Subgroups — #3496×C₂₃₉ #44482266

Order 30592.

1660 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×C₂₃₉	C₂	1	2	yes	maximal, complemented
2	#547×C₂₃₉	C₂	1	4	yes	maximal, complemented
3	#546×C₂₃₉	C₂	1	8	yes	maximal, complemented
4	D₄²×C₂₃₉	C₂	1	4	yes	maximal, complemented
5	#537×C₂₃₉	C₂	1	2	yes	maximal, complemented
6	#534×C₂₃₉	C₂	1	4	yes	maximal, complemented
7	#532×C₂₃₉	C₂	1	2	yes	maximal, complemented
8	C₂×#121×C₂₃₉	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×D₄×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	H(5,𝔽₂)×C₂₃₉	—	2	16	no	—
11	C₂×#41×C₂₃₉	C₂²	1	4	yes	complemented
12	C₂×#41×C₂₃₉	C₂²	1	8	yes	complemented
13	C₂²×D₄×C₂₃₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₂₃₉	C₂²	1	8	yes	complemented
15	C₂²×D₄×C₂₃₉	C₂²	1	8	yes	complemented
16	C₂²×D₄×C₂₃₉	C₂²	1	4	yes	complemented
17	C₂³×C₄×C₂₃₉	C₂²	1	2	yes	complemented
18	C₄⋊Q₈×C₂₃₉	C₂²	1	2	yes	complemented
19	#127×C₂₃₉	C₂²	1	2	yes	complemented
20	#124×C₂₃₉	C₂²	1	4	yes	complemented
21	#123×C₂₃₉	C₂²	1	16	yes	complemented
22	C₂²⋊Q₈×C₂₃₉	C₂²	1	8	yes	complemented
23	#121×C₂₃₉	C₂²	1	4	yes	complemented
24	#121×C₂₃₉	C₂²	1	8	yes	complemented
25	#121×C₂₃₉	C₂²	1	8	yes	complemented
26	#121×C₂₃₉	C₂²	1	8	yes	complemented
27	#121×C₂₃₉	C₂²	1	4	yes	complemented
28	#121×C₂₃₉	C₂²	1	8	yes	complemented
29	#120×C₂₃₉	C₂²	1	16	yes	complemented
30	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
31	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
32	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
33	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
34	C₂×C₄⋊C₄×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄⋊C₄×C₂₃₉	C₂²	1	4	yes	complemented
36	C₂×C₂²⋊C₄×C₂₃₉	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊C₄×C₂₃₉	C₂²	1	8	yes	complemented
38	C₂×C₄²×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
39	C₂⁴×C₂₃₉	C₂³	1	8	yes	—
40	C₂⁴×C₂₃₉	C₂³	1	2	yes	—
41	#41×C₂₃₉	—	2	32	no	—
42	#41×C₂₃₉	—	2	16	no	—
43	C₂×Q₈×C₂₃₉	C₂³	1	4	yes	—
44	C₂×D₄×C₂₃₉	—	2	32	no	—
45	C₂×D₄×C₂₃₉	—	2	32	no	—
46	C₂×D₄×C₂₃₉	—	4	8	no	—
47	C₂×D₄×C₂₃₉	D₄	1	8	yes	complemented
48	C₂×D₄×C₂₃₉	C₂³	1	4	yes	—
49	C₂×D₄×C₂₃₉	C₂³	1	16	yes	—
50	C₂×D₄×C₂₃₉	C₂³	1	8	yes	—
51	C₂×D₄×C₂₃₉	C₂³	1	4	yes	—
52	C₂×D₄×C₂₃₉	C₂³	1	4	yes	—
53	C₂×D₄×C₂₃₉	C₂³	1	8	yes	—
54	C₂×D₄×C₂₃₉	C₂³	1	4	yes	—
55	C₂²×C₄×C₂₃₉	—	4	4	no	—
56	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₂₃₉	C₂³	1	8	yes	—
58	C₂²×C₄×C₂₃₉	C₂³	1	4	yes	—
59	C₂²×C₄×C₂₃₉	C₂³	1	8	yes	—
60	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂₃₉	C₂³	1	4	yes	—
62	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
63	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
64	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
65	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
66	C₄⋊C₄×C₂₃₉	C₂³	1	8	yes	—
67	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
68	C₂²⋊C₄×C₂₃₉	C₂³	1	8	yes	—
69	C₂²⋊C₄×C₂₃₉	C₂³	1	8	yes	—
70	C₂²⋊C₄×C₂₃₉	C₂³	1	16	yes	—
71	C₂²⋊C₄×C₂₃₉	C₂³	1	8	yes	—
72	C₄²×C₂₃₉	C₂³	1	2	yes	—
73	C₄²×C₂₃₉	C₂³	1	2	yes	—
74	C₂³×C₂₃₉	—	2	16	no	—
75	C₂³×C₂₃₉	—	4	2	no	—
76	C₂³×C₂₃₉	—	4	2	no	—
77	C₂³×C₂₃₉	—	4	8	no	—
78	C₂³×C₂₃₉	—	4	8	no	—
79	C₂³×C₂₃₉	C₂×D₄	1	8	yes	complemented
80	C₂³×C₂₃₉	C₂⁴	1	8	yes	—
81	C₂³×C₂₃₉	C₂⁴	1	4	yes	—
82	C₂³×C₂₃₉	C₂⁴	1	1	yes	characteristic
83	Q₈×C₂₃₉	—	2	8	no	—
84	D₄×C₂₃₉	—	2	32	no	—
85	D₄×C₂₃₉	—	2	16	no	—
86	D₄×C₂₃₉	—	2	8	no	—
87	D₄×C₂₃₉	—	2	8	no	—
88	D₄×C₂₃₉	—	4	8	no	—
89	D₄×C₂₃₉	—	4	4	no	—
90	D₄×C₂₃₉	C₂×D₄	1	16	yes	complemented
91	C₂×C₄×C₂₃₉	—	2	16	no	—
92	C₂×C₄×C₂₃₉	—	2	16	no	—
93	C₂×C₄×C₂₃₉	—	2	2	no	—
94	C₂×C₄×C₂₃₉	—	2	8	no	—
95	C₂×C₄×C₂₃₉	—	4	4	no	—
96	C₂×C₄×C₂₃₉	—	4	2	no	—
97	C₂×C₄×C₂₃₉	—	4	1	no	—
98	C₂×C₄×C₂₃₉	C₂×D₄	1	4	yes	complemented
99	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
100	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₄×C₂₃₉	C₂⁴	1	4	yes	—
102	C₂×C₄×C₂₃₉	C₂⁴	1	8	yes	—
103	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
104	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
105	C₂²×C₂₃₉	—	2	1	no	—
106	C₂²×C₂₃₉	—	2	4	no	—
107	C₂²×C₂₃₉	—	2	1	no	—
108	C₂²×C₂₃₉	—	2	4	no	—
109	C₂²×C₂₃₉	—	2	8	no	—
110	C₂²×C₂₃₉	—	2	8	no	—
111	C₂²×C₂₃₉	—	2	8	no	—
112	C₂²×C₂₃₉	—	4	8	no	—
113	C₂²×C₂₃₉	—	8	16	no	—
114	C₂²×C₂₃₉	C₂²×D₄	1	8	yes	—
115	C₂²×C₂₃₉	C₂²×D₄	1	2	yes	—
116	C₂²×C₂₃₉	C₂⁵	1	1	yes	characteristic
117	C₄×C₂₃₉	—	2	8	no	—
118	C₄×C₂₃₉	—	2	1	no	—
119	C₄×C₂₃₉	—	2	4	no	—
120	C₄×C₂₃₉	—	2	2	no	—
121	C₄×C₂₃₉	C₂²×D₄	1	4	yes	—
122	C₄×C₂₃₉	H(5,𝔽₂)	1	2	yes	complemented
123	C₂×C₂₃₉	—	2	2	no	—
124	C₂×C₂₃₉	—	2	8	no	—
125	C₂×C₂₃₉	—	4	8	no	—
126	C₂×C₂₃₉	C₂³×D₄	1	1	yes	characteristic
127	C₂×C₂₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
128	C₂×C₂₃₉	#585	1	1	yes	characteristic
129	C₂₃₉	#3496	1	1	yes	characteristic, direct product factor, Sylow
130	#3496	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂×H(5,𝔽₂)	C₂×C₂₃₉	1	2	yes	complemented
132	#547	C₂×C₂₃₉	1	4	yes	complemented
133	#546	C₂×C₂₃₉	1	8	yes	complemented
134	D₄²	C₂×C₂₃₉	1	4	yes	complemented
135	#537	C₂×C₂₃₉	1	2	yes	complemented
136	#534	C₂×C₂₃₉	1	4	yes	complemented
137	#532	C₂×C₂₃₉	1	2	yes	complemented
138	C₂×#121	C₂×C₂₃₉	1	4	yes	complemented
139	C₂×C₄×D₄	C₂×C₂₃₉	1	1	yes	characteristic, complemented
140	H(5,𝔽₂)	—	2	16	no	—
141	C₂×#41	C₂²×C₂₃₉	1	4	yes	complemented
142	C₂×#41	C₂²×C₂₃₉	1	8	yes	complemented
143	C₂²×D₄	C₂²×C₂₃₉	1	1	yes	characteristic
144	C₂²×D₄	C₂²×C₂₃₉	1	8	yes	complemented
145	C₂²×D₄	C₂²×C₂₃₉	1	8	yes	complemented
146	C₂²×D₄	C₂²×C₂₃₉	1	4	yes	complemented
147	C₂³×C₄	C₂²×C₂₃₉	1	2	yes	complemented
148	C₄⋊Q₈	C₂²×C₂₃₉	1	2	yes	complemented
149	#127	C₂²×C₂₃₉	1	2	yes	complemented
150	#124	C₂²×C₂₃₉	1	4	yes	complemented
151	#123	C₂²×C₂₃₉	1	16	yes	complemented
152	C₂²⋊Q₈	C₂²×C₂₃₉	1	8	yes	complemented
153	#121	C₂²×C₂₃₉	1	4	yes	complemented
154	#121	C₂²×C₂₃₉	1	8	yes	complemented
155	#121	C₂²×C₂₃₉	1	8	yes	complemented
156	#121	C₂²×C₂₃₉	1	8	yes	complemented
157	#121	C₂²×C₂₃₉	1	4	yes	complemented
158	#121	C₂²×C₂₃₉	1	8	yes	complemented
159	#120	C₂²×C₂₃₉	1	16	yes	complemented
160	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
161	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
162	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
163	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
164	C₂×C₄⋊C₄	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
165	C₂×C₄⋊C₄	C₂²×C₂₃₉	1	4	yes	complemented
166	C₂×C₂²⋊C₄	C₂²×C₂₃₉	1	2	yes	complemented
167	C₂×C₂²⋊C₄	C₂²×C₂₃₉	1	8	yes	complemented
168	C₂×C₄²	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
169	C₂⁴	C₂³×C₂₃₉	1	8	yes	—
170	C₂⁴	C₂³×C₂₃₉	1	2	yes	—
171	#41	—	2	32	no	—
172	#41	—	2	16	no	—
173	C₂×Q₈	C₂³×C₂₃₉	1	4	yes	—
174	C₂×D₄	—	2	32	no	—
175	C₂×D₄	—	2	32	no	—
176	C₂×D₄	—	4	8	no	—
177	C₂×D₄	D₄×C₂₃₉	1	8	yes	complemented
178	C₂×D₄	C₂³×C₂₃₉	1	4	yes	—
179	C₂×D₄	C₂³×C₂₃₉	1	16	yes	—
180	C₂×D₄	C₂³×C₂₃₉	1	8	yes	—
181	C₂×D₄	C₂³×C₂₃₉	1	4	yes	—
182	C₂×D₄	C₂³×C₂₃₉	1	4	yes	—
183	C₂×D₄	C₂³×C₂₃₉	1	8	yes	—
184	C₂×D₄	C₂³×C₂₃₉	1	4	yes	—
185	C₂²×C₄	—	4	4	no	—
186	C₂²×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
187	C₂²×C₄	C₂³×C₂₃₉	1	8	yes	—
188	C₂²×C₄	C₂³×C₂₃₉	1	4	yes	—
189	C₂²×C₄	C₂³×C₂₃₉	1	8	yes	—
190	C₂²×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
191	C₂²×C₄	C₂³×C₂₃₉	1	4	yes	—
192	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
193	C₂²×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
194	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
195	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
196	C₄⋊C₄	C₂³×C₂₃₉	1	8	yes	—
197	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
198	C₂²⋊C₄	C₂³×C₂₃₉	1	8	yes	—
199	C₂²⋊C₄	C₂³×C₂₃₉	1	8	yes	—
200	C₂²⋊C₄	C₂³×C₂₃₉	1	16	yes	—
201	C₂²⋊C₄	C₂³×C₂₃₉	1	8	yes	—
202	C₄²	C₂³×C₂₃₉	1	2	yes	—
203	C₄²	C₂³×C₂₃₉	1	2	yes	—
204	C₂³	—	2	16	no	—
205	C₂³	—	4	2	no	—
206	C₂³	—	4	2	no	—
207	C₂³	—	4	8	no	—
208	C₂³	—	4	8	no	—
209	C₂³	C₂×D₄×C₂₃₉	1	8	yes	complemented
210	C₂³	C₂⁴×C₂₃₉	1	8	yes	—
211	C₂³	C₂⁴×C₂₃₉	1	4	yes	—
212	C₂³	C₂⁴×C₂₃₉	1	1	yes	characteristic
213	Q₈	—	2	8	no	—
214	D₄	—	2	32	no	—
215	D₄	—	2	16	no	—
216	D₄	—	2	8	no	—
217	D₄	—	2	8	no	—
218	D₄	—	4	8	no	—
219	D₄	—	4	4	no	—
220	D₄	C₂×D₄×C₂₃₉	1	16	yes	complemented
221	C₂×C₄	—	2	16	no	—
222	C₂×C₄	—	2	16	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	8	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	C₂×D₄×C₂₃₉	1	4	yes	complemented
229	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
230	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
231	C₂×C₄	C₂⁴×C₂₃₉	1	4	yes	—
232	C₂×C₄	C₂⁴×C₂₃₉	1	8	yes	—
233	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
234	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
235	C₂²	—	2	1	no	—
236	C₂²	—	2	4	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	4	no	—
239	C₂²	—	2	8	no	—
240	C₂²	—	2	8	no	—
241	C₂²	—	2	8	no	—
242	C₂²	—	4	8	no	—
243	C₂²	—	8	16	no	—
244	C₂²	C₂²×D₄×C₂₃₉	1	8	yes	—
245	C₂²	C₂²×D₄×C₂₃₉	1	2	yes	—
246	C₂²	C₂⁵×C₂₃₉	1	1	yes	characteristic
247	C₄	—	2	8	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	4	no	—
250	C₄	—	2	2	no	—
251	C₄	C₂²×D₄×C₂₃₉	1	4	yes	—
252	C₄	H(5,𝔽₂)×C₂₃₉	1	2	yes	complemented
253	C₂	—	2	2	no	—
254	C₂	—	2	8	no	—
255	C₂	—	4	8	no	—
256	C₂	C₂³×D₄×C₂₃₉	1	1	yes	characteristic
257	C₂	C₂×H(5,𝔽₂)×C₂₃₉	1	1	yes	characteristic
258	C₂	#585×C₂₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×C₂₃₉	C₂	semidirect
2. #547×C₂₃₉	C₂	semidirect
3. #546×C₂₃₉	C₂	semidirect
4. D₄²×C₂₃₉	C₂	semidirect
5. #537×C₂₃₉	C₂	semidirect
6. #534×C₂₃₉	C₂	semidirect
7. #532×C₂₃₉	C₂	semidirect
8. C₂×#121×C₂₃₉	C₂	semidirect
9. C₂×C₄×D₄×C₂₃₉	C₂	semidirect
11. C₂×#41×C₂₃₉	C₂²	semidirect
12. C₂×#41×C₂₃₉	C₂²	semidirect
14. C₂²×D₄×C₂₃₉	C₂²	semidirect
15. C₂²×D₄×C₂₃₉	C₂²	semidirect
16. C₂²×D₄×C₂₃₉	C₂²	semidirect
17. C₂³×C₄×C₂₃₉	C₂²	semidirect
18. C₄⋊Q₈×C₂₃₉	C₂²	semidirect
19. #127×C₂₃₉	C₂²	semidirect
20. #124×C₂₃₉	C₂²	semidirect
21. #123×C₂₃₉	C₂²	semidirect
22. C₂²⋊Q₈×C₂₃₉	C₂²	semidirect
23. #121×C₂₃₉	C₂²	semidirect
24. #121×C₂₃₉	C₂²	semidirect
25. #121×C₂₃₉	C₂²	semidirect
26. #121×C₂₃₉	C₂²	semidirect
27. #121×C₂₃₉	C₂²	semidirect
28. #121×C₂₃₉	C₂²	semidirect
29. #120×C₂₃₉	C₂²	semidirect
30. C₄×D₄×C₂₃₉	C₂²	semidirect
31. C₄×D₄×C₂₃₉	C₂²	semidirect
32. C₄×D₄×C₂₃₉	C₂²	semidirect
33. C₄×D₄×C₂₃₉	C₂²	semidirect
34. C₂×C₄⋊C₄×C₂₃₉	C₂²	semidirect
35. C₂×C₄⋊C₄×C₂₃₉	C₂²	semidirect
36. C₂×C₂²⋊C₄×C₂₃₉	C₂²	semidirect
37. C₂×C₂²⋊C₄×C₂₃₉	C₂²	semidirect
38. C₂×C₄²×C₂₃₉	C₂²	semidirect
47. C₂×D₄×C₂₃₉	D₄	semidirect
79. C₂³×C₂₃₉	C₂×D₄	semidirect
90. D₄×C₂₃₉	C₂×D₄	semidirect
98. C₂×C₄×C₂₃₉	C₂×D₄	semidirect
122. C₄×C₂₃₉	H(5,𝔽₂)	semidirect
129. C₂₃₉	#3496	direct (N × H)
130. #3496	C₂₃₉	direct (N × H)
131. C₂×H(5,𝔽₂)	C₂×C₂₃₉	semidirect
132. #547	C₂×C₂₃₉	semidirect
133. #546	C₂×C₂₃₉	semidirect
134. D₄²	C₂×C₂₃₉	semidirect
135. #537	C₂×C₂₃₉	semidirect
136. #534	C₂×C₂₃₉	semidirect
137. #532	C₂×C₂₃₉	semidirect
138. C₂×#121	C₂×C₂₃₉	semidirect
139. C₂×C₄×D₄	C₂×C₂₃₉	semidirect
141. C₂×#41	C₂²×C₂₃₉	semidirect
142. C₂×#41	C₂²×C₂₃₉	semidirect
144. C₂²×D₄	C₂²×C₂₃₉	semidirect
145. C₂²×D₄	C₂²×C₂₃₉	semidirect
146. C₂²×D₄	C₂²×C₂₃₉	semidirect
147. C₂³×C₄	C₂²×C₂₃₉	semidirect
148. C₄⋊Q₈	C₂²×C₂₃₉	semidirect
149. #127	C₂²×C₂₃₉	semidirect
150. #124	C₂²×C₂₃₉	semidirect
151. #123	C₂²×C₂₃₉	semidirect
152. C₂²⋊Q₈	C₂²×C₂₃₉	semidirect
153. #121	C₂²×C₂₃₉	semidirect
154. #121	C₂²×C₂₃₉	semidirect
155. #121	C₂²×C₂₃₉	semidirect
156. #121	C₂²×C₂₃₉	semidirect
157. #121	C₂²×C₂₃₉	semidirect
158. #121	C₂²×C₂₃₉	semidirect
159. #120	C₂²×C₂₃₉	semidirect
160. C₄×D₄	C₂²×C₂₃₉	semidirect
161. C₄×D₄	C₂²×C₂₃₉	semidirect
162. C₄×D₄	C₂²×C₂₃₉	semidirect
163. C₄×D₄	C₂²×C₂₃₉	semidirect
164. C₂×C₄⋊C₄	C₂²×C₂₃₉	semidirect
165. C₂×C₄⋊C₄	C₂²×C₂₃₉	semidirect
166. C₂×C₂²⋊C₄	C₂²×C₂₃₉	semidirect
167. C₂×C₂²⋊C₄	C₂²×C₂₃₉	semidirect
168. C₂×C₄²	C₂²×C₂₃₉	semidirect
177. C₂×D₄	D₄×C₂₃₉	semidirect
209. C₂³	C₂×D₄×C₂₃₉	semidirect
220. D₄	C₂×D₄×C₂₃₉	semidirect
228. C₂×C₄	C₂×D₄×C₂₃₉	semidirect
252. C₄	H(5,𝔽₂)×C₂₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×H(5,𝔽₂)×C₂₃₉	2
#547×C₂₃₉	2
#546×C₂₃₉	2
D₄²×C₂₃₉	2
#537×C₂₃₉	2
#534×C₂₃₉	2
#532×C₂₃₉	2
C₂×#121×C₂₃₉	2
C₂×C₄×D₄×C₂₃₉	2
#3496	239

Subgroups — #3496×C239 #44482266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3496×C₂₃₉ #44482266