Subgroups — C₂×C₂₃×#2901 #19207718

Order 5888.

4946 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2901	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#421	C₂	1	6	yes	maximal, complemented
6	C₂²×C₂₃×#104	C₂	1	6	yes	maximal, complemented
7	C₂₃×#585	—	2	4	no	—
8	C₂₃×#585	—	2	4	no	—
9	C₂₃×#585	C₄	1	8	yes	complemented
10	C₂₃×#585	C₂²	1	8	yes	—
11	C₂×C₂₃×2₋¹⁺⁴	—	2	1	no	—
12	C₂×C₂₃×2₋¹⁺⁴	C₄	1	4	yes	complemented
13	C₂×C₂₃×H(5,𝔽₂)	—	2	3	no	—
14	C₂×C₂₃×H(5,𝔽₂)	C₄	1	4	yes	complemented
15	C₂²×#41×C₂₃	—	2	4	no	—
16	C₂²×#41×C₂₃	C₂²	1	6	yes	—
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#568	—	2	4	no	—
19	C₂₃×#568	C₂²	1	8	yes	complemented
20	C₂×C₂₃×#131	—	2	4	no	—
21	C₂²×M₁₆×C₂₃	C₂²	1	6	yes	complemented
22	C₄×#41×C₂₃	—	2	4	no	—
23	C₄×#41×C₂₃	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
25	C₂×C₄×D₄×C₂₃	—	2	3	no	—
26	C₂×C₂₃×#117	C₂²	1	3	yes	complemented
27	C₂²×C₄²×C₂₃	C₂²	1	3	yes	complemented
28	C₂₃×#421	C₂²	1	48	yes	complemented
29	C₂×C₂₃×#104	C₂²	1	4	yes	complemented
30	C₂×C₂₃×#104	C₂²	1	12	yes	complemented
31	C₂×C₂₃×#104	C₂²	1	48	yes	complemented
32	C₂₃×2₋¹⁺⁴	—	2	16	no	—
33	C₂₃×2₋¹⁺⁴	—	2	8	no	—
34	C₂₃×2₋¹⁺⁴	—	2	8	no	—
35	C₂₃×2₋¹⁺⁴	C₂×C₄	1	32	yes	complemented
36	C₂₃×H(5,𝔽₂)	—	2	16	no	—
37	C₂₃×H(5,𝔽₂)	—	2	24	no	—
38	C₂₃×H(5,𝔽₂)	—	2	24	no	—
39	C₂₃×H(5,𝔽₂)	C₂×C₄	1	32	yes	complemented
40	C₂×#41×C₂₃	—	2	32	no	—
41	C₂×#41×C₂₃	—	2	32	no	—
42	C₂×#41×C₂₃	—	2	4	no	—
43	C₂×#41×C₂₃	—	2	12	no	—
44	C₂×#41×C₂₃	—	2	6	no	—
45	C₂×#41×C₂₃	—	2	6	no	—
46	C₂×#41×C₂₃	—	2	12	no	—
47	C₂×#41×C₂₃	—	2	12	no	—
48	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
49	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
50	C₂×#41×C₂₃	C₂×C₄	1	12	yes	complemented
51	C₂×#41×C₂₃	C₂×C₄	1	24	yes	complemented
52	C₂×#41×C₂₃	D₄	1	4	yes	—
53	C₂×#41×C₂₃	D₄	1	4	yes	—
54	C₂×#41×C₂₃	D₄	1	4	yes	—
55	C₂×#41×C₂₃	C₂³	1	4	yes	—
56	C₂×#41×C₂₃	C₂³	1	24	yes	—
57	C₂×#41×C₂₃	C₂³	1	4	yes	—
58	C₂²×Q₈×C₂₃	—	2	4	no	—
59	C₂²×Q₈×C₂₃	C₂×C₄	1	6	yes	complemented
60	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₂₃	—	2	6	no	—
62	C₂²×D₄×C₂₃	—	2	12	no	—
63	C₂²×D₄×C₂₃	C₂×C₄	1	6	yes	complemented
64	C₂²×D₄×C₂₃	D₄	1	3	yes	—
65	C₂³×C₄×C₂₃	—	2	6	no	—
66	C₂³×C₄×C₂₃	—	2	3	no	—
67	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
68	C₂₃×#131	—	2	32	no	—
69	C₂×M₁₆×C₂₃	—	2	6	no	—
70	C₂×M₁₆×C₂₃	—	2	12	no	—
71	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
72	C₂×M₁₆×C₂₃	C₂³	1	24	yes	complemented
73	C₂²×C₈×C₂₃	—	2	6	no	—
74	C₄×Q₈×C₂₃	—	2	8	no	—
75	C₄×D₄×C₂₃	—	2	24	no	—
76	C₂₃×#117	—	2	6	no	—
77	C₂₃×#117	C₂³	1	12	yes	complemented
78	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
79	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
80	C₂×C₄²×C₂₃	—	2	3	no	—
81	C₂×C₄²×C₂₃	—	2	6	no	—
82	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
84	C₂×C₄²×C₂₃	C₂³	1	12	yes	complemented
85	C₂₃×#104	C₂³	1	16	yes	complemented
86	C₂₃×#104	C₂³	1	48	yes	complemented
87	C₂⁴×C₂₃	—	2	6	no	—
88	C₂⁴×C₂₃	C₂×D₄	1	3	yes	—
89	#41×C₂₃	—	2	32	no	—
90	#41×C₂₃	—	2	96	no	—
91	#41×C₂₃	—	2	24	no	—
92	#41×C₂₃	—	2	24	no	—
93	#41×C₂₃	—	2	24	no	—
94	#41×C₂₃	—	2	4	no	—
95	#41×C₂₃	—	2	24	no	—
96	#41×C₂₃	—	2	4	no	—
97	#41×C₂₃	—	2	24	no	—
98	#41×C₂₃	C₂²⋊C₄	1	16	yes	—
99	#41×C₂₃	C₂²⋊C₄	1	16	yes	—
100	#41×C₂₃	C₂²×C₄	1	8	yes	—
101	#41×C₂₃	C₂²×C₄	1	16	yes	—
102	#41×C₂₃	C₂²×C₄	1	48	yes	complemented
103	#41×C₂₃	C₂×D₄	1	16	yes	—
104	#41×C₂₃	C₂⁴	1	8	yes	—
105	C₂×Q₈×C₂₃	—	2	32	no	—
106	C₂×Q₈×C₂₃	—	2	6	no	—
107	C₂×Q₈×C₂₃	—	2	12	no	—
108	C₂×Q₈×C₂₃	C₂²⋊C₄	1	4	yes	—
109	C₂×Q₈×C₂₃	C₂²⋊C₄	1	4	yes	—
110	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
111	C₂×Q₈×C₂₃	C₂²×C₄	1	24	yes	complemented
112	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₂₃	—	2	12	no	—
114	C₂×D₄×C₂₃	—	2	24	no	—
115	C₂×D₄×C₂₃	—	2	4	no	—
116	C₂×D₄×C₂₃	—	2	24	no	—
117	C₂×D₄×C₂₃	—	2	96	no	—
118	C₂×D₄×C₂₃	—	2	6	no	—
119	C₂×D₄×C₂₃	—	2	12	no	—
120	C₂×D₄×C₂₃	C₂²⋊C₄	1	12	yes	—
121	C₂×D₄×C₂₃	C₂²⋊C₄	1	12	yes	—
122	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
123	C₂×D₄×C₂₃	C₂²×C₄	1	24	yes	complemented
124	C₂×D₄×C₂₃	C₂×D₄	1	12	yes	—
125	C₂²×C₄×C₂₃	—	2	6	no	—
126	C₂²×C₄×C₂₃	—	2	1	no	—
127	C₂²×C₄×C₂₃	—	2	12	no	—
128	C₂²×C₄×C₂₃	—	2	24	no	—
129	C₂²×C₄×C₂₃	—	2	24	no	—
130	C₂²×C₄×C₂₃	—	2	4	no	—
131	C₂²×C₄×C₂₃	—	2	3	no	—
132	C₂²×C₄×C₂₃	—	2	12	no	—
133	C₂²×C₄×C₂₃	—	4	12	no	—
134	C₂²×C₄×C₂₃	C₂²×C₄	1	6	yes	—
135	C₂²×C₄×C₂₃	C₂²×C₄	1	6	yes	—
136	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
137	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
138	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
139	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
140	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
141	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
142	M₁₆×C₂₃	—	2	4	no	—
143	M₁₆×C₂₃	—	2	24	no	—
144	M₁₆×C₂₃	C₂⁴	1	8	yes	—
145	C₂×C₈×C₂₃	—	2	24	no	—
146	C₂×C₈×C₂₃	—	2	4	no	—
147	C₄⋊C₄×C₂₃	—	2	12	no	—
148	C₂²⋊C₄×C₂₃	—	2	12	no	—
149	C₄²×C₂₃	—	2	1	no	—
150	C₄²×C₂₃	—	2	3	no	—
151	C₄²×C₂₃	—	2	12	no	—
152	C₄²×C₂₃	C₂⁴	1	2	yes	—
153	C₄²×C₂₃	C₂⁴	1	6	yes	—
154	C₂×#2901	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₂₃	—	2	4	no	—
156	C₂³×C₂₃	—	2	24	no	—
157	C₂³×C₂₃	—	4	6	no	—
158	C₂³×C₂₃	—	8	12	no	—
159	C₂³×C₂₃	C₂×C₂²⋊C₄	1	6	yes	—
160	C₂³×C₂₃	C₂×C₂²⋊C₄	1	6	yes	—
161	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
162	C₂³×C₂₃	C₂²×D₄	1	6	yes	—
163	Q₈×C₂₃	—	2	4	no	—
164	Q₈×C₂₃	—	2	24	no	—
165	Q₈×C₂₃	C₂×C₂²⋊C₄	1	16	yes	—
166	Q₈×C₂₃	C₂³×C₄	1	8	yes	—
167	D₄×C₂₃	—	2	8	no	—
168	D₄×C₂₃	—	2	48	no	—
169	D₄×C₂₃	—	2	8	no	—
170	D₄×C₂₃	—	2	4	no	—
171	D₄×C₂₃	—	2	24	no	—
172	D₄×C₂₃	C₂×C₂²⋊C₄	1	48	yes	—
173	D₄×C₂₃	C₂³×C₄	1	8	yes	—
174	C₂×C₄×C₂₃	—	2	4	no	—
175	C₂×C₄×C₂₃	—	2	4	no	—
176	C₂×C₄×C₂₃	—	2	24	no	—
177	C₂×C₄×C₂₃	—	2	2	no	—
178	C₂×C₄×C₂₃	—	2	8	no	—
179	C₂×C₄×C₂₃	—	2	48	no	—
180	C₂×C₄×C₂₃	—	2	8	no	—
181	C₂×C₄×C₂₃	—	2	6	no	—
182	C₂×C₄×C₂₃	—	4	24	no	—
183	C₂×C₄×C₂₃	—	4	6	no	—
184	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	6	yes	—
185	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
186	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
187	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	6	yes	—
188	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₂₃	C₂³×C₄	1	12	yes	—
191	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
194	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
197	C₈×C₂₃	—	2	8	no	—
198	C₂×#585	C₂×C₂₃	1	1	yes	characteristic
199	C₂×#568	C₂×C₂₃	1	1	yes	characteristic, complemented
200	C₂×C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
201	#2901	C₂×C₂₃	1	16	yes	direct product factor
202	C₂×#421	C₂×C₂₃	1	6	yes	complemented
203	C₂²×#104	C₂×C₂₃	1	6	yes	complemented
204	C₂²×C₂₃	—	2	2	no	—
205	C₂²×C₂₃	—	2	12	no	—
206	C₂²×C₂₃	—	2	8	no	—
207	C₂²×C₂₃	—	4	6	no	—
208	C₂²×C₂₃	—	4	6	no	—
209	C₂²×C₂₃	—	4	8	no	—
210	C₂²×C₂₃	—	8	24	no	—
211	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
212	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₂₃	—	2	4	no	—
216	C₄×C₂₃	—	2	8	no	—
217	C₄×C₂₃	—	4	6	no	—
218	C₄×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
219	C₄×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
220	C₄×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₄×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
222	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
223	#585	—	2	4	no	—
224	#585	—	2	4	no	—
225	#585	C₄×C₂₃	1	8	yes	complemented
226	#585	C₂²×C₂₃	1	8	yes	—
227	C₂×2₋¹⁺⁴	—	2	1	no	—
228	C₂×2₋¹⁺⁴	C₄×C₂₃	1	4	yes	complemented
229	C₂×H(5,𝔽₂)	—	2	3	no	—
230	C₂×H(5,𝔽₂)	C₄×C₂₃	1	4	yes	complemented
231	C₂²×#41	—	2	4	no	—
232	C₂²×#41	C₂²×C₂₃	1	6	yes	—
233	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
234	#568	—	2	4	no	—
235	#568	C₂²×C₂₃	1	8	yes	complemented
236	C₂×#131	—	2	4	no	—
237	C₂²×M₁₆	C₂²×C₂₃	1	6	yes	complemented
238	C₄×#41	—	2	4	no	—
239	C₄×#41	C₂²×C₂₃	1	8	yes	complemented
240	C₂×C₄×Q₈	—	2	1	no	—
241	C₂×C₄×D₄	—	2	3	no	—
242	C₂×#117	C₂²×C₂₃	1	3	yes	complemented
243	C₂²×C₄²	C₂²×C₂₃	1	3	yes	complemented
244	#421	C₂²×C₂₃	1	48	yes	complemented
245	C₂×#104	C₂²×C₂₃	1	4	yes	complemented
246	C₂×#104	C₂²×C₂₃	1	12	yes	complemented
247	C₂×#104	C₂²×C₂₃	1	48	yes	complemented
248	C₂×C₂₃	—	2	1	no	—
249	C₂×C₂₃	—	2	1	no	—
250	C₂×C₂₃	—	2	12	no	—
251	C₂×C₂₃	—	4	8	no	—
252	C₂×C₂₃	#2901	1	2	yes	direct product factor
253	C₂×C₂₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
254	2₋¹⁺⁴	—	2	16	no	—
255	2₋¹⁺⁴	—	2	8	no	—
256	2₋¹⁺⁴	—	2	8	no	—
257	2₋¹⁺⁴	C₂×C₄×C₂₃	1	32	yes	complemented
258	H(5,𝔽₂)	—	2	16	no	—
259	H(5,𝔽₂)	—	2	24	no	—
260	H(5,𝔽₂)	—	2	24	no	—
261	H(5,𝔽₂)	C₂×C₄×C₂₃	1	32	yes	complemented
262	C₂×#41	—	2	32	no	—
263	C₂×#41	—	2	32	no	—
264	C₂×#41	—	2	4	no	—
265	C₂×#41	—	2	12	no	—
266	C₂×#41	—	2	6	no	—
267	C₂×#41	—	2	6	no	—
268	C₂×#41	—	2	12	no	—
269	C₂×#41	—	2	12	no	—
270	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
271	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
272	C₂×#41	C₂×C₄×C₂₃	1	12	yes	complemented
273	C₂×#41	C₂×C₄×C₂₃	1	24	yes	complemented
274	C₂×#41	D₄×C₂₃	1	4	yes	—
275	C₂×#41	D₄×C₂₃	1	4	yes	—
276	C₂×#41	D₄×C₂₃	1	4	yes	—
277	C₂×#41	C₂³×C₂₃	1	4	yes	—
278	C₂×#41	C₂³×C₂₃	1	24	yes	—
279	C₂×#41	C₂³×C₂₃	1	4	yes	—
280	C₂²×Q₈	—	2	4	no	—
281	C₂²×Q₈	C₂×C₄×C₂₃	1	6	yes	complemented
282	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
283	C₂²×D₄	—	2	6	no	—
284	C₂²×D₄	—	2	12	no	—
285	C₂²×D₄	C₂×C₄×C₂₃	1	6	yes	complemented
286	C₂²×D₄	D₄×C₂₃	1	3	yes	—
287	C₂³×C₄	—	2	6	no	—
288	C₂³×C₄	—	2	3	no	—
289	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
290	#131	—	2	32	no	—
291	C₂×M₁₆	—	2	6	no	—
292	C₂×M₁₆	—	2	12	no	—
293	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
294	C₂×M₁₆	C₂³×C₂₃	1	24	yes	complemented
295	C₂²×C₈	—	2	6	no	—
296	C₄×Q₈	—	2	8	no	—
297	C₄×D₄	—	2	24	no	—
298	#117	—	2	6	no	—
299	#117	C₂³×C₂₃	1	12	yes	complemented
300	C₂×C₄⋊C₄	—	2	3	no	—
301	C₂×C₂²⋊C₄	—	2	3	no	—
302	C₂×C₄²	—	2	3	no	—
303	C₂×C₄²	—	2	6	no	—
304	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
305	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₂₃	1	12	yes	complemented
307	#104	C₂³×C₂₃	1	16	yes	complemented
308	#104	C₂³×C₂₃	1	48	yes	complemented
309	C₂₃	C₂×#2901	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	—	2	6	no	—
311	C₂⁴	C₂×D₄×C₂₃	1	3	yes	—
312	#41	—	2	32	no	—
313	#41	—	2	96	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	—	2	24	no	—
317	#41	—	2	24	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	#41	—	2	24	no	—
321	#41	C₂²⋊C₄×C₂₃	1	16	yes	—
322	#41	C₂²⋊C₄×C₂₃	1	16	yes	—
323	#41	C₂²×C₄×C₂₃	1	8	yes	—
324	#41	C₂²×C₄×C₂₃	1	16	yes	—
325	#41	C₂²×C₄×C₂₃	1	48	yes	complemented
326	#41	C₂×D₄×C₂₃	1	16	yes	—
327	#41	C₂⁴×C₂₃	1	8	yes	—
328	C₂×Q₈	—	2	32	no	—
329	C₂×Q₈	—	2	6	no	—
330	C₂×Q₈	—	2	12	no	—
331	C₂×Q₈	C₂²⋊C₄×C₂₃	1	4	yes	—
332	C₂×Q₈	C₂²⋊C₄×C₂₃	1	4	yes	—
333	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
334	C₂×Q₈	C₂²×C₄×C₂₃	1	24	yes	complemented
335	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
336	C₂×D₄	—	2	12	no	—
337	C₂×D₄	—	2	24	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	24	no	—
340	C₂×D₄	—	2	96	no	—
341	C₂×D₄	—	2	6	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	C₂²⋊C₄×C₂₃	1	12	yes	—
344	C₂×D₄	C₂²⋊C₄×C₂₃	1	12	yes	—
345	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
346	C₂×D₄	C₂²×C₄×C₂₃	1	24	yes	complemented
347	C₂×D₄	C₂×D₄×C₂₃	1	12	yes	—
348	C₂²×C₄	—	2	6	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	12	no	—
351	C₂²×C₄	—	2	24	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	24	no	—
354	C₂²×C₄	—	2	3	no	—
355	C₂²×C₄	—	2	12	no	—
356	C₂²×C₄	—	4	12	no	—
357	C₂²×C₄	C₂²×C₄×C₂₃	1	6	yes	—
358	C₂²×C₄	C₂²×C₄×C₂₃	1	6	yes	—
359	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
360	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
361	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
362	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
363	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	24	no	—
367	M₁₆	C₂⁴×C₂₃	1	8	yes	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	24	no	—
370	C₄⋊C₄	—	2	12	no	—
371	C₂²⋊C₄	—	2	12	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	3	no	—
374	C₄²	—	2	12	no	—
375	C₄²	C₂⁴×C₂₃	1	2	yes	—
376	C₄²	C₂⁴×C₂₃	1	6	yes	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	24	no	—
379	C₂³	—	4	6	no	—
380	C₂³	—	8	12	no	—
381	C₂³	C₂×C₂²⋊C₄×C₂₃	1	6	yes	—
382	C₂³	C₂×C₂²⋊C₄×C₂₃	1	6	yes	—
383	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
384	C₂³	C₂²×D₄×C₂₃	1	6	yes	—
385	Q₈	—	2	4	no	—
386	Q₈	—	2	24	no	—
387	Q₈	C₂×C₂²⋊C₄×C₂₃	1	16	yes	—
388	Q₈	C₂³×C₄×C₂₃	1	8	yes	—
389	D₄	—	2	8	no	—
390	D₄	—	2	8	no	—
391	D₄	—	2	48	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	24	no	—
394	D₄	C₂×C₂²⋊C₄×C₂₃	1	48	yes	—
395	D₄	C₂³×C₄×C₂₃	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	24	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	48	no	—
403	C₂×C₄	—	2	6	no	—
404	C₂×C₄	—	4	24	no	—
405	C₂×C₄	—	4	6	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	6	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	6	yes	—
410	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
411	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₄×C₂₃	1	12	yes	—
413	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
415	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
418	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
419	C₈	—	2	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	12	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	4	6	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	8	24	no	—
427	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
428	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
429	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
430	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
431	C₄	—	2	4	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	6	no	—
434	C₄	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
435	C₄	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
436	C₄	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
437	C₄	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
438	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	2	12	no	—
442	C₂	—	4	8	no	—
443	C₂	C₂₃×#2901	1	2	yes	direct product factor
444	C₂	C₂³×C₂²⋊C₄×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
prime radical	C₂×C₂₃×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#568	C₂	semidirect
3. C₂×C₄×#41×C₂₃	C₂	semidirect
4. C₂₃×#2901	C₂	direct (N × H)
5. C₂×C₂₃×#421	C₂	semidirect
6. C₂²×C₂₃×#104	C₂	semidirect
9. C₂₃×#585	C₄	semidirect
12. C₂×C₂₃×2₋¹⁺⁴	C₄	semidirect
14. C₂×C₂₃×H(5,𝔽₂)	C₄	semidirect
19. C₂₃×#568	C₂²	semidirect
21. C₂²×M₁₆×C₂₃	C₂²	semidirect
23. C₄×#41×C₂₃	C₂²	semidirect
26. C₂×C₂₃×#117	C₂²	semidirect
27. C₂²×C₄²×C₂₃	C₂²	semidirect
28. C₂₃×#421	C₂²	semidirect
29. C₂×C₂₃×#104	C₂²	semidirect
30. C₂×C₂₃×#104	C₂²	semidirect
31. C₂×C₂₃×#104	C₂²	semidirect
35. C₂₃×2₋¹⁺⁴	C₂×C₄	semidirect
39. C₂₃×H(5,𝔽₂)	C₂×C₄	semidirect
50. C₂×#41×C₂₃	C₂×C₄	semidirect
51. C₂×#41×C₂₃	C₂×C₄	semidirect
59. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
63. C₂²×D₄×C₂₃	C₂×C₄	semidirect
72. C₂×M₁₆×C₂₃	C₂³	semidirect
77. C₂₃×#117	C₂³	semidirect
84. C₂×C₄²×C₂₃	C₂³	semidirect
85. C₂₃×#104	C₂³	semidirect
86. C₂₃×#104	C₂³	semidirect
102. #41×C₂₃	C₂²×C₄	semidirect
111. C₂×Q₈×C₂₃	C₂²×C₄	semidirect
123. C₂×D₄×C₂₃	C₂²×C₄	semidirect
154. C₂×#2901	C₂₃	direct (N × H)
199. C₂×#568	C₂×C₂₃	semidirect
200. C₂×C₄×#41	C₂×C₂₃	semidirect
201. #2901	C₂×C₂₃	direct (N × H)
202. C₂×#421	C₂×C₂₃	semidirect
203. C₂²×#104	C₂×C₂₃	semidirect
225. #585	C₄×C₂₃	semidirect
228. C₂×2₋¹⁺⁴	C₄×C₂₃	semidirect
230. C₂×H(5,𝔽₂)	C₄×C₂₃	semidirect
235. #568	C₂²×C₂₃	semidirect
237. C₂²×M₁₆	C₂²×C₂₃	semidirect
239. C₄×#41	C₂²×C₂₃	semidirect
242. C₂×#117	C₂²×C₂₃	semidirect
243. C₂²×C₄²	C₂²×C₂₃	semidirect
244. #421	C₂²×C₂₃	semidirect
245. C₂×#104	C₂²×C₂₃	semidirect
246. C₂×#104	C₂²×C₂₃	semidirect
247. C₂×#104	C₂²×C₂₃	semidirect
252. C₂×C₂₃	#2901	direct (N × H)
257. 2₋¹⁺⁴	C₂×C₄×C₂₃	semidirect
261. H(5,𝔽₂)	C₂×C₄×C₂₃	semidirect
272. C₂×#41	C₂×C₄×C₂₃	semidirect
273. C₂×#41	C₂×C₄×C₂₃	semidirect
281. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
285. C₂²×D₄	C₂×C₄×C₂₃	semidirect
294. C₂×M₁₆	C₂³×C₂₃	semidirect
299. #117	C₂³×C₂₃	semidirect
306. C₂×C₄²	C₂³×C₂₃	semidirect
307. #104	C₂³×C₂₃	semidirect
308. #104	C₂³×C₂₃	semidirect
309. C₂₃	C₂×#2901	direct (N × H)
325. #41	C₂²×C₄×C₂₃	semidirect
334. C₂×Q₈	C₂²×C₄×C₂₃	semidirect
346. C₂×D₄	C₂²×C₄×C₂₃	semidirect
443. C₂	C₂₃×#2901	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×#585	2
C₂×C₂₃×#568	2
C₂×C₄×#41×C₂₃	2
C₂₃×#2901	2
C₂×C₂₃×#421	2
C₂²×C₂₃×#104	2
C₂×#2901	23

Subgroups — C2×C23×#2901 #19207718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2901 #19207718