Subgroups — C₂×C₂₃×#3199 #19208369

Order 5888.

2506 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×#535	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3199	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#482	C₂	1	4	yes	maximal, complemented
4	C₂×C₂₃×#469	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#447	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
10	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
11	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
14	C₂₃×#535	—	2	8	no	—
15	C₂₃×#535	C₂²	1	16	yes	complemented
16	C₂×C₂₃×#127	—	2	2	no	—
17	C₂×C₂₃×#124	—	2	2	no	—
18	C₂×C₂₃×#121	C₂²	1	4	yes	—
19	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
20	C₂×C₂₃×#120	—	2	2	no	—
21	C₂×C₂₃×#120	—	2	2	no	—
22	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
23	C₂₃×#482	C₂²	1	32	yes	complemented
24	C₂₃×#469	C₂²	1	16	yes	complemented
25	C₂₃×#466	C₂²	1	16	yes	complemented
26	C₂₃×#447	C₂²	1	32	yes	complemented
27	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
28	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
30	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
31	C₂₃×#408	C₂²	1	8	yes	complemented
32	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
33	C₂⁵×C₂₃	—	2	2	no	—
34	C₂×#41×C₂₃	—	4	2	no	—
35	C₂×#41×C₂₃	—	4	2	no	—
36	C₂×#41×C₂₃	D₄	1	4	yes	—
37	C₂×#41×C₂₃	C₂³	1	4	yes	—
38	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₂₃	—	2	4	no	—
40	C₂²×D₄×C₂₃	—	2	4	no	—
41	C₂²×D₄×C₂₃	—	2	2	no	—
42	C₂²×D₄×C₂₃	—	2	4	no	—
43	C₂²×D₄×C₂₃	—	4	4	no	—
44	C₂²×D₄×C₂₃	—	4	4	no	—
45	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₂₃	D₄	1	2	yes	—
47	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
48	C₂²×D₄×C₂₃	C₂³	1	8	yes	complemented
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
51	C₂×D₈×C₂₃	—	4	4	no	—
52	C₂×D₈×C₂₃	—	4	4	no	—
53	C₂×D₈×C₂₃	C₂³	1	8	yes	—
54	C₂×D₈×C₂₃	C₂³	1	8	yes	—
55	C₂×M₁₆×C₂₃	—	4	2	no	—
56	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
57	C₂²×C₈×C₂₃	—	4	2	no	—
58	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₂₃	C₂³	1	4	yes	complemented
61	C₂₃×#127	—	2	16	no	—
62	C₂₃×#124	—	2	16	no	—
63	C₂₃×#121	—	2	8	no	—
64	C₂₃×#121	—	2	8	no	—
65	C₂₃×#121	C₂³	1	16	yes	—
66	C₂₃×#121	C₂³	1	16	yes	complemented
67	C₂₃×#120	—	2	16	no	—
68	C₂₃×#120	—	2	16	no	—
69	C₂₃×#117	—	2	4	no	—
70	C₂₃×#117	C₂³	1	8	yes	complemented
71	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂₃×#107	C₂³	1	8	yes	complemented
77	C₂₃×#106	C₂³	1	8	yes	complemented
78	C₂₃×#102	C₂³	1	16	yes	complemented
79	C₂₃×#102	C₂³	1	16	yes	complemented
80	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
81	C₂⁴×C₂₃	—	2	4	no	—
82	C₂⁴×C₂₃	—	2	8	no	—
83	C₂⁴×C₂₃	—	4	8	no	—
84	C₂⁴×C₂₃	—	8	8	no	—
85	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
86	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
87	#41×C₂₃	—	4	8	no	—
88	#41×C₂₃	—	4	4	no	—
89	#41×C₂₃	—	4	4	no	—
90	C₂×Q₈×C₂₃	—	4	2	no	—
91	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₂₃	—	2	16	no	—
93	C₂×D₄×C₂₃	—	2	16	no	—
94	C₂×D₄×C₂₃	—	2	4	no	—
95	C₂×D₄×C₂₃	—	2	8	no	—
96	C₂×D₄×C₂₃	—	2	8	no	—
97	C₂×D₄×C₂₃	—	2	8	no	—
98	C₂×D₄×C₂₃	—	4	8	no	—
99	C₂×D₄×C₂₃	—	4	8	no	—
100	C₂×D₄×C₂₃	—	4	4	no	—
101	C₂×D₄×C₂₃	—	4	2	no	—
102	C₂×D₄×C₂₃	—	4	8	no	—
103	C₂×D₄×C₂₃	—	4	16	no	—
104	C₂×D₄×C₂₃	—	8	8	no	—
105	C₂×D₄×C₂₃	—	8	8	no	—
106	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₂₃	C₂×D₄	1	8	yes	—
108	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₂₃	—	2	2	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	4	no	—
112	C₂²×C₄×C₂₃	—	2	4	no	—
113	C₂²×C₄×C₂₃	—	2	4	no	—
114	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
121	D₈×C₂₃	—	4	8	no	—
122	D₈×C₂₃	—	4	8	no	—
123	M₁₆×C₂₃	—	4	4	no	—
124	C₂×C₈×C₂₃	—	2	4	no	—
125	C₂×C₈×C₂₃	—	2	4	no	—
126	C₂×C₈×C₂₃	—	4	4	no	—
127	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
128	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
129	C₄⋊C₄×C₂₃	—	2	4	no	—
130	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
131	C₂²⋊C₄×C₂₃	—	2	8	no	—
132	C₂²⋊C₄×C₂₃	—	2	16	no	—
133	C₂²⋊C₄×C₂₃	—	2	16	no	—
134	C₄²×C₂₃	—	2	8	no	—
135	C₂×#3199	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₂₃	—	2	4	no	—
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	2	4	no	—
139	C₂³×C₂₃	—	2	8	no	—
140	C₂³×C₂₃	—	2	8	no	—
141	C₂³×C₂₃	—	4	16	no	—
142	C₂³×C₂₃	—	4	8	no	—
143	C₂³×C₂₃	—	4	8	no	—
144	C₂³×C₂₃	—	4	8	no	—
145	C₂³×C₂₃	—	8	16	no	—
146	C₂³×C₂₃	—	8	32	no	—
147	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
148	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
149	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₂₃	—	4	4	no	—
151	D₄×C₂₃	—	2	8	no	—
152	D₄×C₂₃	—	2	8	no	—
153	D₄×C₂₃	—	4	8	no	—
154	D₄×C₂₃	—	4	4	no	—
155	D₄×C₂₃	—	4	16	no	—
156	D₄×C₂₃	—	4	8	no	—
157	D₄×C₂₃	—	8	16	no	—
158	D₄×C₂₃	—	8	16	no	—
159	C₂×C₄×C₂₃	—	2	4	no	—
160	C₂×C₄×C₂₃	—	2	2	no	—
161	C₂×C₄×C₂₃	—	2	8	no	—
162	C₂×C₄×C₂₃	—	2	4	no	—
163	C₂×C₄×C₂₃	—	2	2	no	—
164	C₂×C₄×C₂₃	—	2	2	no	—
165	C₂×C₄×C₂₃	—	2	4	no	—
166	C₂×C₄×C₂₃	—	2	4	no	—
167	C₂×C₄×C₂₃	—	2	8	no	—
168	C₂×C₄×C₂₃	—	4	8	no	—
169	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
173	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
174	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
175	C₈×C₂₃	—	2	4	no	—
176	C₈×C₂₃	—	2	4	no	—
177	C₂×#535	C₂×C₂₃	1	2	yes	complemented
178	#3199	C₂×C₂₃	1	16	yes	direct product factor
179	C₂×#482	C₂×C₂₃	1	4	yes	complemented
180	C₂×#469	C₂×C₂₃	1	2	yes	complemented
181	C₂×#466	C₂×C₂₃	1	2	yes	complemented
182	C₂×#447	C₂×C₂₃	1	4	yes	complemented
183	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
184	C₂²×C₂₃	—	2	4	no	—
185	C₂²×C₂₃	—	2	2	no	—
186	C₂²×C₂₃	—	2	4	no	—
187	C₂²×C₂₃	—	2	8	no	—
188	C₂²×C₂₃	—	4	4	no	—
189	C₂²×C₂₃	—	4	8	no	—
190	C₂²×C₂₃	—	4	8	no	—
191	C₂²×C₂₃	—	4	8	no	—
192	C₂²×C₂₃	—	4	8	no	—
193	C₂²×C₂₃	—	8	32	no	—
194	C₂²×C₂₃	—	8	16	no	—
195	C₂²×C₂₃	#534	1	2	yes	—
196	C₂²×C₂₃	#576	1	4	yes	—
197	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
198	C₄×C₂₃	—	2	4	no	—
199	C₄×C₂₃	—	2	2	no	—
200	C₄×C₂₃	—	4	8	no	—
201	C₄×C₂₃	#534	1	2	yes	—
202	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
203	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
205	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
206	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
207	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
208	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
209	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
210	#535	—	2	8	no	—
211	#535	C₂²×C₂₃	1	16	yes	complemented
212	C₂×#127	—	2	2	no	—
213	C₂×#124	—	2	2	no	—
214	C₂×#121	C₂²×C₂₃	1	4	yes	—
215	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
216	C₂×#120	—	2	2	no	—
217	C₂×#120	—	2	2	no	—
218	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
219	#482	C₂²×C₂₃	1	32	yes	complemented
220	#469	C₂²×C₂₃	1	16	yes	complemented
221	#466	C₂²×C₂₃	1	16	yes	complemented
222	#447	C₂²×C₂₃	1	32	yes	complemented
223	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
224	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
225	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
226	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
227	#408	C₂²×C₂₃	1	8	yes	complemented
228	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
229	C₂×C₂₃	—	4	2	no	—
230	C₂×C₂₃	—	4	4	no	—
231	C₂×C₂₃	—	8	8	no	—
232	C₂×C₂₃	#3199	1	4	yes	direct product factor
233	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
234	C₂×C₂₃	C₂×#576	1	2	yes	—
235	C₂⁵	—	2	2	no	—
236	C₂×#41	—	4	2	no	—
237	C₂×#41	—	4	2	no	—
238	C₂×#41	D₄×C₂₃	1	4	yes	—
239	C₂×#41	C₂³×C₂₃	1	4	yes	—
240	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
241	C₂²×D₄	—	2	4	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	4	no	—
245	C₂²×D₄	—	4	4	no	—
246	C₂²×D₄	—	4	4	no	—
247	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
248	C₂²×D₄	D₄×C₂₃	1	2	yes	—
249	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
250	C₂²×D₄	C₂³×C₂₃	1	8	yes	complemented
251	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
252	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
253	C₂×D₈	—	4	4	no	—
254	C₂×D₈	—	4	4	no	—
255	C₂×D₈	C₂³×C₂₃	1	8	yes	—
256	C₂×D₈	C₂³×C₂₃	1	8	yes	—
257	C₂×M₁₆	—	4	2	no	—
258	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
259	C₂²×C₈	—	4	2	no	—
260	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₂₃	1	4	yes	complemented
263	#127	—	2	16	no	—
264	#124	—	2	16	no	—
265	#121	—	2	8	no	—
266	#121	—	2	8	no	—
267	#121	C₂³×C₂₃	1	16	yes	—
268	#121	C₂³×C₂₃	1	16	yes	complemented
269	#120	—	2	16	no	—
270	#120	—	2	16	no	—
271	#117	—	2	4	no	—
272	#117	C₂³×C₂₃	1	8	yes	complemented
273	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₄²	—	2	2	no	—
278	#107	C₂³×C₂₃	1	8	yes	complemented
279	#106	C₂³×C₂₃	1	8	yes	complemented
280	#102	C₂³×C₂₃	1	16	yes	complemented
281	#102	C₂³×C₂₃	1	16	yes	complemented
282	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	complemented
283	C₂₃	C₂×#3199	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	4	8	no	—
287	C₂⁴	—	8	8	no	—
288	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
289	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
290	#41	—	4	8	no	—
291	#41	—	4	4	no	—
292	#41	—	4	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	4	16	no	—
307	C₂×D₄	—	8	8	no	—
308	C₂×D₄	—	8	8	no	—
309	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
310	C₂×D₄	C₂×D₄×C₂₃	1	8	yes	—
311	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
324	D₈	—	4	8	no	—
325	D₈	—	4	8	no	—
326	M₁₆	—	4	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	4	4	no	—
330	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
331	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	16	no	—
336	C₂²⋊C₄	—	2	16	no	—
337	C₄²	—	2	8	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	4	16	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	8	no	—
346	C₂³	—	4	8	no	—
347	C₂³	—	8	16	no	—
348	C₂³	—	8	32	no	—
349	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
350	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
351	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
352	Q₈	—	4	4	no	—
353	D₄	—	2	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	16	no	—
358	D₄	—	4	8	no	—
359	D₄	—	8	16	no	—
360	D₄	—	8	16	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	4	8	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	8	32	no	—
389	C₂²	—	8	16	no	—
390	C₂²	C₂₃×#534	1	2	yes	—
391	C₂²	C₂₃×#576	1	4	yes	—
392	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	8	no	—
396	C₄	C₂₃×#534	1	2	yes	—
397	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
398	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	4	2	no	—
401	C₂	—	8	8	no	—
402	C₂	C₂₃×#3199	1	4	yes	direct product factor
403	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
404	C₂	C₂×C₂₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#535	C₂	semidirect
2. C₂₃×#3199	C₂	direct (N × H)
3. C₂×C₂₃×#482	C₂	semidirect
4. C₂×C₂₃×#469	C₂	semidirect
5. C₂×C₂₃×#466	C₂	semidirect
6. C₂×C₂₃×#447	C₂	semidirect
7. C₂×C₂₃×#408	C₂	semidirect
9. C₂³×D₄×C₂₃	C₂²	semidirect
12. C₂²×M₁₆×C₂₃	C₂²	semidirect
13. C₂³×C₈×C₂₃	C₂²	semidirect
15. C₂₃×#535	C₂²	semidirect
19. C₂×C₂₃×#121	C₂²	semidirect
22. C₂×C₂₃×#117	C₂²	semidirect
23. C₂₃×#482	C₂²	semidirect
24. C₂₃×#469	C₂²	semidirect
25. C₂₃×#466	C₂²	semidirect
26. C₂₃×#447	C₂²	semidirect
27. C₂×C₂₃×#107	C₂²	semidirect
28. C₂×C₂₃×#106	C₂²	semidirect
29. C₂×C₂₃×#102	C₂²	semidirect
30. C₂×C₂₃×#102	C₂²	semidirect
31. C₂₃×#408	C₂²	semidirect
32. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
48. C₂²×D₄×C₂₃	C₂³	semidirect
56. C₂×M₁₆×C₂₃	C₂³	semidirect
60. C₂²×C₈×C₂₃	C₂³	semidirect
66. C₂₃×#121	C₂³	semidirect
70. C₂₃×#117	C₂³	semidirect
76. C₂₃×#107	C₂³	semidirect
77. C₂₃×#106	C₂³	semidirect
78. C₂₃×#102	C₂³	semidirect
79. C₂₃×#102	C₂³	semidirect
80. C₂₃×C₂²⋊C₈	C₂³	semidirect
135. C₂×#3199	C₂₃	direct (N × H)
177. C₂×#535	C₂×C₂₃	semidirect
178. #3199	C₂×C₂₃	direct (N × H)
179. C₂×#482	C₂×C₂₃	semidirect
180. C₂×#469	C₂×C₂₃	semidirect
181. C₂×#466	C₂×C₂₃	semidirect
182. C₂×#447	C₂×C₂₃	semidirect
183. C₂×#408	C₂×C₂₃	semidirect
205. C₂³×D₄	C₂²×C₂₃	semidirect
208. C₂²×M₁₆	C₂²×C₂₃	semidirect
209. C₂³×C₈	C₂²×C₂₃	semidirect
211. #535	C₂²×C₂₃	semidirect
215. C₂×#121	C₂²×C₂₃	semidirect
218. C₂×#117	C₂²×C₂₃	semidirect
219. #482	C₂²×C₂₃	semidirect
220. #469	C₂²×C₂₃	semidirect
221. #466	C₂²×C₂₃	semidirect
222. #447	C₂²×C₂₃	semidirect
223. C₂×#107	C₂²×C₂₃	semidirect
224. C₂×#106	C₂²×C₂₃	semidirect
225. C₂×#102	C₂²×C₂₃	semidirect
226. C₂×#102	C₂²×C₂₃	semidirect
227. #408	C₂²×C₂₃	semidirect
228. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
232. C₂×C₂₃	#3199	direct (N × H)
250. C₂²×D₄	C₂³×C₂₃	semidirect
258. C₂×M₁₆	C₂³×C₂₃	semidirect
262. C₂²×C₈	C₂³×C₂₃	semidirect
268. #121	C₂³×C₂₃	semidirect
272. #117	C₂³×C₂₃	semidirect
278. #107	C₂³×C₂₃	semidirect
279. #106	C₂³×C₂₃	semidirect
280. #102	C₂³×C₂₃	semidirect
281. #102	C₂³×C₂₃	semidirect
282. C₂²⋊C₈	C₂³×C₂₃	semidirect
283. C₂₃	C₂×#3199	direct (N × H)
402. C₂	C₂₃×#3199	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×#535	2
C₂₃×#3199	2
C₂×C₂₃×#482	2
C₂×C₂₃×#469	2
C₂×C₂₃×#466	2
C₂×C₂₃×#447	2
C₂×C₂₃×#408	2
C₂×#3199	23

Subgroups — C2×C23×#3199 #19208369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3199 #19208369