Subgroups — C₂₃×#8079 #19155705

Order 5888.

634 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1301	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₂₃	—	2	1	no	—
6	C₂²×M₁₆×C₂₃	—	2	1	no	—
7	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#431	—	2	1	no	—
9	C₂₃×#431	—	2	1	no	—
10	C₂₃×#431	C₄	1	2	yes	—
11	C₂₃×#431	C₂²	1	2	yes	—
12	C₂₃×#423	—	2	1	no	—
13	C₂₃×#423	—	2	1	no	—
14	C₂₃×#423	—	2	1	no	—
15	C₂₃×#423	—	2	1	no	—
16	C₂₃×#423	C₄	1	2	yes	—
17	C₂₃×#423	C₄	1	2	yes	—
18	C₂₃×#423	C₄	1	2	yes	—
19	C₂₃×#423	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
21	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
22	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
23	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	—
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊C₈	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₂₃	—	2	1	no	—
27	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂×M₁₆×C₂₃	—	2	2	no	—
32	C₂×M₁₆×C₂₃	—	2	2	no	—
33	C₂×M₁₆×C₂₃	—	2	2	no	—
34	C₂×M₁₆×C₂₃	—	4	2	no	—
35	C₂×M₁₆×C₂₃	—	4	2	no	—
36	C₂×M₁₆×C₂₃	—	4	2	no	—
37	C₂×M₁₆×C₂₃	—	4	2	no	—
38	C₂²×C₈×C₂₃	—	2	2	no	—
39	C₂²×C₈×C₂₃	—	2	2	no	—
40	C₂²×C₈×C₂₃	—	2	2	no	—
41	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
53	C₂₃×C₄⋊C₈	—	2	2	no	—
54	C₂₃×C₄⋊C₈	—	2	2	no	—
55	C₂₃×C₄⋊C₈	—	2	2	no	—
56	C₂₃×C₄⋊C₈	—	2	2	no	—
57	C₂₃×C₄⋊C₈	—	2	2	no	—
58	C₂₃×C₄⋊C₈	—	2	2	no	—
59	C₂₃×C₄⋊C₈	—	2	2	no	—
60	C₂₃×C₄⋊C₈	—	2	2	no	—
61	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₂₃×C₂²⋊C₈	—	2	2	no	—
64	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₄×C₈×C₂₃	—	2	2	no	—
66	C₄×C₈×C₂₃	—	2	2	no	—
67	C₂⁴×C₂₃	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₂₃	—	4	2	no	—
69	C₂²×C₄×C₂₃	—	4	2	no	—
70	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	D₈	1	2	yes	—
86	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
89	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
92	M₁₆×C₂₃	—	4	4	no	—
93	M₁₆×C₂₃	—	4	4	no	—
94	M₁₆×C₂₃	—	4	4	no	—
95	M₁₆×C₂₃	—	4	2	no	—
96	M₁₆×C₂₃	—	4	2	no	—
97	C₂×C₈×C₂₃	—	2	4	no	—
98	C₂×C₈×C₂₃	—	2	4	no	—
99	C₂×C₈×C₂₃	—	2	4	no	—
100	C₂×C₈×C₂₃	—	4	4	no	—
101	C₂×C₈×C₂₃	—	4	4	no	—
102	C₂×C₈×C₂₃	—	4	2	no	—
103	C₂×C₈×C₂₃	—	4	2	no	—
104	C₄²×C₂₃	C₄²	1	1	yes	characteristic
105	C₄²×C₂₃	C₄²	1	1	yes	characteristic
106	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
120	#8079	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₂₃	—	4	1	no	—
122	C₂³×C₂₃	—	4	1	no	—
123	C₂³×C₂₃	#95	1	1	yes	characteristic
124	C₂³×C₂₃	#95	1	1	yes	characteristic
125	C₂³×C₂₃	#106	1	2	yes	—
126	C₂³×C₂₃	#107	1	2	yes	—
127	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	—	2	2	no	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	4	1	no	—
135	C₂×C₄×C₂₃	—	4	1	no	—
136	C₂×C₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	—	4	1	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	1	no	—
140	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
141	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
142	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
143	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
144	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
145	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₂₃	#102	1	2	yes	—
147	C₂×C₄×C₂₃	#102	1	2	yes	—
148	C₂×C₄×C₂₃	#102	1	2	yes	—
149	C₂×C₄×C₂₃	#102	1	2	yes	—
150	C₂×C₄×C₂₃	#103	1	2	yes	—
151	C₂×C₄×C₂₃	#103	1	2	yes	—
152	C₂×C₄×C₂₃	#103	1	2	yes	—
153	C₂×C₄×C₂₃	#103	1	2	yes	—
154	C₂×C₄×C₂₃	#106	1	2	yes	—
155	C₂×C₄×C₂₃	#107	1	2	yes	—
156	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
166	C₈×C₂₃	—	4	4	no	—
167	C₈×C₂₃	—	4	4	no	—
168	C₈×C₂₃	—	4	4	no	—
169	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
170	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
171	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
172	#1301	C₂×C₂₃	1	4	yes	complemented
173	C₂²×C₂₃	—	2	1	no	—
174	C₂²×C₂₃	—	2	1	no	—
175	C₂²×C₂₃	—	2	1	no	—
176	C₂²×C₂₃	—	2	1	no	—
177	C₂²×C₂₃	—	2	1	no	—
178	C₂²×C₂₃	—	2	1	no	—
179	C₂²×C₂₃	—	4	2	no	—
180	C₂²×C₂₃	—	4	2	no	—
181	C₂²×C₂₃	#340	1	2	yes	—
182	C₂²×C₂₃	#340	1	2	yes	—
183	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
184	C₂²×C₂₃	C₂×#106	1	1	yes	characteristic
185	C₂²×C₂₃	C₂×#107	1	1	yes	characteristic
186	C₄×C₂₃	—	2	1	no	—
187	C₄×C₂₃	—	2	1	no	—
188	C₄×C₂₃	—	2	1	no	—
189	C₄×C₂₃	—	2	1	no	—
190	C₄×C₂₃	—	2	1	no	—
191	C₄×C₂₃	—	2	1	no	—
192	C₄×C₂₃	#340	1	2	yes	—
193	C₄×C₂₃	#340	1	2	yes	—
194	C₄×C₂₃	#344	1	2	yes	—
195	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
196	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
197	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
198	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
199	C₄×C₂₃	#430	1	2	yes	—
200	C₂²×M₁₆	—	2	1	no	—
201	C₂²×M₁₆	—	2	1	no	—
202	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
203	#431	—	2	1	no	—
204	#431	—	2	1	no	—
205	#431	C₄×C₂₃	1	2	yes	—
206	#431	C₂²×C₂₃	1	2	yes	—
207	#423	—	2	1	no	—
208	#423	—	2	1	no	—
209	#423	—	2	1	no	—
210	#423	—	2	1	no	—
211	#423	C₄×C₂₃	1	2	yes	—
212	#423	C₄×C₂₃	1	2	yes	—
213	#423	C₄×C₂₃	1	2	yes	—
214	#423	C₂²×C₂₃	1	2	yes	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	—	2	1	no	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
220	C₂×C₂²⋊C₈	C₄×C₂₃	1	2	yes	—
221	C₂×C₄×C₈	—	2	1	no	—
222	C₂×C₂₃	—	2	2	no	—
223	C₂×C₂₃	—	2	2	no	—
224	C₂×C₂₃	—	2	1	no	—
225	C₂×C₂₃	—	2	1	no	—
226	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
227	C₂×C₂₃	#1738	1	1	yes	characteristic
228	C₂×C₂₃	C₂×#344	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
231	C₂³×C₄	Q₈×C₂₃	1	1	yes	characteristic
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	4	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂×M₁₆	—	4	2	no	—
239	C₂×M₁₆	—	4	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
246	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
253	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
264	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	2	2	no	—
269	C₂₃	#8079	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	C₄⋊C₄×C₂₃	1	1	yes	characteristic
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
274	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
287	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
288	C₂²×C₄	D₈×C₂₃	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
290	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
291	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
295	M₁₆	—	4	4	no	—
296	M₁₆	—	4	4	no	—
297	M₁₆	—	4	4	no	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₄²	C₄²×C₂₃	1	1	yes	characteristic
308	C₄²	C₄²×C₂₃	1	1	yes	characteristic
309	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
310	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
311	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
312	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
313	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
314	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
315	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
316	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
317	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
318	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
319	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
320	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₂₃×#95	1	1	yes	characteristic
326	C₂³	C₂₃×#95	1	1	yes	characteristic
327	C₂³	C₂₃×#106	1	2	yes	—
328	C₂³	C₂₃×#107	1	2	yes	—
329	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
343	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
344	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
345	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
346	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
347	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
348	C₂×C₄	C₂₃×#102	1	2	yes	—
349	C₂×C₄	C₂₃×#102	1	2	yes	—
350	C₂×C₄	C₂₃×#102	1	2	yes	—
351	C₂×C₄	C₂₃×#102	1	2	yes	—
352	C₂×C₄	C₂₃×#103	1	2	yes	—
353	C₂×C₄	C₂₃×#103	1	2	yes	—
354	C₂×C₄	C₂₃×#103	1	2	yes	—
355	C₂×C₄	C₂₃×#103	1	2	yes	—
356	C₂×C₄	C₂₃×#106	1	2	yes	—
357	C₂×C₄	C₂₃×#107	1	2	yes	—
358	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
364	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
366	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
367	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	4	4	no	—
370	C₈	—	4	4	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₂₃×#340	1	2	yes	—
380	C₂²	C₂₃×#340	1	2	yes	—
381	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
382	C₂²	C₂×C₂₃×#106	1	1	yes	characteristic
383	C₂²	C₂×C₂₃×#107	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	C₂₃×#340	1	2	yes	—
391	C₄	C₂₃×#340	1	2	yes	—
392	C₄	C₂₃×#344	1	2	yes	—
393	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
394	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
395	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
396	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
397	C₄	C₂₃×#430	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	C₂×C₂₃×#340	1	1	yes	characteristic
403	C₂	C₂₃×#1738	1	1	yes	characteristic
404	C₂	C₂×C₂₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×#95
prime radical	C₂⁴×C₂₃	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1301	C₂	semidirect
120. #8079	C₂₃	direct (N × H)
172. #1301	C₂×C₂₃	semidirect
269. C₂₃	#8079	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×#431	2
C₂×C₂₃×#423	2
C₂₃×#1301	2
#8079	23

Subgroups — C23×#8079 #19155705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8079 #19155705