Subgroups — C₁₃₉×#29416 #48024012

Order 35584.

784 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	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal
2	#2075×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2035×C₁₃₉	C₂	1	2	yes	maximal
4	#2001×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1927×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1920×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1878×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1863×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1817×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
12	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	#391×C₁₃₉	C₂²	1	2	yes	—
22	#389×C₁₃₉	C₂²	1	2	yes	—
23	#387×C₁₃₉	—	2	2	no	—
24	#385×C₁₃₉	—	2	2	no	—
25	#380×C₁₃₉	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₃₉	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
29	#340×C₁₃₉	C₂²	1	1	yes	characteristic
30	#340×C₁₃₉	C₂²	1	2	yes	—
31	#340×C₁₃₉	C₂²	1	2	yes	—
32	#340×C₁₃₉	C₂²	1	1	yes	characteristic
33	#336×C₁₃₉	C₂²	1	2	yes	—
34	#336×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
40	C₂×Q₁₆×C₁₃₉	—	4	1	no	—
41	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
45	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
46	C₄×Q₈×C₁₃₉	—	4	2	no	—
47	C₄×Q₈×C₁₃₉	—	4	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄²×C₁₃₉	—	2	2	no	—
57	C₂×C₄²×C₁₃₉	—	2	2	no	—
58	C₂×C₄²×C₁₃₉	—	4	1	no	—
59	C₂×C₄²×C₁₃₉	—	4	1	no	—
60	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
62	#107×C₁₃₉	—	4	1	no	—
63	#106×C₁₃₉	—	2	4	no	—
64	#103×C₁₃₉	—	2	4	no	—
65	#103×C₁₃₉	—	2	4	no	—
66	#103×C₁₃₉	—	4	2	no	—
67	C₂²⋊C₈×C₁₃₉	—	4	1	no	—
68	C₂²⋊C₈×C₁₃₉	—	4	1	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	#95×C₁₃₉	—	2	2	no	—
71	#95×C₁₃₉	—	2	2	no	—
72	#95×C₁₃₉	—	2	2	no	—
73	#95×C₁₃₉	—	2	2	no	—
74	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
75	C₂×Q₈×C₁₃₉	—	2	2	no	—
76	C₂×Q₈×C₁₃₉	—	2	2	no	—
77	C₂×Q₈×C₁₃₉	—	2	2	no	—
78	C₂×Q₈×C₁₃₉	—	2	2	no	—
79	C₂×Q₈×C₁₃₉	—	2	2	no	—
80	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	2	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	1	no	—
88	C₂²×C₄×C₁₃₉	—	2	1	no	—
89	C₂²×C₄×C₁₃₉	—	2	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	4	1	no	—
92	C₂²×C₄×C₁₃₉	—	4	1	no	—
93	C₂²×C₄×C₁₃₉	—	4	1	no	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₁₃₉	—	4	4	no	—
99	C₂×C₈×C₁₃₉	—	2	2	no	—
100	C₂×C₈×C₁₃₉	—	2	2	no	—
101	C₂×C₈×C₁₃₉	—	2	2	no	—
102	C₂×C₈×C₁₃₉	—	2	2	no	—
103	C₂×C₈×C₁₃₉	—	2	2	no	—
104	C₂×C₈×C₁₃₉	—	2	1	no	—
105	C₂×C₈×C₁₃₉	—	2	1	no	—
106	C₄⋊C₄×C₁₃₉	—	2	8	no	—
107	C₄⋊C₄×C₁₃₉	—	2	2	no	—
108	C₄⋊C₄×C₁₃₉	—	2	2	no	—
109	C₄⋊C₄×C₁₃₉	—	2	2	no	—
110	C₄⋊C₄×C₁₃₉	—	2	2	no	—
111	C₄⋊C₄×C₁₃₉	—	2	2	no	—
112	C₄⋊C₄×C₁₃₉	—	4	4	no	—
113	C₄⋊C₄×C₁₃₉	—	4	4	no	—
114	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
115	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
116	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
117	C₄²×C₁₃₉	—	2	2	no	—
118	C₄²×C₁₃₉	—	2	2	no	—
119	C₄²×C₁₃₉	—	4	2	no	—
120	C₄²×C₁₃₉	—	4	4	no	—
121	C₄²×C₁₃₉	—	4	4	no	—
122	C₂³×C₁₃₉	—	2	2	no	—
123	C₂³×C₁₃₉	—	2	1	no	—
124	C₂³×C₁₃₉	—	2	2	no	—
125	C₂³×C₁₃₉	—	2	1	no	—
126	C₂³×C₁₃₉	#135	1	2	yes	—
127	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₁₃₉	—	2	4	no	—
129	Q₈×C₁₃₉	—	2	4	no	—
130	Q₈×C₁₃₉	—	4	2	no	—
131	Q₈×C₁₃₉	—	4	2	no	—
132	C₂×C₄×C₁₃₉	—	2	2	no	—
133	C₂×C₄×C₁₃₉	—	2	2	no	—
134	C₂×C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	1	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	4	4	no	—
142	C₂×C₄×C₁₃₉	—	4	4	no	—
143	C₂×C₄×C₁₃₉	—	4	2	no	—
144	C₂×C₄×C₁₃₉	—	4	2	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	1	no	—
148	C₂×C₄×C₁₃₉	—	4	2	no	—
149	C₂×C₄×C₁₃₉	—	4	1	no	—
150	C₂×C₄×C₁₃₉	—	4	2	no	—
151	C₂×C₄×C₁₃₉	—	4	2	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	—	4	2	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	#137	1	4	yes	—
157	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
158	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₁₃₉	—	4	1	no	—
162	C₈×C₁₃₉	—	4	2	no	—
163	C₈×C₁₃₉	—	4	1	no	—
164	C₂²×C₁₃₉	—	2	4	no	—
165	C₂²×C₁₃₉	—	2	2	no	—
166	C₂²×C₁₃₉	—	4	1	no	—
167	C₂²×C₁₃₉	—	4	2	no	—
168	C₂²×C₁₃₉	—	4	1	no	—
169	C₂²×C₁₃₉	#525	1	2	yes	—
170	C₂²×C₁₃₉	#534	1	1	yes	characteristic
171	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
172	C₂²×C₁₃₉	C₂×#137	1	2	yes	—
173	C₂²×C₁₃₉	#575	1	1	yes	characteristic
174	C₄×C₁₃₉	—	2	4	no	—
175	C₄×C₁₃₉	—	4	1	no	—
176	C₄×C₁₃₉	—	4	4	no	—
177	C₄×C₁₃₉	—	4	4	no	—
178	C₄×C₁₃₉	—	4	2	no	—
179	C₄×C₁₃₉	—	8	2	no	—
180	C₄×C₁₃₉	—	8	2	no	—
181	C₄×C₁₃₉	#551	1	1	yes	characteristic
182	C₄×C₁₃₉	#553	1	2	yes	—
183	C₄×C₁₃₉	#559	1	1	yes	characteristic
184	C₂×C₁₃₉	—	4	2	no	—
185	C₂×C₁₃₉	#2600	1	1	yes	characteristic
186	C₂×C₁₃₉	#3108	1	2	yes	—
187	C₂×C₁₃₉	#3116	1	2	yes	—
188	C₂×C₁₃₉	#3191	1	1	yes	characteristic
189	C₂×C₁₃₉	#3195	1	1	yes	characteristic
190	#29416	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₉	#29416	1	1	yes	characteristic, direct product factor, Sylow
192	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	—
193	#2075	C₂×C₁₃₉	1	1	yes	characteristic
194	#2035	C₂×C₁₃₉	1	2	yes	—
195	#2001	C₂×C₁₃₉	1	1	yes	characteristic
196	#1927	C₂×C₁₃₉	1	2	yes	complemented
197	#1920	C₂×C₁₃₉	1	2	yes	complemented
198	#1878	C₂×C₁₃₉	1	2	yes	complemented
199	#1863	C₂×C₁₃₉	1	2	yes	complemented
200	#1817	C₂×C₁₃₉	1	1	yes	characteristic
201	C₂²×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
204	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
205	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
206	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
207	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
208	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
209	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
211	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
212	#391	C₂²×C₁₃₉	1	2	yes	—
213	#389	C₂²×C₁₃₉	1	2	yes	—
214	#387	—	2	2	no	—
215	#385	—	2	2	no	—
216	#380	C₂²×C₁₃₉	1	2	yes	—
217	C₄×C₄⋊C₄	—	2	2	no	—
218	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
219	C₄×C₂²⋊C₄	—	2	2	no	—
220	#340	C₂²×C₁₃₉	1	2	yes	—
221	#340	C₂²×C₁₃₉	1	1	yes	characteristic
222	#340	C₂²×C₁₃₉	1	2	yes	—
223	#340	C₂²×C₁₃₉	1	1	yes	characteristic
224	#336	C₂²×C₁₃₉	1	2	yes	—
225	#336	C₂²×C₁₃₉	1	2	yes	—
226	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
227	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
230	C₂×Q₁₆	—	2	4	no	—
231	C₂×Q₁₆	—	4	1	no	—
232	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₄×Q₈	—	4	2	no	—
238	C₄×Q₈	—	4	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	—	4	1	no	—
250	C₂×C₄²	—	4	1	no	—
251	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
253	#107	—	4	1	no	—
254	#106	—	2	4	no	—
255	#103	—	2	4	no	—
256	#103	—	2	4	no	—
257	#103	—	4	2	no	—
258	C₂²⋊C₈	—	4	1	no	—
259	C₂²⋊C₈	—	4	1	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
289	Q₁₆	—	4	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
306	C₂²⋊C₄	—	2	8	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	4	no	—
312	C₄²	—	4	4	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	1	no	—
317	C₂³	#135×C₁₃₉	1	2	yes	—
318	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
319	Q₈	—	2	4	no	—
320	Q₈	—	2	4	no	—
321	Q₈	—	4	2	no	—
322	Q₈	—	4	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	#137×C₁₃₉	1	4	yes	—
348	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
349	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
350	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
351	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
352	C₈	—	4	1	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	1	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	#525×C₁₃₉	1	2	yes	—
361	C₂²	#534×C₁₃₉	1	1	yes	characteristic
362	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
363	C₂²	C₂×#137×C₁₃₉	1	2	yes	—
364	C₂²	#575×C₁₃₉	1	1	yes	characteristic
365	C₄	—	2	4	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	4	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	#551×C₁₃₉	1	1	yes	characteristic
373	C₄	#553×C₁₃₉	1	2	yes	—
374	C₄	#559×C₁₃₉	1	1	yes	characteristic
375	C₂	—	4	2	no	—
376	C₂	#2600×C₁₃₉	1	1	yes	characteristic
377	C₂	#3108×C₁₃₉	1	2	yes	—
378	C₂	#3116×C₁₃₉	1	2	yes	—
379	C₂	#3191×C₁₃₉	1	1	yes	characteristic
380	C₂	#3195×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. #1927×C₁₃₉	C₂	semidirect
6. #1920×C₁₃₉	C₂	semidirect
7. #1878×C₁₃₉	C₂	semidirect
8. #1863×C₁₃₉	C₂	semidirect
190. #29416	C₁₃₉	direct (N × H)
191. C₁₃₉	#29416	direct (N × H)
196. #1927	C₂×C₁₃₉	semidirect
197. #1920	C₂×C₁₃₉	semidirect
198. #1878	C₂×C₁₃₉	semidirect
199. #1863	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊Q₈×C₁₃₉	2
#2075×C₁₃₉	2
#2035×C₁₃₉	2
#2001×C₁₃₉	2
#1927×C₁₃₉	2
#1920×C₁₃₉	2
#1878×C₁₃₉	2
#1863×C₁₃₉	2
#1817×C₁₃₉	2
#29416	139

Subgroups — C139×#29416 #48024012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29416 #48024012