Subgroups — C₁₃₉×#13958 #48008554

Order 35584.

2078 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#381×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1445×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1445×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1434×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	C₂²⋊#95×C₁₃₉	C₂	1	4	yes	maximal
8	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×#117×C₁₃₉	—	2	4	no	—
11	C₂×#117×C₁₃₉	—	2	4	no	—
12	C₂×#117×C₁₃₉	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	4	no	—
19	C₂×#95×C₁₃₉	—	2	4	no	—
20	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
25	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
26	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₉	—	2	8	no	—
28	C₂³×C₄×C₁₃₉	—	2	4	no	—
29	C₂³×C₄×C₁₃₉	—	2	8	no	—
30	C₂³×C₄×C₁₃₉	—	2	8	no	—
31	C₂³×C₄×C₁₃₉	—	4	4	no	—
32	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
34	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	#117×C₁₃₉	—	2	32	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
47	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
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	C₂×C₄	1	8	yes	—
53	C₂×C₄²×C₁₃₉	—	2	4	no	—
54	C₂×C₄²×C₁₃₉	—	2	4	no	—
55	C₂×C₄²×C₁₃₉	C₂×C₄	1	8	yes	complemented
56	#95×C₁₃₉	—	2	4	no	—
57	#95×C₁₃₉	—	2	4	no	—
58	#95×C₁₃₉	—	2	4	no	—
59	#95×C₁₃₉	—	2	4	no	—
60	#95×C₁₃₉	—	2	16	no	—
61	#95×C₁₃₉	—	4	8	no	—
62	C₂⁴×C₁₃₉	—	2	4	no	—
63	C₂⁴×C₁₃₉	—	2	2	no	—
64	C₂⁴×C₁₃₉	—	2	2	no	—
65	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
66	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
67	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
68	C₂⁴×C₁₃₉	#41	1	8	yes	—
69	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₉	—	2	16	no	—
71	C₂²×C₄×C₁₃₉	—	2	16	no	—
72	C₂²×C₄×C₁₃₉	—	2	16	no	—
73	C₂²×C₄×C₁₃₉	—	2	4	no	—
74	C₂²×C₄×C₁₃₉	—	2	4	no	—
75	C₂²×C₄×C₁₃₉	—	2	16	no	—
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	8	no	—
82	C₂²×C₄×C₁₃₉	—	2	4	no	—
83	C₂²×C₄×C₁₃₉	—	2	8	no	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	8	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	8	no	—
89	C₂²×C₄×C₁₃₉	—	2	8	no	—
90	C₂²×C₄×C₁₃₉	—	2	4	no	—
91	C₂²×C₄×C₁₃₉	—	2	4	no	—
92	C₂²×C₄×C₁₃₉	—	4	32	no	—
93	C₂²×C₄×C₁₃₉	—	4	8	no	—
94	C₂²×C₄×C₁₃₉	—	4	8	no	—
95	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	16	yes	—
96	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
105	C₄⋊C₄×C₁₃₉	—	2	8	no	—
106	C₄⋊C₄×C₁₃₉	—	2	8	no	—
107	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
108	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
109	C₄²×C₁₃₉	—	2	16	no	—
110	C₂³×C₁₃₉	—	2	4	no	—
111	C₂³×C₁₃₉	—	2	4	no	—
112	C₂³×C₁₃₉	—	2	4	no	—
113	C₂³×C₁₃₉	—	2	4	no	—
114	C₂³×C₁₃₉	—	2	2	no	—
115	C₂³×C₁₃₉	—	2	2	no	—
116	C₂³×C₁₃₉	—	2	4	no	—
117	C₂³×C₁₃₉	—	2	16	no	—
118	C₂³×C₁₃₉	—	2	16	no	—
119	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
120	C₂³×C₁₃₉	#117	1	8	yes	—
121	C₂³×C₁₃₉	#123	1	8	yes	—
122	C₂³×C₁₃₉	#123	1	8	yes	—
123	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
124	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
125	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
126	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
127	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
128	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
129	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
130	C₂×C₄×C₁₃₉	—	2	4	no	—
131	C₂×C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	32	no	—
137	C₂×C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₄×C₁₃₉	—	2	8	no	—
141	C₂×C₄×C₁₃₉	—	2	8	no	—
142	C₂×C₄×C₁₃₉	—	2	16	no	—
143	C₂×C₄×C₁₃₉	—	4	32	no	—
144	C₂×C₄×C₁₃₉	—	4	4	no	—
145	C₂×C₄×C₁₃₉	—	4	4	no	—
146	C₂×C₄×C₁₃₉	—	4	4	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	4	no	—
149	C₂×C₄×C₁₃₉	—	4	2	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	4	8	no	—
152	C₂×C₄×C₁₃₉	—	4	4	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	4	4	no	—
155	C₂×C₄×C₁₃₉	—	4	8	no	—
156	C₂×C₄×C₁₃₉	—	4	8	no	—
157	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
158	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂²×C₁₃₉	—	2	4	no	—
160	C₂²×C₁₃₉	—	2	16	no	—
161	C₂²×C₁₃₉	—	2	8	no	—
162	C₂²×C₁₃₉	—	2	8	no	—
163	C₂²×C₁₃₉	—	2	16	no	—
164	C₂²×C₁₃₉	—	2	4	no	—
165	C₂²×C₁₃₉	#381	1	8	yes	—
166	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₁₃₉	C₂×#117	1	2	yes	—
168	C₂²×C₁₃₉	C₄×#41	1	2	yes	—
169	C₂²×C₁₃₉	#520	1	2	yes	—
170	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
171	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
172	C₂²×C₁₃₉	#525	1	2	yes	—
173	C₂²×C₁₃₉	#532	1	2	yes	—
174	C₂²×C₁₃₉	#535	1	1	yes	characteristic
175	C₂²×C₁₃₉	#536	1	1	yes	characteristic
176	C₂²×C₁₃₉	#537	1	2	yes	—
177	C₂²×C₁₃₉	#551	1	8	yes	—
178	C₂²×C₁₃₉	#552	1	8	yes	—
179	C₄×C₁₃₉	—	2	4	no	—
180	C₄×C₁₃₉	—	2	4	no	—
181	C₄×C₁₃₉	—	4	4	no	—
182	C₄×C₁₃₉	—	4	8	no	—
183	C₄×C₁₃₉	—	4	4	no	—
184	C₄×C₁₃₉	—	8	4	no	—
185	C₂×C₁₃₉	—	2	8	no	—
186	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
187	C₂×C₁₃₉	#2297	1	1	yes	characteristic
188	C₂×C₁₃₉	#2311	1	1	yes	characteristic
189	C₂×C₁₃₉	#2343	1	4	yes	—
190	C₂×C₁₃₉	#2482	1	2	yes	—
191	C₂×C₁₃₉	#2484	1	2	yes	—
192	C₂×C₁₃₉	#2498	1	4	yes	—
193	#13958	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₁₃₉	#13958	1	1	yes	characteristic, direct product factor, Sylow
195	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic
196	C₂×#381	C₂×C₁₃₉	1	1	yes	characteristic
197	C₂²×#95	C₂×C₁₃₉	1	1	yes	characteristic
198	#1445	C₂×C₁₃₉	1	2	yes	complemented
199	#1445	C₂×C₁₃₉	1	2	yes	complemented
200	#1434	C₂×C₁₃₉	1	4	yes	complemented
201	C₂²⋊#95	C₂×C₁₃₉	1	4	yes	—
202	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
203	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
204	C₂×#117	—	2	4	no	—
205	C₂×#117	—	2	4	no	—
206	C₂×#117	C₄×C₁₃₉	1	8	yes	complemented
207	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
209	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
211	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
212	#381	—	2	4	no	—
213	C₂×#95	—	2	4	no	—
214	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
215	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
216	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
217	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
218	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
219	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
220	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
221	C₂³×C₄	—	2	8	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	—	2	8	no	—
224	C₂³×C₄	—	2	8	no	—
225	C₂³×C₄	—	4	4	no	—
226	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
227	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
228	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
229	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
230	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
233	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
235	#117	—	2	32	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₂²⋊C₄	—	2	8	no	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	—	2	4	no	—
249	C₂×C₄²	C₂×C₄×C₁₃₉	1	8	yes	complemented
250	#95	—	2	4	no	—
251	#95	—	2	4	no	—
252	#95	—	2	4	no	—
253	#95	—	2	4	no	—
254	#95	—	2	16	no	—
255	#95	—	4	8	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	2	no	—
258	C₂⁴	—	2	2	no	—
259	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
260	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
261	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
262	C₂⁴	#41×C₁₃₉	1	8	yes	—
263	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
264	C₂²×C₄	—	2	16	no	—
265	C₂²×C₄	—	2	16	no	—
266	C₂²×C₄	—	2	16	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	16	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	4	32	no	—
287	C₂²×C₄	—	4	8	no	—
288	C₂²×C₄	—	4	8	no	—
289	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	16	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	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
298	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₂²⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	—	4	8	no	—
303	C₄²	—	2	16	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	16	no	—
312	C₂³	—	2	16	no	—
313	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
314	C₂³	#117×C₁₃₉	1	8	yes	—
315	C₂³	#123×C₁₃₉	1	8	yes	—
316	C₂³	#123×C₁₃₉	1	8	yes	—
317	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
318	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
319	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
320	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
321	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
322	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
323	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	32	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	16	no	—
337	C₂×C₄	—	4	32	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	16	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	8	no	—
358	C₂²	—	2	16	no	—
359	C₂²	#381×C₁₃₉	1	8	yes	—
360	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
361	C₂²	C₂×#117×C₁₃₉	1	2	yes	—
362	C₂²	C₄×#41×C₁₃₉	1	2	yes	—
363	C₂²	#520×C₁₃₉	1	2	yes	—
364	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
365	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
366	C₂²	#525×C₁₃₉	1	2	yes	—
367	C₂²	#532×C₁₃₉	1	2	yes	—
368	C₂²	#535×C₁₃₉	1	1	yes	characteristic
369	C₂²	#536×C₁₃₉	1	1	yes	characteristic
370	C₂²	#537×C₁₃₉	1	2	yes	—
371	C₂²	#551×C₁₃₉	1	8	yes	—
372	C₂²	#552×C₁₃₉	1	8	yes	—
373	C₄	—	2	4	no	—
374	C₄	—	2	4	no	—
375	C₄	—	4	4	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	8	no	—
378	C₄	—	8	4	no	—
379	C₂	—	2	8	no	—
380	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
381	C₂	#2297×C₁₃₉	1	1	yes	characteristic
382	C₂	#2311×C₁₃₉	1	1	yes	characteristic
383	C₂	#2343×C₁₃₉	1	4	yes	—
384	C₂	#2482×C₁₃₉	1	2	yes	—
385	C₂	#2484×C₁₃₉	1	2	yes	—
386	C₂	#2498×C₁₃₉	1	4	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
4. #1445×C₁₃₉	C₂	semidirect
5. #1445×C₁₃₉	C₂	semidirect
6. #1434×C₁₃₉	C₂	semidirect
12. C₂×#117×C₁₃₉	C₄	semidirect
46. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
47. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
55. C₂×C₄²×C₁₃₉	C₂×C₄	semidirect
193. #13958	C₁₃₉	direct (N × H)
194. C₁₃₉	#13958	direct (N × H)
198. #1445	C₂×C₁₃₉	semidirect
199. #1445	C₂×C₁₃₉	semidirect
200. #1434	C₂×C₁₃₉	semidirect
206. C₂×#117	C₄×C₁₃₉	semidirect
240. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
241. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
249. C₂×C₄²	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#117×C₁₃₉	2
C₂×#381×C₁₃₉	2
C₂²×#95×C₁₃₉	2
#1445×C₁₃₉	2
#1434×C₁₃₉	2
C₂²⋊#95×C₁₃₉	2
#13958	139

Subgroups — C139×#13958 #48008554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#13958 #48008554