Subgroups — C₁₃₉×#13965 #48008561

Order 35584.

2150 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#385×C₁₃₉	C₂	1	4	yes	maximal
2	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1444×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	C₄⋊#95×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	8	yes	—
10	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
14	#385×C₁₃₉	—	2	16	no	—
15	#380×C₁₃₉	—	2	4	no	—
16	C₄×C₂²⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
17	C₂×#95×C₁₃₉	—	2	4	no	—
18	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
23	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₉	—	2	4	no	—
25	C₂³×C₄×C₁₃₉	—	2	8	no	—
26	C₂³×C₄×C₁₃₉	—	2	8	no	—
27	C₂³×C₄×C₁₃₉	—	4	4	no	—
28	C₂³×C₄×C₁₃₉	—	4	4	no	—
29	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
31	C₂³×C₄×C₁₃₉	Q₈	1	4	yes	—
32	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
39	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
42	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
43	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
44	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
45	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	—
46	C₂×C₂²⋊C₄×C₁₃₉	Q₈	1	8	yes	—
47	C₂×C₄²×C₁₃₉	—	4	4	no	—
48	C₂×C₄²×C₁₃₉	C₂×C₄	1	8	yes	complemented
49	#95×C₁₃₉	—	2	4	no	—
50	#95×C₁₃₉	—	2	4	no	—
51	#95×C₁₃₉	—	2	4	no	—
52	#95×C₁₃₉	—	2	16	no	—
53	#95×C₁₃₉	C₂×C₄	1	8	yes	complemented
54	C₂⁴×C₁₃₉	—	2	4	no	—
55	C₂⁴×C₁₃₉	—	2	4	no	—
56	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
57	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
58	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
59	C₂⁴×C₁₃₉	C₂×Q₈	1	4	yes	—
60	C₂⁴×C₁₃₉	C₂×Q₈	1	2	yes	—
61	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
62	C₂²×C₄×C₁₃₉	—	2	8	no	—
63	C₂²×C₄×C₁₃₉	—	2	8	no	—
64	C₂²×C₄×C₁₃₉	—	2	4	no	—
65	C₂²×C₄×C₁₃₉	—	2	4	no	—
66	C₂²×C₄×C₁₃₉	—	2	16	no	—
67	C₂²×C₄×C₁₃₉	—	2	4	no	—
68	C₂²×C₄×C₁₃₉	—	2	8	no	—
69	C₂²×C₄×C₁₃₉	—	2	4	no	—
70	C₂²×C₄×C₁₃₉	—	2	8	no	—
71	C₂²×C₄×C₁₃₉	—	2	4	no	—
72	C₂²×C₄×C₁₃₉	—	2	4	no	—
73	C₂²×C₄×C₁₃₉	—	2	4	no	—
74	C₂²×C₄×C₁₃₉	—	2	8	no	—
75	C₂²×C₄×C₁₃₉	—	2	8	no	—
76	C₂²×C₄×C₁₃₉	—	4	8	no	—
77	C₂²×C₄×C₁₃₉	—	4	8	no	—
78	C₂²×C₄×C₁₃₉	—	4	8	no	—
79	C₂²×C₄×C₁₃₉	—	4	32	no	—
80	C₂²×C₄×C₁₃₉	—	4	8	no	—
81	C₂²×C₄×C₁₃₉	—	4	8	no	—
82	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	16	yes	complemented
83	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
85	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
88	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
90	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
93	C₄⋊C₄×C₁₃₉	—	4	32	no	—
94	C₄⋊C₄×C₁₃₉	—	4	8	no	—
95	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
96	C₂²⋊C₄×C₁₃₉	C₄⋊C₄	1	32	yes	complemented
97	C₄²×C₁₃₉	—	4	8	no	—
98	C₂³×C₁₃₉	—	2	4	no	—
99	C₂³×C₁₃₉	—	2	4	no	—
100	C₂³×C₁₃₉	—	2	4	no	—
101	C₂³×C₁₃₉	—	2	4	no	—
102	C₂³×C₁₃₉	—	2	4	no	—
103	C₂³×C₁₃₉	—	2	4	no	—
104	C₂³×C₁₃₉	—	2	16	no	—
105	C₂³×C₁₃₉	—	2	16	no	—
106	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	8	yes	—
107	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
108	C₂³×C₁₃₉	#127	1	4	yes	—
109	C₂³×C₁₃₉	C₄⋊Q₈	1	4	yes	—
110	C₂³×C₁₃₉	C₄⋊Q₈	1	8	yes	—
111	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
112	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
113	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
114	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
115	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
116	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
117	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
118	C₂×C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄×C₁₃₉	—	2	4	no	—
120	C₂×C₄×C₁₃₉	—	2	8	no	—
121	C₂×C₄×C₁₃₉	—	2	4	no	—
122	C₂×C₄×C₁₃₉	—	2	4	no	—
123	C₂×C₄×C₁₃₉	—	2	4	no	—
124	C₂×C₄×C₁₃₉	—	2	4	no	—
125	C₂×C₄×C₁₃₉	—	2	4	no	—
126	C₂×C₄×C₁₃₉	—	2	16	no	—
127	C₂×C₄×C₁₃₉	—	2	16	no	—
128	C₂×C₄×C₁₃₉	—	2	8	no	—
129	C₂×C₄×C₁₃₉	—	2	16	no	—
130	C₂×C₄×C₁₃₉	—	4	16	no	—
131	C₂×C₄×C₁₃₉	—	4	32	no	—
132	C₂×C₄×C₁₃₉	—	4	4	no	—
133	C₂×C₄×C₁₃₉	—	4	4	no	—
134	C₂×C₄×C₁₃₉	—	4	8	no	—
135	C₂×C₄×C₁₃₉	—	4	4	no	—
136	C₂×C₄×C₁₃₉	—	4	4	no	—
137	C₂×C₄×C₁₃₉	—	4	4	no	—
138	C₂×C₄×C₁₃₉	—	4	8	no	—
139	C₂×C₄×C₁₃₉	—	4	8	no	—
140	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	16	yes	—
141	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
142	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
143	C₂²×C₁₃₉	—	2	4	no	—
144	C₂²×C₁₃₉	—	2	8	no	—
145	C₂²×C₁₃₉	—	2	16	no	—
146	C₂²×C₁₃₉	—	2	8	no	—
147	C₂²×C₁₃₉	—	2	16	no	—
148	C₂²×C₁₃₉	—	2	4	no	—
149	C₂²×C₁₃₉	#384	1	8	yes	—
150	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	2	yes	—
152	C₂²×C₁₃₉	C₄×#41	1	2	yes	—
153	C₂²×C₁₃₉	#518	1	2	yes	—
154	C₂²×C₁₃₉	#525	1	2	yes	—
155	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
156	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
157	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	2	yes	—
158	C₂²×C₁₃₉	#533	1	2	yes	—
159	C₂²×C₁₃₉	#534	1	2	yes	—
160	C₂²×C₁₃₉	#543	1	2	yes	—
161	C₂²×C₁₃₉	#546	1	8	yes	—
162	C₂²×C₁₃₉	#554	1	8	yes	—
163	C₄×C₁₃₉	—	2	4	no	—
164	C₄×C₁₃₉	—	2	4	no	—
165	C₄×C₁₃₉	—	2	16	no	—
166	C₄×C₁₃₉	—	4	8	no	—
167	C₄×C₁₃₉	—	8	4	no	—
168	C₂×C₁₃₉	—	2	8	no	—
169	C₂×C₁₃₉	C₂×#384	1	1	yes	characteristic
170	C₂×C₁₃₉	#2296	1	1	yes	characteristic
171	C₂×C₁₃₉	#2315	1	1	yes	characteristic
172	C₂×C₁₃₉	#2349	1	4	yes	—
173	C₂×C₁₃₉	#2539	1	2	yes	—
174	C₂×C₁₃₉	#2549	1	4	yes	—
175	C₂×C₁₃₉	#2583	1	2	yes	—
176	#13965	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃₉	#13965	1	1	yes	characteristic, direct product factor, Sylow
178	C₂×#385	C₂×C₁₃₉	1	4	yes	—
179	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
180	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
181	C₂²×#95	C₂×C₁₃₉	1	1	yes	characteristic
182	#1444	C₂×C₁₃₉	1	4	yes	complemented
183	C₄⋊#95	C₂×C₁₃₉	1	4	yes	complemented
184	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
185	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
186	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	8	yes	—
187	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
190	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
191	#385	—	2	16	no	—
192	#380	—	2	4	no	—
193	C₄×C₂²⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
194	C₂×#95	—	2	4	no	—
195	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
196	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
197	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
198	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
199	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
200	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
201	C₂³×C₄	—	2	4	no	—
202	C₂³×C₄	—	2	8	no	—
203	C₂³×C₄	—	2	8	no	—
204	C₂³×C₄	—	4	4	no	—
205	C₂³×C₄	—	4	4	no	—
206	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
207	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
208	C₂³×C₄	Q₈×C₁₃₉	1	4	yes	—
209	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
210	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
211	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
212	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	16	no	—
216	C₂×C₄⋊C₄	—	2	16	no	—
217	C₂×C₄⋊C₄	—	4	8	no	—
218	C₂×C₄⋊C₄	—	4	4	no	—
219	C₂×C₂²⋊C₄	—	2	4	no	—
220	C₂×C₂²⋊C₄	—	2	8	no	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
222	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	—
223	C₂×C₂²⋊C₄	Q₈×C₁₃₉	1	8	yes	—
224	C₂×C₄²	—	4	4	no	—
225	C₂×C₄²	C₂×C₄×C₁₃₉	1	8	yes	complemented
226	#95	—	2	4	no	—
227	#95	—	2	4	no	—
228	#95	—	2	4	no	—
229	#95	—	2	16	no	—
230	#95	C₂×C₄×C₁₃₉	1	8	yes	complemented
231	C₂⁴	—	2	4	no	—
232	C₂⁴	—	2	4	no	—
233	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
234	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
235	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
236	C₂⁴	C₂×Q₈×C₁₃₉	1	4	yes	—
237	C₂⁴	C₂×Q₈×C₁₃₉	1	2	yes	—
238	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
239	C₂²×C₄	—	2	8	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	16	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	4	8	no	—
254	C₂²×C₄	—	4	8	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	—	4	32	no	—
257	C₂²×C₄	—	4	8	no	—
258	C₂²×C₄	—	4	8	no	—
259	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	16	yes	complemented
260	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
266	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
267	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
268	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
269	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
270	C₄⋊C₄	—	4	32	no	—
271	C₄⋊C₄	—	4	8	no	—
272	C₂²⋊C₄	—	4	8	no	—
273	C₂²⋊C₄	C₄⋊C₄×C₁₃₉	1	32	yes	complemented
274	C₄²	—	4	8	no	—
275	C₂³	—	2	4	no	—
276	C₂³	—	2	4	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	16	no	—
282	C₂³	—	2	16	no	—
283	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	8	yes	—
284	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
285	C₂³	#127×C₁₃₉	1	4	yes	—
286	C₂³	C₄⋊Q₈×C₁₃₉	1	8	yes	—
287	C₂³	C₄⋊Q₈×C₁₃₉	1	4	yes	—
288	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
289	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
290	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
291	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
292	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
293	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
294	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	4	16	no	—
308	C₂×C₄	—	4	32	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	8	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	16	yes	—
318	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
319	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	16	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	8	no	—
325	C₂²	—	2	16	no	—
326	C₂²	#384×C₁₃₉	1	8	yes	—
327	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
328	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	2	yes	—
329	C₂²	C₄×#41×C₁₃₉	1	2	yes	—
330	C₂²	#518×C₁₃₉	1	2	yes	—
331	C₂²	#525×C₁₃₉	1	2	yes	—
332	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
333	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	2	yes	—
334	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
335	C₂²	#533×C₁₃₉	1	2	yes	—
336	C₂²	#534×C₁₃₉	1	2	yes	—
337	C₂²	#543×C₁₃₉	1	2	yes	—
338	C₂²	#546×C₁₃₉	1	8	yes	—
339	C₂²	#554×C₁₃₉	1	8	yes	—
340	C₄	—	2	4	no	—
341	C₄	—	2	4	no	—
342	C₄	—	2	16	no	—
343	C₄	—	4	8	no	—
344	C₄	—	8	4	no	—
345	C₂	—	2	8	no	—
346	C₂	C₂×#384×C₁₃₉	1	1	yes	characteristic
347	C₂	#2296×C₁₃₉	1	1	yes	characteristic
348	C₂	#2315×C₁₃₉	1	1	yes	characteristic
349	C₂	#2349×C₁₃₉	1	4	yes	—
350	C₂	#2539×C₁₃₉	1	2	yes	—
351	C₂	#2549×C₁₃₉	1	4	yes	—
352	C₂	#2583×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. #1444×C₁₃₉	C₂	semidirect
6. C₄⋊#95×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊C₄×C₁₃₉	C₄	semidirect
48. C₂×C₄²×C₁₃₉	C₂×C₄	semidirect
53. #95×C₁₃₉	C₂×C₄	semidirect
82. C₂²×C₄×C₁₃₉	C₄⋊C₄	semidirect
96. C₂²⋊C₄×C₁₃₉	C₄⋊C₄	semidirect
176. #13965	C₁₃₉	direct (N × H)
177. C₁₃₉	#13965	direct (N × H)
182. #1444	C₂×C₁₃₉	semidirect
183. C₄⋊#95	C₂×C₁₃₉	semidirect
193. C₄×C₂²⋊C₄	C₄×C₁₃₉	semidirect
225. C₂×C₄²	C₂×C₄×C₁₃₉	semidirect
230. #95	C₂×C₄×C₁₃₉	semidirect
259. C₂²×C₄	C₄⋊C₄×C₁₃₉	semidirect
273. C₂²⋊C₄	C₄⋊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×#385×C₁₃₉	2
C₂×#380×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
C₂²×#95×C₁₃₉	2
#1444×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#13965	139

Subgroups — C139×#13965 #48008561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#13965 #48008561