Subgroups — C₂₃×#60235 #19207861

Order 5888.

2094 conjugacy classes of subgroups.

The subgroup lattice has 936 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	C₂₃×#2981	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2980	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2979	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2977	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2976	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2929	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2924	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2880	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#131	C₂²	1	2	yes	—
19	C₂×C₂₃×#131	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#537	C₄	1	2	yes	—
25	C₂₃×#537	C₄	1	2	yes	—
26	C₂₃×#536	C₄	1	1	yes	characteristic
27	C₂₃×#536	C₄	1	1	yes	characteristic
28	C₂₃×#536	C₄	1	2	yes	—
29	C₂₃×#535	C₄	1	2	yes	—
30	C₂₃×#535	C₄	1	1	yes	characteristic
31	C₂₃×#535	C₄	1	1	yes	characteristic
32	C₂₃×#534	C₄	1	2	yes	—
33	C₂₃×#534	C₄	1	2	yes	—
34	C₂₃×#532	C₂²	1	2	yes	—
35	C₂₃×#532	C₂²	1	2	yes	—
36	C₂₃×#525	C₂²	1	2	yes	—
37	C₂₃×#525	C₂²	1	2	yes	—
38	C₂₃×#525	C₂²	1	2	yes	—
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
41	C₂₃×#436	C₂²	1	4	yes	complemented
42	C₂₃×#436	C₂²	1	4	yes	complemented
43	C₂₃×#436	C₂²	1	4	yes	complemented
44	C₂₃×#436	C₂²	1	4	yes	complemented
45	C₂₃×#435	C₂²	1	4	yes	complemented
46	C₂₃×#435	C₂²	1	4	yes	complemented
47	C₂₃×#435	C₂²	1	4	yes	complemented
48	C₂₃×#435	C₂²	1	4	yes	complemented
49	C₂₃×#435	C₂²	1	4	yes	complemented
50	C₂₃×#435	C₂²	1	4	yes	complemented
51	C₂₃×#435	C₂²	1	4	yes	complemented
52	C₂₃×#435	C₂²	1	4	yes	complemented
53	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
54	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
55	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
56	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
57	C₂₃×#433	C₂²	1	4	yes	complemented
58	C₂₃×#433	C₂²	1	4	yes	complemented
59	C₂₃×#432	C₂²	1	4	yes	complemented
60	C₂₃×#431	C₂²	1	4	yes	complemented
61	C₂₃×#424	C₂²	1	2	yes	complemented
62	C₂₃×#424	C₂²	1	2	yes	complemented
63	C₂₃×#408	C₂²	1	2	yes	—
64	C₂₃×#408	C₂²	1	2	yes	—
65	C₂₃×#408	C₂²	1	2	yes	—
66	C₂₃×#408	C₂²	1	2	yes	—
67	C₂₃×#408	C₂²	1	1	yes	characteristic
68	C₂₃×#408	C₂²	1	2	yes	—
69	C₂₃×#408	C₂²	1	1	yes	characteristic
70	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#408	C₂²	1	2	yes	complemented
72	C₂₃×#408	C₂²	1	4	yes	complemented
73	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#408	C₂²	1	4	yes	complemented
75	C₂₃×#408	C₂²	1	2	yes	complemented
76	C₂₃×#408	C₂²	1	2	yes	complemented
77	C₂₃×#407	C₂²	1	2	yes	—
78	C₂₃×#407	C₂²	1	2	yes	complemented
79	C₂₃×#407	C₂²	1	4	yes	complemented
80	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
81	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
82	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
83	C₂₃×#405	C₂²	1	2	yes	complemented
84	C₂₃×#405	C₂²	1	2	yes	complemented
85	C₂×#41×C₂₃	—	4	2	no	—
86	C₂×#41×C₂₃	—	4	2	no	—
87	C₂×#41×C₂₃	—	4	2	no	—
88	C₂×#41×C₂₃	—	4	2	no	—
89	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
90	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
91	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
92	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
94	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	2	yes	—
96	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
103	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
104	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
105	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
106	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
107	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂₃×#131	—	4	4	no	—
113	C₂₃×#131	—	4	4	no	—
114	C₂×M₁₆×C₂₃	—	4	2	no	—
115	C₂×M₁₆×C₂₃	—	4	2	no	—
116	C₂×M₁₆×C₂₃	—	4	2	no	—
117	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
118	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
125	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
126	C₂²×C₈×C₂₃	—	4	2	no	—
127	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
128	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
129	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
131	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
135	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
136	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
138	C₂₃×#127	C₂×C₄	1	2	yes	—
139	C₂₃×#127	C₂×C₄	1	2	yes	—
140	C₂₃×#124	C₂×C₄	1	2	yes	—
141	C₂₃×#124	C₂×C₄	1	2	yes	—
142	C₂₃×#124	C₂×C₄	1	2	yes	—
143	C₂₃×#124	C₂×C₄	1	2	yes	—
144	C₂₃×#123	C₂×C₄	1	4	yes	—
145	C₂₃×#123	C₂×C₄	1	4	yes	—
146	C₂₃×#123	C₂×C₄	1	2	yes	—
147	C₂₃×#123	C₂×C₄	1	2	yes	—
148	C₂₃×#123	C₂×C₄	1	2	yes	—
149	C₂₃×#123	C₂×C₄	1	2	yes	—
150	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
151	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
153	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
154	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
155	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
156	C₂₃×#121	C₂×C₄	1	2	yes	—
157	C₂₃×#121	C₂×C₄	1	2	yes	—
158	C₂₃×#121	C₂×C₄	1	2	yes	—
159	C₂₃×#121	C₂×C₄	1	2	yes	—
160	C₂₃×#121	C₂×C₄	1	4	yes	—
161	C₂₃×#121	C₂×C₄	1	4	yes	—
162	C₂₃×#121	C₂×C₄	1	4	yes	—
163	C₂₃×#121	C₂×C₄	1	4	yes	—
164	C₂₃×#121	C₂×C₄	1	4	yes	—
165	C₂₃×#121	C₂×C₄	1	4	yes	—
166	C₂₃×#120	C₂×C₄	1	4	yes	—
167	C₂₃×#120	C₂×C₄	1	4	yes	—
168	C₂₃×#120	C₂×C₄	1	2	yes	—
169	C₂₃×#120	C₂×C₄	1	2	yes	—
170	C₂₃×#120	C₂×C₄	1	2	yes	—
171	C₂₃×#120	C₂×C₄	1	2	yes	—
172	C₄×D₄×C₂₃	C₂³	1	4	yes	—
173	C₄×D₄×C₂₃	C₂³	1	4	yes	—
174	C₄×D₄×C₂₃	C₂³	1	4	yes	—
175	C₄×D₄×C₂₃	C₂³	1	4	yes	—
176	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
177	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
178	C₂₃×#117	C₂×C₄	1	2	yes	—
179	C₂₃×#117	C₂³	1	2	yes	—
180	C₂₃×#117	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
183	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
184	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
185	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
186	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
187	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
199	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
201	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
202	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
203	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
204	C₂₃×#97	C₂³	1	4	yes	—
205	C₂₃×#97	C₂³	1	4	yes	—
206	C₄×C₈×C₂₃	C₂³	1	4	yes	—
207	C₄×C₈×C₂₃	C₂³	1	4	yes	—
208	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
209	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
210	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
211	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
212	#41×C₂₃	—	2	4	no	—
213	#41×C₂₃	—	2	4	no	—
214	#41×C₂₃	—	4	2	no	—
215	#41×C₂₃	—	4	2	no	—
216	#41×C₂₃	—	4	2	no	—
217	#41×C₂₃	—	4	2	no	—
218	#41×C₂₃	—	4	1	no	—
219	#41×C₂₃	—	4	1	no	—
220	#41×C₂₃	—	4	1	no	—
221	#41×C₂₃	—	4	1	no	—
222	#41×C₂₃	—	4	1	no	—
223	#41×C₂₃	—	4	1	no	—
224	#41×C₂₃	—	4	2	no	—
225	#41×C₂₃	—	4	2	no	—
226	#41×C₂₃	—	4	1	no	—
227	#41×C₂₃	—	4	1	no	—
228	#41×C₂₃	—	4	4	no	—
229	#41×C₂₃	—	4	4	no	—
230	C₂×Q₈×C₂₃	—	4	2	no	—
231	C₂×Q₈×C₂₃	—	4	2	no	—
232	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
233	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
234	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
235	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
236	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
237	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
238	C₂×D₄×C₂₃	—	4	2	no	—
239	C₂×D₄×C₂₃	—	4	2	no	—
240	C₂×D₄×C₂₃	—	4	2	no	—
241	C₂×D₄×C₂₃	—	4	2	no	—
242	C₂×D₄×C₂₃	—	4	4	no	—
243	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
244	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
245	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
246	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
247	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
248	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
249	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
250	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
251	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
252	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
253	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
254	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
255	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
256	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
257	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
258	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
259	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
260	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
261	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
262	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	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	—	4	2	no	—
270	C₂²×C₄×C₂₃	—	4	2	no	—
271	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
281	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
282	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	M₁₆×C₂₃	—	2	4	no	—
292	M₁₆×C₂₃	—	2	4	no	—
293	M₁₆×C₂₃	—	4	1	no	—
294	M₁₆×C₂₃	—	4	2	no	—
295	M₁₆×C₂₃	—	4	1	no	—
296	M₁₆×C₂₃	—	4	2	no	—
297	M₁₆×C₂₃	—	4	2	no	—
298	M₁₆×C₂₃	—	4	4	no	—
299	M₁₆×C₂₃	—	4	4	no	—
300	C₂×C₈×C₂₃	—	2	4	no	—
301	C₂×C₈×C₂₃	—	2	4	no	—
302	C₂×C₈×C₂₃	—	4	1	no	—
303	C₂×C₈×C₂₃	—	4	2	no	—
304	C₂×C₈×C₂₃	—	4	1	no	—
305	C₂×C₈×C₂₃	—	4	2	no	—
306	C₂×C₈×C₂₃	—	4	2	no	—
307	C₂×C₈×C₂₃	—	4	4	no	—
308	C₂×C₈×C₂₃	—	4	4	no	—
309	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
310	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
313	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
314	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
316	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
317	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
318	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
319	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
320	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
322	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
323	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
324	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
325	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
326	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
327	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
328	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
329	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
330	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
331	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
332	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
333	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
334	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
335	C₄²×C₂₃	C₂⁴	1	4	yes	—
336	#60235	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	4	2	no	—
341	C₂³×C₂₃	—	4	2	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	4	2	no	—
344	C₂³×C₂₃	—	4	4	no	—
345	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
346	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
347	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
348	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
349	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
350	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
351	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
352	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
353	Q₈×C₂₃	—	2	4	no	—
354	Q₈×C₂₃	—	4	1	no	—
355	Q₈×C₂₃	—	4	1	no	—
356	Q₈×C₂₃	—	4	1	no	—
357	Q₈×C₂₃	—	4	1	no	—
358	Q₈×C₂₃	—	4	2	no	—
359	D₄×C₂₃	—	2	8	no	—
360	D₄×C₂₃	—	2	4	no	—
361	D₄×C₂₃	—	4	1	no	—
362	D₄×C₂₃	—	4	1	no	—
363	D₄×C₂₃	—	4	1	no	—
364	D₄×C₂₃	—	4	1	no	—
365	D₄×C₂₃	—	4	2	no	—
366	D₄×C₂₃	—	4	1	no	—
367	D₄×C₂₃	—	4	1	no	—
368	D₄×C₂₃	—	4	1	no	—
369	D₄×C₂₃	—	4	1	no	—
370	D₄×C₂₃	—	4	1	no	—
371	D₄×C₂₃	—	4	1	no	—
372	D₄×C₂₃	—	4	1	no	—
373	D₄×C₂₃	—	4	1	no	—
374	D₄×C₂₃	—	4	4	no	—
375	D₄×C₂₃	—	4	4	no	—
376	D₄×C₂₃	—	4	4	no	—
377	D₄×C₂₃	—	4	4	no	—
378	D₄×C₂₃	—	4	4	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	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	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	1	no	—
392	C₂×C₄×C₂₃	—	2	4	no	—
393	C₂×C₄×C₂₃	—	2	4	no	—
394	C₂×C₄×C₂₃	—	2	1	no	—
395	C₂×C₄×C₂₃	—	2	1	no	—
396	C₂×C₄×C₂₃	—	2	1	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	1	no	—
399	C₂×C₄×C₂₃	—	2	1	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	1	no	—
402	C₂×C₄×C₂₃	—	4	2	no	—
403	C₂×C₄×C₂₃	—	4	4	no	—
404	C₂×C₄×C₂₃	—	4	4	no	—
405	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
406	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
407	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
408	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
409	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
410	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
411	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
412	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
414	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
415	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
416	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
418	C₈×C₂₃	—	2	2	no	—
419	C₈×C₂₃	—	2	2	no	—
420	C₈×C₂₃	—	2	2	no	—
421	C₈×C₂₃	—	2	2	no	—
422	C₈×C₂₃	—	2	4	no	—
423	C₈×C₂₃	—	2	4	no	—
424	#3449	C₂×C₂₃	1	1	yes	characteristic
425	#2981	C₂×C₂₃	1	4	yes	complemented
426	#2980	C₂×C₂₃	1	2	yes	complemented
427	#2979	C₂×C₂₃	1	2	yes	complemented
428	#2978	C₂×C₂₃	1	2	yes	complemented
429	#2977	C₂×C₂₃	1	2	yes	complemented
430	#2976	C₂×C₂₃	1	4	yes	complemented
431	#2933	C₂×C₂₃	1	2	yes	complemented
432	#2933	C₂×C₂₃	1	2	yes	complemented
433	#2930	C₂×C₂₃	1	2	yes	complemented
434	#2929	C₂×C₂₃	1	2	yes	complemented
435	#2924	C₂×C₂₃	1	2	yes	complemented
436	#2880	C₂×C₂₃	1	2	yes	complemented
437	#2879	C₂×C₂₃	1	1	yes	characteristic, complemented
438	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	2	1	no	—
441	C₂²×C₂₃	—	2	1	no	—
442	C₂²×C₂₃	—	2	1	no	—
443	C₂²×C₂₃	—	2	1	no	—
444	C₂²×C₂₃	—	2	1	no	—
445	C₂²×C₂₃	—	2	1	no	—
446	C₂²×C₂₃	—	2	4	no	—
447	C₂²×C₂₃	—	2	2	no	—
448	C₂²×C₂₃	—	2	2	no	—
449	C₂²×C₂₃	—	2	2	no	—
450	C₂²×C₂₃	—	2	2	no	—
451	C₂²×C₂₃	—	2	2	no	—
452	C₂²×C₂₃	—	2	4	no	—
453	C₂²×C₂₃	—	2	4	no	—
454	C₂²×C₂₃	—	2	2	no	—
455	C₂²×C₂₃	—	4	4	no	—
456	C₂²×C₂₃	—	8	2	no	—
457	C₂²×C₂₃	—	8	2	no	—
458	C₂²×C₂₃	—	8	4	no	—
459	C₂²×C₂₃	#518	1	2	yes	—
460	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
461	C₄×C₂₃	—	2	1	no	—
462	C₄×C₂₃	—	2	1	no	—
463	C₄×C₂₃	—	2	1	no	—
464	C₄×C₂₃	—	2	1	no	—
465	C₄×C₂₃	—	2	1	no	—
466	C₄×C₂₃	—	2	1	no	—
467	C₄×C₂₃	—	2	4	no	—
468	C₄×C₂₃	—	2	4	no	—
469	C₄×C₂₃	—	2	4	no	—
470	C₄×C₂₃	#518	1	2	yes	—
471	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×#131	C₂²×C₂₃	1	2	yes	—
476	C₂×#131	C₂²×C₂₃	1	2	yes	—
477	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
480	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#537	C₄×C₂₃	1	2	yes	—
482	#537	C₄×C₂₃	1	2	yes	—
483	#536	C₄×C₂₃	1	1	yes	characteristic
484	#536	C₄×C₂₃	1	1	yes	characteristic
485	#536	C₄×C₂₃	1	2	yes	—
486	#535	C₄×C₂₃	1	2	yes	—
487	#535	C₄×C₂₃	1	1	yes	characteristic
488	#535	C₄×C₂₃	1	1	yes	characteristic
489	#534	C₄×C₂₃	1	2	yes	—
490	#534	C₄×C₂₃	1	2	yes	—
491	#532	C₂²×C₂₃	1	2	yes	—
492	#532	C₂²×C₂₃	1	2	yes	—
493	#525	C₂²×C₂₃	1	2	yes	—
494	#525	C₂²×C₂₃	1	2	yes	—
495	#525	C₂²×C₂₃	1	2	yes	—
496	#525	C₂²×C₂₃	1	2	yes	—
497	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
498	#436	C₂²×C₂₃	1	4	yes	complemented
499	#436	C₂²×C₂₃	1	4	yes	complemented
500	#436	C₂²×C₂₃	1	4	yes	complemented
501	#436	C₂²×C₂₃	1	4	yes	complemented
502	#435	C₂²×C₂₃	1	4	yes	complemented
503	#435	C₂²×C₂₃	1	4	yes	complemented
504	#435	C₂²×C₂₃	1	4	yes	complemented
505	#435	C₂²×C₂₃	1	4	yes	complemented
506	#435	C₂²×C₂₃	1	4	yes	complemented
507	#435	C₂²×C₂₃	1	4	yes	complemented
508	#435	C₂²×C₂₃	1	4	yes	complemented
509	#435	C₂²×C₂₃	1	4	yes	complemented
510	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
511	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
512	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
513	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
514	#433	C₂²×C₂₃	1	4	yes	complemented
515	#433	C₂²×C₂₃	1	4	yes	complemented
516	#432	C₂²×C₂₃	1	4	yes	complemented
517	#431	C₂²×C₂₃	1	4	yes	complemented
518	#424	C₂²×C₂₃	1	2	yes	complemented
519	#424	C₂²×C₂₃	1	2	yes	complemented
520	#408	C₂²×C₂₃	1	2	yes	—
521	#408	C₂²×C₂₃	1	1	yes	characteristic
522	#408	C₂²×C₂₃	1	1	yes	characteristic
523	#408	C₂²×C₂₃	1	2	yes	—
524	#408	C₂²×C₂₃	1	2	yes	—
525	#408	C₂²×C₂₃	1	2	yes	—
526	#408	C₂²×C₂₃	1	2	yes	—
527	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#408	C₂²×C₂₃	1	2	yes	complemented
530	#408	C₂²×C₂₃	1	2	yes	complemented
531	#408	C₂²×C₂₃	1	2	yes	complemented
532	#408	C₂²×C₂₃	1	4	yes	complemented
533	#408	C₂²×C₂₃	1	4	yes	complemented
534	#407	C₂²×C₂₃	1	2	yes	—
535	#407	C₂²×C₂₃	1	2	yes	complemented
536	#407	C₂²×C₂₃	1	4	yes	complemented
537	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
538	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
539	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
540	#405	C₂²×C₂₃	1	2	yes	complemented
541	#405	C₂²×C₂₃	1	2	yes	complemented
542	C₂×C₂₃	—	2	2	no	—
543	C₂×C₂₃	—	4	1	no	—
544	C₂×C₂₃	—	4	1	no	—
545	C₂×C₂₃	—	4	1	no	—
546	C₂×C₂₃	—	4	1	no	—
547	C₂×C₂₃	—	4	1	no	—
548	C₂×C₂₃	—	4	4	no	—
549	C₂×C₂₃	—	4	1	no	—
550	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
551	C₂×C₂₃	#3573	1	2	yes	—
552	C₂×#41	—	4	2	no	—
553	C₂×#41	—	4	2	no	—
554	C₂×#41	—	4	2	no	—
555	C₂×#41	—	4	2	no	—
556	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
557	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
558	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
559	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
560	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
561	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
562	C₂×#41	C₂³×C₂₃	1	2	yes	—
563	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
564	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
566	C₂×#41	C₂³×C₂₃	1	2	yes	—
567	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
568	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
569	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
570	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
571	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
572	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
573	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
574	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
579	#131	—	4	4	no	—
580	#131	—	4	4	no	—
581	C₂×M₁₆	—	4	2	no	—
582	C₂×M₁₆	—	4	2	no	—
583	C₂×M₁₆	—	4	2	no	—
584	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
585	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
586	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
588	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
589	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
590	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
591	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
592	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
593	C₂²×C₈	—	4	2	no	—
594	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
595	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
596	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
598	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
599	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
600	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
601	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
602	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
603	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
604	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
605	#127	C₂×C₄×C₂₃	1	2	yes	—
606	#127	C₂×C₄×C₂₃	1	2	yes	—
607	#124	C₂×C₄×C₂₃	1	2	yes	—
608	#124	C₂×C₄×C₂₃	1	2	yes	—
609	#124	C₂×C₄×C₂₃	1	2	yes	—
610	#124	C₂×C₄×C₂₃	1	2	yes	—
611	#123	C₂×C₄×C₂₃	1	4	yes	—
612	#123	C₂×C₄×C₂₃	1	4	yes	—
613	#123	C₂×C₄×C₂₃	1	2	yes	—
614	#123	C₂×C₄×C₂₃	1	2	yes	—
615	#123	C₂×C₄×C₂₃	1	2	yes	—
616	#123	C₂×C₄×C₂₃	1	2	yes	—
617	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
618	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
619	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
620	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
621	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
622	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
623	#121	C₂×C₄×C₂₃	1	2	yes	—
624	#121	C₂×C₄×C₂₃	1	2	yes	—
625	#121	C₂×C₄×C₂₃	1	2	yes	—
626	#121	C₂×C₄×C₂₃	1	2	yes	—
627	#121	C₂×C₄×C₂₃	1	4	yes	—
628	#121	C₂×C₄×C₂₃	1	4	yes	—
629	#121	C₂×C₄×C₂₃	1	4	yes	—
630	#121	C₂×C₄×C₂₃	1	4	yes	—
631	#121	C₂×C₄×C₂₃	1	4	yes	—
632	#121	C₂×C₄×C₂₃	1	4	yes	—
633	#120	C₂×C₄×C₂₃	1	4	yes	—
634	#120	C₂×C₄×C₂₃	1	4	yes	—
635	#120	C₂×C₄×C₂₃	1	2	yes	—
636	#120	C₂×C₄×C₂₃	1	2	yes	—
637	#120	C₂×C₄×C₂₃	1	2	yes	—
638	#120	C₂×C₄×C₂₃	1	2	yes	—
639	C₄×D₄	C₂³×C₂₃	1	4	yes	—
640	C₄×D₄	C₂³×C₂₃	1	4	yes	—
641	C₄×D₄	C₂³×C₂₃	1	4	yes	—
642	C₄×D₄	C₂³×C₂₃	1	4	yes	—
643	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
644	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
645	#117	C₂×C₄×C₂₃	1	2	yes	—
646	#117	C₂³×C₂₃	1	2	yes	—
647	#117	C₂³×C₂₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
651	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
652	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
654	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
655	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
656	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
659	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
660	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
662	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
663	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
665	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
667	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
670	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
671	#97	C₂³×C₂₃	1	4	yes	—
672	#97	C₂³×C₂₃	1	4	yes	—
673	C₄×C₈	C₂³×C₂₃	1	4	yes	—
674	C₄×C₈	C₂³×C₂₃	1	4	yes	—
675	C₂₃	#60235	1	1	yes	characteristic, direct product factor, Sylow
676	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
677	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
678	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
679	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	4	2	no	—
683	#41	—	4	2	no	—
684	#41	—	4	2	no	—
685	#41	—	4	2	no	—
686	#41	—	4	1	no	—
687	#41	—	4	1	no	—
688	#41	—	4	1	no	—
689	#41	—	4	1	no	—
690	#41	—	4	1	no	—
691	#41	—	4	1	no	—
692	#41	—	4	2	no	—
693	#41	—	4	2	no	—
694	#41	—	4	1	no	—
695	#41	—	4	1	no	—
696	#41	—	4	4	no	—
697	#41	—	4	4	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
701	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
702	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
703	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
704	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
705	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
712	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
713	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
714	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
715	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
716	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
717	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
718	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
719	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
720	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
721	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
722	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
723	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
724	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
725	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
726	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
727	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
728	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
729	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
730	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
740	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
741	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
742	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
743	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
746	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
747	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
748	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
749	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
750	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
758	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
759	M₁₆	—	2	4	no	—
760	M₁₆	—	2	4	no	—
761	M₁₆	—	4	1	no	—
762	M₁₆	—	4	2	no	—
763	M₁₆	—	4	1	no	—
764	M₁₆	—	4	2	no	—
765	M₁₆	—	4	2	no	—
766	M₁₆	—	4	4	no	—
767	M₁₆	—	4	4	no	—
768	C₂×C₈	—	2	4	no	—
769	C₂×C₈	—	2	4	no	—
770	C₂×C₈	—	4	1	no	—
771	C₂×C₈	—	4	2	no	—
772	C₂×C₈	—	4	1	no	—
773	C₂×C₈	—	4	2	no	—
774	C₂×C₈	—	4	2	no	—
775	C₂×C₈	—	4	4	no	—
776	C₂×C₈	—	4	4	no	—
777	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
778	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
780	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
781	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
782	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
783	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
784	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
785	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
786	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
787	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
788	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
789	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
790	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
791	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
792	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
793	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
794	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
795	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
796	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
797	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
798	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
799	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
800	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
801	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
802	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
803	C₄²	C₂⁴×C₂₃	1	4	yes	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	4	no	—
812	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
813	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
814	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
815	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
816	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
817	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
818	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
819	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
820	Q₈	—	2	4	no	—
821	Q₈	—	4	1	no	—
822	Q₈	—	4	1	no	—
823	Q₈	—	4	1	no	—
824	Q₈	—	4	1	no	—
825	Q₈	—	4	2	no	—
826	D₄	—	2	8	no	—
827	D₄	—	2	4	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	2	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	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	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	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	—	4	2	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
873	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
874	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
875	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
876	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
877	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
878	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
879	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
880	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
881	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
882	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
883	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
884	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
885	C₈	—	2	2	no	—
886	C₈	—	2	2	no	—
887	C₈	—	2	2	no	—
888	C₈	—	2	2	no	—
889	C₈	—	2	4	no	—
890	C₈	—	2	4	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	4	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	8	2	no	—
909	C₂²	—	8	2	no	—
910	C₂²	—	8	4	no	—
911	C₂²	C₂₃×#518	1	2	yes	—
912	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	4	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	4	no	—
922	C₄	C₂₃×#518	1	2	yes	—
923	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
924	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
925	C₂	—	2	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	4	1	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	1	no	—
930	C₂	—	4	1	no	—
931	C₂	—	4	1	no	—
932	C₂	—	4	4	no	—
933	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
934	C₂	C₂₃×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2981	C₂	semidirect
3. C₂₃×#2980	C₂	semidirect
4. C₂₃×#2979	C₂	semidirect
5. C₂₃×#2978	C₂	semidirect
6. C₂₃×#2977	C₂	semidirect
7. C₂₃×#2976	C₂	semidirect
8. C₂₃×#2933	C₂	semidirect
9. C₂₃×#2933	C₂	semidirect
10. C₂₃×#2930	C₂	semidirect
11. C₂₃×#2929	C₂	semidirect
12. C₂₃×#2924	C₂	semidirect
13. C₂₃×#2880	C₂	semidirect
14. C₂₃×#2879	C₂	semidirect
15. C₂×C₂₃×#408	C₂	semidirect
20. C₂²×M₁₆×C₂₃	C₂²	semidirect
21. C₂²×M₁₆×C₂₃	C₂²	semidirect
22. C₂²×M₁₆×C₂₃	C₂²	semidirect
23. C₂³×C₈×C₂₃	C₂²	semidirect
41. C₂₃×#436	C₂²	semidirect
42. C₂₃×#436	C₂²	semidirect
43. C₂₃×#436	C₂²	semidirect
44. C₂₃×#436	C₂²	semidirect
45. C₂₃×#435	C₂²	semidirect
46. C₂₃×#435	C₂²	semidirect
47. C₂₃×#435	C₂²	semidirect
48. C₂₃×#435	C₂²	semidirect
49. C₂₃×#435	C₂²	semidirect
50. C₂₃×#435	C₂²	semidirect
51. C₂₃×#435	C₂²	semidirect
52. C₂₃×#435	C₂²	semidirect
53. C₈×D₄×C₂₃	C₂²	semidirect
54. C₈×D₄×C₂₃	C₂²	semidirect
55. C₈×D₄×C₂₃	C₂²	semidirect
56. C₈×D₄×C₂₃	C₂²	semidirect
57. C₂₃×#433	C₂²	semidirect
58. C₂₃×#433	C₂²	semidirect
59. C₂₃×#432	C₂²	semidirect
60. C₂₃×#431	C₂²	semidirect
61. C₂₃×#424	C₂²	semidirect
62. C₂₃×#424	C₂²	semidirect
70. C₂₃×#408	C₂²	semidirect
71. C₂₃×#408	C₂²	semidirect
72. C₂₃×#408	C₂²	semidirect
73. C₂₃×#408	C₂²	semidirect
74. C₂₃×#408	C₂²	semidirect
75. C₂₃×#408	C₂²	semidirect
76. C₂₃×#408	C₂²	semidirect
78. C₂₃×#407	C₂²	semidirect
79. C₂₃×#407	C₂²	semidirect
81. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
82. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
83. C₂₃×#405	C₂²	semidirect
84. C₂₃×#405	C₂²	semidirect
336. #60235	C₂₃	direct (N × H)
425. #2981	C₂×C₂₃	semidirect
426. #2980	C₂×C₂₃	semidirect
427. #2979	C₂×C₂₃	semidirect
428. #2978	C₂×C₂₃	semidirect
429. #2977	C₂×C₂₃	semidirect
430. #2976	C₂×C₂₃	semidirect
431. #2933	C₂×C₂₃	semidirect
432. #2933	C₂×C₂₃	semidirect
433. #2930	C₂×C₂₃	semidirect
434. #2929	C₂×C₂₃	semidirect
435. #2924	C₂×C₂₃	semidirect
436. #2880	C₂×C₂₃	semidirect
437. #2879	C₂×C₂₃	semidirect
438. C₂×#408	C₂×C₂₃	semidirect
477. C₂²×M₁₆	C₂²×C₂₃	semidirect
478. C₂²×M₁₆	C₂²×C₂₃	semidirect
479. C₂²×M₁₆	C₂²×C₂₃	semidirect
480. C₂³×C₈	C₂²×C₂₃	semidirect
498. #436	C₂²×C₂₃	semidirect
499. #436	C₂²×C₂₃	semidirect
500. #436	C₂²×C₂₃	semidirect
501. #436	C₂²×C₂₃	semidirect
502. #435	C₂²×C₂₃	semidirect
503. #435	C₂²×C₂₃	semidirect
504. #435	C₂²×C₂₃	semidirect
505. #435	C₂²×C₂₃	semidirect
506. #435	C₂²×C₂₃	semidirect
507. #435	C₂²×C₂₃	semidirect
508. #435	C₂²×C₂₃	semidirect
509. #435	C₂²×C₂₃	semidirect
510. C₈×D₄	C₂²×C₂₃	semidirect
511. C₈×D₄	C₂²×C₂₃	semidirect
512. C₈×D₄	C₂²×C₂₃	semidirect
513. C₈×D₄	C₂²×C₂₃	semidirect
514. #433	C₂²×C₂₃	semidirect
515. #433	C₂²×C₂₃	semidirect
516. #432	C₂²×C₂₃	semidirect
517. #431	C₂²×C₂₃	semidirect
518. #424	C₂²×C₂₃	semidirect
519. #424	C₂²×C₂₃	semidirect
527. #408	C₂²×C₂₃	semidirect
528. #408	C₂²×C₂₃	semidirect
529. #408	C₂²×C₂₃	semidirect
530. #408	C₂²×C₂₃	semidirect
531. #408	C₂²×C₂₃	semidirect
532. #408	C₂²×C₂₃	semidirect
533. #408	C₂²×C₂₃	semidirect
535. #407	C₂²×C₂₃	semidirect
536. #407	C₂²×C₂₃	semidirect
538. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
539. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
540. #405	C₂²×C₂₃	semidirect
541. #405	C₂²×C₂₃	semidirect
675. C₂₃	#60235	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
C₂₃×#2981	2
C₂₃×#2980	2
C₂₃×#2979	2
C₂₃×#2978	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2933	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂₃×#2924	2
C₂₃×#2880	2
C₂₃×#2879	2
C₂×C₂₃×#408	2
#60235	23

Subgroups — C23×#60235 #19207861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60235 #19207861