Subgroups — C₁₃₉×#20011 #48014607

Order 35584.

572 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	#3360×C₁₃₉	C₂	1	2	yes	maximal
2	#3342×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3338×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1710×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1684×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1675×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1673×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1643×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1638×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#556×C₁₃₉	C₂²	1	2	yes	—
13	#554×C₁₃₉	C₂²	1	2	yes	—
14	#500×C₁₃₉	C₂²	1	1	yes	characteristic
15	#500×C₁₃₉	C₂²	1	1	yes	characteristic
16	#488×C₁₃₉	—	2	2	no	—
17	#487×C₁₃₉	C₂²	1	2	yes	—
18	#487×C₁₃₉	C₂²	1	2	yes	—
19	#485×C₁₃₉	—	2	2	no	—
20	#484×C₁₃₉	—	2	2	no	—
21	#479×C₁₃₉	—	2	2	no	—
22	#477×C₁₃₉	C₂²	1	2	yes	—
23	#476×C₁₃₉	C₂²	1	2	yes	—
24	#475×C₁₃₉	C₂²	1	2	yes	—
25	#467×C₁₃₉	—	2	1	no	—
26	#467×C₁₃₉	—	2	1	no	—
27	#463×C₁₃₉	—	2	2	no	—
28	#461×C₁₃₉	C₂²	1	2	yes	—
29	C₈×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₄×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₄×SD₁₆×C₁₃₉	—	2	2	no	—
32	C₄×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	#427×C₁₃₉	—	2	1	no	—
36	C₂×#107×C₁₃₉	—	2	1	no	—
37	#335×C₁₃₉	C₂²	1	1	yes	characteristic
38	#335×C₁₃₉	C₂²	1	1	yes	characteristic
39	#333×C₁₃₉	C₂²	1	2	yes	—
40	#332×C₁₃₉	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₉	C₂²	1	2	yes	—
42	D₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₃₉	D₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
47	C₂×D₈×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₉	—	2	1	no	—
49	C₂²×C₈×C₁₃₉	—	2	1	no	—
50	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
52	#126×C₁₃₉	—	4	2	no	—
53	#125×C₁₃₉	—	2	2	no	—
54	#124×C₁₃₉	—	2	2	no	—
55	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
56	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
57	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
58	C₄×Q₈×C₁₃₉	—	2	2	no	—
59	C₄×Q₈×C₁₃₉	C₂³	1	2	yes	—
60	C₄×D₄×C₁₃₉	—	2	2	no	—
61	C₄×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	#117×C₁₃₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
65	#107×C₁₃₉	—	2	1	no	—
66	#107×C₁₃₉	—	2	1	no	—
67	#107×C₁₃₉	—	2	1	no	—
68	#107×C₁₃₉	—	2	1	no	—
69	#107×C₁₃₉	—	2	2	no	—
70	#107×C₁₃₉	D₄	1	1	yes	characteristic
71	#107×C₁₃₉	D₄	1	1	yes	characteristic
72	#106×C₁₃₉	—	2	2	no	—
73	#106×C₁₃₉	—	2	2	no	—
74	C₄⋊C₈×C₁₃₉	—	2	2	no	—
75	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₁₃₉	C₂³	1	2	yes	—
78	#103×C₁₃₉	—	2	2	no	—
79	#103×C₁₃₉	—	2	2	no	—
80	#103×C₁₃₉	—	2	2	no	—
81	#103×C₁₃₉	—	2	2	no	—
82	#103×C₁₃₉	—	2	2	no	—
83	#103×C₁₃₉	—	4	2	no	—
84	#103×C₁₃₉	D₄	1	2	yes	—
85	#102×C₁₃₉	—	2	2	no	—
86	#102×C₁₃₉	D₄	1	1	yes	characteristic
87	#102×C₁₃₉	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
89	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
90	C₄×C₈×C₁₃₉	—	2	2	no	—
91	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₉	—	2	2	no	—
95	C₂×Q₈×C₁₃₉	—	2	2	no	—
96	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	—	2	1	no	—
100	C₂²×C₄×C₁₃₉	—	2	1	no	—
101	C₂²×C₄×C₁₃₉	—	4	2	no	—
102	Q₁₆×C₁₃₉	—	2	2	no	—
103	SD₁₆×C₁₃₉	—	4	4	no	—
104	D₈×C₁₃₉	—	2	2	no	—
105	C₂×C₈×C₁₃₉	—	2	2	no	—
106	C₂×C₈×C₁₃₉	—	2	1	no	—
107	C₂×C₈×C₁₃₉	—	2	1	no	—
108	C₂×C₈×C₁₃₉	—	2	1	no	—
109	C₂×C₈×C₁₃₉	—	4	2	no	—
110	C₂×C₈×C₁₃₉	—	4	2	no	—
111	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₁₃₉	—	2	2	no	—
116	C₄⋊C₄×C₁₃₉	—	2	2	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	2	2	no	—
119	C₄⋊C₄×C₁₃₉	—	2	2	no	—
120	C₄⋊C₄×C₁₃₉	—	4	2	no	—
121	C₄⋊C₄×C₁₃₉	—	4	2	no	—
122	C₄⋊C₄×C₁₃₉	—	4	2	no	—
123	C₄⋊C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
127	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
128	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
129	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
131	C₄²×C₁₃₉	—	2	2	no	—
132	C₄²×C₁₃₉	—	4	2	no	—
133	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
134	C₂³×C₁₃₉	—	2	1	no	—
135	C₂³×C₁₃₉	—	2	1	no	—
136	Q₈×C₁₃₉	—	2	2	no	—
137	Q₈×C₁₃₉	—	2	2	no	—
138	Q₈×C₁₃₉	—	4	2	no	—
139	Q₈×C₁₃₉	—	4	2	no	—
140	Q₈×C₁₃₉	—	8	2	no	—
141	D₄×C₁₃₉	—	2	1	no	—
142	D₄×C₁₃₉	—	2	1	no	—
143	D₄×C₁₃₉	—	2	1	no	—
144	D₄×C₁₃₉	#135	1	2	yes	—
145	C₂×C₄×C₁₃₉	—	2	2	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	1	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	4	1	no	—
150	C₂×C₄×C₁₃₉	—	4	1	no	—
151	C₂×C₄×C₁₃₉	—	4	1	no	—
152	C₂×C₄×C₁₃₉	—	4	1	no	—
153	C₂×C₄×C₁₃₉	—	4	2	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	16	2	no	—
156	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
159	C₈×C₁₃₉	—	2	1	no	—
160	C₈×C₁₃₉	—	2	1	no	—
161	C₈×C₁₃₉	—	2	1	no	—
162	C₈×C₁₃₉	—	4	1	no	—
163	C₈×C₁₃₉	—	4	1	no	—
164	C₈×C₁₃₉	—	4	1	no	—
165	C₈×C₁₃₉	—	4	2	no	—
166	C₈×C₁₃₉	#135	1	2	yes	—
167	C₂²×C₁₃₉	—	2	2	no	—
168	C₂²×C₁₃₉	—	4	1	no	—
169	C₂²×C₁₃₉	—	4	1	no	—
170	C₂²×C₁₃₉	—	4	1	no	—
171	C₂²×C₁₃₉	—	4	1	no	—
172	C₂²×C₁₃₉	—	4	1	no	—
173	C₂²×C₁₃₉	D₄²	1	1	yes	characteristic
174	C₄×C₁₃₉	—	2	1	no	—
175	C₄×C₁₃₉	—	4	1	no	—
176	C₄×C₁₃₉	—	4	1	no	—
177	C₄×C₁₃₉	—	4	2	no	—
178	C₄×C₁₃₉	—	4	2	no	—
179	C₄×C₁₃₉	—	8	2	no	—
180	C₄×C₁₃₉	—	8	2	no	—
181	C₄×C₁₃₉	C₂×#135	1	1	yes	characteristic
182	C₄×C₁₃₉	C₂×#135	1	1	yes	characteristic
183	C₄×C₁₃₉	#578	1	1	yes	characteristic
184	C₄×C₁₃₉	#578	1	1	yes	characteristic
185	C₂×C₁₃₉	—	4	2	no	—
186	C₂×C₁₃₉	—	8	1	no	—
187	C₂×C₁₃₉	#3283	1	1	yes	characteristic
188	C₂×C₁₃₉	#3285	1	1	yes	characteristic
189	C₂×C₁₃₉	#3290	1	1	yes	characteristic
190	#20011	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₉	#20011	1	1	yes	characteristic, direct product factor, Sylow
192	#3360	C₂×C₁₃₉	1	2	yes	—
193	#3342	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	#3338	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	#1710	C₂×C₁₃₉	1	1	yes	characteristic, complemented
196	#1684	C₂×C₁₃₉	1	2	yes	complemented
197	#1675	C₂×C₁₃₉	1	1	yes	characteristic, complemented
198	#1673	C₂×C₁₃₉	1	1	yes	characteristic, complemented
199	#1643	C₂×C₁₃₉	1	2	yes	complemented
200	#1638	C₂×C₁₃₉	1	2	yes	complemented
201	C₈×Q₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
202	C₈×D₈	C₂×C₁₃₉	1	1	yes	characteristic
203	#556	C₂²×C₁₃₉	1	2	yes	—
204	#554	C₂²×C₁₃₉	1	2	yes	—
205	#500	C₂²×C₁₃₉	1	1	yes	characteristic
206	#500	C₂²×C₁₃₉	1	1	yes	characteristic
207	#488	—	2	2	no	—
208	#487	C₂²×C₁₃₉	1	2	yes	—
209	#487	C₂²×C₁₃₉	1	2	yes	—
210	#485	—	2	2	no	—
211	#484	—	2	2	no	—
212	#479	—	2	2	no	—
213	#477	C₂²×C₁₃₉	1	2	yes	—
214	#476	C₂²×C₁₃₉	1	2	yes	—
215	#475	C₂²×C₁₃₉	1	2	yes	—
216	#467	—	2	1	no	—
217	#467	—	2	1	no	—
218	#463	—	2	2	no	—
219	#461	C₂²×C₁₃₉	1	2	yes	—
220	C₈×Q₈	C₂²×C₁₃₉	1	2	yes	—
221	C₄×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₄×SD₁₆	—	2	2	no	—
223	C₄×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
224	C₈×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
225	C₈×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
226	#427	—	2	1	no	—
227	C₂×#107	—	2	1	no	—
228	#335	C₂²×C₁₃₉	1	1	yes	characteristic
229	#335	C₂²×C₁₃₉	1	1	yes	characteristic
230	#333	C₂²×C₁₃₉	1	2	yes	—
231	#332	C₂²×C₁₃₉	1	2	yes	—
232	Q₈⋊C₈	C₂²×C₁₃₉	1	2	yes	—
233	D₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
234	D₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
235	C₈²	C₂²×C₁₃₉	1	1	yes	characteristic
236	C₂×Q₁₆	D₄×C₁₃₉	1	1	yes	characteristic
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×D₈	D₄×C₁₃₉	1	1	yes	characteristic
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
243	#126	—	4	2	no	—
244	#125	—	2	2	no	—
245	#124	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₂²⋊Q₈	—	4	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	C₂³×C₁₃₉	1	2	yes	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
253	C₄×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	#107	—	2	1	no	—
257	#107	—	2	1	no	—
258	#107	—	2	1	no	—
259	#107	—	2	1	no	—
260	#107	—	2	2	no	—
261	#107	D₄×C₁₃₉	1	1	yes	characteristic
262	#107	D₄×C₁₃₉	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	#106	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
267	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
268	C₄⋊C₈	C₂³×C₁₃₉	1	2	yes	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	4	2	no	—
275	#103	D₄×C₁₃₉	1	2	yes	—
276	#102	—	2	2	no	—
277	#102	D₄×C₁₃₉	1	1	yes	characteristic
278	#102	D₄×C₁₃₉	1	1	yes	characteristic
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
288	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
289	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	2	no	—
293	Q₁₆	—	2	2	no	—
294	SD₁₆	—	4	4	no	—
295	D₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
315	C₄⋊C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
316	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	2	no	—
324	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	Q₈	—	2	2	no	—
328	Q₈	—	2	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	8	2	no	—
332	D₄	—	2	1	no	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	#135×C₁₃₉	1	2	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	16	2	no	—
347	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	4	1	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	1	no	—
356	C₈	—	4	2	no	—
357	C₈	#135×C₁₃₉	1	2	yes	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	D₄²×C₁₃₉	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	C₂×#135×C₁₃₉	1	1	yes	characteristic
373	C₄	C₂×#135×C₁₃₉	1	1	yes	characteristic
374	C₄	#578×C₁₃₉	1	1	yes	characteristic
375	C₄	#578×C₁₃₉	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	8	1	no	—
378	C₂	#3283×C₁₃₉	1	1	yes	characteristic
379	C₂	#3285×C₁₃₉	1	1	yes	characteristic
380	C₂	#3290×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
prime radical	C₂×D₈×C₁₃₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #3342×C₁₃₉	C₂	semidirect
3. #3338×C₁₃₉	C₂	semidirect
4. #1710×C₁₃₉	C₂	semidirect
5. #1684×C₁₃₉	C₂	semidirect
6. #1675×C₁₃₉	C₂	semidirect
7. #1673×C₁₃₉	C₂	semidirect
8. #1643×C₁₃₉	C₂	semidirect
9. #1638×C₁₃₉	C₂	semidirect
10. C₈×Q₁₆×C₁₃₉	C₂	semidirect
190. #20011	C₁₃₉	direct (N × H)
191. C₁₃₉	#20011	direct (N × H)
193. #3342	C₂×C₁₃₉	semidirect
194. #3338	C₂×C₁₃₉	semidirect
195. #1710	C₂×C₁₃₉	semidirect
196. #1684	C₂×C₁₃₉	semidirect
197. #1675	C₂×C₁₃₉	semidirect
198. #1673	C₂×C₁₃₉	semidirect
199. #1643	C₂×C₁₃₉	semidirect
200. #1638	C₂×C₁₃₉	semidirect
201. C₈×Q₁₆	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3360×C₁₃₉	2
#3342×C₁₃₉	2
#3338×C₁₃₉	2
#1710×C₁₃₉	2
#1684×C₁₃₉	2
#1675×C₁₃₉	2
#1673×C₁₃₉	2
#1643×C₁₃₉	2
#1638×C₁₃₉	2
C₈×Q₁₆×C₁₃₉	2
C₈×D₈×C₁₃₉	2
#20011	139

Subgroups — C139×#20011 #48014607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20011 #48014607