Subgroups — C₂²×#385×C₁₃₉ #48028609

Order 35584.

8670 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂³×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#385×C₁₃₉	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#95×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₃₉	—	2	8	no	—
9	C₂⁴×C₄×C₁₃₉	—	2	16	no	—
10	C₂⁴×C₄×C₁₃₉	C₂²	1	12	yes	—
11	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₃₉	—	2	16	no	—
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	24	yes	complemented
17	C₂²×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
18	C₂²×C₂²⋊C₄×C₁₃₉	C₄	1	16	yes	complemented
19	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	12	yes	—
20	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	12	yes	—
21	#385×C₁₃₉	C₂²	1	64	yes	direct product factor
22	C₂×#95×C₁₃₉	C₂²	1	24	yes	complemented
23	C₂⁵×C₁₃₉	—	2	8	no	—
24	C₂⁵×C₁₃₉	—	2	8	no	—
25	C₂⁵×C₁₃₉	C₂×C₄	1	8	yes	—
26	C₂⁵×C₁₃₉	D₄	1	8	yes	—
27	C₂⁵×C₁₃₉	Q₈	1	8	yes	—
28	C₂⁵×C₁₃₉	C₂³	1	6	yes	—
29	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₉	—	2	128	no	—
31	C₂³×C₄×C₁₃₉	—	2	8	no	—
32	C₂³×C₄×C₁₃₉	—	2	48	no	—
33	C₂³×C₄×C₁₃₉	—	2	8	no	—
34	C₂³×C₄×C₁₃₉	—	2	8	no	—
35	C₂³×C₄×C₁₃₉	—	2	8	no	—
36	C₂³×C₄×C₁₃₉	—	2	96	no	—
37	C₂³×C₄×C₁₃₉	—	2	4	no	—
38	C₂³×C₄×C₁₃₉	—	2	4	no	—
39	C₂³×C₄×C₁₃₉	—	2	8	no	—
40	C₂³×C₄×C₁₃₉	—	2	8	no	—
41	C₂³×C₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
42	C₂³×C₄×C₁₃₉	D₄	1	16	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
44	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
45	C₂³×C₄×C₁₃₉	C₂³	1	16	yes	—
46	C₂³×C₄×C₁₃₉	C₂³	1	12	yes	—
47	C₂³×C₄×C₁₃₉	C₂³	1	12	yes	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	96	no	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	32	yes	complemented
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	48	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	96	yes	complemented
52	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
53	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
54	#95×C₁₃₉	C₂³	1	32	yes	complemented
55	C₂⁴×C₁₃₉	—	2	64	no	—
56	C₂⁴×C₁₃₉	—	2	32	no	—
57	C₂⁴×C₁₃₉	—	2	64	no	—
58	C₂⁴×C₁₃₉	—	2	32	no	—
59	C₂⁴×C₁₃₉	—	2	24	no	—
60	C₂⁴×C₁₃₉	—	2	24	no	—
61	C₂⁴×C₁₃₉	C₄⋊C₄	1	64	yes	complemented
62	C₂⁴×C₁₃₉	C₂²×C₄	1	24	yes	—
63	C₂⁴×C₁₃₉	C₂²×C₄	1	4	yes	—
64	C₂⁴×C₁₃₉	C₂×D₄	1	24	yes	—
65	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
66	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
67	C₂⁴×C₁₃₉	C₂×Q₈	1	24	yes	—
68	C₂⁴×C₁₃₉	C₂×Q₈	1	4	yes	—
69	C₂⁴×C₁₃₉	#41	1	8	yes	—
70	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
71	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
72	C₂²×C₄×C₁₃₉	—	2	384	no	—
73	C₂²×C₄×C₁₃₉	—	2	64	no	—
74	C₂²×C₄×C₁₃₉	—	2	64	no	—
75	C₂²×C₄×C₁₃₉	—	2	24	no	—
76	C₂²×C₄×C₁₃₉	—	2	32	no	—
77	C₂²×C₄×C₁₃₉	—	2	24	no	—
78	C₂²×C₄×C₁₃₉	—	2	24	no	—
79	C₂²×C₄×C₁₃₉	—	2	24	no	—
80	C₂²×C₄×C₁₃₉	—	2	64	no	—
81	C₂²×C₄×C₁₃₉	—	2	12	no	—
82	C₂²×C₄×C₁₃₉	—	2	12	no	—
83	C₂²×C₄×C₁₃₉	—	2	24	no	—
84	C₂²×C₄×C₁₃₉	—	2	24	no	—
85	C₂²×C₄×C₁₃₉	—	4	16	no	—
86	C₂²×C₄×C₁₃₉	—	4	16	no	—
87	C₂²×C₄×C₁₃₉	C₂²×C₄	1	48	yes	complemented
88	C₂²×C₄×C₁₃₉	C₂×D₄	1	48	yes	—
89	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
90	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
92	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
93	C₄⋊C₄×C₁₃₉	—	2	64	no	—
94	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
95	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	64	yes	complemented
96	C₂³×C₁₃₉	—	2	96	no	—
97	C₂³×C₁₃₉	—	2	48	no	—
98	C₂³×C₁₃₉	—	2	96	no	—
99	C₂³×C₁₃₉	—	2	48	no	—
100	C₂³×C₁₃₉	—	2	8	no	—
101	C₂³×C₁₃₉	—	2	8	no	—
102	C₂³×C₁₃₉	—	2	256	no	—
103	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	16	yes	—
104	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	96	yes	complemented
105	C₂³×C₁₃₉	C₄×D₄	1	32	yes	—
106	C₂³×C₁₃₉	#120	1	16	yes	—
107	C₂³×C₁₃₉	C₂²⋊Q₈	1	32	yes	—
108	C₂³×C₁₃₉	#123	1	16	yes	—
109	C₂³×C₁₃₉	C₂³×C₄	1	8	yes	—
110	C₂³×C₁₃₉	C₂³×C₄	1	6	yes	—
111	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
112	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
113	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
114	C₂³×C₁₃₉	C₂²×Q₈	1	8	yes	—
115	C₂³×C₁₃₉	C₂²×Q₈	1	6	yes	—
116	C₂³×C₁₃₉	C₂×#41	1	12	yes	—
117	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
118	C₂×C₄×C₁₃₉	—	2	128	no	—
119	C₂×C₄×C₁₃₉	—	2	96	no	—
120	C₂×C₄×C₁₃₉	—	2	96	no	—
121	C₂×C₄×C₁₃₉	—	2	8	no	—
122	C₂×C₄×C₁₃₉	—	2	8	no	—
123	C₂×C₄×C₁₃₉	—	2	8	no	—
124	C₂×C₄×C₁₃₉	—	2	8	no	—
125	C₂×C₄×C₁₃₉	—	2	4	no	—
126	C₂×C₄×C₁₃₉	—	2	4	no	—
127	C₂×C₄×C₁₃₉	—	2	8	no	—
128	C₂×C₄×C₁₃₉	—	2	8	no	—
129	C₂×C₄×C₁₃₉	—	4	24	no	—
130	C₂×C₄×C₁₃₉	—	4	24	no	—
131	C₂×C₄×C₁₃₉	C₂³×C₄	1	16	yes	complemented
132	C₂×C₄×C₁₃₉	C₂²×D₄	1	16	yes	—
133	C₂²×C₁₃₉	—	2	16	no	—
134	C₂²×C₁₃₉	—	2	8	no	—
135	C₂²×C₁₃₉	—	2	16	no	—
136	C₂²×C₁₃₉	—	2	8	no	—
137	C₂²×C₁₃₉	—	2	192	no	—
138	C₂²×C₁₃₉	#385	1	64	yes	direct product factor
139	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	12	yes	—
140	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	16	yes	complemented
141	C₂²×C₁₃₉	C₂×C₄×D₄	1	24	yes	—
142	C₂²×C₁₃₉	C₂×#120	1	12	yes	—
143	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	24	yes	—
144	C₂²×C₁₃₉	C₂×#123	1	12	yes	—
145	C₂²×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
146	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
147	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
148	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
149	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
150	C₄×C₁₃₉	—	2	16	no	—
151	C₄×C₁₃₉	—	2	16	no	—
152	C₄×C₁₃₉	—	4	4	no	—
153	C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₁₃₉	—	2	16	no	—
155	C₂×C₁₃₉	C₂×#385	1	24	yes	direct product factor
156	C₂×C₁₃₉	C₂³×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₁₃₉	C₂²×C₄×D₄	1	2	yes	—
158	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
159	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	2	yes	—
160	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
161	C₂²×#385	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₁₃₉	C₂²×#385	1	1	yes	characteristic, direct product factor, Sylow
163	C₂⁵×C₄	C₂×C₁₃₉	1	1	yes	characteristic
164	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
165	C₂³×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
166	C₂³×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
167	C₂×#385	C₂×C₁₃₉	1	24	yes	direct product factor
168	C₂²×#95	C₂×C₁₃₉	1	2	yes	complemented
169	C₂⁶	C₂²×C₁₃₉	1	1	yes	characteristic
170	C₂⁴×C₄	—	2	8	no	—
171	C₂⁴×C₄	—	2	16	no	—
172	C₂⁴×C₄	C₂²×C₁₃₉	1	12	yes	—
173	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
174	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
175	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
176	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
177	C₂²×C₄⋊C₄	—	2	16	no	—
178	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	24	yes	complemented
179	C₂²×C₂²⋊C₄	—	2	8	no	—
180	C₂²×C₂²⋊C₄	C₄×C₁₃₉	1	16	yes	complemented
181	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	12	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	12	yes	—
183	#385	C₂²×C₁₃₉	1	64	yes	direct product factor
184	C₂×#95	C₂²×C₁₃₉	1	24	yes	complemented
185	C₂⁵	—	2	8	no	—
186	C₂⁵	—	2	8	no	—
187	C₂⁵	C₂×C₄×C₁₃₉	1	8	yes	—
188	C₂⁵	D₄×C₁₃₉	1	8	yes	—
189	C₂⁵	Q₈×C₁₃₉	1	8	yes	—
190	C₂⁵	C₂³×C₁₃₉	1	6	yes	—
191	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
192	C₂³×C₄	—	2	128	no	—
193	C₂³×C₄	—	2	8	no	—
194	C₂³×C₄	—	2	48	no	—
195	C₂³×C₄	—	2	8	no	—
196	C₂³×C₄	—	2	8	no	—
197	C₂³×C₄	—	2	8	no	—
198	C₂³×C₄	—	2	96	no	—
199	C₂³×C₄	—	2	4	no	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	—	2	8	no	—
202	C₂³×C₄	—	2	8	no	—
203	C₂³×C₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
204	C₂³×C₄	D₄×C₁₃₉	1	16	yes	—
205	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
206	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
207	C₂³×C₄	C₂³×C₁₃₉	1	16	yes	—
208	C₂³×C₄	C₂³×C₁₃₉	1	12	yes	—
209	C₂³×C₄	C₂³×C₁₃₉	1	12	yes	—
210	C₂×C₄⋊C₄	—	2	96	no	—
211	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	32	yes	complemented
212	C₂×C₂²⋊C₄	—	2	48	no	—
213	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	96	yes	complemented
214	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
215	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
216	#95	C₂³×C₁₃₉	1	32	yes	complemented
217	C₂⁴	—	2	64	no	—
218	C₂⁴	—	2	32	no	—
219	C₂⁴	—	2	64	no	—
220	C₂⁴	—	2	32	no	—
221	C₂⁴	—	2	24	no	—
222	C₂⁴	—	2	24	no	—
223	C₂⁴	C₄⋊C₄×C₁₃₉	1	64	yes	complemented
224	C₂⁴	C₂²×C₄×C₁₃₉	1	24	yes	—
225	C₂⁴	C₂²×C₄×C₁₃₉	1	4	yes	—
226	C₂⁴	C₂×D₄×C₁₃₉	1	24	yes	—
227	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
228	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
229	C₂⁴	C₂×Q₈×C₁₃₉	1	24	yes	—
230	C₂⁴	C₂×Q₈×C₁₃₉	1	4	yes	—
231	C₂⁴	#41×C₁₃₉	1	8	yes	—
232	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
233	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
234	C₂²×C₄	—	2	384	no	—
235	C₂²×C₄	—	2	64	no	—
236	C₂²×C₄	—	2	64	no	—
237	C₂²×C₄	—	2	24	no	—
238	C₂²×C₄	—	2	32	no	—
239	C₂²×C₄	—	2	24	no	—
240	C₂²×C₄	—	2	24	no	—
241	C₂²×C₄	—	2	24	no	—
242	C₂²×C₄	—	2	64	no	—
243	C₂²×C₄	—	2	12	no	—
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	24	no	—
246	C₂²×C₄	—	2	24	no	—
247	C₂²×C₄	—	4	16	no	—
248	C₂²×C₄	—	4	16	no	—
249	C₂²×C₄	C₂²×C₄×C₁₃₉	1	48	yes	complemented
250	C₂²×C₄	C₂×D₄×C₁₃₉	1	48	yes	—
251	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
252	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
253	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
254	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
255	C₄⋊C₄	—	2	64	no	—
256	C₂²⋊C₄	—	2	32	no	—
257	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	64	yes	complemented
258	C₂³	—	2	96	no	—
259	C₂³	—	2	48	no	—
260	C₂³	—	2	96	no	—
261	C₂³	—	2	48	no	—
262	C₂³	—	2	8	no	—
263	C₂³	—	2	8	no	—
264	C₂³	—	2	256	no	—
265	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	16	yes	—
266	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	96	yes	complemented
267	C₂³	C₄×D₄×C₁₃₉	1	32	yes	—
268	C₂³	#120×C₁₃₉	1	16	yes	—
269	C₂³	C₂²⋊Q₈×C₁₃₉	1	32	yes	—
270	C₂³	#123×C₁₃₉	1	16	yes	—
271	C₂³	C₂³×C₄×C₁₃₉	1	8	yes	—
272	C₂³	C₂³×C₄×C₁₃₉	1	6	yes	—
273	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
274	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
275	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
276	C₂³	C₂²×Q₈×C₁₃₉	1	8	yes	—
277	C₂³	C₂²×Q₈×C₁₃₉	1	6	yes	—
278	C₂³	C₂×#41×C₁₃₉	1	12	yes	—
279	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
280	C₂×C₄	—	2	128	no	—
281	C₂×C₄	—	2	96	no	—
282	C₂×C₄	—	2	96	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	4	24	no	—
292	C₂×C₄	—	4	24	no	—
293	C₂×C₄	C₂³×C₄×C₁₃₉	1	16	yes	complemented
294	C₂×C₄	C₂²×D₄×C₁₃₉	1	16	yes	—
295	C₂²	—	2	192	no	—
296	C₂²	—	2	16	no	—
297	C₂²	—	2	8	no	—
298	C₂²	—	2	16	no	—
299	C₂²	—	2	8	no	—
300	C₂²	#385×C₁₃₉	1	64	yes	direct product factor
301	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	12	yes	—
302	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	16	yes	complemented
303	C₂²	C₂×C₄×D₄×C₁₃₉	1	24	yes	—
304	C₂²	C₂×#120×C₁₃₉	1	12	yes	—
305	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	24	yes	—
306	C₂²	C₂×#123×C₁₃₉	1	12	yes	—
307	C₂²	C₂⁴×C₄×C₁₃₉	1	1	yes	characteristic
308	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
309	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
310	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
311	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
312	C₄	—	2	16	no	—
313	C₄	—	2	16	no	—
314	C₄	—	4	4	no	—
315	C₄	—	4	4	no	—
316	C₂	—	2	16	no	—
317	C₂	C₂×#385×C₁₃₉	1	24	yes	direct product factor
318	C₂	C₂³×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
319	C₂	C₂²×C₄×D₄×C₁₃₉	1	2	yes	—
320	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
321	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	2	yes	—
322	C₂	C₂²×#123×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	C₂⁶×C₁₃₉	C₂²
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
5. C₂×#385×C₁₃₉	C₂	direct (N × H)
6. C₂²×#95×C₁₃₉	C₂	semidirect
16. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
18. C₂²×C₂²⋊C₄×C₁₃₉	C₄	semidirect
21. #385×C₁₃₉	C₂²	direct (N × H)
22. C₂×#95×C₁₃₉	C₂²	semidirect
41. C₂³×C₄×C₁₃₉	C₂×C₄	semidirect
49. C₂×C₄⋊C₄×C₁₃₉	C₂³	semidirect
51. C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	semidirect
54. #95×C₁₃₉	C₂³	semidirect
61. C₂⁴×C₁₃₉	C₄⋊C₄	semidirect
87. C₂²×C₄×C₁₃₉	C₂²×C₄	semidirect
95. C₂²⋊C₄×C₁₃₉	C₂²×C₄	semidirect
104. C₂³×C₁₃₉	C₂×C₄⋊C₄	semidirect
131. C₂×C₄×C₁₃₉	C₂³×C₄	semidirect
138. C₂²×C₁₃₉	#385	direct (N × H)
140. C₂²×C₁₃₉	C₂²×C₄⋊C₄	semidirect
155. C₂×C₁₃₉	C₂×#385	direct (N × H)
161. C₂²×#385	C₁₃₉	direct (N × H)
162. C₁₃₉	C₂²×#385	direct (N × H)
164. C₂³×C₄⋊C₄	C₂×C₁₃₉	semidirect
167. C₂×#385	C₂×C₁₃₉	direct (N × H)
168. C₂²×#95	C₂×C₁₃₉	semidirect
178. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
180. C₂²×C₂²⋊C₄	C₄×C₁₃₉	semidirect
183. #385	C₂²×C₁₃₉	direct (N × H)
184. C₂×#95	C₂²×C₁₃₉	semidirect
203. C₂³×C₄	C₂×C₄×C₁₃₉	semidirect
211. C₂×C₄⋊C₄	C₂³×C₁₃₉	semidirect
213. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	semidirect
216. #95	C₂³×C₁₃₉	semidirect
223. C₂⁴	C₄⋊C₄×C₁₃₉	semidirect
249. C₂²×C₄	C₂²×C₄×C₁₃₉	semidirect
257. C₂²⋊C₄	C₂²×C₄×C₁₃₉	semidirect
266. C₂³	C₂×C₄⋊C₄×C₁₃₉	semidirect
293. C₂×C₄	C₂³×C₄×C₁₃₉	semidirect
300. C₂²	#385×C₁₃₉	direct (N × H)
302. C₂²	C₂²×C₄⋊C₄×C₁₃₉	semidirect
317. C₂	C₂×#385×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
C₂⁵×C₄×C₁₃₉	2
C₂³×C₄⋊C₄×C₁₃₉	2
C₂³×C₂²⋊C₄×C₁₃₉	2
C₂×#385×C₁₃₉	2
C₂²×#95×C₁₃₉	2
C₂²×#385	139

Subgroups — C22×#385×C139 #48028609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#385×C₁₃₉ #48028609