Subgroups — C₁₃₉×#14618 #48009214

Order 35584.

1290 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#399×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1443×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#1440×C₁₃₉	C₂	1	3	yes	maximal
4	#1437×C₁₃₉	C₂	1	3	yes	maximal
5	#1436×C₁₃₉	C₂	1	6	yes	maximal, complemented
6	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
7	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
8	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	3	yes	—
11	#399×C₁₃₉	C₄	1	8	yes	complemented
12	C₂×#95×C₁₃₉	C₂²	1	6	yes	—
13	C₂×#95×C₁₃₉	C₂²	1	6	yes	—
14	C₂×#95×C₁₃₉	C₂²	1	3	yes	—
15	C₂×#95×C₁₃₉	C₂²	1	6	yes	—
16	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
18	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
19	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
20	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
21	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
22	C₂×C₄⋊C₄×C₁₃₉	—	4	3	no	—
23	C₂×C₄⋊C₄×C₁₃₉	—	4	3	no	—
24	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	12	yes	—
25	C₂×C₂²⋊C₄×C₁₃₉	—	2	12	no	—
26	C₂×C₂²⋊C₄×C₁₃₉	—	4	3	no	—
27	C₂×C₂²⋊C₄×C₁₃₉	—	4	3	no	—
28	C₂×C₂²⋊C₄×C₁₃₉	—	4	3	no	—
29	C₂×C₂²⋊C₄×C₁₃₉	—	4	3	no	—
30	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	12	yes	—
31	C₂×C₄²×C₁₃₉	—	4	3	no	—
32	C₂×C₄²×C₁₃₉	—	4	6	no	—
33	#95×C₁₃₉	—	2	12	no	—
34	#95×C₁₃₉	—	2	12	no	—
35	#95×C₁₃₉	—	4	3	no	—
36	#95×C₁₃₉	—	4	6	no	—
37	#95×C₁₃₉	C₂×C₄	1	4	yes	—
38	C₂⁴×C₁₃₉	—	2	6	no	—
39	C₂⁴×C₁₃₉	—	2	3	no	—
40	C₂⁴×C₁₃₉	—	2	3	no	—
41	C₂⁴×C₁₃₉	—	2	2	no	—
42	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
43	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
44	C₂²×C₄×C₁₃₉	—	2	6	no	—
45	C₂²×C₄×C₁₃₉	—	2	6	no	—
46	C₂²×C₄×C₁₃₉	—	2	6	no	—
47	C₂²×C₄×C₁₃₉	—	2	6	no	—
48	C₂²×C₄×C₁₃₉	—	2	6	no	—
49	C₂²×C₄×C₁₃₉	—	2	6	no	—
50	C₂²×C₄×C₁₃₉	—	2	3	no	—
51	C₂²×C₄×C₁₃₉	—	2	6	no	—
52	C₂²×C₄×C₁₃₉	—	2	3	no	—
53	C₂²×C₄×C₁₃₉	—	2	6	no	—
54	C₂²×C₄×C₁₃₉	—	2	6	no	—
55	C₂²×C₄×C₁₃₉	—	2	3	no	—
56	C₂²×C₄×C₁₃₉	—	2	3	no	—
57	C₂²×C₄×C₁₃₉	—	2	6	no	—
58	C₂²×C₄×C₁₃₉	—	2	6	no	—
59	C₂²×C₄×C₁₃₉	—	2	6	no	—
60	C₂²×C₄×C₁₃₉	—	2	2	no	—
61	C₂²×C₄×C₁₃₉	C₂²×C₄	1	6	yes	—
62	C₂²×C₄×C₁₃₉	C₂²×C₄	1	6	yes	—
63	C₂²×C₄×C₁₃₉	#41	1	12	yes	—
64	C₄⋊C₄×C₁₃₉	—	4	12	no	—
65	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
66	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
67	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
68	C₄²×C₁₃₉	—	4	12	no	—
69	C₂³×C₁₃₉	—	2	6	no	—
70	C₂³×C₁₃₉	—	2	6	no	—
71	C₂³×C₁₃₉	—	2	2	no	—
72	C₂³×C₁₃₉	—	4	6	no	—
73	C₂³×C₁₃₉	—	4	6	no	—
74	C₂³×C₁₃₉	—	4	3	no	—
75	C₂³×C₁₃₉	—	4	6	no	—
76	C₂³×C₁₃₉	—	4	3	no	—
77	C₂³×C₁₃₉	—	4	1	no	—
78	C₂³×C₁₃₉	—	4	3	no	—
79	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
80	C₂³×C₁₃₉	C₂×#41	1	6	yes	—
81	C₂³×C₁₃₉	H(5,𝔽₂)	1	3	yes	—
82	C₂³×C₁₃₉	H(5,𝔽₂)	1	3	yes	—
83	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
84	C₂×C₄×C₁₃₉	—	2	12	no	—
85	C₂×C₄×C₁₃₉	—	2	6	no	—
86	C₂×C₄×C₁₃₉	—	2	6	no	—
87	C₂×C₄×C₁₃₉	—	2	12	no	—
88	C₂×C₄×C₁₃₉	—	2	12	no	—
89	C₂×C₄×C₁₃₉	—	2	12	no	—
90	C₂×C₄×C₁₃₉	—	2	12	no	—
91	C₂×C₄×C₁₃₉	—	4	6	no	—
92	C₂×C₄×C₁₃₉	—	4	6	no	—
93	C₂×C₄×C₁₃₉	—	4	3	no	—
94	C₂×C₄×C₁₃₉	—	4	6	no	—
95	C₂×C₄×C₁₃₉	—	4	3	no	—
96	C₂×C₄×C₁₃₉	—	4	6	no	—
97	C₂×C₄×C₁₃₉	—	4	3	no	—
98	C₂×C₄×C₁₃₉	—	4	6	no	—
99	C₂×C₄×C₁₃₉	—	4	6	no	—
100	C₂×C₄×C₁₃₉	—	4	3	no	—
101	C₂×C₄×C₁₃₉	—	4	6	no	—
102	C₂×C₄×C₁₃₉	—	4	6	no	—
103	C₂×C₄×C₁₃₉	—	4	2	no	—
104	C₂²×C₁₃₉	—	4	6	no	—
105	C₂²×C₁₃₉	—	4	6	no	—
106	C₂²×C₁₃₉	—	4	2	no	—
107	C₂²×C₁₃₉	—	8	6	no	—
108	C₂²×C₁₃₉	—	8	2	no	—
109	C₂²×C₁₃₉	C₄×#41	1	3	yes	—
110	C₂²×C₁₃₉	#518	1	3	yes	—
111	C₂²×C₁₃₉	#519	1	1	yes	characteristic
112	C₂²×C₁₃₉	#539	1	6	yes	—
113	C₂²×C₁₃₉	#542	1	6	yes	—
114	C₂²×C₁₃₉	#551	1	3	yes	—
115	C₂²×C₁₃₉	#553	1	6	yes	—
116	C₂²×C₁₃₉	#559	1	3	yes	—
117	C₂²×C₁₃₉	#560	1	3	yes	—
118	C₂²×C₁₃₉	#560	1	1	yes	characteristic
119	C₄×C₁₃₉	—	4	6	no	—
120	C₄×C₁₃₉	—	4	6	no	—
121	C₄×C₁₃₉	—	4	12	no	—
122	C₄×C₁₃₉	—	8	2	no	—
123	C₂×C₁₃₉	—	8	2	no	—
124	C₂×C₁₃₉	#2332	1	3	yes	—
125	C₂×C₁₃₉	#2374	1	3	yes	—
126	C₂×C₁₃₉	#2380	1	1	yes	characteristic
127	C₂×C₁₃₉	#2796	1	6	yes	—
128	C₂×C₁₃₉	#2801	1	2	yes	—
129	#14618	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₁₃₉	#14618	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×#399	C₂×C₁₃₉	1	1	yes	characteristic
132	#1443	C₂×C₁₃₉	1	2	yes	complemented
133	#1440	C₂×C₁₃₉	1	3	yes	—
134	#1437	C₂×C₁₃₉	1	3	yes	—
135	#1436	C₂×C₁₃₉	1	6	yes	complemented
136	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
137	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
138	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
139	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
140	C₂²×C₄²	C₂²×C₁₃₉	1	3	yes	—
141	#399	C₄×C₁₃₉	1	8	yes	complemented
142	C₂×#95	C₂²×C₁₃₉	1	6	yes	—
143	C₂×#95	C₂²×C₁₃₉	1	6	yes	—
144	C₂×#95	C₂²×C₁₃₉	1	3	yes	—
145	C₂×#95	C₂²×C₁₃₉	1	6	yes	—
146	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
147	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
148	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
149	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
150	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
151	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
152	C₂×C₄⋊C₄	—	4	3	no	—
153	C₂×C₄⋊C₄	—	4	3	no	—
154	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	12	yes	—
155	C₂×C₂²⋊C₄	—	2	12	no	—
156	C₂×C₂²⋊C₄	—	4	3	no	—
157	C₂×C₂²⋊C₄	—	4	3	no	—
158	C₂×C₂²⋊C₄	—	4	3	no	—
159	C₂×C₂²⋊C₄	—	4	3	no	—
160	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	12	yes	—
161	C₂×C₄²	—	4	3	no	—
162	C₂×C₄²	—	4	6	no	—
163	#95	—	2	12	no	—
164	#95	—	2	12	no	—
165	#95	—	4	3	no	—
166	#95	—	4	6	no	—
167	#95	C₂×C₄×C₁₃₉	1	4	yes	—
168	C₂⁴	—	2	6	no	—
169	C₂⁴	—	2	3	no	—
170	C₂⁴	—	2	3	no	—
171	C₂⁴	—	2	2	no	—
172	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
173	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
174	C₂²×C₄	—	2	6	no	—
175	C₂²×C₄	—	2	6	no	—
176	C₂²×C₄	—	2	6	no	—
177	C₂²×C₄	—	2	6	no	—
178	C₂²×C₄	—	2	6	no	—
179	C₂²×C₄	—	2	6	no	—
180	C₂²×C₄	—	2	3	no	—
181	C₂²×C₄	—	2	6	no	—
182	C₂²×C₄	—	2	3	no	—
183	C₂²×C₄	—	2	6	no	—
184	C₂²×C₄	—	2	6	no	—
185	C₂²×C₄	—	2	3	no	—
186	C₂²×C₄	—	2	3	no	—
187	C₂²×C₄	—	2	6	no	—
188	C₂²×C₄	—	2	6	no	—
189	C₂²×C₄	—	2	6	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	C₂²×C₄×C₁₃₉	1	6	yes	—
192	C₂²×C₄	C₂²×C₄×C₁₃₉	1	6	yes	—
193	C₂²×C₄	#41×C₁₃₉	1	12	yes	—
194	C₄⋊C₄	—	4	12	no	—
195	C₂²⋊C₄	—	4	12	no	—
196	C₂²⋊C₄	—	4	12	no	—
197	C₂²⋊C₄	—	4	4	no	—
198	C₄²	—	4	12	no	—
199	C₂³	—	2	6	no	—
200	C₂³	—	2	6	no	—
201	C₂³	—	2	2	no	—
202	C₂³	—	4	6	no	—
203	C₂³	—	4	6	no	—
204	C₂³	—	4	3	no	—
205	C₂³	—	4	6	no	—
206	C₂³	—	4	3	no	—
207	C₂³	—	4	1	no	—
208	C₂³	—	4	3	no	—
209	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
210	C₂³	C₂×#41×C₁₃₉	1	6	yes	—
211	C₂³	H(5,𝔽₂)×C₁₃₉	1	3	yes	—
212	C₂³	H(5,𝔽₂)×C₁₃₉	1	3	yes	—
213	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
214	C₂×C₄	—	2	12	no	—
215	C₂×C₄	—	2	6	no	—
216	C₂×C₄	—	2	6	no	—
217	C₂×C₄	—	2	12	no	—
218	C₂×C₄	—	2	12	no	—
219	C₂×C₄	—	2	12	no	—
220	C₂×C₄	—	2	12	no	—
221	C₂×C₄	—	4	6	no	—
222	C₂×C₄	—	4	6	no	—
223	C₂×C₄	—	4	3	no	—
224	C₂×C₄	—	4	6	no	—
225	C₂×C₄	—	4	6	no	—
226	C₂×C₄	—	4	3	no	—
227	C₂×C₄	—	4	6	no	—
228	C₂×C₄	—	4	3	no	—
229	C₂×C₄	—	4	6	no	—
230	C₂×C₄	—	4	3	no	—
231	C₂×C₄	—	4	6	no	—
232	C₂×C₄	—	4	6	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂²	—	4	6	no	—
235	C₂²	—	4	6	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	8	6	no	—
238	C₂²	—	8	2	no	—
239	C₂²	C₄×#41×C₁₃₉	1	3	yes	—
240	C₂²	#518×C₁₃₉	1	3	yes	—
241	C₂²	#519×C₁₃₉	1	1	yes	characteristic
242	C₂²	#539×C₁₃₉	1	6	yes	—
243	C₂²	#542×C₁₃₉	1	6	yes	—
244	C₂²	#551×C₁₃₉	1	3	yes	—
245	C₂²	#553×C₁₃₉	1	6	yes	—
246	C₂²	#559×C₁₃₉	1	3	yes	—
247	C₂²	#560×C₁₃₉	1	3	yes	—
248	C₂²	#560×C₁₃₉	1	1	yes	characteristic
249	C₄	—	4	12	no	—
250	C₄	—	4	6	no	—
251	C₄	—	4	6	no	—
252	C₄	—	8	2	no	—
253	C₂	—	8	2	no	—
254	C₂	#2332×C₁₃₉	1	3	yes	—
255	C₂	#2374×C₁₃₉	1	3	yes	—
256	C₂	#2380×C₁₃₉	1	1	yes	characteristic
257	C₂	#2796×C₁₃₉	1	6	yes	—
258	C₂	#2801×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
2. #1443×C₁₃₉	C₂	semidirect
5. #1436×C₁₃₉	C₂	semidirect
11. #399×C₁₃₉	C₄	semidirect
129. #14618	C₁₃₉	direct (N × H)
130. C₁₃₉	#14618	direct (N × H)
132. #1443	C₂×C₁₃₉	semidirect
135. #1436	C₂×C₁₃₉	semidirect
141. #399	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×#399×C₁₃₉	2
#1443×C₁₃₉	2
#1440×C₁₃₉	2
#1437×C₁₃₉	2
#1436×C₁₃₉	2
#14618	139

Subgroups — C139×#14618 #48009214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#14618 #48009214