Subgroups — C₁₃₉×#13904 #48008500

Order 35584.

2278 conjugacy classes of subgroups.

The subgroup lattice has 362 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	C₂×#381×C₁₃₉	C₂	1	4	yes	maximal
3	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1445×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	—	2	4	no	—
10	C₂²×C₄⋊C₄×C₁₃₉	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
18	#381×C₁₃₉	—	2	16	no	—
19	#380×C₁₃₉	—	2	4	no	—
20	C₄×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
21	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#95×C₁₃₉	C₂²	1	16	yes	—
24	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
25	C₂³×C₄×C₁₃₉	—	2	8	no	—
26	C₂³×C₄×C₁₃₉	—	2	4	no	—
27	C₂³×C₄×C₁₃₉	—	2	4	no	—
28	C₂³×C₄×C₁₃₉	—	2	8	no	—
29	C₂³×C₄×C₁₃₉	—	2	8	no	—
30	C₂³×C₄×C₁₃₉	C₂×C₄	1	8	yes	—
31	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
33	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₃₉	—	2	32	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
48	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	—
53	C₂×C₄²×C₁₃₉	—	2	4	no	—
54	C₂×C₄²×C₁₃₉	—	2	8	no	—
55	#95×C₁₃₉	—	2	4	no	—
56	#95×C₁₃₉	—	2	4	no	—
57	#95×C₁₃₉	—	2	32	no	—
58	C₂⁴×C₁₃₉	—	2	4	no	—
59	C₂⁴×C₁₃₉	—	2	4	no	—
60	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
61	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
62	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
63	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
64	C₂⁴×C₁₃₉	#41	1	4	yes	—
65	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₉	—	2	4	no	—
67	C₂²×C₄×C₁₃₉	—	2	16	no	—
68	C₂²×C₄×C₁₃₉	—	2	16	no	—
69	C₂²×C₄×C₁₃₉	—	2	16	no	—
70	C₂²×C₄×C₁₃₉	—	2	16	no	—
71	C₂²×C₄×C₁₃₉	—	2	32	no	—
72	C₂²×C₄×C₁₃₉	—	2	8	no	—
73	C₂²×C₄×C₁₃₉	—	2	4	no	—
74	C₂²×C₄×C₁₃₉	—	2	4	no	—
75	C₂²×C₄×C₁₃₉	—	2	4	no	—
76	C₂²×C₄×C₁₃₉	—	2	8	no	—
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	8	no	—
79	C₂²×C₄×C₁₃₉	—	2	8	no	—
80	C₂²×C₄×C₁₃₉	—	2	8	no	—
81	C₂²×C₄×C₁₃₉	—	2	4	no	—
82	C₂²×C₄×C₁₃₉	—	2	8	no	—
83	C₂²×C₄×C₁₃₉	—	2	8	no	—
84	C₂²×C₄×C₁₃₉	—	4	16	no	—
85	C₂²×C₄×C₁₃₉	—	4	8	no	—
86	C₂²×C₄×C₁₃₉	—	4	8	no	—
87	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	16	yes	—
88	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
89	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
97	C₄⋊C₄×C₁₃₉	—	2	16	no	—
98	C₄⋊C₄×C₁₃₉	—	2	16	no	—
99	C₄⋊C₄×C₁₃₉	—	4	8	no	—
100	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
101	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
102	C₄²×C₁₃₉	—	4	8	no	—
103	C₂³×C₁₃₉	—	2	4	no	—
104	C₂³×C₁₃₉	—	2	4	no	—
105	C₂³×C₁₃₉	—	2	4	no	—
106	C₂³×C₁₃₉	—	2	4	no	—
107	C₂³×C₁₃₉	—	2	4	no	—
108	C₂³×C₁₃₉	—	2	4	no	—
109	C₂³×C₁₃₉	—	2	16	no	—
110	C₂³×C₁₃₉	—	2	16	no	—
111	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
112	C₂³×C₁₃₉	C₄×D₄	1	8	yes	—
113	C₂³×C₁₃₉	#121	1	8	yes	—
114	C₂³×C₁₃₉	#124	1	4	yes	—
115	C₂³×C₁₃₉	#127	1	4	yes	—
116	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
117	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
118	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
119	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
120	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
121	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
122	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
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	32	no	—
127	C₂×C₄×C₁₃₉	—	2	8	no	—
128	C₂×C₄×C₁₃₉	—	2	16	no	—
129	C₂×C₄×C₁₃₉	—	2	8	no	—
130	C₂×C₄×C₁₃₉	—	2	16	no	—
131	C₂×C₄×C₁₃₉	—	4	8	no	—
132	C₂×C₄×C₁₃₉	—	4	4	no	—
133	C₂×C₄×C₁₃₉	—	4	4	no	—
134	C₂×C₄×C₁₃₉	—	4	4	no	—
135	C₂×C₄×C₁₃₉	—	4	4	no	—
136	C₂×C₄×C₁₃₉	—	4	8	no	—
137	C₂×C₄×C₁₃₉	—	4	32	no	—
138	C₂×C₄×C₁₃₉	—	4	4	no	—
139	C₂×C₄×C₁₃₉	—	4	4	no	—
140	C₂×C₄×C₁₃₉	—	4	4	no	—
141	C₂×C₄×C₁₃₉	—	4	16	no	—
142	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
143	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₁₃₉	#117	1	8	yes	—
145	C₂×C₄×C₁₃₉	#123	1	8	yes	—
146	C₂×C₄×C₁₃₉	#123	1	8	yes	—
147	C₂²×C₁₃₉	—	2	4	no	—
148	C₂²×C₁₃₉	—	2	16	no	—
149	C₂²×C₁₃₉	—	2	16	no	—
150	C₂²×C₁₃₉	—	2	8	no	—
151	C₂²×C₁₃₉	—	2	8	no	—
152	C₂²×C₁₃₉	—	2	4	no	—
153	C₂²×C₁₃₉	#390	1	8	yes	—
154	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₁₃₉	C₂×#117	1	2	yes	—
156	C₂²×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
157	C₂²×C₁₃₉	#519	1	2	yes	—
158	C₂²×C₁₃₉	C₂×#121	1	2	yes	—
159	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
160	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
161	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
163	C₂²×C₁₃₉	#536	1	2	yes	—
164	C₂²×C₁₃₉	#536	1	2	yes	—
165	C₂²×C₁₃₉	#547	1	8	yes	—
166	C₂²×C₁₃₉	#552	1	8	yes	—
167	C₄×C₁₃₉	—	2	4	no	—
168	C₄×C₁₃₉	—	4	8	no	—
169	C₄×C₁₃₉	—	4	8	no	—
170	C₄×C₁₃₉	—	8	4	no	—
171	C₄×C₁₃₉	#381	1	8	yes	complemented
172	C₂×C₁₃₉	—	2	8	no	—
173	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
174	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
175	C₂×C₁₃₉	#2310	1	1	yes	characteristic
176	C₂×C₁₃₉	#2344	1	4	yes	—
177	C₂×C₁₃₉	#2486	1	4	yes	—
178	C₂×C₁₃₉	#2501	1	2	yes	—
179	C₂×C₁₃₉	#2503	1	2	yes	—
180	#13904	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₉	#13904	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
183	C₂×#381	C₂×C₁₃₉	1	4	yes	—
184	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
185	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
186	#1445	C₂×C₁₃₉	1	4	yes	complemented
187	C₄⋊#95	C₂×C₁₃₉	1	4	yes	complemented
188	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
189	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	—	2	4	no	—
191	C₂²×C₄⋊C₄	—	2	4	no	—
192	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
193	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
196	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
197	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
198	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
199	#381	—	2	16	no	—
200	#380	—	2	4	no	—
201	C₄×C₂²⋊C₄	—	2	4	no	—
202	C₂×#95	C₂²×C₁₃₉	1	16	yes	—
203	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
204	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
205	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
206	C₂³×C₄	—	2	8	no	—
207	C₂³×C₄	—	2	4	no	—
208	C₂³×C₄	—	2	4	no	—
209	C₂³×C₄	—	2	8	no	—
210	C₂³×C₄	—	2	8	no	—
211	C₂³×C₄	C₂×C₄×C₁₃₉	1	8	yes	—
212	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
213	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
214	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
215	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
216	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
217	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
218	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
220	C₂×C₄⋊C₄	—	2	32	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	8	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₂²⋊C₄	—	2	8	no	—
233	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	—	2	8	no	—
236	#95	—	2	4	no	—
237	#95	—	2	4	no	—
238	#95	—	2	32	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	—	2	4	no	—
241	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
242	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
243	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
244	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
245	C₂⁴	#41×C₁₃₉	1	4	yes	—
246	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	16	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	32	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	4	16	no	—
266	C₂²×C₄	—	4	8	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	16	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
277	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
278	C₄⋊C₄	—	2	16	no	—
279	C₄⋊C₄	—	2	16	no	—
280	C₄⋊C₄	—	4	8	no	—
281	C₂²⋊C₄	—	2	16	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₄²	—	4	8	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	16	no	—
292	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
293	C₂³	C₄×D₄×C₁₃₉	1	8	yes	—
294	C₂³	#121×C₁₃₉	1	8	yes	—
295	C₂³	#124×C₁₃₉	1	4	yes	—
296	C₂³	#127×C₁₃₉	1	4	yes	—
297	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
298	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
299	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
300	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
301	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
302	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
303	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	32	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	16	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	32	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
325	C₂×C₄	#117×C₁₃₉	1	8	yes	—
326	C₂×C₄	#123×C₁₃₉	1	8	yes	—
327	C₂×C₄	#123×C₁₃₉	1	8	yes	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	16	no	—
331	C₂²	—	2	16	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	2	8	no	—
334	C₂²	#390×C₁₃₉	1	8	yes	—
335	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
336	C₂²	C₂×#117×C₁₃₉	1	2	yes	—
337	C₂²	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
338	C₂²	#519×C₁₃₉	1	2	yes	—
339	C₂²	C₂×#121×C₁₃₉	1	2	yes	—
340	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
341	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
342	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
343	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
344	C₂²	#536×C₁₃₉	1	2	yes	—
345	C₂²	#536×C₁₃₉	1	2	yes	—
346	C₂²	#547×C₁₃₉	1	8	yes	—
347	C₂²	#552×C₁₃₉	1	8	yes	—
348	C₄	—	2	4	no	—
349	C₄	—	4	8	no	—
350	C₄	—	4	8	no	—
351	C₄	—	8	4	no	—
352	C₄	#381×C₁₃₉	1	8	yes	complemented
353	C₂	—	2	8	no	—
354	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
355	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
356	C₂	#2310×C₁₃₉	1	1	yes	characteristic
357	C₂	#2344×C₁₃₉	1	4	yes	—
358	C₂	#2486×C₁₃₉	1	4	yes	—
359	C₂	#2501×C₁₃₉	1	2	yes	—
360	C₂	#2503×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. #1445×C₁₃₉	C₂	semidirect
6. C₄⋊#95×C₁₃₉	C₂	semidirect
11. C₂²×C₄⋊C₄×C₁₃₉	C₄	semidirect
171. C₄×C₁₃₉	#381	semidirect
180. #13904	C₁₃₉	direct (N × H)
181. C₁₃₉	#13904	direct (N × H)
186. #1445	C₂×C₁₃₉	semidirect
187. C₄⋊#95	C₂×C₁₃₉	semidirect
192. C₂²×C₄⋊C₄	C₄×C₁₃₉	semidirect
352. C₄	#381×C₁₃₉	semidirect

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
C₂×#381×C₁₃₉	2
C₂×#380×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
#1445×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#13904	139

Subgroups — C139×#13904 #48008500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#13904 #48008500