Subgroups — C₂²×#390×C₁₃₉ #48028615

Order 35584.

9534 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂²⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	C₂³×C₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#390×C₁₃₉	C₂	1	24	yes	maximal, direct product factor
6	C₂⁶×C₁₃₉	C₂²	1	2	yes	—
7	C₂³×D₄×C₁₃₉	—	2	8	no	—
8	C₂³×D₄×C₁₃₉	—	2	8	no	—
9	C₂³×D₄×C₁₃₉	C₄	1	16	yes	complemented
10	C₂³×D₄×C₁₃₉	C₂²	1	12	yes	—
11	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	12	yes	complemented
16	C₂²×C₂²⋊C₄×C₁₃₉	—	2	32	no	—
17	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	48	yes	complemented
18	C₂²×C₄²×C₁₃₉	—	2	8	no	—
19	C₂²×C₄²×C₁₃₉	C₂²	1	12	yes	complemented
20	#390×C₁₃₉	C₂²	1	64	yes	direct product factor
21	C₂⁵×C₁₃₉	—	2	16	no	—
22	C₂⁵×C₁₃₉	—	2	8	no	—
23	C₂⁵×C₁₃₉	—	2	8	no	—
24	C₂⁵×C₁₃₉	—	2	16	no	—
25	C₂⁵×C₁₃₉	C₂×C₄	1	16	yes	—
26	C₂⁵×C₁₃₉	C₂³	1	12	yes	—
27	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
28	C₂²×D₄×C₁₃₉	—	2	128	no	—
29	C₂²×D₄×C₁₃₉	—	2	48	no	—
30	C₂²×D₄×C₁₃₉	—	2	48	no	—
31	C₂²×D₄×C₁₃₉	C₂×C₄	1	96	yes	complemented
32	C₂²×D₄×C₁₃₉	C₂³	1	16	yes	—
33	C₂³×C₄×C₁₃₉	—	2	8	no	—
34	C₂³×C₄×C₁₃₉	—	2	8	no	—
35	C₂³×C₄×C₁₃₉	—	2	16	no	—
36	C₂³×C₄×C₁₃₉	—	2	8	no	—
37	C₂³×C₄×C₁₃₉	C₂×C₄	1	8	yes	—
38	C₂³×C₄×C₁₃₉	D₄	1	8	yes	—
39	C₂³×C₄×C₁₃₉	D₄	1	8	yes	—
40	C₂³×C₄×C₁₃₉	D₄	1	16	yes	complemented
41	C₂³×C₄×C₁₃₉	C₂³	1	12	yes	—
42	C₂³×C₄×C₁₃₉	C₂³	1	12	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	48	no	—
45	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	complemented
46	C₂×C₂²⋊C₄×C₁₃₉	—	2	192	no	—
47	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	64	yes	complemented
48	C₂×C₄²×C₁₃₉	—	2	48	no	—
49	C₂×C₄²×C₁₃₉	C₂³	1	16	yes	complemented
50	C₂⁴×C₁₃₉	—	2	64	no	—
51	C₂⁴×C₁₃₉	—	2	128	no	—
52	C₂⁴×C₁₃₉	—	2	48	no	—
53	C₂⁴×C₁₃₉	—	2	24	no	—
54	C₂⁴×C₁₃₉	—	2	24	no	—
55	C₂⁴×C₁₃₉	—	2	48	no	—
56	C₂⁴×C₁₃₉	—	4	64	no	—
57	C₂⁴×C₁₃₉	—	4	32	no	—
58	C₂⁴×C₁₃₉	—	4	32	no	—
59	C₂⁴×C₁₃₉	C₂²×C₄	1	48	yes	—
60	C₂⁴×C₁₃₉	C₂²×C₄	1	4	yes	—
61	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
62	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
63	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
64	C₂⁴×C₁₃₉	#41	1	8	yes	—
65	C₂⁴×C₁₃₉	C₂⁴	1	8	yes	—
66	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
67	C₂×D₄×C₁₃₉	—	2	384	no	—
68	C₂×D₄×C₁₃₉	—	2	32	no	—
69	C₂×D₄×C₁₃₉	—	2	32	no	—
70	C₂×D₄×C₁₃₉	C₂²×C₄	1	64	yes	complemented
71	C₂²×C₄×C₁₃₉	—	2	64	no	—
72	C₂²×C₄×C₁₃₉	—	2	24	no	—
73	C₂²×C₄×C₁₃₉	—	2	24	no	—
74	C₂²×C₄×C₁₃₉	—	2	48	no	—
75	C₂²×C₄×C₁₃₉	—	2	24	no	—
76	C₂²×C₄×C₁₃₉	—	4	32	no	—
77	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	64	yes	complemented
78	C₂²×C₄×C₁₃₉	C₂²×C₄	1	24	yes	—
79	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
80	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	48	yes	complemented
82	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
83	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
84	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
85	C₄⋊C₄×C₁₃₉	—	2	32	no	—
86	C₂²⋊C₄×C₁₃₉	—	2	128	no	—
87	C₄²×C₁₃₉	—	2	32	no	—
88	C₂³×C₁₃₉	—	2	96	no	—
89	C₂³×C₁₃₉	—	2	192	no	—
90	C₂³×C₁₃₉	—	2	16	no	—
91	C₂³×C₁₃₉	—	2	8	no	—
92	C₂³×C₁₃₉	—	2	8	no	—
93	C₂³×C₁₃₉	—	2	16	no	—
94	C₂³×C₁₃₉	—	4	96	no	—
95	C₂³×C₁₃₉	—	4	48	no	—
96	C₂³×C₁₃₉	—	4	48	no	—
97	C₂³×C₁₃₉	—	4	256	no	—
98	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	16	yes	—
99	C₂³×C₁₃₉	C₄×D₄	1	32	yes	—
100	C₂³×C₁₃₉	#121	1	32	yes	—
101	C₂³×C₁₃₉	#124	1	16	yes	—
102	C₂³×C₁₃₉	#127	1	16	yes	—
103	C₂³×C₁₃₉	C₂³×C₄	1	16	yes	—
104	C₂³×C₁₃₉	C₂³×C₄	1	6	yes	—
105	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
106	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
107	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
108	C₂³×C₁₃₉	C₂×#41	1	12	yes	—
109	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
110	D₄×C₁₃₉	—	2	128	no	—
111	C₂×C₄×C₁₃₉	—	2	96	no	—
112	C₂×C₄×C₁₃₉	—	2	8	no	—
113	C₂×C₄×C₁₃₉	—	2	8	no	—
114	C₂×C₄×C₁₃₉	—	2	16	no	—
115	C₂×C₄×C₁₃₉	—	2	8	no	—
116	C₂×C₄×C₁₃₉	—	4	48	no	—
117	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	96	yes	complemented
118	C₂×C₄×C₁₃₉	C₂³×C₄	1	8	yes	—
119	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
120	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
121	C₂×C₄×C₁₃₉	C₂²×D₄	1	16	yes	complemented
122	C₂²×C₁₃₉	—	2	16	no	—
123	C₂²×C₁₃₉	—	2	32	no	—
124	C₂²×C₁₃₉	—	4	16	no	—
125	C₂²×C₁₃₉	—	4	8	no	—
126	C₂²×C₁₃₉	—	4	8	no	—
127	C₂²×C₁₃₉	—	4	192	no	—
128	C₂²×C₁₃₉	#390	1	64	yes	direct product factor
129	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	12	yes	—
130	C₂²×C₁₃₉	C₂×C₄×D₄	1	24	yes	—
131	C₂²×C₁₃₉	C₂×#121	1	24	yes	—
132	C₂²×C₁₃₉	C₂×#124	1	12	yes	—
133	C₂²×C₁₃₉	C₂×#127	1	12	yes	—
134	C₂²×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
135	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
136	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
137	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
138	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
139	C₄×C₁₃₉	—	2	16	no	—
140	C₄×C₁₃₉	—	4	8	no	—
141	C₄×C₁₃₉	C₂²×C₂²⋊C₄	1	16	yes	complemented
142	C₂×C₁₃₉	—	4	16	no	—
143	C₂×C₁₃₉	C₂×#390	1	24	yes	direct product factor
144	C₂×C₁₃₉	C₂³×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₁₃₉	C₂²×C₄×D₄	1	2	yes	—
146	C₂×C₁₃₉	C₂²×#121	1	2	yes	—
147	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
148	C₂×C₁₃₉	C₂²×#127	1	1	yes	characteristic
149	C₂²×#390	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₁₃₉	C₂²×#390	1	1	yes	characteristic, direct product factor, Sylow
151	C₂⁴×D₄	C₂×C₁₃₉	1	1	yes	characteristic
152	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
153	C₂³×C₂²⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
154	C₂³×C₄²	C₂×C₁₃₉	1	1	yes	characteristic, complemented
155	C₂×#390	C₂×C₁₃₉	1	24	yes	direct product factor
156	C₂⁶	C₂²×C₁₃₉	1	2	yes	—
157	C₂³×D₄	—	2	8	no	—
158	C₂³×D₄	—	2	8	no	—
159	C₂³×D₄	C₄×C₁₃₉	1	16	yes	complemented
160	C₂³×D₄	C₂²×C₁₃₉	1	12	yes	—
161	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
162	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
163	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	—	2	8	no	—
165	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	12	yes	complemented
166	C₂²×C₂²⋊C₄	—	2	32	no	—
167	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	48	yes	complemented
168	C₂²×C₄²	—	2	8	no	—
169	C₂²×C₄²	C₂²×C₁₃₉	1	12	yes	complemented
170	#390	C₂²×C₁₃₉	1	64	yes	direct product factor
171	C₂⁵	—	2	16	no	—
172	C₂⁵	—	2	8	no	—
173	C₂⁵	—	2	8	no	—
174	C₂⁵	—	2	16	no	—
175	C₂⁵	C₂×C₄×C₁₃₉	1	16	yes	—
176	C₂⁵	C₂³×C₁₃₉	1	12	yes	—
177	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
178	C₂²×D₄	—	2	128	no	—
179	C₂²×D₄	—	2	48	no	—
180	C₂²×D₄	—	2	48	no	—
181	C₂²×D₄	C₂×C₄×C₁₃₉	1	96	yes	complemented
182	C₂²×D₄	C₂³×C₁₃₉	1	16	yes	—
183	C₂³×C₄	—	2	8	no	—
184	C₂³×C₄	—	2	8	no	—
185	C₂³×C₄	—	2	16	no	—
186	C₂³×C₄	—	2	8	no	—
187	C₂³×C₄	C₂×C₄×C₁₃₉	1	8	yes	—
188	C₂³×C₄	D₄×C₁₃₉	1	8	yes	—
189	C₂³×C₄	D₄×C₁₃₉	1	8	yes	—
190	C₂³×C₄	D₄×C₁₃₉	1	16	yes	complemented
191	C₂³×C₄	C₂³×C₁₃₉	1	12	yes	—
192	C₂³×C₄	C₂³×C₁₃₉	1	12	yes	—
193	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
194	C₂×C₄⋊C₄	—	2	48	no	—
195	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	complemented
196	C₂×C₂²⋊C₄	—	2	192	no	—
197	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	64	yes	complemented
198	C₂×C₄²	—	2	48	no	—
199	C₂×C₄²	C₂³×C₁₃₉	1	16	yes	complemented
200	C₂⁴	—	2	64	no	—
201	C₂⁴	—	2	128	no	—
202	C₂⁴	—	2	48	no	—
203	C₂⁴	—	2	24	no	—
204	C₂⁴	—	2	24	no	—
205	C₂⁴	—	2	48	no	—
206	C₂⁴	—	4	64	no	—
207	C₂⁴	—	4	32	no	—
208	C₂⁴	—	4	32	no	—
209	C₂⁴	C₂²×C₄×C₁₃₉	1	48	yes	—
210	C₂⁴	C₂²×C₄×C₁₃₉	1	4	yes	—
211	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
212	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
213	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
214	C₂⁴	#41×C₁₃₉	1	8	yes	—
215	C₂⁴	C₂⁴×C₁₃₉	1	8	yes	—
216	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
217	C₂×D₄	—	2	384	no	—
218	C₂×D₄	—	2	32	no	—
219	C₂×D₄	—	2	32	no	—
220	C₂×D₄	C₂²×C₄×C₁₃₉	1	64	yes	complemented
221	C₂²×C₄	—	2	64	no	—
222	C₂²×C₄	—	2	24	no	—
223	C₂²×C₄	—	2	24	no	—
224	C₂²×C₄	—	2	48	no	—
225	C₂²×C₄	—	2	24	no	—
226	C₂²×C₄	—	4	32	no	—
227	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	64	yes	complemented
228	C₂²×C₄	C₂²×C₄×C₁₃₉	1	24	yes	—
229	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
230	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
231	C₂²×C₄	C₂×D₄×C₁₃₉	1	48	yes	complemented
232	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
233	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
234	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
235	C₄⋊C₄	—	2	32	no	—
236	C₂²⋊C₄	—	2	128	no	—
237	C₄²	—	2	32	no	—
238	C₂³	—	2	96	no	—
239	C₂³	—	2	192	no	—
240	C₂³	—	2	16	no	—
241	C₂³	—	2	8	no	—
242	C₂³	—	2	8	no	—
243	C₂³	—	2	16	no	—
244	C₂³	—	4	96	no	—
245	C₂³	—	4	48	no	—
246	C₂³	—	4	48	no	—
247	C₂³	—	4	256	no	—
248	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	16	yes	—
249	C₂³	C₄×D₄×C₁₃₉	1	32	yes	—
250	C₂³	#121×C₁₃₉	1	32	yes	—
251	C₂³	#124×C₁₃₉	1	16	yes	—
252	C₂³	#127×C₁₃₉	1	16	yes	—
253	C₂³	C₂³×C₄×C₁₃₉	1	16	yes	—
254	C₂³	C₂³×C₄×C₁₃₉	1	6	yes	—
255	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
256	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
257	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
258	C₂³	C₂×#41×C₁₃₉	1	12	yes	—
259	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
260	D₄	—	2	128	no	—
261	C₂×C₄	—	2	96	no	—
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	2	8	no	—
264	C₂×C₄	—	2	16	no	—
265	C₂×C₄	—	2	8	no	—
266	C₂×C₄	—	4	48	no	—
267	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	96	yes	complemented
268	C₂×C₄	C₂³×C₄×C₁₃₉	1	8	yes	—
269	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
270	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
271	C₂×C₄	C₂²×D₄×C₁₃₉	1	16	yes	complemented
272	C₂²	—	2	16	no	—
273	C₂²	—	2	32	no	—
274	C₂²	—	4	192	no	—
275	C₂²	—	4	16	no	—
276	C₂²	—	4	8	no	—
277	C₂²	—	4	8	no	—
278	C₂²	#390×C₁₃₉	1	64	yes	direct product factor
279	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	12	yes	—
280	C₂²	C₂×C₄×D₄×C₁₃₉	1	24	yes	—
281	C₂²	C₂×#121×C₁₃₉	1	24	yes	—
282	C₂²	C₂×#124×C₁₃₉	1	12	yes	—
283	C₂²	C₂×#127×C₁₃₉	1	12	yes	—
284	C₂²	C₂⁴×C₄×C₁₃₉	1	1	yes	characteristic
285	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
286	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
287	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
288	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
289	C₄	—	2	16	no	—
290	C₄	—	4	8	no	—
291	C₄	C₂²×C₂²⋊C₄×C₁₃₉	1	16	yes	complemented
292	C₂	—	4	16	no	—
293	C₂	C₂×#390×C₁₃₉	1	24	yes	direct product factor
294	C₂	C₂³×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
295	C₂	C₂²×C₄×D₄×C₁₃₉	1	2	yes	—
296	C₂	C₂²×#121×C₁₃₉	1	2	yes	—
297	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
298	C₂	C₂²×#127×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵×C₁₃₉	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₃₉
Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×D₄×C₁₃₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₁₃₉	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₁₃₉	C₂	semidirect
4. C₂³×C₄²×C₁₃₉	C₂	semidirect
5. C₂×#390×C₁₃₉	C₂	direct (N × H)
9. C₂³×D₄×C₁₃₉	C₄	semidirect
15. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
17. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
19. C₂²×C₄²×C₁₃₉	C₂²	semidirect
20. #390×C₁₃₉	C₂²	direct (N × H)
31. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
40. C₂³×C₄×C₁₃₉	D₄	semidirect
45. C₂×C₄⋊C₄×C₁₃₉	C₂³	semidirect
47. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
49. C₂×C₄²×C₁₃₉	C₂³	semidirect
70. C₂×D₄×C₁₃₉	C₂²×C₄	semidirect
77. C₂²×C₄×C₁₃₉	C₂²⋊C₄	semidirect
81. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
117. C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	semidirect
121. C₂×C₄×C₁₃₉	C₂²×D₄	semidirect
128. C₂²×C₁₃₉	#390	direct (N × H)
141. C₄×C₁₃₉	C₂²×C₂²⋊C₄	semidirect
143. C₂×C₁₃₉	C₂×#390	direct (N × H)
149. C₂²×#390	C₁₃₉	direct (N × H)
150. C₁₃₉	C₂²×#390	direct (N × H)
152. C₂³×C₄⋊C₄	C₂×C₁₃₉	semidirect
153. C₂³×C₂²⋊C₄	C₂×C₁₃₉	semidirect
154. C₂³×C₄²	C₂×C₁₃₉	semidirect
155. C₂×#390	C₂×C₁₃₉	direct (N × H)
159. C₂³×D₄	C₄×C₁₃₉	semidirect
165. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
167. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
169. C₂²×C₄²	C₂²×C₁₃₉	semidirect
170. #390	C₂²×C₁₃₉	direct (N × H)
181. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
190. C₂³×C₄	D₄×C₁₃₉	semidirect
195. C₂×C₄⋊C₄	C₂³×C₁₃₉	semidirect
197. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
199. C₂×C₄²	C₂³×C₁₃₉	semidirect
220. C₂×D₄	C₂²×C₄×C₁₃₉	semidirect
227. C₂²×C₄	C₂²⋊C₄×C₁₃₉	semidirect
231. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
267. C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	semidirect
271. C₂×C₄	C₂²×D₄×C₁₃₉	semidirect
278. C₂²	#390×C₁₃₉	direct (N × H)
291. C₄	C₂²×C₂²⋊C₄×C₁₃₉	semidirect
293. C₂	C₂×#390×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₃₉	2
C₂³×C₄⋊C₄×C₁₃₉	2
C₂³×C₂²⋊C₄×C₁₃₉	2
C₂³×C₄²×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₂²×#390	139

Subgroups — C22×#390×C139 #48028615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#390×C₁₃₉ #48028615