Subgroups — C₂₃×#2691 #15670310

Order 2944.

554 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#126	—	2	4	no	—
22	C₂₃×#121	—	2	4	no	—
23	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#95	C₂²	1	1	yes	characteristic
46	C₂₃×#95	C₂²	1	1	yes	characteristic
47	C₂₃×#95	C₂²	1	1	yes	characteristic
48	C₂₃×#95	C₂²	1	1	yes	characteristic
49	C₂₃×#95	C₂²	1	1	yes	characteristic
50	C₂₃×#95	C₂²	1	1	yes	characteristic
51	C₂₃×#95	C₂²	1	1	yes	characteristic
52	C₂₃×#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
54	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
55	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
56	C₂×D₄×C₂₃	—	2	2	no	—
57	C₂×D₄×C₂₃	—	2	2	no	—
58	C₂×D₄×C₂₃	—	2	2	no	—
59	C₂×D₄×C₂₃	—	2	2	no	—
60	C₂×D₄×C₂₃	—	2	2	no	—
61	C₂×D₄×C₂₃	—	2	2	no	—
62	C₂×D₄×C₂₃	—	4	1	no	—
63	C₂×D₄×C₂₃	—	4	1	no	—
64	C₂×D₄×C₂₃	—	4	1	no	—
65	C₂²×C₄×C₂₃	—	2	2	no	—
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	4	1	no	—
68	C₂²×C₄×C₂₃	—	4	1	no	—
69	C₂²×C₄×C₂₃	—	4	1	no	—
70	C₂²×C₄×C₂₃	—	4	1	no	—
71	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₂₃	—	2	2	no	—
84	C₄⋊C₄×C₂₃	—	2	2	no	—
85	C₄⋊C₄×C₂₃	—	2	2	no	—
86	C₄⋊C₄×C₂₃	—	2	2	no	—
87	C₄⋊C₄×C₂₃	—	2	2	no	—
88	C₄⋊C₄×C₂₃	—	4	1	no	—
89	C₄⋊C₄×C₂₃	—	4	1	no	—
90	C₄⋊C₄×C₂₃	—	4	1	no	—
91	C₂²⋊C₄×C₂₃	—	2	2	no	—
92	C₂²⋊C₄×C₂₃	—	2	2	no	—
93	C₂²⋊C₄×C₂₃	—	2	2	no	—
94	C₂²⋊C₄×C₂₃	—	2	2	no	—
95	C₂²⋊C₄×C₂₃	—	4	1	no	—
96	C₂²⋊C₄×C₂₃	—	4	1	no	—
97	C₂²⋊C₄×C₂₃	—	4	1	no	—
98	C₂²⋊C₄×C₂₃	—	4	1	no	—
99	C₂²⋊C₄×C₂₃	—	4	1	no	—
100	C₂²⋊C₄×C₂₃	—	4	1	no	—
101	C₂²⋊C₄×C₂₃	—	4	1	no	—
102	C₂²⋊C₄×C₂₃	—	4	1	no	—
103	C₂²⋊C₄×C₂₃	D₄	1	4	yes	—
104	C₄²×C₂₃	—	2	2	no	—
105	C₂³×C₂₃	—	2	1	no	—
106	C₂³×C₂₃	—	2	1	no	—
107	C₂³×C₂₃	—	2	1	no	—
108	C₂³×C₂₃	—	2	1	no	—
109	C₂³×C₂₃	—	2	1	no	—
110	C₂³×C₂₃	—	2	1	no	—
111	C₂³×C₂₃	—	2	1	no	—
112	C₂³×C₂₃	—	2	1	no	—
113	C₂³×C₂₃	—	2	1	no	—
114	C₂³×C₂₃	—	2	1	no	—
115	C₂³×C₂₃	—	2	1	no	—
116	C₂³×C₂₃	—	2	1	no	—
117	C₂³×C₂₃	—	2	1	no	—
118	C₂³×C₂₃	—	2	1	no	—
119	C₂³×C₂₃	—	2	1	no	—
120	C₂³×C₂₃	—	2	1	no	—
121	C₂³×C₂₃	—	2	1	no	—
122	C₂³×C₂₃	—	2	1	no	—
123	C₂³×C₂₃	—	2	1	no	—
124	C₂³×C₂₃	C₂×D₄	1	2	yes	—
125	C₂³×C₂₃	#41	1	2	yes	—
126	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
127	D₄×C₂₃	—	4	4	no	—
128	D₄×C₂₃	—	4	4	no	—
129	D₄×C₂₃	—	4	4	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	2	1	no	—
147	C₂×C₄×C₂₃	—	2	1	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	2	1	no	—
155	C₂×C₄×C₂₃	—	2	1	no	—
156	C₂×C₄×C₂₃	—	2	1	no	—
157	C₂×C₄×C₂₃	—	2	1	no	—
158	C₂×C₄×C₂₃	—	2	1	no	—
159	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	2	1	no	—
163	C₂×C₄×C₂₃	—	4	4	no	—
164	C₂×C₄×C₂₃	—	4	4	no	—
165	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
166	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
167	C₂×C₄×C₂₃	#41	1	2	yes	—
168	#2691	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₂₃	—	2	2	no	—
170	C₂²×C₂₃	—	2	2	no	—
171	C₂²×C₂₃	—	2	2	no	—
172	C₂²×C₂₃	—	2	2	no	—
173	C₂²×C₂₃	—	2	2	no	—
174	C₂²×C₂₃	—	2	2	no	—
175	C₂²×C₂₃	—	4	1	no	—
176	C₂²×C₂₃	—	4	1	no	—
177	C₂²×C₂₃	—	4	1	no	—
178	C₂²×C₂₃	—	4	1	no	—
179	C₂²×C₂₃	—	4	1	no	—
180	C₂²×C₂₃	—	4	1	no	—
181	C₂²×C₂₃	—	4	1	no	—
182	C₂²×C₂₃	—	4	1	no	—
183	C₂²×C₂₃	—	4	1	no	—
184	C₂²×C₂₃	—	4	1	no	—
185	C₂²×C₂₃	—	4	1	no	—
186	C₂²×C₂₃	—	4	1	no	—
187	C₂²×C₂₃	—	4	1	no	—
188	C₂²×C₂₃	—	4	1	no	—
189	C₂²×C₂₃	—	4	1	no	—
190	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
191	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
192	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
193	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂²×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
197	C₄×C₂₃	—	2	2	no	—
198	C₄×C₂₃	—	2	2	no	—
199	C₄×C₂₃	—	2	2	no	—
200	C₄×C₂₃	—	4	1	no	—
201	C₄×C₂₃	—	4	1	no	—
202	C₄×C₂₃	—	4	1	no	—
203	C₄×C₂₃	—	4	1	no	—
204	C₄×C₂₃	—	4	1	no	—
205	C₄×C₂₃	—	4	1	no	—
206	C₄×C₂₃	—	4	1	no	—
207	C₄×C₂₃	—	4	1	no	—
208	C₄×C₂₃	—	4	1	no	—
209	C₂×#126	C₂×C₂₃	1	1	yes	characteristic, complemented
210	C₂×#121	C₂×C₂₃	1	1	yes	characteristic
211	#398	C₂×C₂₃	1	1	yes	characteristic, complemented
212	#397	C₂×C₂₃	1	1	yes	characteristic, complemented
213	#396	C₂×C₂₃	1	1	yes	characteristic, complemented
214	#394	C₂×C₂₃	1	1	yes	characteristic, complemented
215	#394	C₂×C₂₃	1	1	yes	characteristic, complemented
216	#394	C₂×C₂₃	1	1	yes	characteristic, complemented
217	#390	C₂×C₂₃	1	1	yes	characteristic, complemented
218	#387	C₂×C₂₃	1	1	yes	characteristic, complemented
219	#386	C₂×C₂₃	1	1	yes	characteristic, complemented
220	#386	C₂×C₂₃	1	1	yes	characteristic, complemented
221	#385	C₂×C₂₃	1	1	yes	characteristic, complemented
222	#385	C₂×C₂₃	1	1	yes	characteristic, complemented
223	#380	C₂×C₂₃	1	1	yes	characteristic, complemented
224	C₂×C₂₃	—	4	2	no	—
225	C₂×C₂₃	—	4	2	no	—
226	C₂×C₂₃	—	8	1	no	—
227	C₂×C₂₃	#537	1	1	yes	characteristic
228	C₂×C₂₃	#539	1	1	yes	characteristic
229	C₂×C₂₃	#542	1	1	yes	characteristic
230	C₂×C₂₃	#546	1	1	yes	characteristic
231	C₂×C₂₃	#546	1	1	yes	characteristic
232	C₂×C₂₃	#553	1	1	yes	characteristic
233	C₂×C₂₃	#560	1	1	yes	characteristic
234	C₂²×D₄	C₂²×C₂₃	1	1	yes	characteristic
235	C₂²×D₄	C₂²×C₂₃	1	1	yes	characteristic
236	C₂²×D₄	C₂²×C₂₃	1	1	yes	characteristic
237	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
238	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
239	#126	—	2	4	no	—
240	#121	—	2	4	no	—
241	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
262	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
263	#95	C₂²×C₂₃	1	1	yes	characteristic
264	#95	C₂²×C₂₃	1	1	yes	characteristic
265	#95	C₂²×C₂₃	1	1	yes	characteristic
266	#95	C₂²×C₂₃	1	1	yes	characteristic
267	#95	C₂²×C₂₃	1	1	yes	characteristic
268	#95	C₂²×C₂₃	1	1	yes	characteristic
269	#95	C₂²×C₂₃	1	1	yes	characteristic
270	#95	C₂²×C₂₃	1	1	yes	characteristic
271	C₂₃	#2691	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
273	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
274	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	D₄×C₂₃	1	4	yes	—
323	C₄²	—	2	2	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	C₂×D₄×C₂₃	1	2	yes	—
344	C₂³	#41×C₂₃	1	2	yes	—
345	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
385	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
386	C₂×C₄	#41×C₂₃	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	C₂²×D₄×C₂₃	1	1	yes	characteristic
409	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
410	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
411	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₂	—	4	2	no	—
428	C₂	—	4	2	no	—
429	C₂	—	8	1	no	—
430	C₂	C₂₃×#537	1	1	yes	characteristic
431	C₂	C₂₃×#539	1	1	yes	characteristic
432	C₂	C₂₃×#542	1	1	yes	characteristic
433	C₂	C₂₃×#546	1	1	yes	characteristic
434	C₂	C₂₃×#546	1	1	yes	characteristic
435	C₂	C₂₃×#553	1	1	yes	characteristic
436	C₂	C₂₃×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂
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. C₂×C₂₃×#126	C₂	semidirect
3. C₂₃×#398	C₂	semidirect
4. C₂₃×#397	C₂	semidirect
5. C₂₃×#396	C₂	semidirect
6. C₂₃×#394	C₂	semidirect
7. C₂₃×#394	C₂	semidirect
8. C₂₃×#394	C₂	semidirect
9. C₂₃×#390	C₂	semidirect
10. C₂₃×#387	C₂	semidirect
11. C₂₃×#386	C₂	semidirect
12. C₂₃×#386	C₂	semidirect
13. C₂₃×#385	C₂	semidirect
14. C₂₃×#385	C₂	semidirect
15. C₂₃×#380	C₂	semidirect
168. #2691	C₂₃	direct (N × H)
209. C₂×#126	C₂×C₂₃	semidirect
211. #398	C₂×C₂₃	semidirect
212. #397	C₂×C₂₃	semidirect
213. #396	C₂×C₂₃	semidirect
214. #394	C₂×C₂₃	semidirect
215. #394	C₂×C₂₃	semidirect
216. #394	C₂×C₂₃	semidirect
217. #390	C₂×C₂₃	semidirect
218. #387	C₂×C₂₃	semidirect
219. #386	C₂×C₂₃	semidirect
220. #386	C₂×C₂₃	semidirect
221. #385	C₂×C₂₃	semidirect
222. #385	C₂×C₂₃	semidirect
223. #380	C₂×C₂₃	semidirect
271. C₂₃	#2691	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#126	2
C₂×C₂₃×#121	2
C₂₃×#398	2
C₂₃×#397	2
C₂₃×#396	2
C₂₃×#394	2
C₂₃×#390	2
C₂₃×#387	2
C₂₃×#386	2
C₂₃×#385	2
C₂₃×#380	2
#2691	23

Subgroups — C23×#2691 #15670310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2691 #15670310