Subgroups — C₂₃×#60341 #19207967

Order 5888.

1748 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3482	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2992	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2988	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2985	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2984	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2970	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2968	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2962	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#446	C₂	1	2	yes	maximal, complemented
18	C₂₃×#557	C₄	1	1	yes	characteristic
19	C₂₃×#556	C₄	1	2	yes	—
20	C₂₃×#556	C₄	1	1	yes	characteristic
21	C₂₃×#552	C₄	1	2	yes	—
22	C₂₃×#552	C₄	1	4	yes	—
23	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
24	C₂₃×#548	C₄	1	2	yes	—
25	C₂₃×#547	C₄	1	1	yes	characteristic
26	C₂₃×#547	C₄	1	2	yes	—
27	C₂₃×#533	C₂²	1	1	yes	characteristic
28	C₂₃×#533	C₂²	1	2	yes	—
29	C₂₃×#529	C₂²	1	2	yes	—
30	C₂₃×#529	C₂²	1	4	yes	—
31	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
32	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
33	C₄×#41×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
35	C₂₃×#446	C₂²	1	1	yes	characteristic
36	C₂₃×#446	C₂²	1	2	yes	—
37	C₂₃×#446	C₂²	1	4	yes	—
38	C₂₃×#446	C₂²	1	2	yes	—
39	C₂₃×#446	C₂²	1	4	yes	—
40	C₂₃×#446	C₂²	1	2	yes	—
41	C₂₃×#446	C₂²	1	2	yes	—
42	C₂₃×#446	C₂²	1	4	yes	—
43	C₂₃×#446	C₂²	1	2	yes	—
44	C₂₃×#446	C₂²	1	1	yes	characteristic
45	C₂₃×#446	C₂²	1	4	yes	—
46	C₂₃×#446	C₂²	1	2	yes	—
47	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
48	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
49	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
50	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
51	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
52	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
53	C₂₃×#436	C₂²	1	1	yes	characteristic
54	C₂₃×#436	C₂²	1	1	yes	characteristic
55	C₂₃×#435	C₂²	1	2	yes	—
56	C₂₃×#435	C₂²	1	2	yes	—
57	C₂₃×#435	C₂²	1	4	yes	—
58	C₂₃×#435	C₂²	1	4	yes	—
59	C₂₃×#435	C₂²	1	4	yes	—
60	C₂₃×#435	C₂²	1	4	yes	—
61	C₈×D₄×C₂₃	C₂²	1	2	yes	—
62	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₈×D₄×C₂₃	C₂²	1	2	yes	—
65	C₈×D₄×C₂₃	C₂²	1	4	yes	—
66	C₈×D₄×C₂₃	C₂²	1	2	yes	—
67	C₈×D₄×C₂₃	C₂²	1	4	yes	—
68	C₈×D₄×C₂₃	C₂²	1	2	yes	—
69	C₂₃×#433	C₂²	1	4	yes	—
70	C₂₃×#433	C₂²	1	4	yes	—
71	C₂₃×#433	C₂²	1	4	yes	—
72	C₂₃×#432	C₂²	1	2	yes	—
73	C₂₃×#432	C₂²	1	4	yes	—
74	C₂₃×#432	C₂²	1	2	yes	—
75	C₂₃×#431	C₂²	1	2	yes	—
76	C₂₃×#431	C₂²	1	1	yes	characteristic
77	C₂₃×#431	C₂²	1	2	yes	—
78	C₂₃×#431	C₂²	1	1	yes	characteristic
79	C₂₃×#431	C₂²	1	4	yes	—
80	C₂₃×#424	C₂²	1	2	yes	—
81	C₂₃×#424	C₂²	1	4	yes	—
82	C₂₃×#423	C₂²	1	1	yes	characteristic
83	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	—
84	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
85	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
86	C₂₃×#405	C₂²	1	2	yes	—
87	C₂₃×#405	C₂²	1	4	yes	—
88	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
89	C₂×C₂₃×#97	C₂²	1	4	yes	—
90	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
91	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
92	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
94	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
95	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
96	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
97	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
99	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
105	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
106	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
107	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
108	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
109	C₂₃×#126	C₂×C₄	1	4	yes	—
110	C₂₃×#126	C₂×C₄	1	4	yes	—
111	C₂₃×#126	C₂×C₄	1	4	yes	—
112	C₂₃×#125	C₂×C₄	1	2	yes	—
113	C₂₃×#125	C₂×C₄	1	4	yes	—
114	C₂₃×#125	C₂×C₄	1	2	yes	—
115	C₂₃×#125	C₂×C₄	1	4	yes	—
116	C₂₃×#124	C₂×C₄	1	2	yes	—
117	C₂₃×#124	C₂×C₄	1	4	yes	—
118	C₂₃×#123	C₂×C₄	1	4	yes	—
119	C₂₃×#123	C₂×C₄	1	4	yes	—
120	C₂₃×#123	C₂×C₄	1	4	yes	—
121	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
122	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
123	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
124	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
125	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
126	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
127	C₂₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
128	C₂₃×#121	C₂×C₄	1	2	yes	—
129	C₂₃×#121	C₂×C₄	1	4	yes	—
130	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
131	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
132	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
133	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	—
134	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
135	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
136	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
137	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
138	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
141	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
142	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
143	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
145	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
146	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
147	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₄×D₄×C₂₃	C₂³	1	2	yes	—
149	C₄×D₄×C₂₃	C₂³	1	4	yes	—
150	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₄×D₄×C₂₃	C₂³	1	2	yes	—
152	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
153	C₂₃×#117	C₂×C₄	1	2	yes	—
154	C₂₃×#117	C₂×C₄	1	2	yes	—
155	C₂₃×#117	C₂×C₄	1	4	yes	—
156	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
157	C₂₃×#117	C₂×C₄	1	2	yes	—
158	C₂₃×#117	C₂³	1	2	yes	—
159	C₂₃×#117	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
167	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
168	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
169	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
170	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
172	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
175	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
176	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
182	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
183	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
185	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
186	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
187	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂₃×#97	C₂³	1	2	yes	—
191	C₂₃×#97	C₂³	1	4	yes	—
192	C₂₃×#97	C₂³	1	4	yes	—
193	C₂₃×#97	C₂³	1	4	yes	—
194	C₂₃×#97	C₂³	1	2	yes	—
195	C₂₃×#97	C₂³	1	4	yes	—
196	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₂₃	C₂³	1	2	yes	—
199	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₂₃	C₂³	1	2	yes	—
201	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
202	C₄×C₈×C₂₃	C₂³	1	2	yes	—
203	C₄×C₈×C₂₃	C₂³	1	2	yes	—
204	C₄×C₈×C₂₃	C₂³	1	4	yes	—
205	C₄×C₈×C₂₃	C₂³	1	4	yes	—
206	#41×C₂₃	—	2	4	no	—
207	#41×C₂₃	—	2	8	no	—
208	#41×C₂₃	—	4	2	no	—
209	C₂×Q₈×C₂₃	—	4	4	no	—
210	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
211	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
212	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
213	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
214	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
215	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
216	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
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	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
222	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
227	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	M₁₆×C₂₃	—	2	4	no	—
232	M₁₆×C₂₃	—	4	2	no	—
233	M₁₆×C₂₃	—	4	2	no	—
234	C₂×C₈×C₂₃	—	2	4	no	—
235	C₂×C₈×C₂₃	—	2	2	no	—
236	C₂×C₈×C₂₃	—	4	2	no	—
237	C₂×C₈×C₂₃	—	4	4	no	—
238	C₂×C₈×C₂₃	—	4	1	no	—
239	C₂×C₈×C₂₃	—	4	4	no	—
240	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
244	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
250	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
251	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
252	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
253	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
254	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
255	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
256	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
257	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
258	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
259	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
260	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
263	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
264	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
265	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
266	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
269	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
270	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
271	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
272	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
273	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
274	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
275	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
276	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
277	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
278	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
280	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
281	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
282	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
283	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
284	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
285	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
286	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
287	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
288	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₄²×C₂₃	C₂⁴	1	2	yes	—
291	C₄²×C₂₃	C₂⁴	1	4	yes	—
292	C₄²×C₂₃	C₂⁴	1	2	yes	—
293	#60341	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
295	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
296	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
297	Q₈×C₂₃	—	2	2	no	—
298	Q₈×C₂₃	—	2	4	no	—
299	Q₈×C₂₃	—	2	2	no	—
300	Q₈×C₂₃	—	2	4	no	—
301	Q₈×C₂₃	—	4	4	no	—
302	D₄×C₂₃	—	2	4	no	—
303	D₄×C₂₃	—	2	8	no	—
304	D₄×C₂₃	—	2	2	no	—
305	D₄×C₂₃	—	4	2	no	—
306	D₄×C₂₃	#131	1	4	yes	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	8	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	4	no	—
311	C₂×C₄×C₂₃	—	2	4	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	4	2	no	—
321	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
322	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
323	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
324	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
325	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
330	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
331	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
332	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
334	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
335	C₈×C₂₃	—	2	1	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	—	2	1	no	—
339	C₈×C₂₃	—	2	2	no	—
340	C₈×C₂₃	—	2	4	no	—
341	C₈×C₂₃	—	2	2	no	—
342	C₈×C₂₃	—	2	1	no	—
343	C₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
344	#3482	C₂×C₂₃	1	1	yes	characteristic
345	#2994	C₂×C₂₃	1	2	yes	complemented
346	#2992	C₂×C₂₃	1	4	yes	complemented
347	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2988	C₂×C₂₃	1	2	yes	complemented
350	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#2985	C₂×C₂₃	1	2	yes	complemented
352	#2984	C₂×C₂₃	1	2	yes	complemented
353	#2970	C₂×C₂₃	1	2	yes	complemented
354	#2968	C₂×C₂₃	1	4	yes	complemented
355	#2966	C₂×C₂₃	1	2	yes	complemented
356	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
357	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#2962	C₂×C₂₃	1	2	yes	complemented
359	#2960	C₂×C₂₃	1	1	yes	characteristic, complemented
360	C₂×#446	C₂×C₂₃	1	2	yes	complemented
361	C₂²×C₂₃	—	2	2	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	1	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	1	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	2	1	no	—
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	C₂×#131	1	4	yes	—
370	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
371	C₄×C₂₃	—	2	2	no	—
372	C₄×C₂₃	—	2	1	no	—
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	2	1	no	—
375	C₄×C₂₃	—	2	2	no	—
376	C₄×C₂₃	—	2	2	no	—
377	C₄×C₂₃	—	2	4	no	—
378	C₄×C₂₃	—	2	1	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	2	no	—
381	C₄×C₂₃	—	2	4	no	—
382	C₄×C₂₃	C₂×#131	1	2	yes	—
383	C₄×C₂₃	#568	1	2	yes	—
384	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₄×C₂₃	#585	1	1	yes	characteristic
386	#557	C₄×C₂₃	1	1	yes	characteristic
387	#556	C₄×C₂₃	1	2	yes	—
388	#556	C₄×C₂₃	1	1	yes	characteristic
389	#552	C₄×C₂₃	1	2	yes	—
390	#552	C₄×C₂₃	1	4	yes	—
391	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
392	#548	C₄×C₂₃	1	2	yes	—
393	#547	C₄×C₂₃	1	1	yes	characteristic
394	#547	C₄×C₂₃	1	2	yes	—
395	#533	C₂²×C₂₃	1	1	yes	characteristic
396	#533	C₂²×C₂₃	1	2	yes	—
397	#529	C₂²×C₂₃	1	2	yes	—
398	#529	C₂²×C₂₃	1	4	yes	—
399	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
400	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
401	C₄×#41	C₂²×C₂₃	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
403	#446	C₂²×C₂₃	1	1	yes	characteristic
404	#446	C₂²×C₂₃	1	2	yes	—
405	#446	C₂²×C₂₃	1	4	yes	—
406	#446	C₂²×C₂₃	1	2	yes	—
407	#446	C₂²×C₂₃	1	4	yes	—
408	#446	C₂²×C₂₃	1	2	yes	—
409	#446	C₂²×C₂₃	1	2	yes	—
410	#446	C₂²×C₂₃	1	4	yes	—
411	#446	C₂²×C₂₃	1	2	yes	—
412	#446	C₂²×C₂₃	1	1	yes	characteristic
413	#446	C₂²×C₂₃	1	4	yes	—
414	#446	C₂²×C₂₃	1	2	yes	—
415	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
416	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
417	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
418	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
419	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
420	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
421	#436	C₂²×C₂₃	1	1	yes	characteristic
422	#436	C₂²×C₂₃	1	1	yes	characteristic
423	#435	C₂²×C₂₃	1	2	yes	—
424	#435	C₂²×C₂₃	1	2	yes	—
425	#435	C₂²×C₂₃	1	4	yes	—
426	#435	C₂²×C₂₃	1	4	yes	—
427	#435	C₂²×C₂₃	1	4	yes	—
428	#435	C₂²×C₂₃	1	4	yes	—
429	C₈×D₄	C₂²×C₂₃	1	2	yes	—
430	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
431	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
432	C₈×D₄	C₂²×C₂₃	1	2	yes	—
433	C₈×D₄	C₂²×C₂₃	1	4	yes	—
434	C₈×D₄	C₂²×C₂₃	1	2	yes	—
435	C₈×D₄	C₂²×C₂₃	1	4	yes	—
436	C₈×D₄	C₂²×C₂₃	1	2	yes	—
437	#433	C₂²×C₂₃	1	4	yes	—
438	#433	C₂²×C₂₃	1	4	yes	—
439	#433	C₂²×C₂₃	1	4	yes	—
440	#432	C₂²×C₂₃	1	2	yes	—
441	#432	C₂²×C₂₃	1	4	yes	—
442	#432	C₂²×C₂₃	1	2	yes	—
443	#431	C₂²×C₂₃	1	2	yes	—
444	#431	C₂²×C₂₃	1	1	yes	characteristic
445	#431	C₂²×C₂₃	1	2	yes	—
446	#431	C₂²×C₂₃	1	1	yes	characteristic
447	#431	C₂²×C₂₃	1	4	yes	—
448	#424	C₂²×C₂₃	1	2	yes	—
449	#424	C₂²×C₂₃	1	4	yes	—
450	#423	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	—
452	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
453	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
454	#405	C₂²×C₂₃	1	2	yes	—
455	#405	C₂²×C₂₃	1	4	yes	—
456	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
457	C₂×#97	C₂²×C₂₃	1	4	yes	—
458	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
459	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×C₂₃	—	2	4	no	—
461	C₂×C₂₃	—	4	1	no	—
462	C₂×C₂₃	—	4	2	no	—
463	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×C₂₃	C₂²×#131	1	1	yes	characteristic
465	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
466	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
467	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
468	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
469	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
470	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
471	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
472	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
473	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
476	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
478	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
479	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
480	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
481	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
482	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
483	#126	C₂×C₄×C₂₃	1	4	yes	—
484	#126	C₂×C₄×C₂₃	1	4	yes	—
485	#126	C₂×C₄×C₂₃	1	4	yes	—
486	#125	C₂×C₄×C₂₃	1	2	yes	—
487	#125	C₂×C₄×C₂₃	1	4	yes	—
488	#125	C₂×C₄×C₂₃	1	2	yes	—
489	#125	C₂×C₄×C₂₃	1	4	yes	—
490	#124	C₂×C₄×C₂₃	1	2	yes	—
491	#124	C₂×C₄×C₂₃	1	4	yes	—
492	#123	C₂×C₄×C₂₃	1	4	yes	—
493	#123	C₂×C₄×C₂₃	1	4	yes	—
494	#123	C₂×C₄×C₂₃	1	4	yes	—
495	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
496	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
497	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
498	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
499	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
500	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
501	C₂²⋊Q₈	C₂×C₄×C₂₃	1	4	yes	—
502	#121	C₂×C₄×C₂₃	1	2	yes	—
503	#121	C₂×C₄×C₂₃	1	4	yes	—
504	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
505	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
506	C₄×Q₈	C₂×C₄×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	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
510	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
511	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
512	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
513	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
514	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
515	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
516	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
517	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
518	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
519	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
520	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
521	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₄×D₄	C₂³×C₂₃	1	2	yes	—
523	C₄×D₄	C₂³×C₂₃	1	4	yes	—
524	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
525	C₄×D₄	C₂³×C₂₃	1	2	yes	—
526	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
527	#117	C₂×C₄×C₂₃	1	2	yes	—
528	#117	C₂×C₄×C₂₃	1	2	yes	—
529	#117	C₂×C₄×C₂₃	1	4	yes	—
530	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
531	#117	C₂×C₄×C₂₃	1	2	yes	—
532	#117	C₂³×C₂₃	1	4	yes	—
533	#117	C₂³×C₂₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
536	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
538	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
540	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
542	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
543	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
545	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
547	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
548	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
549	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
550	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
551	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
552	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
554	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
555	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
558	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
560	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
561	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
562	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
563	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
564	#97	C₂³×C₂₃	1	2	yes	—
565	#97	C₂³×C₂₃	1	4	yes	—
566	#97	C₂³×C₂₃	1	4	yes	—
567	#97	C₂³×C₂₃	1	4	yes	—
568	#97	C₂³×C₂₃	1	2	yes	—
569	#97	C₂³×C₂₃	1	4	yes	—
570	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₂₃	1	2	yes	—
573	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₂₃	1	2	yes	—
575	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
576	C₄×C₈	C₂³×C₂₃	1	2	yes	—
577	C₄×C₈	C₂³×C₂₃	1	2	yes	—
578	C₄×C₈	C₂³×C₂₃	1	4	yes	—
579	C₄×C₈	C₂³×C₂₃	1	4	yes	—
580	C₂₃	#60341	1	1	yes	characteristic, direct product factor, Sylow
581	#41	—	2	4	no	—
582	#41	—	2	8	no	—
583	#41	—	4	2	no	—
584	C₂×Q₈	—	4	4	no	—
585	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
586	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
587	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
588	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
589	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
590	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
591	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
592	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
593	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
594	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
596	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
597	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
598	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
602	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	M₁₆	—	2	4	no	—
607	M₁₆	—	4	2	no	—
608	M₁₆	—	4	2	no	—
609	C₂×C₈	—	2	4	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	4	2	no	—
612	C₂×C₈	—	4	4	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	—	4	4	no	—
615	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
619	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
620	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
622	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
623	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
624	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
625	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
627	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
628	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
629	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
630	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
631	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
632	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
633	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
634	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
635	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
636	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
637	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
638	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
639	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
640	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
641	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
642	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
643	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
644	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
645	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
646	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
647	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
648	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
649	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
650	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
651	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
652	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
653	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
654	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
655	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
656	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
657	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
658	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
659	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
660	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
661	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
662	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
663	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
664	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
665	C₄²	C₂⁴×C₂₃	1	2	yes	—
666	C₄²	C₂⁴×C₂₃	1	4	yes	—
667	C₄²	C₂⁴×C₂₃	1	2	yes	—
668	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
669	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
670	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
671	Q₈	—	2	2	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	4	no	—
675	Q₈	—	4	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	8	no	—
678	D₄	—	2	2	no	—
679	D₄	—	4	2	no	—
680	D₄	C₂₃×#131	1	4	yes	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	8	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
696	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
697	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
698	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
699	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
700	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
701	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
702	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
703	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
704	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
705	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
707	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
708	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
709	C₈	—	2	1	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	4	no	—
715	C₈	—	2	2	no	—
716	C₈	—	2	1	no	—
717	C₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	C₂×C₂₃×#131	1	4	yes	—
727	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
728	C₄	—	2	2	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	4	no	—
739	C₄	C₂×C₂₃×#131	1	2	yes	—
740	C₄	C₂₃×#568	1	2	yes	—
741	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
742	C₄	C₂₃×#585	1	1	yes	characteristic
743	C₂	—	2	4	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
747	C₂	C₂²×C₂₃×#131	1	1	yes	characteristic
748	C₂	C₂×C₂₃×#568	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×#3482	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×#2994	C₂	semidirect
3. C₂₃×#2992	C₂	semidirect
4. C₂₃×#2990	C₂	semidirect
5. C₂₃×#2990	C₂	semidirect
6. C₂₃×#2988	C₂	semidirect
7. C₂₃×#2986	C₂	semidirect
8. C₂₃×#2985	C₂	semidirect
9. C₂₃×#2984	C₂	semidirect
10. C₂₃×#2970	C₂	semidirect
11. C₂₃×#2968	C₂	semidirect
12. C₂₃×#2966	C₂	semidirect
13. C₂₃×#2965	C₂	semidirect
14. C₈×#41×C₂₃	C₂	semidirect
15. C₂₃×#2962	C₂	semidirect
16. C₂₃×#2960	C₂	semidirect
17. C₂×C₂₃×#446	C₂	semidirect
293. #60341	C₂₃	direct (N × H)
345. #2994	C₂×C₂₃	semidirect
346. #2992	C₂×C₂₃	semidirect
347. #2990	C₂×C₂₃	semidirect
348. #2990	C₂×C₂₃	semidirect
349. #2988	C₂×C₂₃	semidirect
350. #2986	C₂×C₂₃	semidirect
351. #2985	C₂×C₂₃	semidirect
352. #2984	C₂×C₂₃	semidirect
353. #2970	C₂×C₂₃	semidirect
354. #2968	C₂×C₂₃	semidirect
355. #2966	C₂×C₂₃	semidirect
356. #2965	C₂×C₂₃	semidirect
357. C₈×#41	C₂×C₂₃	semidirect
358. #2962	C₂×C₂₃	semidirect
359. #2960	C₂×C₂₃	semidirect
360. C₂×#446	C₂×C₂₃	semidirect
580. C₂₃	#60341	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×#3482	2
C₂₃×#2994	2
C₂₃×#2992	2
C₂₃×#2990	2
C₂₃×#2988	2
C₂₃×#2986	2
C₂₃×#2985	2
C₂₃×#2984	2
C₂₃×#2970	2
C₂₃×#2968	2
C₂₃×#2966	2
C₂₃×#2965	2
C₈×#41×C₂₃	2
C₂₃×#2962	2
C₂₃×#2960	2
C₂×C₂₃×#446	2
#60341	23

Subgroups — C23×#60341 #19207967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60341 #19207967