Subgroups — C₁₃₉×#20986 #48015582

Order 35584.

1718 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#410×C₁₃₉	C₂	1	2	yes	maximal
4	#2310×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1899×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#1740×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
9	#536×C₁₃₉	—	2	4	no	—
10	#536×C₁₃₉	—	2	4	no	—
11	C₂×C₄⋊Q₈×C₁₃₉	C₄	1	2	yes	complemented
12	C₂×#124×C₁₃₉	C₄	1	2	yes	complemented
13	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
14	C₂×C₂²⋊Q₈×C₁₃₉	C₄	1	4	yes	complemented
15	#519×C₁₃₉	—	2	8	no	—
16	C₂×C₄×Q₈×C₁₃₉	—	2	4	no	—
17	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
21	#410×C₁₃₉	—	2	8	no	—
22	C₂×#99×C₁₃₉	C₂²	1	8	yes	—
23	#391×C₁₃₉	—	2	4	no	—
24	#381×C₁₃₉	C₂²	1	4	yes	—
25	#342×C₁₃₉	C₂²	1	8	yes	—
26	C₂×#41×C₁₃₉	—	2	4	no	—
27	C₂×#41×C₁₃₉	—	2	2	no	—
28	C₂×#41×C₁₃₉	—	2	2	no	—
29	C₂×#41×C₁₃₉	—	2	4	no	—
30	C₂²×Q₈×C₁₃₉	—	2	4	no	—
31	C₂²×Q₈×C₁₃₉	—	2	4	no	—
32	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
34	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₁₃₉	D₄	1	4	yes	—
36	C₂²×Q₈×C₁₃₉	D₄	1	4	yes	—
37	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
43	#124×C₁₃₉	—	2	8	no	—
44	#123×C₁₃₉	—	2	8	no	—
45	#123×C₁₃₉	—	2	8	no	—
46	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
47	C₄×Q₈×C₁₃₉	—	2	32	no	—
48	#117×C₁₃₉	—	2	4	no	—
49	#117×C₁₃₉	—	2	2	no	—
50	#117×C₁₃₉	—	2	2	no	—
51	#117×C₁₃₉	—	2	16	no	—
52	#117×C₁₃₉	—	2	4	no	—
53	#117×C₁₃₉	—	2	4	no	—
54	#117×C₁₃₉	D₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
60	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
61	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
64	C₂×C₄²×C₁₃₉	—	2	4	no	—
65	C₂×C₄²×C₁₃₉	—	2	2	no	—
66	C₂×C₄²×C₁₃₉	—	2	2	no	—
67	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
68	#99×C₁₃₉	—	2	16	no	—
69	#95×C₁₃₉	—	2	8	no	—
70	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
72	#41×C₁₃₉	—	4	4	no	—
73	#41×C₁₃₉	—	4	4	no	—
74	#41×C₁₃₉	—	4	4	no	—
75	#41×C₁₃₉	—	4	4	no	—
76	C₂×Q₈×C₁₃₉	—	2	2	no	—
77	C₂×Q₈×C₁₃₉	—	2	8	no	—
78	C₂×Q₈×C₁₃₉	—	2	8	no	—
79	C₂×Q₈×C₁₃₉	—	2	4	no	—
80	C₂×Q₈×C₁₃₉	—	2	8	no	—
81	C₂×Q₈×C₁₃₉	—	2	8	no	—
82	C₂×Q₈×C₁₃₉	—	2	8	no	—
83	C₂×Q₈×C₁₃₉	—	2	8	no	—
84	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	8	yes	—
85	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	8	yes	—
86	C₂×D₄×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	2	2	no	—
89	C₂×D₄×C₁₃₉	—	2	4	no	—
90	C₂×D₄×C₁₃₉	—	2	2	no	—
91	C₂×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	4	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	4	no	—
96	C₂²×C₄×C₁₃₉	—	2	8	no	—
97	C₂²×C₄×C₁₃₉	—	2	4	no	—
98	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
109	C₄⋊C₄×C₁₃₉	—	2	16	no	—
110	C₄⋊C₄×C₁₃₉	—	2	4	no	—
111	C₄⋊C₄×C₁₃₉	—	2	16	no	—
112	C₄⋊C₄×C₁₃₉	—	2	8	no	—
113	C₄⋊C₄×C₁₃₉	—	4	4	no	—
114	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
116	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
118	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
121	C₄²×C₁₃₉	—	2	16	no	—
122	C₄²×C₁₃₉	—	2	4	no	—
123	C₄²×C₁₃₉	—	2	8	no	—
124	C₄²×C₁₃₉	—	4	4	no	—
125	C₂³×C₁₃₉	—	2	2	no	—
126	C₂³×C₁₃₉	—	2	4	no	—
127	C₂³×C₁₃₉	—	4	2	no	—
128	C₂³×C₁₃₉	—	4	4	no	—
129	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
130	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
131	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
132	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
133	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
134	Q₈×C₁₃₉	—	2	16	no	—
135	Q₈×C₁₃₉	—	2	16	no	—
136	Q₈×C₁₃₉	—	4	4	no	—
137	D₄×C₁₃₉	—	4	2	no	—
138	D₄×C₁₃₉	—	4	4	no	—
139	D₄×C₁₃₉	—	4	2	no	—
140	D₄×C₁₃₉	—	4	4	no	—
141	C₂×C₄×C₁₃₉	—	2	8	no	—
142	C₂×C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₄×C₁₃₉	—	2	8	no	—
144	C₂×C₄×C₁₃₉	—	2	4	no	—
145	C₂×C₄×C₁₃₉	—	2	4	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	4	no	—
148	C₂×C₄×C₁₃₉	—	2	8	no	—
149	C₂×C₄×C₁₃₉	—	4	8	no	—
150	C₂×C₄×C₁₃₉	—	4	8	no	—
151	C₂×C₄×C₁₃₉	—	4	4	no	—
152	C₂×C₄×C₁₃₉	—	4	8	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	—
155	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
158	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
159	C₂×C₄×C₁₃₉	#120	1	4	yes	—
160	C₂×C₄×C₁₃₉	#121	1	4	yes	—
161	C₂×C₄×C₁₃₉	#121	1	4	yes	—
162	C₂×C₄×C₁₃₉	#123	1	4	yes	—
163	C₂²×C₁₃₉	—	2	2	no	—
164	C₂²×C₁₃₉	—	2	2	no	—
165	C₂²×C₁₃₉	—	2	2	no	—
166	C₂²×C₁₃₉	—	4	2	no	—
167	C₂²×C₁₃₉	—	4	2	no	—
168	C₂²×C₁₃₉	—	4	4	no	—
169	C₂²×C₁₃₉	—	4	2	no	—
170	C₂²×C₁₃₉	—	8	4	no	—
171	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
173	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
174	C₂²×C₁₃₉	C₂×#121	1	2	yes	—
175	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
176	C₄×C₁₃₉	—	2	8	no	—
177	C₄×C₁₃₉	—	4	8	no	—
178	C₄×C₁₃₉	—	4	4	no	—
179	C₄×C₁₃₉	—	4	2	no	—
180	C₄×C₁₃₉	—	8	4	no	—
181	C₄×C₁₃₉	#386	1	4	yes	—
182	C₄×C₁₃₉	#386	1	4	yes	—
183	C₂×C₁₃₉	—	2	1	no	—
184	C₂×C₁₃₉	—	2	2	no	—
185	C₂×C₁₃₉	—	2	2	no	—
186	C₂×C₁₃₉	—	2	1	no	—
187	C₂×C₁₃₉	—	8	2	no	—
188	C₂×C₁₃₉	C₂×#386	1	1	yes	characteristic
189	C₂×C₁₃₉	#2884	1	2	yes	—
190	#20986	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₉	#20986	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic
193	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	C₂×#410	C₂×C₁₃₉	1	2	yes	—
195	#2310	C₂×C₁₃₉	1	1	yes	characteristic, complemented
196	#1899	C₂×C₁₃₉	1	8	yes	complemented
197	#1740	C₂×C₁₃₉	1	2	yes	complemented
198	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
199	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
200	#536	—	2	4	no	—
201	#536	—	2	4	no	—
202	C₂×C₄⋊Q₈	C₄×C₁₃₉	1	2	yes	complemented
203	C₂×#124	C₄×C₁₃₉	1	2	yes	complemented
204	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
205	C₂×C₂²⋊Q₈	C₄×C₁₃₉	1	4	yes	complemented
206	#519	—	2	8	no	—
207	C₂×C₄×Q₈	—	2	4	no	—
208	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
209	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
210	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
211	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
212	#410	—	2	8	no	—
213	C₂×#99	C₂²×C₁₃₉	1	8	yes	—
214	#391	—	2	4	no	—
215	#381	C₂²×C₁₃₉	1	4	yes	—
216	#342	C₂²×C₁₃₉	1	8	yes	—
217	C₂×#41	—	2	2	no	—
218	C₂×#41	—	2	2	no	—
219	C₂×#41	—	2	4	no	—
220	C₂×#41	—	2	4	no	—
221	C₂²×Q₈	—	2	4	no	—
222	C₂²×Q₈	—	2	4	no	—
223	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
224	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
225	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
226	C₂²×Q₈	D₄×C₁₃₉	1	4	yes	—
227	C₂²×Q₈	D₄×C₁₃₉	1	4	yes	—
228	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
229	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
230	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
233	C₄⋊Q₈	—	2	8	no	—
234	#124	—	2	8	no	—
235	#123	—	2	8	no	—
236	#123	—	2	8	no	—
237	C₂²⋊Q₈	—	2	16	no	—
238	C₄×Q₈	—	2	32	no	—
239	#117	—	2	4	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	16	no	—
243	#117	—	2	4	no	—
244	#117	—	2	4	no	—
245	#117	D₄×C₁₃₉	1	8	yes	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
259	#99	—	2	16	no	—
260	#95	—	2	8	no	—
261	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
262	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
263	#41	—	4	4	no	—
264	#41	—	4	4	no	—
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	2	8	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	2	8	no	—
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	8	yes	—
276	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	8	yes	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
299	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
300	C₄⋊C₄	—	2	16	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
312	C₄²	—	2	16	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	8	no	—
315	C₄²	—	4	4	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	4	no	—
320	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
321	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
322	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
323	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
324	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
325	Q₈	—	2	16	no	—
326	Q₈	—	2	16	no	—
327	Q₈	—	4	4	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
348	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
349	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
350	C₂×C₄	#120×C₁₃₉	1	4	yes	—
351	C₂×C₄	#121×C₁₃₉	1	4	yes	—
352	C₂×C₄	#121×C₁₃₉	1	4	yes	—
353	C₂×C₄	#123×C₁₃₉	1	4	yes	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	8	4	no	—
362	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
363	C₂²	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
364	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
365	C₂²	C₂×#121×C₁₃₉	1	2	yes	—
366	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
367	C₄	—	2	8	no	—
368	C₄	—	4	8	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	4	no	—
371	C₄	—	8	4	no	—
372	C₄	#386×C₁₃₉	1	4	yes	—
373	C₄	#386×C₁₃₉	1	4	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	1	no	—
378	C₂	—	8	2	no	—
379	C₂	C₂×#386×C₁₃₉	1	1	yes	characteristic
380	C₂	#2884×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂³×Q₈×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#519×C₁₃₉	C₂	semidirect
4. #2310×C₁₃₉	C₂	semidirect
5. #1899×C₁₃₉	C₂	semidirect
6. #1740×C₁₃₉	C₂	semidirect
11. C₂×C₄⋊Q₈×C₁₃₉	C₄	semidirect
12. C₂×#124×C₁₃₉	C₄	semidirect
14. C₂×C₂²⋊Q₈×C₁₃₉	C₄	semidirect
190. #20986	C₁₃₉	direct (N × H)
191. C₁₃₉	#20986	direct (N × H)
193. C₂×#519	C₂×C₁₃₉	semidirect
195. #2310	C₂×C₁₃₉	semidirect
196. #1899	C₂×C₁₃₉	semidirect
197. #1740	C₂×C₁₃₉	semidirect
202. C₂×C₄⋊Q₈	C₄×C₁₃₉	semidirect
203. C₂×#124	C₄×C₁₃₉	semidirect
205. C₂×C₂²⋊Q₈	C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₁₃₉	2
C₂×#519×C₁₃₉	2
C₂×#410×C₁₃₉	2
#2310×C₁₃₉	2
#1899×C₁₃₉	2
#1740×C₁₃₉	2
#20986	139

Subgroups — C139×#20986 #48015582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20986 #48015582