Subgroups — C₂₃×#60273 #19207899

Order 5888.

1826 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2993	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2991	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2989	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2924	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2905	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×#131	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
21	C₂₃×#556	C₄	1	1	yes	characteristic
22	C₂₃×#555	C₄	1	1	yes	characteristic
23	C₂₃×#554	C₄	1	1	yes	characteristic
24	C₂₃×#553	C₄	1	2	yes	—
25	C₂₃×#552	C₄	1	2	yes	—
26	C₂₃×#552	C₄	1	2	yes	—
27	C₂₃×#551	C₄	1	4	yes	—
28	C₂₃×#547	C₄	1	1	yes	characteristic
29	C₂₃×#546	C₄	1	2	yes	—
30	C₂₃×#533	C₂²	1	1	yes	characteristic
31	C₂₃×#529	C₂²	1	2	yes	—
32	C₂₃×#529	C₂²	1	4	yes	—
33	C₂₃×#525	C₂²	1	2	yes	—
34	C₄×#41×C₂₃	C₂²	1	2	yes	—
35	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#117	C₂²	1	2	yes	—
38	C₂₃×#446	C₂²	1	2	yes	complemented
39	C₂₃×#446	C₂²	1	2	yes	complemented
40	C₂₃×#446	C₂²	1	2	yes	complemented
41	C₂₃×#446	C₂²	1	4	yes	complemented
42	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
43	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
44	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
45	C₂₃×#436	C₂²	1	1	yes	characteristic
46	C₂₃×#436	C₂²	1	1	yes	characteristic
47	C₂₃×#436	C₂²	1	1	yes	characteristic
48	C₂₃×#436	C₂²	1	2	yes	—
49	C₂₃×#436	C₂²	1	1	yes	characteristic
50	C₂₃×#436	C₂²	1	2	yes	—
51	C₂₃×#436	C₂²	1	2	yes	—
52	C₂₃×#436	C₂²	1	4	yes	complemented
53	C₂₃×#436	C₂²	1	4	yes	complemented
54	C₂₃×#436	C₂²	1	4	yes	complemented
55	C₂₃×#435	C₂²	1	4	yes	—
56	C₂₃×#435	C₂²	1	4	yes	complemented
57	C₂₃×#435	C₂²	1	4	yes	complemented
58	C₂₃×#435	C₂²	1	4	yes	complemented
59	C₂₃×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₂₃	C₂²	1	2	yes	—
61	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
62	C₂₃×#433	C₂²	1	2	yes	complemented
63	C₂₃×#433	C₂²	1	2	yes	complemented
64	C₂₃×#433	C₂²	1	4	yes	complemented
65	C₂₃×#433	C₂²	1	4	yes	complemented
66	C₂₃×#432	C₂²	1	4	yes	complemented
67	C₂₃×#431	C₂²	1	2	yes	complemented
68	C₂₃×#431	C₂²	1	2	yes	complemented
69	C₂₃×#431	C₂²	1	4	yes	complemented
70	C₂₃×#424	C₂²	1	1	yes	characteristic
71	C₂₃×#424	C₂²	1	1	yes	characteristic
72	C₂₃×#424	C₂²	1	2	yes	—
73	C₂₃×#424	C₂²	1	2	yes	—
74	C₂₃×#424	C₂²	1	2	yes	—
75	C₂₃×#424	C₂²	1	4	yes	complemented
76	C₂₃×#424	C₂²	1	4	yes	complemented
77	C₂₃×#424	C₂²	1	4	yes	complemented
78	C₂₃×#423	C₂²	1	1	yes	characteristic
79	C₂₃×#423	C₂²	1	4	yes	complemented
80	C₂₃×#423	C₂²	1	2	yes	complemented
81	C₂₃×#423	C₂²	1	4	yes	complemented
82	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
83	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
84	C₂₃×#408	C₂²	1	1	yes	characteristic
85	C₂₃×#408	C₂²	1	1	yes	characteristic
86	C₂₃×#407	C₂²	1	2	yes	—
87	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
88	C₂₃×#405	C₂²	1	2	yes	—
89	C₂₃×#405	C₂²	1	2	yes	—
90	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
92	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
93	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
96	C₂₃×#131	—	4	4	no	—
97	C₂×M₁₆×C₂₃	—	4	4	no	—
98	C₂×M₁₆×C₂₃	—	4	4	no	—
99	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
108	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
112	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
113	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₂₃×#126	C₂×C₄	1	4	yes	—
116	C₂₃×#126	C₂×C₄	1	4	yes	—
117	C₂₃×#126	C₂×C₄	1	4	yes	—
118	C₂₃×#125	C₂×C₄	1	4	yes	—
119	C₂₃×#125	C₂×C₄	1	2	yes	—
120	C₂₃×#125	C₂×C₄	1	2	yes	—
121	C₂₃×#124	C₂×C₄	1	4	yes	—
122	C₂₃×#124	C₂×C₄	1	2	yes	—
123	C₂₃×#123	C₂×C₄	1	4	yes	—
124	C₂₃×#123	C₂×C₄	1	4	yes	—
125	C₂₃×#123	C₂×C₄	1	4	yes	—
126	C₂₃×#123	C₂×C₄	1	4	yes	—
127	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
128	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
130	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
131	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
132	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
133	C₂₃×#121	C₂×C₄	1	2	yes	—
134	C₂₃×#121	C₂×C₄	1	2	yes	—
135	C₂₃×#121	C₂×C₄	1	4	yes	—
136	C₂₃×#121	C₂×C₄	1	2	yes	—
137	C₂₃×#120	C₂×C₄	1	4	yes	—
138	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
140	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
142	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
143	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
145	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
146	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
147	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
148	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
149	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
151	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₂₃	C₂³	1	4	yes	—
154	C₄×D₄×C₂₃	C₂³	1	2	yes	—
155	C₄×D₄×C₂₃	C₂³	1	4	yes	—
156	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂₃×#117	C₂×C₄	1	4	yes	—
158	C₂₃×#117	C₂×C₄	1	4	yes	—
159	C₂₃×#117	C₂×C₄	1	2	yes	—
160	C₂₃×#117	C₂×C₄	1	2	yes	—
161	C₂₃×#117	C₂×C₄	1	2	yes	—
162	C₂₃×#117	C₂³	1	2	yes	—
163	C₂₃×#117	C₂³	1	1	yes	characteristic
164	C₂₃×#117	C₂³	1	4	yes	—
165	C₂₃×#117	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
171	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
179	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
180	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊C₈	C₂³	1	4	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	2	yes	—
188	C₂₃×C₄⋊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	2	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	4	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	2	yes	—
198	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
199	C₂₃×#97	C₂³	1	2	yes	—
200	C₂₃×#97	C₂³	1	4	yes	—
201	C₂₃×#97	C₂³	1	4	yes	—
202	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
206	C₄×C₈×C₂₃	C₂³	1	2	yes	—
207	C₄×C₈×C₂₃	C₂³	1	4	yes	—
208	C₄×C₈×C₂₃	C₂³	1	4	yes	—
209	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
210	#41×C₂₃	—	2	2	no	—
211	#41×C₂₃	—	2	2	no	—
212	#41×C₂₃	—	4	4	no	—
213	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
214	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
215	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
216	C₂×D₄×C₂₃	—	4	2	no	—
217	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
219	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
221	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
222	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
224	C₂²×C₄×C₂₃	—	2	4	no	—
225	C₂²×C₄×C₂₃	—	2	4	no	—
226	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
233	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
234	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
235	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
239	M₁₆×C₂₃	—	2	2	no	—
240	M₁₆×C₂₃	—	2	4	no	—
241	M₁₆×C₂₃	—	2	2	no	—
242	M₁₆×C₂₃	—	4	2	no	—
243	M₁₆×C₂₃	—	4	2	no	—
244	M₁₆×C₂₃	—	4	2	no	—
245	M₁₆×C₂₃	—	4	2	no	—
246	M₁₆×C₂₃	—	4	4	no	—
247	M₁₆×C₂₃	—	4	4	no	—
248	C₂×C₈×C₂₃	—	2	2	no	—
249	C₂×C₈×C₂₃	—	2	4	no	—
250	C₂×C₈×C₂₃	—	2	2	no	—
251	C₂×C₈×C₂₃	—	4	4	no	—
252	C₂×C₈×C₂₃	—	4	4	no	—
253	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
254	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
255	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
263	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
264	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
265	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
266	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
268	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
269	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
270	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
271	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
272	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
273	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
274	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
279	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
280	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
284	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
285	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
286	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
287	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
288	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
289	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
291	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
293	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
294	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
295	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
296	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
297	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
298	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
299	C₄²×C₂₃	C₂⁴	1	2	yes	—
300	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₂₃	C₂⁴	1	4	yes	—
303	#60273	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₂₃	—	2	4	no	—
305	C₂³×C₂₃	—	4	2	no	—
306	C₂³×C₂₃	—	4	2	no	—
307	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
308	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
309	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
310	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
311	Q₈×C₂₃	—	2	2	no	—
312	Q₈×C₂₃	—	2	4	no	—
313	Q₈×C₂₃	—	4	2	no	—
314	D₄×C₂₃	—	2	4	no	—
315	D₄×C₂₃	—	2	2	no	—
316	D₄×C₂₃	—	2	2	no	—
317	D₄×C₂₃	—	2	2	no	—
318	D₄×C₂₃	—	4	2	no	—
319	D₄×C₂₃	—	4	4	no	—
320	D₄×C₂₃	—	4	4	no	—
321	C₂×C₄×C₂₃	—	2	4	no	—
322	C₂×C₄×C₂₃	—	2	4	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	4	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	4	2	no	—
333	C₂×C₄×C₂₃	—	4	4	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	4	no	—
336	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
338	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
340	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
341	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
343	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
344	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
345	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
346	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
351	C₈×C₂₃	—	2	2	no	—
352	C₈×C₂₃	—	2	1	no	—
353	C₈×C₂₃	—	2	1	no	—
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	2	4	no	—
357	C₈×C₂₃	—	2	1	no	—
358	C₈×C₂₃	—	2	1	no	—
359	C₈×C₂₃	—	2	2	no	—
360	#3475	C₂×C₂₃	1	1	yes	characteristic
361	#2995	C₂×C₂₃	1	4	yes	complemented
362	#2994	C₂×C₂₃	1	2	yes	complemented
363	#2993	C₂×C₂₃	1	2	yes	complemented
364	#2993	C₂×C₂₃	1	4	yes	complemented
365	#2991	C₂×C₂₃	1	2	yes	complemented
366	#2989	C₂×C₂₃	1	2	yes	complemented
367	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#2960	C₂×C₂₃	1	1	yes	characteristic, complemented
369	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#2933	C₂×C₂₃	1	2	yes	complemented
371	#2930	C₂×C₂₃	1	2	yes	complemented
372	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#2924	C₂×C₂₃	1	2	yes	complemented
374	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#2905	C₂×C₂₃	1	2	yes	complemented
377	C₂²×C₂₃	—	2	1	no	—
378	C₂²×C₂₃	—	2	1	no	—
379	C₂²×C₂₃	—	2	2	no	—
380	C₂²×C₂₃	—	2	2	no	—
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	2	2	no	—
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	2	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	2	2	no	—
388	C₂²×C₂₃	—	8	4	no	—
389	C₂²×C₂₃	#520	1	2	yes	—
390	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
391	C₄×C₂₃	—	2	2	no	—
392	C₄×C₂₃	—	2	2	no	—
393	C₄×C₂₃	—	2	2	no	—
394	C₄×C₂₃	—	2	2	no	—
395	C₄×C₂₃	—	2	1	no	—
396	C₄×C₂₃	—	2	4	no	—
397	C₄×C₂₃	—	2	1	no	—
398	C₄×C₂₃	—	2	2	no	—
399	C₄×C₂₃	—	2	4	no	—
400	C₄×C₂₃	—	2	1	no	—
401	C₄×C₂₃	#520	1	2	yes	—
402	C₄×C₂₃	#568	1	2	yes	—
403	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
404	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂×#131	C₂²×C₂₃	1	2	yes	—
406	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
407	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
408	#556	C₄×C₂₃	1	1	yes	characteristic
409	#555	C₄×C₂₃	1	1	yes	characteristic
410	#554	C₄×C₂₃	1	1	yes	characteristic
411	#553	C₄×C₂₃	1	2	yes	—
412	#552	C₄×C₂₃	1	2	yes	—
413	#552	C₄×C₂₃	1	2	yes	—
414	#551	C₄×C₂₃	1	4	yes	—
415	#547	C₄×C₂₃	1	1	yes	characteristic
416	#546	C₄×C₂₃	1	2	yes	—
417	#533	C₂²×C₂₃	1	1	yes	characteristic
418	#529	C₂²×C₂₃	1	2	yes	—
419	#529	C₂²×C₂₃	1	4	yes	—
420	#525	C₂²×C₂₃	1	2	yes	—
421	C₄×#41	C₂²×C₂₃	1	2	yes	—
422	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#117	C₂²×C₂₃	1	2	yes	—
425	#446	C₂²×C₂₃	1	2	yes	complemented
426	#446	C₂²×C₂₃	1	2	yes	complemented
427	#446	C₂²×C₂₃	1	2	yes	complemented
428	#446	C₂²×C₂₃	1	4	yes	complemented
429	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
430	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
431	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
432	#436	C₂²×C₂₃	1	1	yes	characteristic
433	#436	C₂²×C₂₃	1	1	yes	characteristic
434	#436	C₂²×C₂₃	1	1	yes	characteristic
435	#436	C₂²×C₂₃	1	2	yes	—
436	#436	C₂²×C₂₃	1	1	yes	characteristic
437	#436	C₂²×C₂₃	1	2	yes	—
438	#436	C₂²×C₂₃	1	2	yes	—
439	#436	C₂²×C₂₃	1	4	yes	complemented
440	#436	C₂²×C₂₃	1	4	yes	complemented
441	#436	C₂²×C₂₃	1	4	yes	complemented
442	#435	C₂²×C₂₃	1	4	yes	—
443	#435	C₂²×C₂₃	1	4	yes	complemented
444	#435	C₂²×C₂₃	1	4	yes	complemented
445	#435	C₂²×C₂₃	1	4	yes	complemented
446	#435	C₂²×C₂₃	1	4	yes	complemented
447	C₈×D₄	C₂²×C₂₃	1	2	yes	—
448	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
449	#433	C₂²×C₂₃	1	2	yes	complemented
450	#433	C₂²×C₂₃	1	2	yes	complemented
451	#433	C₂²×C₂₃	1	4	yes	complemented
452	#433	C₂²×C₂₃	1	4	yes	complemented
453	#432	C₂²×C₂₃	1	4	yes	complemented
454	#431	C₂²×C₂₃	1	2	yes	complemented
455	#431	C₂²×C₂₃	1	2	yes	complemented
456	#431	C₂²×C₂₃	1	4	yes	complemented
457	#424	C₂²×C₂₃	1	1	yes	characteristic
458	#424	C₂²×C₂₃	1	2	yes	—
459	#424	C₂²×C₂₃	1	2	yes	—
460	#424	C₂²×C₂₃	1	2	yes	—
461	#424	C₂²×C₂₃	1	1	yes	characteristic
462	#424	C₂²×C₂₃	1	4	yes	complemented
463	#424	C₂²×C₂₃	1	4	yes	complemented
464	#424	C₂²×C₂₃	1	4	yes	complemented
465	#423	C₂²×C₂₃	1	1	yes	characteristic
466	#423	C₂²×C₂₃	1	4	yes	complemented
467	#423	C₂²×C₂₃	1	4	yes	complemented
468	#423	C₂²×C₂₃	1	2	yes	complemented
469	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
471	#408	C₂²×C₂₃	1	1	yes	characteristic
472	#408	C₂²×C₂₃	1	1	yes	characteristic
473	#407	C₂²×C₂₃	1	2	yes	—
474	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
475	#405	C₂²×C₂₃	1	2	yes	—
476	#405	C₂²×C₂₃	1	2	yes	—
477	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×C₂₃	—	2	2	no	—
480	C₂×C₂₃	—	4	2	no	—
481	C₂×C₂₃	—	4	2	no	—
482	C₂×C₂₃	—	4	2	no	—
483	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
484	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
485	C₂×C₂₃	#3573	1	1	yes	characteristic
486	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
487	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
488	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
490	#131	—	4	4	no	—
491	C₂×M₁₆	—	4	4	no	—
492	C₂×M₁₆	—	4	4	no	—
493	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
495	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
497	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
498	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
499	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
500	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
501	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
502	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
504	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
506	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
507	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
509	#126	C₂×C₄×C₂₃	1	4	yes	—
510	#126	C₂×C₄×C₂₃	1	4	yes	—
511	#126	C₂×C₄×C₂₃	1	4	yes	—
512	#125	C₂×C₄×C₂₃	1	4	yes	—
513	#125	C₂×C₄×C₂₃	1	2	yes	—
514	#125	C₂×C₄×C₂₃	1	2	yes	—
515	#124	C₂×C₄×C₂₃	1	2	yes	—
516	#124	C₂×C₄×C₂₃	1	4	yes	—
517	#123	C₂×C₄×C₂₃	1	4	yes	—
518	#123	C₂×C₄×C₂₃	1	4	yes	—
519	#123	C₂×C₄×C₂₃	1	4	yes	—
520	#123	C₂×C₄×C₂₃	1	4	yes	—
521	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
522	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
523	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
524	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
525	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
526	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
527	#121	C₂×C₄×C₂₃	1	2	yes	—
528	#121	C₂×C₄×C₂₃	1	2	yes	—
529	#121	C₂×C₄×C₂₃	1	4	yes	—
530	#121	C₂×C₄×C₂₃	1	2	yes	—
531	#120	C₂×C₄×C₂₃	1	4	yes	—
532	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
533	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
534	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
535	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
536	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
537	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
538	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
539	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
540	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
541	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
542	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
543	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
544	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
545	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
546	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
547	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
548	C₄×D₄	C₂³×C₂₃	1	2	yes	—
549	C₄×D₄	C₂³×C₂₃	1	4	yes	—
550	C₄×D₄	C₂³×C₂₃	1	4	yes	—
551	#117	C₂×C₄×C₂₃	1	4	yes	—
552	#117	C₂×C₄×C₂₃	1	2	yes	—
553	#117	C₂×C₄×C₂₃	1	2	yes	—
554	#117	C₂×C₄×C₂₃	1	4	yes	—
555	#117	C₂×C₄×C₂₃	1	2	yes	—
556	#117	C₂³×C₂₃	1	1	yes	characteristic
557	#117	C₂³×C₂₃	1	2	yes	—
558	#117	C₂³×C₂₃	1	4	yes	—
559	#117	C₂³×C₂₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
566	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
568	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
569	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
570	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
571	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
572	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
573	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
574	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
575	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
576	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
577	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
578	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
579	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
580	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
581	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
582	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
586	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
587	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
591	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
592	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
593	#97	C₂³×C₂₃	1	2	yes	—
594	#97	C₂³×C₂₃	1	4	yes	—
595	#97	C₂³×C₂₃	1	4	yes	—
596	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
599	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
600	C₄×C₈	C₂³×C₂₃	1	2	yes	—
601	C₄×C₈	C₂³×C₂₃	1	4	yes	—
602	C₄×C₈	C₂³×C₂₃	1	4	yes	—
603	C₂₃	#60273	1	1	yes	characteristic, direct product factor, Sylow
604	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
605	#41	—	2	2	no	—
606	#41	—	2	2	no	—
607	#41	—	4	4	no	—
608	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
609	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
610	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
613	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
614	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
615	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
616	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
617	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
618	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
623	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
624	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
625	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
626	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
627	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
628	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
629	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
634	M₁₆	—	2	2	no	—
635	M₁₆	—	2	4	no	—
636	M₁₆	—	2	2	no	—
637	M₁₆	—	4	2	no	—
638	M₁₆	—	4	2	no	—
639	M₁₆	—	4	2	no	—
640	M₁₆	—	4	2	no	—
641	M₁₆	—	4	4	no	—
642	M₁₆	—	4	4	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	4	4	no	—
647	C₂×C₈	—	4	4	no	—
648	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
649	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
650	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
654	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
656	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
657	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
658	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
659	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
660	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
661	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
662	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
663	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
664	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
665	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
666	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
668	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
669	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
670	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
671	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
672	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
673	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
674	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
683	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
684	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
688	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
689	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
690	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
691	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
692	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
693	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
694	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
695	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
696	C₄²	C₂⁴×C₂₃	1	4	yes	—
697	C₄²	C₂⁴×C₂₃	1	2	yes	—
698	C₂³	—	2	4	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
702	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
703	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
704	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
705	Q₈	—	2	4	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	2	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	4	no	—
714	D₄	—	4	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
731	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
732	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
734	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
735	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
736	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
737	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
738	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
740	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
741	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
742	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
743	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
744	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
745	C₈	—	2	2	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	2	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₂₃×#520	1	2	yes	—
767	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	1	no	—
778	C₄	C₂₃×#520	1	2	yes	—
779	C₄	C₂₃×#568	1	2	yes	—
780	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
781	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
782	C₂	—	2	2	no	—
783	C₂	—	4	2	no	—
784	C₂	—	4	2	no	—
785	C₂	—	4	2	no	—
786	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
787	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
788	C₂	C₂₃×#3573	1	1	yes	characteristic

	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×#3475	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×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2993	C₂	semidirect
6. C₂₃×#2991	C₂	semidirect
7. C₂₃×#2989	C₂	semidirect
8. C₂₃×#2962	C₂	semidirect
9. C₂₃×#2960	C₂	semidirect
10. D₄×M₁₆×C₂₃	C₂	semidirect
11. C₂₃×#2933	C₂	semidirect
12. C₂₃×#2930	C₂	semidirect
13. C₂×C₂₃×#436	C₂	semidirect
14. C₂₃×#2924	C₂	semidirect
15. C₂₃×#2922	C₂	semidirect
16. C₂₃×#2906	C₂	semidirect
17. C₂₃×#2905	C₂	semidirect
38. C₂₃×#446	C₂²	semidirect
39. C₂₃×#446	C₂²	semidirect
40. C₂₃×#446	C₂²	semidirect
41. C₂₃×#446	C₂²	semidirect
42. C₈×Q₈×C₂₃	C₂²	semidirect
43. C₈×Q₈×C₂₃	C₂²	semidirect
44. C₈×Q₈×C₂₃	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
53. C₂₃×#436	C₂²	semidirect
54. C₂₃×#436	C₂²	semidirect
56. C₂₃×#435	C₂²	semidirect
57. C₂₃×#435	C₂²	semidirect
58. C₂₃×#435	C₂²	semidirect
59. C₂₃×#435	C₂²	semidirect
61. C₈×D₄×C₂₃	C₂²	semidirect
62. C₂₃×#433	C₂²	semidirect
63. C₂₃×#433	C₂²	semidirect
64. C₂₃×#433	C₂²	semidirect
65. C₂₃×#433	C₂²	semidirect
66. C₂₃×#432	C₂²	semidirect
67. C₂₃×#431	C₂²	semidirect
68. C₂₃×#431	C₂²	semidirect
69. C₂₃×#431	C₂²	semidirect
75. C₂₃×#424	C₂²	semidirect
76. C₂₃×#424	C₂²	semidirect
77. C₂₃×#424	C₂²	semidirect
79. C₂₃×#423	C₂²	semidirect
80. C₂₃×#423	C₂²	semidirect
81. C₂₃×#423	C₂²	semidirect
83. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
303. #60273	C₂₃	direct (N × H)
361. #2995	C₂×C₂₃	semidirect
362. #2994	C₂×C₂₃	semidirect
363. #2993	C₂×C₂₃	semidirect
364. #2993	C₂×C₂₃	semidirect
365. #2991	C₂×C₂₃	semidirect
366. #2989	C₂×C₂₃	semidirect
367. #2962	C₂×C₂₃	semidirect
368. #2960	C₂×C₂₃	semidirect
369. D₄×M₁₆	C₂×C₂₃	semidirect
370. #2933	C₂×C₂₃	semidirect
371. #2930	C₂×C₂₃	semidirect
372. C₂×#436	C₂×C₂₃	semidirect
373. #2924	C₂×C₂₃	semidirect
374. #2922	C₂×C₂₃	semidirect
375. #2906	C₂×C₂₃	semidirect
376. #2905	C₂×C₂₃	semidirect
425. #446	C₂²×C₂₃	semidirect
426. #446	C₂²×C₂₃	semidirect
427. #446	C₂²×C₂₃	semidirect
428. #446	C₂²×C₂₃	semidirect
429. C₈×Q₈	C₂²×C₂₃	semidirect
430. C₈×Q₈	C₂²×C₂₃	semidirect
431. C₈×Q₈	C₂²×C₂₃	semidirect
439. #436	C₂²×C₂₃	semidirect
440. #436	C₂²×C₂₃	semidirect
441. #436	C₂²×C₂₃	semidirect
443. #435	C₂²×C₂₃	semidirect
444. #435	C₂²×C₂₃	semidirect
445. #435	C₂²×C₂₃	semidirect
446. #435	C₂²×C₂₃	semidirect
448. C₈×D₄	C₂²×C₂₃	semidirect
449. #433	C₂²×C₂₃	semidirect
450. #433	C₂²×C₂₃	semidirect
451. #433	C₂²×C₂₃	semidirect
452. #433	C₂²×C₂₃	semidirect
453. #432	C₂²×C₂₃	semidirect
454. #431	C₂²×C₂₃	semidirect
455. #431	C₂²×C₂₃	semidirect
456. #431	C₂²×C₂₃	semidirect
462. #424	C₂²×C₂₃	semidirect
463. #424	C₂²×C₂₃	semidirect
464. #424	C₂²×C₂₃	semidirect
466. #423	C₂²×C₂₃	semidirect
467. #423	C₂²×C₂₃	semidirect
468. #423	C₂²×C₂₃	semidirect
470. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
603. C₂₃	#60273	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×#3475	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2991	2
C₂₃×#2989	2
C₂₃×#2962	2
C₂₃×#2960	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2930	2
C₂×C₂₃×#436	2
C₂₃×#2924	2
C₂₃×#2922	2
C₂₃×#2906	2
C₂₃×#2905	2
#60273	23

Subgroups — C23×#60273 #19207899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60273 #19207899