Group #48002901 — subgroups

Subgroups — C₁₃₉×#8305 #48002901

Order 35584.

1154 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1817×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#323×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	C₂³×Q₈×C₁₃₉	C₄	1	1	yes	characteristic
5	C₂³×D₄×C₁₃₉	C₄	1	1	yes	characteristic
6	C₂×#124×C₁₃₉	—	2	8	no	—
7	C₂×#124×C₁₃₉	—	2	4	no	—
8	C₂²×C₂²⋊C₄×C₁₃₉	C₄	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
12	#336×C₁₃₉	—	2	4	no	—
13	#323×C₁₃₉	—	2	8	no	—
14	C₂⁵×C₁₃₉	C₂×C₄	1	2	yes	—
15	C₂²×Q₈×C₁₃₉	—	2	4	no	—
16	C₂²×Q₈×C₁₃₉	—	2	2	no	—
17	C₂²×Q₈×C₁₃₉	—	4	4	no	—
18	C₂²×D₄×C₁₃₉	—	2	4	no	—
19	C₂²×D₄×C₁₃₉	—	2	2	no	—
20	C₂²×D₄×C₁₃₉	—	4	4	no	—
21	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₃₉	—	2	4	no	—
26	#124×C₁₃₉	—	2	32	no	—
27	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
30	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
31	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
32	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	—
33	C₂×C₄²×C₁₃₉	—	2	4	no	—
34	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
35	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
36	C₂⁴×C₁₃₉	—	2	2	no	—
37	C₂⁴×C₁₃₉	—	2	2	no	—
38	C₂⁴×C₁₃₉	—	2	8	no	—
39	C₂⁴×C₁₃₉	—	4	4	no	—
40	C₂⁴×C₁₃₉	—	4	4	no	—
41	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
42	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×Q₈×C₁₃₉	—	2	8	no	—
44	C₂×Q₈×C₁₃₉	—	4	16	no	—
45	C₂×Q₈×C₁₃₉	—	4	4	no	—
46	C₂×Q₈×C₁₃₉	—	4	4	no	—
47	C₂×D₄×C₁₃₉	—	2	8	no	—
48	C₂×D₄×C₁₃₉	—	4	16	no	—
49	C₂×D₄×C₁₃₉	—	4	4	no	—
50	C₂×D₄×C₁₃₉	—	4	4	no	—
51	C₂²×C₄×C₁₃₉	—	2	2	no	—
52	C₂²×C₄×C₁₃₉	—	2	4	no	—
53	C₂²×C₄×C₁₃₉	—	2	2	no	—
54	C₂²×C₄×C₁₃₉	—	2	2	no	—
55	C₂²×C₄×C₁₃₉	—	2	2	no	—
56	C₂²×C₄×C₁₃₉	—	2	4	no	—
57	C₂²×C₄×C₁₃₉	—	4	2	no	—
58	C₂²×C₄×C₁₃₉	—	4	4	no	—
59	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
62	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
64	C₂×C₈×C₁₃₉	—	4	8	no	—
65	C₂×C₈×C₁₃₉	—	4	4	no	—
66	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
67	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
68	C₄²×C₁₃₉	—	2	8	no	—
69	C₂³×C₁₃₉	—	2	2	no	—
70	C₂³×C₁₃₉	—	2	2	no	—
71	C₂³×C₁₃₉	—	2	4	no	—
72	C₂³×C₁₃₉	—	2	8	no	—
73	C₂³×C₁₃₉	—	4	4	no	—
74	C₂³×C₁₃₉	—	4	4	no	—
75	C₂³×C₁₃₉	—	4	4	no	—
76	C₂³×C₁₃₉	—	4	4	no	—
77	C₂³×C₁₃₉	—	4	4	no	—
78	C₂³×C₁₃₉	—	4	4	no	—
79	C₂³×C₁₃₉	—	4	4	no	—
80	C₂³×C₁₃₉	—	4	4	no	—
81	C₂³×C₁₃₉	—	8	16	no	—
82	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
83	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂³×C₁₃₉	#131	1	4	yes	—
85	Q₈×C₁₃₉	—	4	16	no	—
86	D₄×C₁₃₉	—	4	16	no	—
87	C₂×C₄×C₁₃₉	—	2	8	no	—
88	C₂×C₄×C₁₃₉	—	2	2	no	—
89	C₂×C₄×C₁₃₉	—	2	4	no	—
90	C₂×C₄×C₁₃₉	—	2	2	no	—
91	C₂×C₄×C₁₃₉	—	2	2	no	—
92	C₂×C₄×C₁₃₉	—	2	4	no	—
93	C₂×C₄×C₁₃₉	—	2	4	no	—
94	C₂×C₄×C₁₃₉	—	4	4	no	—
95	C₂×C₄×C₁₃₉	—	4	4	no	—
96	C₂×C₄×C₁₃₉	—	4	4	no	—
97	C₂×C₄×C₁₃₉	—	4	4	no	—
98	C₂×C₄×C₁₃₉	—	4	4	no	—
99	C₂×C₄×C₁₃₉	#100	1	4	yes	—
100	C₂×C₄×C₁₃₉	#120	1	4	yes	—
101	C₈×C₁₃₉	—	8	4	no	—
102	C₂²×C₁₃₉	—	2	8	no	—
103	C₂²×C₁₃₉	—	2	2	no	—
104	C₂²×C₁₃₉	—	2	2	no	—
105	C₂²×C₁₃₉	—	4	4	no	—
106	C₂²×C₁₃₉	—	4	4	no	—
107	C₂²×C₁₃₉	—	4	4	no	—
108	C₂²×C₁₃₉	—	8	8	no	—
109	C₂²×C₁₃₉	—	8	8	no	—
110	C₂²×C₁₃₉	—	8	8	no	—
111	C₂²×C₁₃₉	#379	1	1	yes	characteristic
112	C₂²×C₁₃₉	#408	1	4	yes	—
113	C₂²×C₁₃₉	#408	1	2	yes	—
114	C₂²×C₁₃₉	#410	1	2	yes	—
115	C₂²×C₁₃₉	C₂×#100	1	2	yes	—
116	C₄×C₁₃₉	—	2	4	no	—
117	C₄×C₁₃₉	—	2	4	no	—
118	C₄×C₁₃₉	—	4	2	no	—
119	C₄×C₁₃₉	—	4	4	no	—
120	C₂×C₁₃₉	—	2	4	no	—
121	C₂×C₁₃₉	—	8	4	no	—
122	C₂×C₁₃₉	#1469	1	4	yes	—
123	C₂×C₁₃₉	#1780	1	1	yes	characteristic
124	C₂×C₁₃₉	#1782	1	1	yes	characteristic
125	C₂×C₁₃₉	#1783	1	1	yes	characteristic
126	#8305	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₁₃₉	#8305	1	1	yes	characteristic, direct product factor, Sylow
128	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic
129	#1817	C₂×C₁₃₉	1	2	yes	complemented
130	C₂×#323	C₂×C₁₃₉	1	4	yes	complemented
131	C₂³×Q₈	C₄×C₁₃₉	1	1	yes	characteristic
132	C₂³×D₄	C₄×C₁₃₉	1	1	yes	characteristic
133	C₂×#124	—	2	8	no	—
134	C₂×#124	—	2	4	no	—
135	C₂²×C₂²⋊C₄	C₄×C₁₃₉	1	2	yes	—
136	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
137	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
138	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
139	#336	—	2	4	no	—
140	#323	—	2	8	no	—
141	C₂⁵	C₂×C₄×C₁₃₉	1	2	yes	—
142	C₂²×Q₈	—	2	4	no	—
143	C₂²×Q₈	—	2	2	no	—
144	C₂²×Q₈	—	4	4	no	—
145	C₂²×D₄	—	2	4	no	—
146	C₂²×D₄	—	2	2	no	—
147	C₂²×D₄	—	4	4	no	—
148	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
149	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
150	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
151	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
152	C₂²×C₈	—	2	4	no	—
153	#124	—	2	32	no	—
154	C₂×C₂²⋊C₄	—	2	4	no	—
155	C₂×C₂²⋊C₄	—	2	4	no	—
156	C₂×C₂²⋊C₄	—	2	4	no	—
157	C₂×C₂²⋊C₄	—	2	4	no	—
158	C₂×C₂²⋊C₄	—	2	4	no	—
159	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	—
160	C₂×C₄²	—	2	4	no	—
161	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
162	C₂²⋊C₈	—	2	8	no	—
163	C₂⁴	—	2	2	no	—
164	C₂⁴	—	2	2	no	—
165	C₂⁴	—	2	8	no	—
166	C₂⁴	—	4	4	no	—
167	C₂⁴	—	4	4	no	—
168	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
169	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
170	C₂×Q₈	—	2	8	no	—
171	C₂×Q₈	—	4	16	no	—
172	C₂×Q₈	—	4	4	no	—
173	C₂×Q₈	—	4	4	no	—
174	C₂×D₄	—	2	8	no	—
175	C₂×D₄	—	4	16	no	—
176	C₂×D₄	—	4	4	no	—
177	C₂×D₄	—	4	4	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	4	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	4	4	no	—
186	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
187	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
188	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
189	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
190	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
191	C₂×C₈	—	4	8	no	—
192	C₂×C₈	—	4	4	no	—
193	C₂²⋊C₄	—	2	16	no	—
194	C₂²⋊C₄	—	2	16	no	—
195	C₄²	—	2	8	no	—
196	C₂³	—	2	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	2	4	no	—
199	C₂³	—	2	8	no	—
200	C₂³	—	4	4	no	—
201	C₂³	—	4	4	no	—
202	C₂³	—	4	4	no	—
203	C₂³	—	4	4	no	—
204	C₂³	—	4	4	no	—
205	C₂³	—	4	4	no	—
206	C₂³	—	4	4	no	—
207	C₂³	—	4	4	no	—
208	C₂³	—	8	16	no	—
209	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
210	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
211	C₂³	#131×C₁₃₉	1	4	yes	—
212	Q₈	—	4	16	no	—
213	D₄	—	4	16	no	—
214	C₂×C₄	—	2	8	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	4	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	#100×C₁₃₉	1	4	yes	—
227	C₂×C₄	#120×C₁₃₉	1	4	yes	—
228	C₈	—	8	4	no	—
229	C₂²	—	2	2	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	2	8	no	—
232	C₂²	—	4	4	no	—
233	C₂²	—	4	4	no	—
234	C₂²	—	4	4	no	—
235	C₂²	—	8	8	no	—
236	C₂²	—	8	8	no	—
237	C₂²	—	8	8	no	—
238	C₂²	#379×C₁₃₉	1	1	yes	characteristic
239	C₂²	#408×C₁₃₉	1	4	yes	—
240	C₂²	#408×C₁₃₉	1	2	yes	—
241	C₂²	#410×C₁₃₉	1	2	yes	—
242	C₂²	C₂×#100×C₁₃₉	1	2	yes	—
243	C₄	—	2	4	no	—
244	C₄	—	2	4	no	—
245	C₄	—	4	2	no	—
246	C₄	—	4	4	no	—
247	C₂	—	2	4	no	—
248	C₂	—	8	4	no	—
249	C₂	#1469×C₁₃₉	1	4	yes	—
250	C₂	#1780×C₁₃₉	1	1	yes	characteristic
251	C₂	#1782×C₁₃₉	1	1	yes	characteristic
252	C₂	#1783×C₁₃₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#124×C₁₃₉

C₂

yes

maximal, characteristic

#1817×C₁₃₉

C₂

yes

maximal, complemented

C₂×#323×C₁₃₉

C₂

yes

maximal, complemented

C₂³×Q₈×C₁₃₉

C₄

yes

characteristic

C₂³×D₄×C₁₃₉

C₄

yes

characteristic

C₂×#124×C₁₃₉

—

C₂×#124×C₁₃₉

—

C₂²×C₂²⋊C₄×C₁₃₉

C₄

yes

—

C₂²×C₂²⋊C₄×C₁₃₉

C₂²

yes

—

C₂²×C₄²×C₁₃₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₁₃₉

C₂²

yes

—

#336×C₁₃₉

—

#323×C₁₃₉

—

C₂⁵×C₁₃₉

C₂×C₄

yes

—

C₂²×Q₈×C₁₃₉

—

C₂²×Q₈×C₁₃₉

—

C₂²×Q₈×C₁₃₉

—

C₂²×D₄×C₁₃₉

—

C₂²×D₄×C₁₃₉

—

C₂²×D₄×C₁₃₉

—

C₂³×C₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₃₉

C₂×C₄

yes

—

C₂³×C₄×C₁₃₉

C₂³

yes

characteristic

C₂²×C₈×C₁₃₉

—

#124×C₁₃₉

—

C₂×C₂²⋊C₄×C₁₃₉

—

C₂×C₂²⋊C₄×C₁₃₉

—

C₂×C₂²⋊C₄×C₁₃₉

—

C₂×C₂²⋊C₄×C₁₃₉

—

C₂×C₂²⋊C₄×C₁₃₉

—

C₂×C₂²⋊C₄×C₁₃₉

D₄

yes

—

C₂×C₄²×C₁₃₉

—

C₂×C₄²×C₁₃₉

D₄

yes

—

C₂²⋊C₈×C₁₃₉

—

C₂⁴×C₁₃₉

—

C₂⁴×C₁₃₉

—

C₂⁴×C₁₃₉

—

C₂⁴×C₁₃₉

—

C₂⁴×C₁₃₉

—

C₂⁴×C₁₃₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₃₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×Q₈×C₁₃₉

—

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

—

C₂×D₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃₉

C₂×D₄

yes

—

C₂²×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂²⋊C₄×C₁₃₉

—

C₂²⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₃₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₃₉

#131

yes

—

Q₈×C₁₃₉

—

D₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

#100

yes

—

100

C₂×C₄×C₁₃₉

#120

yes

—

101

C₈×C₁₃₉

—

102

C₂²×C₁₃₉

—

103

C₂²×C₁₃₉

—

104

C₂²×C₁₃₉

—

105

C₂²×C₁₃₉

—

106

C₂²×C₁₃₉

—

107

C₂²×C₁₃₉

—

108

C₂²×C₁₃₉

—

109

C₂²×C₁₃₉

—

110

C₂²×C₁₃₉

—

111

C₂²×C₁₃₉

#379

yes

characteristic

112

C₂²×C₁₃₉

#408

yes

—

113

C₂²×C₁₃₉

#408

yes

—

114

C₂²×C₁₃₉

#410

yes

—

115

C₂²×C₁₃₉

C₂×#100

yes

—

116

C₄×C₁₃₉

—

117

C₄×C₁₃₉

—

118

C₄×C₁₃₉

—

119

C₄×C₁₃₉

—

120

C₂×C₁₃₉

—

121

C₂×C₁₃₉

—

122

C₂×C₁₃₉

#1469

yes

—

123

C₂×C₁₃₉

#1780

yes

characteristic

124

C₂×C₁₃₉

#1782

yes

characteristic

125

C₂×C₁₃₉

#1783

yes

characteristic

126

#8305

C₁₃₉

yes

maximal, characteristic, direct product factor, Sylow

127

C₁₃₉

#8305

yes

characteristic, direct product factor, Sylow

128

C₂²×#124

C₂×C₁₃₉

yes

characteristic

129

#1817

C₂×C₁₃₉

yes

complemented

130

C₂×#323

C₂×C₁₃₉

yes

complemented

131

C₂³×Q₈

C₄×C₁₃₉

yes

characteristic

132

C₂³×D₄

C₄×C₁₃₉

yes

characteristic

133

C₂×#124

—

134

C₂×#124

—

135

C₂²×C₂²⋊C₄

C₄×C₁₃₉

yes

—

136

C₂²×C₂²⋊C₄

C₂²×C₁₃₉

yes

—

137

C₂²×C₄²

C₂²×C₁₃₉

yes

characteristic

138

C₂×C₂²⋊C₈

C₂²×C₁₃₉

yes

—

139

#336

—

140

#323

—

141

C₂⁵

C₂×C₄×C₁₃₉

yes

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×Q₈

—

145

C₂²×D₄

—

146

C₂²×D₄

—

147

C₂²×D₄

—

148

C₂³×C₄

C₂×C₄×C₁₃₉

yes

characteristic

149

C₂³×C₄

C₂×C₄×C₁₃₉

yes

characteristic

150

C₂³×C₄

C₂×C₄×C₁₃₉

yes

—

151

C₂³×C₄

C₂³×C₁₃₉

yes

characteristic

152

C₂²×C₈

—

153

#124

—

154

C₂×C₂²⋊C₄

—

155

C₂×C₂²⋊C₄

—

156

C₂×C₂²⋊C₄

—

157

C₂×C₂²⋊C₄

—

158

C₂×C₂²⋊C₄

—

159

C₂×C₂²⋊C₄

D₄×C₁₃₉

yes

—

160

C₂×C₄²

—

161

C₂×C₄²

D₄×C₁₃₉

yes

—

162

C₂²⋊C₈

—

163

C₂⁴

—

164

C₂⁴

—

165

C₂⁴

—

166

C₂⁴

—

167

C₂⁴

—

168

C₂⁴

C₂²⋊C₄×C₁₃₉

yes

—

169

C₂⁴

C₂²×C₄×C₁₃₉

yes

characteristic

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂²⋊C₄×C₁₃₉

yes

—

187

C₂²×C₄

C₂²⋊C₄×C₁₃₉

yes

—

188

C₂²×C₄

C₂²⋊C₄×C₁₃₉

yes

—

189

C₂²×C₄

C₂×D₄×C₁₃₉

yes

—

190

C₂²×C₄

C₂×D₄×C₁₃₉

yes

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

195

C₄²

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

C₂×C₂²⋊C₄×C₁₃₉

yes

—

210

C₂³

C₂×C₂²⋊C₄×C₁₃₉

yes

characteristic

211

C₂³

#131×C₁₃₉

yes

—

212

Q₈

—

213

D₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

#100×C₁₃₉

yes

—

227

C₂×C₄

#120×C₁₃₉

yes

—

228

C₈

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

#379×C₁₃₉

yes

characteristic

239

C₂²

#408×C₁₃₉

yes

—

240

C₂²

#408×C₁₃₉

yes

—

241

C₂²

#410×C₁₃₉

yes

—

242

C₂²

C₂×#100×C₁₃₉

yes

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₂

—

248

C₂

—

249

C₂

#1469×C₁₃₉

yes

—

250

C₂

#1780×C₁₃₉

yes

characteristic

251

C₂

#1782×C₁₃₉

yes

characteristic

252

C₂

#1783×C₁₃₉

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃₉

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₁₃₉

Frattini, cosocle

C₂³×C₄

C₂³×C₁₃₉

prime radical

C₂³×D₄×C₁₃₉

C₄

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

N	H ≅ G/N	type
2. #1817×C₁₃₉	C₂	semidirect
3. C₂×#323×C₁₃₉	C₂	semidirect
126. #8305	C₁₃₉	direct (N × H)
127. C₁₃₉	#8305	direct (N × H)
129. #1817	C₂×C₁₃₉	semidirect
130. C₂×#323	C₂×C₁₃₉	semidirect

H ≅ G/N

type

2. #1817×C₁₃₉

C₂

semidirect

3. C₂×#323×C₁₃₉

C₂

semidirect

126. #8305

C₁₃₉

direct (N × H)

127. C₁₃₉

#8305

direct (N × H)

129. #1817

C₂×C₁₃₉

semidirect

130. C₂×#323

C₂×C₁₃₉

semidirect

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

subgroup	index
C₂²×#124×C₁₃₉	2
#1817×C₁₃₉	2
C₂×#323×C₁₃₉	2
#8305	139

subgroup

index

C₂²×#124×C₁₃₉

#1817×C₁₃₉

C₂×#323×C₁₃₉

#8305

139

Subgroups — C₁₃₉×#8305 #48002901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C139×#8305 #48002901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#8305 #48002901