂₃	—	4	1	no	—
463	C₄×C₂₃	—	4	1	no	—
464	C₄×C₂₃	—	4	2	no	—
465	C₄×C₂₃	—	4	1	no	—
466	C₄×C₂₃	—	4	2	no	—
467	C₄×C₂₃	—	4	1	no	—
468	C₄×C₂₃	—	4	1	no	—
469	C₄×C₂₃	—	4	2	no	—
470	C₄×C₂₃	#519	1	4	yes	—
471	#544	C₄×C₂₃	1	16	yes	complemented
472	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
475	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×#125	C₂²×C₂₃	1	2	yes	—
477	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
479	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
480	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
481	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
482	C₂×#117	C₂²×C₂₃	1	2	yes	—
483	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
486	#391	C₂²×C₂₃	1	2	yes	—
487	#391	C₂²×C₂₃	1	2	yes	—
488	#391	C₂²×C₂₃	1	2	yes	—
489	#391	C₂²×C₂₃	1	2	yes	—
490	#391	C₂²×C₂₃	1	2	yes	—
491	#391	C₂²×C₂₃	1	2	yes	—
492	#389	C₂²×C₂₃	1	1	yes	characteristic
493	#389	C₂²×C₂₃	1	1	yes	characteristic
494	#389	C₂²×C₂₃	1	2	yes	—
495	#389	C₂²×C₂₃	1	1	yes	characteristic
496	#389	C₂²×C₂₃	1	1	yes	characteristic
497	#389	C₂²×C₂₃	1	2	yes	—
498	#389	C₂²×C₂₃	1	2	yes	—
499	#389	C₂²×C₂₃	1	1	yes	characteristic
500	#389	C₂²×C₂₃	1	1	yes	characteristic
501	#389	C₂²×C₂₃	1	2	yes	—
502	#389	C₂²×C₂₃	1	1	yes	characteristic
503	#389	C₂²×C₂₃	1	1	yes	characteristic
504	#389	C₂²×C₂₃	1	2	yes	—
505	#389	C₂²×C₂₃	1	2	yes	—
506	#388	C₂²×C₂₃	1	2	yes	—
507	#388	C₂²×C₂₃	1	2	yes	—
508	#388	C₂²×C₂₃	1	1	yes	characteristic
509	#388	C₂²×C₂₃	1	2	yes	—
510	#388	C₂²×C₂₃	1	2	yes	—
511	#388	C₂²×C₂₃	1	1	yes	characteristic
512	#388	C₂²×C₂₃	1	2	yes	—
513	#388	C₂²×C₂₃	1	2	yes	—
514	#388	C₂²×C₂₃	1	1	yes	characteristic
515	#388	C₂²×C₂₃	1	1	yes	characteristic
516	#387	C₂²×C₂₃	1	2	yes	—
517	#387	C₂²×C₂₃	1	2	yes	—
518	#387	C₂²×C₂₃	1	2	yes	—
519	#387	C₂²×C₂₃	1	2	yes	—
520	#387	C₂²×C₂₃	1	2	yes	—
521	#387	C₂²×C₂₃	1	2	yes	—
522	#387	C₂²×C₂₃	1	2	yes	—
523	#387	C₂²×C₂₃	1	2	yes	—
524	#387	C₂²×C₂₃	1	2	yes	—
525	#387	C₂²×C₂₃	1	2	yes	—
526	#387	C₂²×C₂₃	1	1	yes	characteristic
527	#387	C₂²×C₂₃	1	1	yes	characteristic
528	#387	C₂²×C₂₃	1	2	yes	—
529	#387	C₂²×C₂₃	1	2	yes	—
530	#387	C₂²×C₂₃	1	2	yes	—
531	#387	C₂²×C₂₃	1	2	yes	—
532	#387	C₂²×C₂₃	1	2	yes	—
533	#387	C₂²×C₂₃	1	2	yes	—
534	#387	C₂²×C₂₃	1	2	yes	—
535	#387	C₂²×C₂₃	1	2	yes	—
536	#387	C₂²×C₂₃	1	1	yes	characteristic
537	#387	C₂²×C₂₃	1	1	yes	characteristic
538	#384	C₂²×C₂₃	1	1	yes	characteristic
539	#383	C₂²×C₂₃	1	2	yes	—
540	#383	C₂²×C₂₃	1	2	yes	—
541	#382	C₂²×C₂₃	1	1	yes	characteristic
542	#381	C₂²×C₂₃	1	2	yes	—
543	#380	C₂²×C₂₃	1	1	yes	characteristic
544	#380	C₂²×C₂₃	1	1	yes	characteristic
545	#380	C₂²×C₂₃	1	2	yes	—
546	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
549	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
550	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
561	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
566	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
568	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
569	#376	C₂²×C₂₃	1	1	yes	characteristic
570	C₄³	C₂²×C₂₃	1	1	yes	characteristic
571	C₂×C₂₃	—	4	2	no	—
572	C₂×C₂₃	C₂×#519	1	1	yes	characteristic
573	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
575	C₂×C₂₃	#3552	1	1	yes	characteristic
576	C₂×C₂₃	#3555	1	1	yes	characteristic
577	C₂×C₂₃	#3559	1	1	yes	characteristic
578	C₂×C₂₃	#3565	1	1	yes	characteristic
579	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
580	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
581	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
583	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
584	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
585	C₄⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
586	#125	C₂×C₄×C₂₃	1	8	yes	—
587	#125	C₂×C₄×C₂₃	1	16	yes	—
588	#125	C₂×C₄×C₂₃	1	8	yes	—
589	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
590	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
591	C₄×Q₈	—	4	4	no	—
592	C₄×Q₈	—	4	4	no	—
593	#117	—	4	4	no	—
594	#117	C₂×C₄×C₂₃	1	8	yes	—
595	#117	C₂×C₄×C₂₃	1	8	yes	—
596	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	—
597	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
649	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
652	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
658	#95	C₂³×C₂₃	1	1	yes	characteristic
659	#95	C₂³×C₂₃	1	1	yes	characteristic
660	#95	C₂³×C₂₃	1	1	yes	characteristic
661	#95	C₂³×C₂₃	1	1	yes	characteristic
662	#95	C₂³×C₂₃	1	1	yes	characteristic
663	#95	C₂³×C₂₃	1	1	yes	characteristic
664	#95	C₂³×C₂₃	1	2	yes	—
665	#95	C₂³×C₂₃	1	1	yes	characteristic
666	#95	C₂³×C₂₃	1	1	yes	characteristic
667	#95	C₂³×C₂₃	1	2	yes	—
668	#95	C₂³×C₂₃	1	1	yes	characteristic
669	#95	C₂³×C₂₃	1	1	yes	characteristic
670	#95	C₂³×C₂₃	1	2	yes	—
671	#95	C₂³×C₂₃	1	2	yes	—
672	#95	C₂³×C₂₃	1	2	yes	—
673	#95	C₂³×C₂₃	1	2	yes	—
674	#95	C₂³×C₂₃	1	2	yes	—
675	#95	C₂³×C₂₃	1	2	yes	—
676	#95	C₂³×C₂₃	1	2	yes	—
677	#95	C₂³×C₂₃	1	2	yes	—
678	#95	C₂³×C₂₃	1	2	yes	—
679	#95	C₂³×C₂₃	1	2	yes	—
680	#95	C₂³×C₂₃	1	2	yes	—
681	#95	C₂³×C₂₃	1	2	yes	—
682	#95	C₂³×C₂₃	1	2	yes	—
683	#95	C₂³×C₂₃	1	2	yes	—
684	#95	C₂³×C₂₃	1	2	yes	—
685	#95	C₂³×C₂₃	1	2	yes	—
686	#95	C₂³×C₂₃	1	2	yes	—
687	#95	C₂³×C₂₃	1	2	yes	—
688	#95	C₂³×C₂₃	1	1	yes	characteristic
689	#95	C₂³×C₂₃	1	2	yes	—
690	#95	C₂³×C₂₃	1	1	yes	characteristic
691	#95	C₂³×C₂₃	1	2	yes	—
692	C₂₃	#34434	1	1	yes	characteristic, direct product factor, Sylow
693	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
694	C₂×Q₈	—	4	2	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	C₂²×C₄×C₂₃	1	8	yes	—
699	C₂×Q₈	C₂²×C₄×C₂₃	1	8	yes	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
705	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
706	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
747	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
748	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
749	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
750	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
751	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
752	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
753	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
754	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
755	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
756	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
757	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
758	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
766	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
767	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	1	no	—
786	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
787	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
788	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
796	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
797	Q₈	—	4	8	no	—
798	Q₈	—	4	8	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	8	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
854	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
855	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
857	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
858	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
859	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
860	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
861	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
862	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
863	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
864	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
865	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
866	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
875	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
879	C₂²	C₂₃×#585	1	1	yes	characteristic
880	C₂²	C₂₃×#585	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	C₂₃×#519	1	4	yes	—
903	C₂	—	4	2	no	—
904	C₂	C₂×C₂₃×#519	1	1	yes	characteristic
905	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
906	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
907	C₂	C₂₃×#3552	1	1	yes	characteristic
908	C₂	C₂₃×#3555	1	1	yes	characteristic
909	C₂	C₂₃×#3559	1	1	yes	characteristic
910	C₂	C₂₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁴×C₂₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2381	C₂	semidirect
4. C₂₃×#2370	C₂	semidirect
5. C₂₃×#2370	C₂	semidirect
6. C₂₃×#2369	C₂	semidirect
7. C₂₃×#2365	C₂	semidirect
8. C₂₃×#2365	C₂	semidirect
14. C₂₃×#2336	C₂	semidirect
15. C₂₃×#2336	C₂	semidirect
17. C₂₃×#2331	C₂	semidirect
18. C₂₃×#2330	C₂	semidirect
21. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
22. C₄×C₂₃×#125	C₂	semidirect
24. C₂₃×#544	C₄	semidirect
333. #34434	C₂₃	direct (N × H)
413. #2381	C₂×C₂₃	semidirect
415. #2370	C₂×C₂₃	semidirect
416. #2370	C₂×C₂₃	semidirect
417. #2369	C₂×C₂₃	semidirect
418. #2365	C₂×C₂₃	semidirect
419. #2365	C₂×C₂₃	semidirect
425. #2336	C₂×C₂₃	semidirect
426. #2336	C₂×C₂₃	semidirect
428. #2331	C₂×C₂₃	semidirect
429. #2330	C₂×C₂₃	semidirect
432. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
433. C₄×#125	C₂×C₂₃	semidirect
471. #544	C₄×C₂₃	semidirect
692. C₂₃	#34434	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#544	2
C₂₃×#2381	2
C₂₃×#2378	2
C₂₃×#2370	2
C₂₃×#2369	2
C₂₃×#2365	2
C₂₃×#2362	2
C₂₃×#2347	2
C₂₃×#2345	2
C₂₃×#2344	2
C₂₃×#2336	2
C₂₃×#2332	2
C₂₃×#2331	2
C₂₃×#2330	2
C₂₃×#2323	2
C₂₃×#2314	2
C₄×C₂₃×C₄⋊Q₈	2
C₄×C₂₃×#125	2
C₂₃×#2298	2
#34434	23

Subgroups — C23×#34434 #19182060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34434 #19182060