Subgroups — C₂×#1824×C₁₃₉ #48015294

Order 35584.

1878 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1824×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₁₃₉	—	2	1	no	—
7	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₃₉	—	2	2	no	—
10	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
11	C₂²×C₄⋊C₄×C₁₃₉	—	2	4	no	—
12	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
17	C₂×C₂²⋊C₈×C₁₃₉	—	2	4	no	—
18	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
19	#380×C₁₃₉	—	2	2	no	—
20	#380×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#95×C₁₃₉	—	2	1	no	—
22	#340×C₁₃₉	C₂²	1	16	yes	complemented
23	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₉	—	2	8	no	—
25	C₂³×C₄×C₁₃₉	—	2	8	no	—
26	C₂³×C₄×C₁₃₉	—	2	4	no	—
27	C₂³×C₄×C₁₃₉	—	2	2	no	—
28	C₂³×C₄×C₁₃₉	—	2	2	no	—
29	C₂³×C₄×C₁₃₉	—	4	8	no	—
30	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
31	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
32	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃₉	—	2	4	no	—
37	C₂²×C₈×C₁₃₉	—	2	8	no	—
38	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
39	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
53	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
54	#95×C₁₃₉	—	2	4	no	—
55	C₂⁴×C₁₃₉	—	2	4	no	—
56	C₂⁴×C₁₃₉	—	2	4	no	—
57	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
58	C₂⁴×C₁₃₉	SD₁₆	1	4	yes	—
59	C₂⁴×C₁₃₉	Q₁₆	1	4	yes	—
60	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
61	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃₉	—	2	4	no	—
63	C₂²×C₄×C₁₃₉	—	2	16	no	—
64	C₂²×C₄×C₁₃₉	—	2	8	no	—
65	C₂²×C₄×C₁₃₉	—	2	16	no	—
66	C₂²×C₄×C₁₃₉	—	2	8	no	—
67	C₂²×C₄×C₁₃₉	—	2	8	no	—
68	C₂²×C₄×C₁₃₉	—	2	16	no	—
69	C₂²×C₄×C₁₃₉	—	2	4	no	—
70	C₂²×C₄×C₁₃₉	—	2	4	no	—
71	C₂²×C₄×C₁₃₉	—	4	16	no	—
72	C₂²×C₄×C₁₃₉	—	4	32	no	—
73	C₂²×C₄×C₁₃₉	—	4	8	no	—
74	C₂²×C₄×C₁₃₉	—	4	4	no	—
75	C₂²×C₄×C₁₃₉	—	4	4	no	—
76	C₂²×C₄×C₁₃₉	—	4	4	no	—
77	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
78	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
79	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
83	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
86	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₁₃₉	—	2	4	no	—
88	C₂×C₈×C₁₃₉	—	2	8	no	—
89	C₂×C₈×C₁₃₉	—	4	8	no	—
90	C₄⋊C₄×C₁₃₉	—	2	8	no	—
91	C₄⋊C₄×C₁₃₉	—	2	16	no	—
92	C₄⋊C₄×C₁₃₉	—	2	4	no	—
93	C₄⋊C₄×C₁₃₉	—	2	8	no	—
94	C₄⋊C₄×C₁₃₉	—	4	4	no	—
95	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
96	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
97	C₂³×C₁₃₉	—	2	4	no	—
98	C₂³×C₁₃₉	—	2	4	no	—
99	C₂³×C₁₃₉	—	2	8	no	—
100	C₂³×C₁₃₉	—	2	8	no	—
101	C₂³×C₁₃₉	—	2	16	no	—
102	C₂³×C₁₃₉	—	2	16	no	—
103	C₂³×C₁₃₉	#103	1	16	yes	—
104	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
105	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
106	C₂³×C₁₃₉	#123	1	4	yes	—
107	C₂³×C₁₃₉	C₂×SD₁₆	1	4	yes	—
108	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
109	C₂³×C₁₃₉	C₂×Q₁₆	1	4	yes	—
110	C₂³×C₁₃₉	C₂×Q₁₆	1	2	yes	—
111	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
112	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₃₉	—	2	4	no	—
114	C₂×C₄×C₁₃₉	—	2	8	no	—
115	C₂×C₄×C₁₃₉	—	2	8	no	—
116	C₂×C₄×C₁₃₉	—	2	8	no	—
117	C₂×C₄×C₁₃₉	—	2	16	no	—
118	C₂×C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄×C₁₃₉	—	4	32	no	—
120	C₂×C₄×C₁₃₉	—	4	8	no	—
121	C₂×C₄×C₁₃₉	—	4	16	no	—
122	C₂×C₄×C₁₃₉	—	4	4	no	—
123	C₂×C₄×C₁₃₉	—	4	4	no	—
124	C₂×C₄×C₁₃₉	—	4	4	no	—
125	C₂×C₄×C₁₃₉	—	8	8	no	—
126	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
127	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₃₉	#117	1	8	yes	—
129	C₂×C₄×C₁₃₉	#123	1	8	yes	—
130	C₂×C₄×C₁₃₉	#123	1	4	yes	—
131	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
134	C₈×C₁₃₉	—	4	4	no	—
135	C₂²×C₁₃₉	—	2	8	no	—
136	C₂²×C₁₃₉	—	2	8	no	—
137	C₂²×C₁₃₉	—	2	32	no	—
138	C₂²×C₁₃₉	—	2	4	no	—
139	C₂²×C₁₃₉	—	2	4	no	—
140	C₂²×C₁₃₉	#381	1	4	yes	—
141	C₂²×C₁₃₉	C₂×#103	1	8	yes	—
142	C₂²×C₁₃₉	C₂×#103	1	4	yes	—
143	C₂²×C₁₃₉	#418	1	4	yes	—
144	C₂²×C₁₃₉	#481	1	8	yes	—
145	C₂²×C₁₃₉	#484	1	8	yes	—
146	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
148	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
149	C₂²×C₁₃₉	C₂²×Q₁₆	1	1	yes	characteristic
150	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
151	C₄×C₁₃₉	—	2	4	no	—
152	C₄×C₁₃₉	—	4	8	no	—
153	C₄×C₁₃₉	—	8	4	no	—
154	C₄×C₁₃₉	#381	1	4	yes	—
155	C₄×C₁₃₉	C₂×#117	1	2	yes	—
156	C₄×C₁₃₉	C₂×#123	1	2	yes	—
157	C₂×C₁₃₉	—	2	8	no	—
158	C₂×C₁₃₉	#1824	1	8	yes	direct product factor
159	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
160	C₂×C₁₃₉	C₂²×#103	1	1	yes	characteristic
161	C₂×C₁₃₉	C₂×#418	1	1	yes	characteristic
162	C₂×C₁₃₉	C₂×#481	1	2	yes	—
163	C₂×C₁₃₉	C₂×#484	1	2	yes	—
164	C₂×#1824	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₁₃₉	C₂×#1824	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
167	C₂²×C₂²⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic
168	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
169	#1824	C₂×C₁₃₉	1	8	yes	direct product factor
170	C₂×#340	C₂×C₁₃₉	1	4	yes	complemented
171	C₂⁴×C₄	—	2	1	no	—
172	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
173	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
174	C₂²×C₄⋊C₄	—	2	1	no	—
175	C₂²×C₄⋊C₄	—	2	2	no	—
176	C₂²×C₄⋊C₄	—	2	4	no	—
177	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
178	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
181	C₂²×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₂²⋊C₈	—	2	4	no	—
183	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
184	#380	—	2	2	no	—
185	#380	C₂²×C₁₃₉	1	4	yes	—
186	C₂×#95	—	2	1	no	—
187	#340	C₂²×C₁₃₉	1	16	yes	complemented
188	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
189	C₂³×C₄	—	2	8	no	—
190	C₂³×C₄	—	2	8	no	—
191	C₂³×C₄	—	2	2	no	—
192	C₂³×C₄	—	2	4	no	—
193	C₂³×C₄	—	2	2	no	—
194	C₂³×C₄	—	4	8	no	—
195	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
196	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
197	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
198	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
199	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
200	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	8	no	—
203	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
204	C₂×C₄⋊C₄	—	2	16	no	—
205	C₂×C₄⋊C₄	—	2	8	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	8	no	—
210	C₂×C₄⋊C₄	—	2	8	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
214	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
216	C₂×C₂²⋊C₄	—	2	4	no	—
217	C₂×C₂²⋊C₄	—	4	4	no	—
218	C₂²⋊C₈	—	2	8	no	—
219	#95	—	2	4	no	—
220	C₂⁴	—	2	4	no	—
221	C₂⁴	—	2	4	no	—
222	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
223	C₂⁴	SD₁₆×C₁₃₉	1	4	yes	—
224	C₂⁴	Q₁₆×C₁₃₉	1	4	yes	—
225	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
226	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	16	no	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	16	no	—
231	C₂²×C₄	—	2	8	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	16	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	4	32	no	—
237	C₂²×C₄	—	4	16	no	—
238	C₂²×C₄	—	4	8	no	—
239	C₂²×C₄	—	4	4	no	—
240	C₂²×C₄	—	4	4	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
243	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
246	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
247	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
248	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
249	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
250	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
251	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	8	no	—
254	C₂×C₈	—	4	8	no	—
255	C₄⋊C₄	—	2	8	no	—
256	C₄⋊C₄	—	2	16	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	8	no	—
259	C₄⋊C₄	—	4	4	no	—
260	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
261	C₂²⋊C₄	—	4	8	no	—
262	C₂³	—	2	8	no	—
263	C₂³	—	2	16	no	—
264	C₂³	—	2	16	no	—
265	C₂³	—	2	4	no	—
266	C₂³	—	2	4	no	—
267	C₂³	—	2	8	no	—
268	C₂³	#103×C₁₃₉	1	16	yes	—
269	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
270	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
271	C₂³	#123×C₁₃₉	1	4	yes	—
272	C₂³	C₂×SD₁₆×C₁₃₉	1	4	yes	—
273	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
274	C₂³	C₂×Q₁₆×C₁₃₉	1	4	yes	—
275	C₂³	C₂×Q₁₆×C₁₃₉	1	2	yes	—
276	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
277	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	16	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	4	32	no	—
285	C₂×C₄	—	4	16	no	—
286	C₂×C₄	—	4	8	no	—
287	C₂×C₄	—	4	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	8	8	no	—
291	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
292	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
293	C₂×C₄	#117×C₁₃₉	1	8	yes	—
294	C₂×C₄	#123×C₁₃₉	1	8	yes	—
295	C₂×C₄	#123×C₁₃₉	1	4	yes	—
296	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
297	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
298	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
299	C₈	—	4	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	2	8	no	—
303	C₂²	—	2	32	no	—
304	C₂²	—	2	4	no	—
305	C₂²	#381×C₁₃₉	1	4	yes	—
306	C₂²	C₂×#103×C₁₃₉	1	8	yes	—
307	C₂²	C₂×#103×C₁₃₉	1	4	yes	—
308	C₂²	#418×C₁₃₉	1	4	yes	—
309	C₂²	#481×C₁₃₉	1	8	yes	—
310	C₂²	#484×C₁₃₉	1	8	yes	—
311	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
312	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
313	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
314	C₂²	C₂²×Q₁₆×C₁₃₉	1	1	yes	characteristic
315	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
316	C₄	—	2	4	no	—
317	C₄	—	4	8	no	—
318	C₄	—	8	4	no	—
319	C₄	#381×C₁₃₉	1	4	yes	—
320	C₄	C₂×#117×C₁₃₉	1	2	yes	—
321	C₄	C₂×#123×C₁₃₉	1	2	yes	—
322	C₂	—	2	8	no	—
323	C₂	#1824×C₁₃₉	1	8	yes	direct product factor
324	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
325	C₂	C₂²×#103×C₁₃₉	1	1	yes	characteristic
326	C₂	C₂×#418×C₁₃₉	1	1	yes	characteristic
327	C₂	C₂×#481×C₁₃₉	1	2	yes	—
328	C₂	C₂×#484×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. #1824×C₁₃₉	C₂	direct (N × H)
5. C₂×#340×C₁₃₉	C₂	semidirect
12. C₂²×C₄⋊C₄×C₁₃₉	C₄	semidirect
22. #340×C₁₃₉	C₂²	semidirect
48. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
158. C₂×C₁₃₉	#1824	direct (N × H)
164. C₂×#1824	C₁₃₉	direct (N × H)
165. C₁₃₉	C₂×#1824	direct (N × H)
169. #1824	C₂×C₁₃₉	direct (N × H)
170. C₂×#340	C₂×C₁₃₉	semidirect
177. C₂²×C₄⋊C₄	C₄×C₁₃₉	semidirect
187. #340	C₂²×C₁₃₉	semidirect
213. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
323. C₂	#1824×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
C₂³×C₄⋊C₄×C₁₃₉	2
C₂²×C₂²⋊C₈×C₁₃₉	2
C₂×#380×C₁₃₉	2
#1824×C₁₃₉	2
C₂×#340×C₁₃₉	2
C₂×#1824	139

Subgroups — C2×#1824×C139 #48015294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1824×C₁₃₉ #48015294