Subgroups — C₂₃×#36747 #19184373

Order 5888.

2146 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2848	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2784	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2780	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2780	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2748	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2748	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2732	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2692	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2692	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2683	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2626	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2438	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2438	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2437	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2437	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2309	C₂	1	1	yes	maximal, characteristic
18	C₂₃×#2308	C₂	1	1	yes	maximal, characteristic
19	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic
20	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#400	C₂²	1	2	yes	complemented
35	C₂₃×#400	C₂²	1	2	yes	complemented
36	C₂₃×#399	C₂²	1	2	yes	complemented
37	C₂₃×#399	C₂²	1	2	yes	complemented
38	C₂₃×#399	C₂²	1	2	yes	complemented
39	C₂₃×#399	C₂²	1	2	yes	complemented
40	C₂₃×#398	C₂²	1	2	yes	complemented
41	C₂₃×#398	C₂²	1	2	yes	complemented
42	C₂₃×#398	C₂²	1	2	yes	complemented
43	C₂₃×#398	C₂²	1	2	yes	complemented
44	C₂₃×#396	C₂²	1	2	yes	complemented
45	C₂₃×#396	C₂²	1	2	yes	complemented
46	C₂₃×#396	C₂²	1	2	yes	complemented
47	C₂₃×#396	C₂²	1	2	yes	complemented
48	C₂₃×#396	C₂²	1	2	yes	complemented
49	C₂₃×#396	C₂²	1	2	yes	complemented
50	C₂₃×#396	C₂²	1	2	yes	complemented
51	C₂₃×#396	C₂²	1	2	yes	complemented
52	C₂₃×#395	C₂²	1	2	yes	complemented
53	C₂₃×#395	C₂²	1	2	yes	complemented
54	C₂₃×#393	C₂²	1	2	yes	complemented
55	C₂₃×#393	C₂²	1	2	yes	complemented
56	C₂₃×#393	C₂²	1	2	yes	complemented
57	C₂₃×#393	C₂²	1	2	yes	complemented
58	C₂₃×#391	C₂²	1	2	yes	complemented
59	C₂₃×#391	C₂²	1	2	yes	complemented
60	C₂₃×#390	C₂²	1	1	yes	characteristic
61	C₂₃×#390	C₂²	1	1	yes	characteristic
62	C₂₃×#390	C₂²	1	2	yes	—
63	C₂₃×#390	C₂²	1	2	yes	—
64	C₂₃×#390	C₂²	1	1	yes	characteristic
65	C₂₃×#390	C₂²	1	1	yes	characteristic
66	C₂₃×#389	C₂²	1	2	yes	complemented
67	C₂₃×#389	C₂²	1	2	yes	complemented
68	C₂₃×#387	C₂²	1	2	yes	complemented
69	C₂₃×#387	C₂²	1	2	yes	complemented
70	C₂₃×#387	C₂²	1	2	yes	complemented
71	C₂₃×#387	C₂²	1	2	yes	complemented
72	C₂₃×#386	C₂²	1	1	yes	characteristic
73	C₂₃×#386	C₂²	1	1	yes	characteristic
74	C₂₃×#386	C₂²	1	1	yes	characteristic
75	C₂₃×#386	C₂²	1	2	yes	—
76	C₂₃×#386	C₂²	1	2	yes	—
77	C₂₃×#386	C₂²	1	2	yes	—
78	C₂₃×#386	C₂²	1	1	yes	characteristic
79	C₂₃×#386	C₂²	1	2	yes	—
80	C₂₃×#386	C₂²	1	1	yes	characteristic
81	C₂₃×#386	C₂²	1	1	yes	characteristic
82	C₂₃×#386	C₂²	1	1	yes	characteristic
83	C₂₃×#386	C₂²	1	1	yes	characteristic
84	C₂₃×#385	C₂²	1	2	yes	—
85	C₂₃×#385	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	—
88	C₂₃×#385	C₂²	1	2	yes	complemented
89	C₂₃×#385	C₂²	1	2	yes	complemented
90	C₂₃×#385	C₂²	1	2	yes	complemented
91	C₂₃×#385	C₂²	1	2	yes	complemented
92	C₂₃×#385	C₂²	1	2	yes	complemented
93	C₂₃×#385	C₂²	1	2	yes	complemented
94	C₂₃×#385	C₂²	1	2	yes	complemented
95	C₂₃×#385	C₂²	1	2	yes	complemented
96	C₂₃×#381	C₂²	1	2	yes	—
97	C₂₃×#380	C₂²	1	2	yes	—
98	C₂₃×#380	C₂²	1	2	yes	—
99	C₂₃×#380	C₂²	1	2	yes	complemented
100	C₂₃×#380	C₂²	1	2	yes	complemented
101	C₂₃×#380	C₂²	1	2	yes	complemented
102	C₂₃×#380	C₂²	1	2	yes	complemented
103	C₂₃×#379	C₂²	1	2	yes	—
104	C₂₃×#379	C₂²	1	2	yes	—
105	C₂₃×#379	C₂²	1	2	yes	—
106	C₂×C₂₃×#95	C₂²	1	2	yes	—
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
110	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	—	4	2	no	—
112	C₂²×D₄×C₂₃	—	4	2	no	—
113	C₂²×D₄×C₂₃	Q₈	1	8	yes	complemented
114	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₂₃	—	4	4	no	—
119	C₂³×C₄×C₂₃	—	4	2	no	—
120	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂₃×C₂²⋊Q₈	—	4	4	no	—
130	C₂₃×C₂²⋊Q₈	—	4	4	no	—
131	C₂₃×C₂²⋊Q₈	—	4	4	no	—
132	C₂₃×C₂²⋊Q₈	—	4	4	no	—
133	C₂₃×C₂²⋊Q₈	—	4	4	no	—
134	C₂₃×C₂²⋊Q₈	—	4	4	no	—
135	C₂₃×#117	—	4	2	no	—
136	C₂₃×#117	—	4	2	no	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
159	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
160	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
161	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	C₂³	1	2	yes	—
207	C₂₃×#95	C₂³	1	2	yes	—
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂₃×#95	C₂³	1	2	yes	—
211	C₂⁴×C₂₃	—	2	2	no	—
212	C₂⁴×C₂₃	—	2	2	no	—
213	C₂⁴×C₂₃	—	2	2	no	—
214	C₂⁴×C₂₃	—	2	2	no	—
215	C₂⁴×C₂₃	—	4	2	no	—
216	C₂⁴×C₂₃	—	4	2	no	—
217	C₂⁴×C₂₃	—	4	2	no	—
218	C₂⁴×C₂₃	—	4	2	no	—
219	C₂⁴×C₂₃	C₂×Q₈	1	4	yes	—
220	C₂⁴×C₂₃	C₂×Q₈	1	4	yes	—
221	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
226	C₂×Q₈×C₂₃	—	2	4	no	—
227	C₂×Q₈×C₂₃	—	4	2	no	—
228	C₂×Q₈×C₂₃	—	4	2	no	—
229	C₂×Q₈×C₂₃	—	4	2	no	—
230	C₂×Q₈×C₂₃	—	4	2	no	—
231	C₂×Q₈×C₂₃	—	4	2	no	—
232	C₂×D₄×C₂₃	—	4	16	no	—
233	C₂×D₄×C₂₃	—	4	1	no	—
234	C₂×D₄×C₂₃	—	4	1	no	—
235	C₂×D₄×C₂₃	—	4	1	no	—
236	C₂×D₄×C₂₃	—	4	1	no	—
237	C₂×D₄×C₂₃	—	4	1	no	—
238	C₂×D₄×C₂₃	—	4	1	no	—
239	C₂×D₄×C₂₃	—	4	1	no	—
240	C₂×D₄×C₂₃	—	4	1	no	—
241	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
242	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
243	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
244	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	4	no	—
248	C₂²×C₄×C₂₃	—	2	4	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	—	2	4	no	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	4	1	no	—
253	C₂²×C₄×C₂₃	—	4	2	no	—
254	C₂²×C₄×C₂₃	—	4	2	no	—
255	C₂²×C₄×C₂₃	—	4	2	no	—
256	C₂²×C₄×C₂₃	—	4	2	no	—
257	C₂²×C₄×C₂₃	—	4	1	no	—
258	C₂²×C₄×C₂₃	—	4	1	no	—
259	C₂²×C₄×C₂₃	—	4	2	no	—
260	C₂²×C₄×C₂₃	—	4	2	no	—
261	C₂²×C₄×C₂₃	—	4	1	no	—
262	C₂²×C₄×C₂₃	—	4	2	no	—
263	C₂²×C₄×C₂₃	—	4	2	no	—
264	C₂²×C₄×C₂₃	—	4	2	no	—
265	C₂²×C₄×C₂₃	—	4	2	no	—
266	C₂²×C₄×C₂₃	—	4	2	no	—
267	C₂²×C₄×C₂₃	—	4	16	no	—
268	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₂₃	—	2	4	no	—
284	C₄⋊C₄×C₂₃	—	2	4	no	—
285	C₄⋊C₄×C₂₃	—	2	4	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	1	no	—
290	C₄⋊C₄×C₂₃	—	4	2	no	—
291	C₄⋊C₄×C₂₃	—	4	1	no	—
292	C₄⋊C₄×C₂₃	—	4	2	no	—
293	C₄⋊C₄×C₂₃	—	4	2	no	—
294	C₄⋊C₄×C₂₃	—	4	2	no	—
295	C₄⋊C₄×C₂₃	—	4	2	no	—
296	C₄⋊C₄×C₂₃	—	4	2	no	—
297	C₄⋊C₄×C₂₃	—	4	2	no	—
298	C₄⋊C₄×C₂₃	—	4	2	no	—
299	C₄⋊C₄×C₂₃	—	4	2	no	—
300	C₄⋊C₄×C₂₃	—	4	2	no	—
301	C₄⋊C₄×C₂₃	—	4	2	no	—
302	C₄⋊C₄×C₂₃	—	4	2	no	—
303	C₄⋊C₄×C₂₃	—	4	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	4	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	4	1	no	—
311	C₂²⋊C₄×C₂₃	—	4	2	no	—
312	C₂²⋊C₄×C₂₃	—	4	2	no	—
313	C₂²⋊C₄×C₂₃	—	4	1	no	—
314	C₂²⋊C₄×C₂₃	—	4	2	no	—
315	C₂²⋊C₄×C₂₃	—	4	1	no	—
316	C₂²⋊C₄×C₂₃	—	4	2	no	—
317	C₂²⋊C₄×C₂₃	—	4	1	no	—
318	C₂²⋊C₄×C₂₃	—	4	2	no	—
319	C₂²⋊C₄×C₂₃	—	4	2	no	—
320	C₂²⋊C₄×C₂₃	—	4	2	no	—
321	C₂²⋊C₄×C₂₃	—	4	2	no	—
322	C₂²⋊C₄×C₂₃	—	4	2	no	—
323	C₂²⋊C₄×C₂₃	—	4	2	no	—
324	C₂²⋊C₄×C₂₃	—	4	2	no	—
325	C₂²⋊C₄×C₂₃	—	4	2	no	—
326	C₂²⋊C₄×C₂₃	—	4	2	no	—
327	C₂²⋊C₄×C₂₃	—	4	2	no	—
328	C₂²⋊C₄×C₂₃	—	4	2	no	—
329	C₂²⋊C₄×C₂₃	—	4	2	no	—
330	C₄²×C₂₃	—	4	1	no	—
331	C₄²×C₂₃	—	4	2	no	—
332	C₄²×C₂₃	—	4	1	no	—
333	#36747	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₂₃	—	2	2	no	—
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	8	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	1	no	—
342	C₂³×C₂₃	—	2	1	no	—
343	C₂³×C₂₃	—	2	1	no	—
344	C₂³×C₂₃	—	2	1	no	—
345	C₂³×C₂₃	—	2	1	no	—
346	C₂³×C₂₃	—	2	1	no	—
347	C₂³×C₂₃	—	2	1	no	—
348	C₂³×C₂₃	—	2	1	no	—
349	C₂³×C₂₃	—	2	2	no	—
350	C₂³×C₂₃	—	2	2	no	—
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	—	2	2	no	—
353	C₂³×C₂₃	—	2	8	no	—
354	C₂³×C₂₃	—	4	8	no	—
355	C₂³×C₂₃	—	4	8	no	—
356	C₂³×C₂₃	—	4	4	no	—
357	C₂³×C₂₃	—	4	4	no	—
358	C₂³×C₂₃	—	4	8	no	—
359	C₂³×C₂₃	—	8	2	no	—
360	C₂³×C₂₃	—	8	2	no	—
361	C₂³×C₂₃	—	8	4	no	—
362	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
363	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
364	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
365	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
366	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
367	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
368	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
369	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
370	Q₈×C₂₃	—	8	4	no	—
371	Q₈×C₂₃	—	8	4	no	—
372	D₄×C₂₃	—	4	4	no	—
373	D₄×C₂₃	—	4	4	no	—
374	D₄×C₂₃	—	4	4	no	—
375	D₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	2	8	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	1	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	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	2	no	—
410	C₂×C₄×C₂₃	—	2	2	no	—
411	C₂×C₄×C₂₃	—	2	2	no	—
412	C₂×C₄×C₂₃	—	2	2	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	4	4	no	—
417	C₂×C₄×C₂₃	—	4	8	no	—
418	C₂×C₄×C₂₃	—	4	8	no	—
419	C₂×C₄×C₂₃	—	4	4	no	—
420	C₂×C₄×C₂₃	—	8	4	no	—
421	C₂×C₄×C₂₃	—	8	2	no	—
422	C₂×C₄×C₂₃	—	8	2	no	—
423	C₂×C₄×C₂₃	—	8	4	no	—
424	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
425	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
426	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
427	#2848	C₂×C₂₃	1	2	yes	complemented
428	#2804	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#2784	C₂×C₂₃	1	2	yes	complemented
430	#2780	C₂×C₂₃	1	2	yes	complemented
431	#2780	C₂×C₂₃	1	2	yes	complemented
432	#2748	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#2748	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#2732	C₂×C₂₃	1	2	yes	complemented
435	#2692	C₂×C₂₃	1	2	yes	complemented
436	#2692	C₂×C₂₃	1	2	yes	complemented
437	#2683	C₂×C₂₃	1	1	yes	characteristic, complemented
438	#2626	C₂×C₂₃	1	2	yes	complemented
439	#2438	C₂×C₂₃	1	2	yes	complemented
440	#2438	C₂×C₂₃	1	2	yes	complemented
441	#2437	C₂×C₂₃	1	2	yes	complemented
442	#2437	C₂×C₂₃	1	2	yes	complemented
443	#2309	C₂×C₂₃	1	1	yes	characteristic
444	#2308	C₂×C₂₃	1	1	yes	characteristic
445	C₂×#386	C₂×C₂₃	1	1	yes	characteristic
446	C₂²×C₂₃	—	2	4	no	—
447	C₂²×C₂₃	—	2	2	no	—
448	C₂²×C₂₃	—	2	2	no	—
449	C₂²×C₂₃	—	2	4	no	—
450	C₂²×C₂₃	—	2	2	no	—
451	C₂²×C₂₃	—	2	2	no	—
452	C₂²×C₂₃	—	2	2	no	—
453	C₂²×C₂₃	—	2	2	no	—
454	C₂²×C₂₃	—	2	4	no	—
455	C₂²×C₂₃	—	2	4	no	—
456	C₂²×C₂₃	—	2	4	no	—
457	C₂²×C₂₃	—	2	4	no	—
458	C₂²×C₂₃	—	4	16	no	—
459	C₂²×C₂₃	—	4	1	no	—
460	C₂²×C₂₃	—	4	1	no	—
461	C₂²×C₂₃	—	4	1	no	—
462	C₂²×C₂₃	—	4	1	no	—
463	C₂²×C₂₃	—	4	1	no	—
464	C₂²×C₂₃	—	4	1	no	—
465	C₂²×C₂₃	—	4	1	no	—
466	C₂²×C₂₃	—	4	1	no	—
467	C₂²×C₂₃	—	4	2	no	—
468	C₂²×C₂₃	—	4	2	no	—
469	C₂²×C₂₃	—	4	2	no	—
470	C₂²×C₂₃	—	4	2	no	—
471	C₂²×C₂₃	—	8	8	no	—
472	C₂²×C₂₃	#543	1	4	yes	—
473	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
474	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
477	C₂²×C₂₃	#585	1	2	yes	—
478	C₄×C₂₃	—	2	2	no	—
479	C₄×C₂₃	—	2	2	no	—
480	C₄×C₂₃	—	2	4	no	—
481	C₄×C₂₃	—	4	2	no	—
482	C₄×C₂₃	—	4	2	no	—
483	C₄×C₂₃	—	4	2	no	—
484	C₄×C₂₃	—	4	2	no	—
485	C₄×C₂₃	—	4	2	no	—
486	C₄×C₂₃	—	4	2	no	—
487	C₄×C₂₃	—	4	2	no	—
488	C₄×C₂₃	—	4	2	no	—
489	C₄×C₂₃	—	4	2	no	—
490	C₄×C₂₃	—	4	2	no	—
491	C₄×C₂₃	—	4	2	no	—
492	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
493	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
496	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
497	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
498	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
499	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
500	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
501	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
502	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
503	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
504	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
505	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
506	#400	C₂²×C₂₃	1	2	yes	complemented
507	#400	C₂²×C₂₃	1	2	yes	complemented
508	#399	C₂²×C₂₃	1	2	yes	complemented
509	#399	C₂²×C₂₃	1	2	yes	complemented
510	#399	C₂²×C₂₃	1	2	yes	complemented
511	#399	C₂²×C₂₃	1	2	yes	complemented
512	#398	C₂²×C₂₃	1	2	yes	complemented
513	#398	C₂²×C₂₃	1	2	yes	complemented
514	#398	C₂²×C₂₃	1	2	yes	complemented
515	#398	C₂²×C₂₃	1	2	yes	complemented
516	#396	C₂²×C₂₃	1	2	yes	complemented
517	#396	C₂²×C₂₃	1	2	yes	complemented
518	#396	C₂²×C₂₃	1	2	yes	complemented
519	#396	C₂²×C₂₃	1	2	yes	complemented
520	#396	C₂²×C₂₃	1	2	yes	complemented
521	#396	C₂²×C₂₃	1	2	yes	complemented
522	#396	C₂²×C₂₃	1	2	yes	complemented
523	#396	C₂²×C₂₃	1	2	yes	complemented
524	#395	C₂²×C₂₃	1	2	yes	complemented
525	#395	C₂²×C₂₃	1	2	yes	complemented
526	#393	C₂²×C₂₃	1	2	yes	complemented
527	#393	C₂²×C₂₃	1	2	yes	complemented
528	#393	C₂²×C₂₃	1	2	yes	complemented
529	#393	C₂²×C₂₃	1	2	yes	complemented
530	#391	C₂²×C₂₃	1	2	yes	complemented
531	#391	C₂²×C₂₃	1	2	yes	complemented
532	#390	C₂²×C₂₃	1	1	yes	characteristic
533	#390	C₂²×C₂₃	1	1	yes	characteristic
534	#390	C₂²×C₂₃	1	2	yes	—
535	#390	C₂²×C₂₃	1	2	yes	—
536	#390	C₂²×C₂₃	1	1	yes	characteristic
537	#390	C₂²×C₂₃	1	1	yes	characteristic
538	#389	C₂²×C₂₃	1	2	yes	complemented
539	#389	C₂²×C₂₃	1	2	yes	complemented
540	#387	C₂²×C₂₃	1	2	yes	complemented
541	#387	C₂²×C₂₃	1	2	yes	complemented
542	#387	C₂²×C₂₃	1	2	yes	complemented
543	#387	C₂²×C₂₃	1	2	yes	complemented
544	#386	C₂²×C₂₃	1	1	yes	characteristic
545	#386	C₂²×C₂₃	1	2	yes	—
546	#386	C₂²×C₂₃	1	2	yes	—
547	#386	C₂²×C₂₃	1	1	yes	characteristic
548	#386	C₂²×C₂₃	1	1	yes	characteristic
549	#386	C₂²×C₂₃	1	1	yes	characteristic
550	#386	C₂²×C₂₃	1	1	yes	characteristic
551	#386	C₂²×C₂₃	1	1	yes	characteristic
552	#386	C₂²×C₂₃	1	2	yes	—
553	#386	C₂²×C₂₃	1	2	yes	—
554	#386	C₂²×C₂₃	1	1	yes	characteristic
555	#386	C₂²×C₂₃	1	1	yes	characteristic
556	#385	C₂²×C₂₃	1	2	yes	—
557	#385	C₂²×C₂₃	1	2	yes	—
558	#385	C₂²×C₂₃	1	2	yes	—
559	#385	C₂²×C₂₃	1	2	yes	—
560	#385	C₂²×C₂₃	1	2	yes	complemented
561	#385	C₂²×C₂₃	1	2	yes	complemented
562	#385	C₂²×C₂₃	1	2	yes	complemented
563	#385	C₂²×C₂₃	1	2	yes	complemented
564	#385	C₂²×C₂₃	1	2	yes	complemented
565	#385	C₂²×C₂₃	1	2	yes	complemented
566	#385	C₂²×C₂₃	1	2	yes	complemented
567	#385	C₂²×C₂₃	1	2	yes	complemented
568	#381	C₂²×C₂₃	1	2	yes	—
569	#380	C₂²×C₂₃	1	2	yes	—
570	#380	C₂²×C₂₃	1	2	yes	—
571	#380	C₂²×C₂₃	1	2	yes	complemented
572	#380	C₂²×C₂₃	1	2	yes	complemented
573	#380	C₂²×C₂₃	1	2	yes	complemented
574	#380	C₂²×C₂₃	1	2	yes	complemented
575	#379	C₂²×C₂₃	1	2	yes	—
576	#379	C₂²×C₂₃	1	2	yes	—
577	#379	C₂²×C₂₃	1	2	yes	—
578	C₂×#95	C₂²×C₂₃	1	2	yes	—
579	C₂×C₂₃	—	2	4	no	—
580	C₂×C₂₃	—	4	2	no	—
581	C₂×C₂₃	—	4	2	no	—
582	C₂×C₂₃	—	4	2	no	—
583	C₂×C₂₃	—	4	2	no	—
584	C₂×C₂₃	C₂×#543	1	1	yes	characteristic
585	C₂×C₂₃	#3501	1	2	yes	—
586	C₂×C₂₃	#3532	1	1	yes	characteristic
587	C₂×C₂₃	#3533	1	1	yes	characteristic
588	C₂×C₂₃	#3542	1	2	yes	—
589	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
590	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
591	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
592	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₂²×D₄	—	4	2	no	—
594	C₂²×D₄	—	4	2	no	—
595	C₂²×D₄	Q₈×C₂₃	1	8	yes	complemented
596	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
600	C₂³×C₄	—	4	4	no	—
601	C₂³×C₄	—	4	2	no	—
602	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
603	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
606	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
607	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
609	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂²⋊Q₈	—	4	4	no	—
612	C₂²⋊Q₈	—	4	4	no	—
613	C₂²⋊Q₈	—	4	4	no	—
614	C₂²⋊Q₈	—	4	4	no	—
615	C₂²⋊Q₈	—	4	4	no	—
616	C₂²⋊Q₈	—	4	4	no	—
617	#117	—	4	2	no	—
618	#117	—	4	2	no	—
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₂²⋊C₄	—	4	4	no	—
641	C₂×C₂²⋊C₄	—	4	2	no	—
642	C₂×C₂²⋊C₄	—	4	2	no	—
643	C₂×C₂²⋊C₄	—	4	2	no	—
644	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
689	#95	C₂³×C₂₃	1	2	yes	—
690	#95	C₂³×C₂₃	1	2	yes	—
691	#95	C₂³×C₂₃	1	2	yes	—
692	#95	C₂³×C₂₃	1	2	yes	—
693	C₂₃	#36747	1	1	yes	characteristic, direct product factor, Sylow
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	2	no	—
696	C₂⁴	—	2	2	no	—
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	4	2	no	—
699	C₂⁴	—	4	2	no	—
700	C₂⁴	—	4	2	no	—
701	C₂⁴	—	4	2	no	—
702	C₂⁴	C₂×Q₈×C₂₃	1	4	yes	—
703	C₂⁴	C₂×Q₈×C₂₃	1	4	yes	—
704	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
705	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
707	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
708	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×D₄	—	4	16	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	1	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
725	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
726	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
727	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	16	no	—
751	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
752	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	1	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	4	1	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	1	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	1	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	1	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₄²	—	4	1	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	1	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	8	no	—
835	C₂³	—	2	8	no	—
836	C₂³	—	4	8	no	—
837	C₂³	—	4	8	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	4	8	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	2	no	—
843	C₂³	—	8	4	no	—
844	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
845	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
846	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
847	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
848	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
849	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
850	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
851	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
852	Q₈	—	8	4	no	—
853	Q₈	—	8	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	4	no	—
856	D₄	—	4	4	no	—
857	D₄	—	4	4	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	8	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	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	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	4	8	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	4	no	—
906	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
907	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
908	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
909	C₂²	—	2	4	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	4	16	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	8	8	no	—
935	C₂²	C₂₃×#543	1	4	yes	—
936	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
937	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
938	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
939	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
940	C₂²	C₂₃×#585	1	2	yes	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₂	—	2	4	no	—
956	C₂	—	4	2	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	4	2	no	—
960	C₂	C₂×C₂₃×#543	1	1	yes	characteristic
961	C₂	C₂₃×#3501	1	2	yes	—
962	C₂	C₂₃×#3532	1	1	yes	characteristic
963	C₂	C₂₃×#3533	1	1	yes	characteristic
964	C₂	C₂₃×#3542	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2848	C₂	semidirect
2. C₂₃×#2804	C₂	semidirect
3. C₂₃×#2784	C₂	semidirect
4. C₂₃×#2780	C₂	semidirect
5. C₂₃×#2780	C₂	semidirect
6. C₂₃×#2748	C₂	semidirect
7. C₂₃×#2748	C₂	semidirect
8. C₂₃×#2732	C₂	semidirect
9. C₂₃×#2692	C₂	semidirect
10. C₂₃×#2692	C₂	semidirect
11. C₂₃×#2683	C₂	semidirect
12. C₂₃×#2626	C₂	semidirect
13. C₂₃×#2438	C₂	semidirect
14. C₂₃×#2438	C₂	semidirect
15. C₂₃×#2437	C₂	semidirect
16. C₂₃×#2437	C₂	semidirect
24. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
34. C₂₃×#400	C₂²	semidirect
35. C₂₃×#400	C₂²	semidirect
36. C₂₃×#399	C₂²	semidirect
37. C₂₃×#399	C₂²	semidirect
38. C₂₃×#399	C₂²	semidirect
39. C₂₃×#399	C₂²	semidirect
40. C₂₃×#398	C₂²	semidirect
41. C₂₃×#398	C₂²	semidirect
42. C₂₃×#398	C₂²	semidirect
43. C₂₃×#398	C₂²	semidirect
44. C₂₃×#396	C₂²	semidirect
45. C₂₃×#396	C₂²	semidirect
46. C₂₃×#396	C₂²	semidirect
47. C₂₃×#396	C₂²	semidirect
48. C₂₃×#396	C₂²	semidirect
49. C₂₃×#396	C₂²	semidirect
50. C₂₃×#396	C₂²	semidirect
51. C₂₃×#396	C₂²	semidirect
52. C₂₃×#395	C₂²	semidirect
53. C₂₃×#395	C₂²	semidirect
54. C₂₃×#393	C₂²	semidirect
55. C₂₃×#393	C₂²	semidirect
56. C₂₃×#393	C₂²	semidirect
57. C₂₃×#393	C₂²	semidirect
58. C₂₃×#391	C₂²	semidirect
59. C₂₃×#391	C₂²	semidirect
66. C₂₃×#389	C₂²	semidirect
67. C₂₃×#389	C₂²	semidirect
68. C₂₃×#387	C₂²	semidirect
69. C₂₃×#387	C₂²	semidirect
70. C₂₃×#387	C₂²	semidirect
71. C₂₃×#387	C₂²	semidirect
88. C₂₃×#385	C₂²	semidirect
89. C₂₃×#385	C₂²	semidirect
90. C₂₃×#385	C₂²	semidirect
91. C₂₃×#385	C₂²	semidirect
92. C₂₃×#385	C₂²	semidirect
93. C₂₃×#385	C₂²	semidirect
94. C₂₃×#385	C₂²	semidirect
95. C₂₃×#385	C₂²	semidirect
99. C₂₃×#380	C₂²	semidirect
100. C₂₃×#380	C₂²	semidirect
101. C₂₃×#380	C₂²	semidirect
102. C₂₃×#380	C₂²	semidirect
113. C₂²×D₄×C₂₃	Q₈	semidirect
333. #36747	C₂₃	direct (N × H)
427. #2848	C₂×C₂₃	semidirect
428. #2804	C₂×C₂₃	semidirect
429. #2784	C₂×C₂₃	semidirect
430. #2780	C₂×C₂₃	semidirect
431. #2780	C₂×C₂₃	semidirect
432. #2748	C₂×C₂₃	semidirect
433. #2748	C₂×C₂₃	semidirect
434. #2732	C₂×C₂₃	semidirect
435. #2692	C₂×C₂₃	semidirect
436. #2692	C₂×C₂₃	semidirect
437. #2683	C₂×C₂₃	semidirect
438. #2626	C₂×C₂₃	semidirect
439. #2438	C₂×C₂₃	semidirect
440. #2438	C₂×C₂₃	semidirect
441. #2437	C₂×C₂₃	semidirect
442. #2437	C₂×C₂₃	semidirect
496. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
497. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
498. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
499. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
506. #400	C₂²×C₂₃	semidirect
507. #400	C₂²×C₂₃	semidirect
508. #399	C₂²×C₂₃	semidirect
509. #399	C₂²×C₂₃	semidirect
510. #399	C₂²×C₂₃	semidirect
511. #399	C₂²×C₂₃	semidirect
512. #398	C₂²×C₂₃	semidirect
513. #398	C₂²×C₂₃	semidirect
514. #398	C₂²×C₂₃	semidirect
515. #398	C₂²×C₂₃	semidirect
516. #396	C₂²×C₂₃	semidirect
517. #396	C₂²×C₂₃	semidirect
518. #396	C₂²×C₂₃	semidirect
519. #396	C₂²×C₂₃	semidirect
520. #396	C₂²×C₂₃	semidirect
521. #396	C₂²×C₂₃	semidirect
522. #396	C₂²×C₂₃	semidirect
523. #396	C₂²×C₂₃	semidirect
524. #395	C₂²×C₂₃	semidirect
525. #395	C₂²×C₂₃	semidirect
526. #393	C₂²×C₂₃	semidirect
527. #393	C₂²×C₂₃	semidirect
528. #393	C₂²×C₂₃	semidirect
529. #393	C₂²×C₂₃	semidirect
530. #391	C₂²×C₂₃	semidirect
531. #391	C₂²×C₂₃	semidirect
538. #389	C₂²×C₂₃	semidirect
539. #389	C₂²×C₂₃	semidirect
540. #387	C₂²×C₂₃	semidirect
541. #387	C₂²×C₂₃	semidirect
542. #387	C₂²×C₂₃	semidirect
543. #387	C₂²×C₂₃	semidirect
560. #385	C₂²×C₂₃	semidirect
561. #385	C₂²×C₂₃	semidirect
562. #385	C₂²×C₂₃	semidirect
563. #385	C₂²×C₂₃	semidirect
564. #385	C₂²×C₂₃	semidirect
565. #385	C₂²×C₂₃	semidirect
566. #385	C₂²×C₂₃	semidirect
567. #385	C₂²×C₂₃	semidirect
571. #380	C₂²×C₂₃	semidirect
572. #380	C₂²×C₂₃	semidirect
573. #380	C₂²×C₂₃	semidirect
574. #380	C₂²×C₂₃	semidirect
595. C₂²×D₄	Q₈×C₂₃	semidirect
693. C₂₃	#36747	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×#2848	2
C₂₃×#2804	2
C₂₃×#2784	2
C₂₃×#2780	2
C₂₃×#2748	2
C₂₃×#2732	2
C₂₃×#2692	2
C₂₃×#2683	2
C₂₃×#2626	2
C₂₃×#2438	2
C₂₃×#2437	2
C₂₃×#2309	2
C₂₃×#2308	2
C₂×C₂₃×#386	2
#36747	23

Subgroups — C23×#36747 #19184373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36747 #19184373