Subgroups — C₁₃₉×#13853 #48008449

Order 35584.

1942 conjugacy classes of subgroups.

The subgroup lattice has 230 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×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
3	#1445×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#1440×C₁₃₉	C₂	1	4	yes	maximal
5	C₄×#95×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂×#117×C₁₃₉	—	2	8	no	—
8	C₂×#117×C₁₃₉	C₄	1	8	yes	complemented
9	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
11	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₃₉	C₂²	1	4	yes	—
13	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
14	C₄×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
15	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#95×C₁₃₉	C₂²	1	16	yes	—
17	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
18	C₂³×C₄×C₁₃₉	—	2	8	no	—
19	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₃₉	D₄	1	8	yes	—
21	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
22	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
23	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
25	#117×C₁₃₉	—	2	32	no	—
26	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
29	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
30	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
31	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
32	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
33	C₂×C₄²×C₁₃₉	—	2	8	no	—
34	C₂×C₄²×C₁₃₉	—	2	8	no	—
35	C₂×C₄²×C₁₃₉	—	2	16	no	—
36	C₂×C₄²×C₁₃₉	C₂×C₄	1	8	yes	—
37	#95×C₁₃₉	—	2	8	no	—
38	#95×C₁₃₉	—	2	32	no	—
39	C₂⁴×C₁₃₉	—	2	8	no	—
40	C₂⁴×C₁₃₉	—	2	4	no	—
41	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
42	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
43	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
44	C₂²×C₄×C₁₃₉	—	2	4	no	—
45	C₂²×C₄×C₁₃₉	—	2	16	no	—
46	C₂²×C₄×C₁₃₉	—	2	32	no	—
47	C₂²×C₄×C₁₃₉	—	2	8	no	—
48	C₂²×C₄×C₁₃₉	—	2	4	no	—
49	C₂²×C₄×C₁₃₉	—	2	4	no	—
50	C₂²×C₄×C₁₃₉	—	2	16	no	—
51	C₂²×C₄×C₁₃₉	—	2	16	no	—
52	C₂²×C₄×C₁₃₉	—	2	16	no	—
53	C₂²×C₄×C₁₃₉	—	2	8	no	—
54	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	16	yes	—
55	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
56	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
57	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
59	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
60	C₂²×C₄×C₁₃₉	#41	1	16	yes	—
61	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
62	C₄⋊C₄×C₁₃₉	—	2	16	no	—
63	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
64	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
65	C₄²×C₁₃₉	—	2	16	no	—
66	C₄²×C₁₃₉	—	4	16	no	—
67	C₂³×C₁₃₉	—	2	4	no	—
68	C₂³×C₁₃₉	—	2	8	no	—
69	C₂³×C₁₃₉	—	2	8	no	—
70	C₂³×C₁₃₉	—	2	8	no	—
71	C₂³×C₁₃₉	—	2	8	no	—
72	C₂³×C₁₃₉	—	4	16	no	—
73	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
74	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
75	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
76	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
77	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
78	C₂×C₄×C₁₃₉	—	2	4	no	—
79	C₂×C₄×C₁₃₉	—	2	8	no	—
80	C₂×C₄×C₁₃₉	—	2	32	no	—
81	C₂×C₄×C₁₃₉	—	2	8	no	—
82	C₂×C₄×C₁₃₉	—	2	16	no	—
83	C₂×C₄×C₁₃₉	—	2	16	no	—
84	C₂×C₄×C₁₃₉	—	2	32	no	—
85	C₂×C₄×C₁₃₉	—	4	8	no	—
86	C₂×C₄×C₁₃₉	—	4	8	no	—
87	C₂×C₄×C₁₃₉	—	4	16	no	—
88	C₂×C₄×C₁₃₉	—	4	8	no	—
89	C₂×C₄×C₁₃₉	—	4	8	no	—
90	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
91	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
92	C₂×C₄×C₁₃₉	#117	1	8	yes	—
93	C₂×C₄×C₁₃₉	#123	1	16	yes	—
94	C₂²×C₁₃₉	—	2	4	no	—
95	C₂²×C₁₃₉	—	2	8	no	—
96	C₂²×C₁₃₉	—	4	16	no	—
97	C₂²×C₁₃₉	—	4	8	no	—
98	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₁₃₉	C₂×#117	1	2	yes	—
100	C₂²×C₁₃₉	C₄×#41	1	4	yes	—
101	C₂²×C₁₃₉	C₂×#123	1	4	yes	—
102	C₂²×C₁₃₉	#525	1	4	yes	—
103	C₂²×C₁₃₉	#529	1	16	yes	—
104	C₂²×C₁₃₉	#532	1	4	yes	—
105	C₄×C₁₃₉	—	2	4	no	—
106	C₄×C₁₃₉	—	4	16	no	—
107	C₄×C₁₃₉	—	4	8	no	—
108	C₄×C₁₃₉	#381	1	8	yes	—
109	C₂×C₁₃₉	—	4	4	no	—
110	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
111	C₂×C₁₃₉	#2297	1	2	yes	—
112	C₂×C₁₃₉	#2298	1	4	yes	—
113	C₂×C₁₃₉	#2395	1	8	yes	—
114	#13853	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₁₃₉	#13853	1	1	yes	characteristic, direct product factor, Sylow
116	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic
117	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	—
118	#1445	C₂×C₁₃₉	1	4	yes	complemented
119	#1440	C₂×C₁₃₉	1	4	yes	—
120	C₄×#95	C₂×C₁₃₉	1	4	yes	complemented
121	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
122	C₂×#117	—	2	8	no	—
123	C₂×#117	C₄×C₁₃₉	1	8	yes	complemented
124	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
125	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
126	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
127	C₂²×C₄²	C₂²×C₁₃₉	1	4	yes	—
128	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
129	C₄×C₂²⋊C₄	—	2	8	no	—
130	C₂×#95	C₂²×C₁₃₉	1	16	yes	—
131	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
132	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
133	C₂³×C₄	—	2	8	no	—
134	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
135	C₂³×C₄	D₄×C₁₃₉	1	8	yes	—
136	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
137	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
138	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
139	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
140	#117	—	2	32	no	—
141	C₂×C₄⋊C₄	—	2	4	no	—
142	C₂×C₄⋊C₄	—	2	4	no	—
143	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
144	C₂×C₂²⋊C₄	—	2	8	no	—
145	C₂×C₂²⋊C₄	—	2	8	no	—
146	C₂×C₂²⋊C₄	—	2	16	no	—
147	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
148	C₂×C₄²	—	2	8	no	—
149	C₂×C₄²	—	2	8	no	—
150	C₂×C₄²	—	2	16	no	—
151	C₂×C₄²	C₂×C₄×C₁₃₉	1	8	yes	—
152	#95	—	2	8	no	—
153	#95	—	2	32	no	—
154	C₂⁴	—	2	8	no	—
155	C₂⁴	—	2	4	no	—
156	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
157	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
158	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	2	16	no	—
161	C₂²×C₄	—	2	32	no	—
162	C₂²×C₄	—	2	8	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	2	4	no	—
165	C₂²×C₄	—	2	16	no	—
166	C₂²×C₄	—	2	16	no	—
167	C₂²×C₄	—	2	16	no	—
168	C₂²×C₄	—	2	8	no	—
169	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	16	yes	—
170	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
171	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
172	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
173	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
174	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
175	C₂²×C₄	#41×C₁₃₉	1	16	yes	—
176	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
177	C₄⋊C₄	—	2	16	no	—
178	C₂²⋊C₄	—	2	32	no	—
179	C₂²⋊C₄	—	2	16	no	—
180	C₄²	—	2	16	no	—
181	C₄²	—	4	16	no	—
182	C₂³	—	2	4	no	—
183	C₂³	—	2	8	no	—
184	C₂³	—	2	8	no	—
185	C₂³	—	2	8	no	—
186	C₂³	—	2	8	no	—
187	C₂³	—	4	16	no	—
188	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
189	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
190	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
191	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
192	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	32	no	—
196	C₂×C₄	—	2	8	no	—
197	C₂×C₄	—	2	16	no	—
198	C₂×C₄	—	2	16	no	—
199	C₂×C₄	—	2	32	no	—
200	C₂×C₄	—	4	8	no	—
201	C₂×C₄	—	4	8	no	—
202	C₂×C₄	—	4	16	no	—
203	C₂×C₄	—	4	8	no	—
204	C₂×C₄	—	4	8	no	—
205	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
206	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
207	C₂×C₄	#117×C₁₃₉	1	8	yes	—
208	C₂×C₄	#123×C₁₃₉	1	16	yes	—
209	C₂²	—	2	4	no	—
210	C₂²	—	2	8	no	—
211	C₂²	—	4	8	no	—
212	C₂²	—	4	16	no	—
213	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
214	C₂²	C₂×#117×C₁₃₉	1	2	yes	—
215	C₂²	C₄×#41×C₁₃₉	1	4	yes	—
216	C₂²	C₂×#123×C₁₃₉	1	4	yes	—
217	C₂²	#525×C₁₃₉	1	4	yes	—
218	C₂²	#529×C₁₃₉	1	16	yes	—
219	C₂²	#532×C₁₃₉	1	4	yes	—
220	C₄	—	2	4	no	—
221	C₄	—	4	8	no	—
222	C₄	—	4	16	no	—
223	C₄	#381×C₁₃₉	1	8	yes	—
224	C₂	—	4	4	no	—
225	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
226	C₂	#2297×C₁₃₉	1	2	yes	—
227	C₂	#2298×C₁₃₉	1	4	yes	—
228	C₂	#2395×C₁₃₉	1	8	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #1445×C₁₃₉	C₂	semidirect
5. C₄×#95×C₁₃₉	C₂	semidirect
8. C₂×#117×C₁₃₉	C₄	semidirect
114. #13853	C₁₃₉	direct (N × H)
115. C₁₃₉	#13853	direct (N × H)
118. #1445	C₂×C₁₃₉	semidirect
120. C₄×#95	C₂×C₁₃₉	semidirect
123. C₂×#117	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×C₄×C₂²⋊C₄×C₁₃₉	2
#1445×C₁₃₉	2
#1440×C₁₃₉	2
C₄×#95×C₁₃₉	2
#13853	139

Subgroups — C139×#13853 #48008449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#13853 #48008449