Subgroups — C₁₃₉×#20845 #48015441

Order 35584.

1558 conjugacy classes of subgroups.

The subgroup lattice has 354 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×#428×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#407×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2280×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1854×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#1736×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
9	C₂×#117×C₁₃₉	—	2	2	no	—
10	C₂×#117×C₁₃₉	—	2	8	no	—
11	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
16	C₂²×C₄²×C₁₃₉	—	2	1	no	—
17	#428×C₁₃₉	—	2	8	no	—
18	C₂×#107×C₁₃₉	C₂²	1	4	yes	complemented
19	C₂×#106×C₁₃₉	C₂²	1	4	yes	complemented
20	#407×C₁₃₉	C₄	1	8	yes	complemented
21	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
22	#381×C₁₃₉	—	2	1	no	—
23	#380×C₁₃₉	C₂²	1	4	yes	—
24	#379×C₁₃₉	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
26	#340×C₁₃₉	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃₉	—	2	4	no	—
29	C₂³×C₄×C₁₃₉	—	2	4	no	—
30	C₂³×C₄×C₁₃₉	—	2	2	no	—
31	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₃₉	Q₈	1	4	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₃₉	—	2	4	no	—
38	C₂×M₁₆×C₁₃₉	—	2	4	no	—
39	C₂×M₁₆×C₁₃₉	C₂×C₄	1	8	yes	—
40	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
41	#117×C₁₃₉	—	2	16	no	—
42	#117×C₁₃₉	—	2	16	no	—
43	#117×C₁₃₉	—	2	4	no	—
44	#117×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
56	C₂×C₄²×C₁₃₉	—	2	8	no	—
57	C₂×C₄²×C₁₃₉	—	2	4	no	—
58	C₂×C₄²×C₁₃₉	—	2	1	no	—
59	C₂×C₄²×C₁₃₉	—	2	1	no	—
60	#107×C₁₃₉	—	2	8	no	—
61	#106×C₁₃₉	—	2	8	no	—
62	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	16	yes	complemented
63	#95×C₁₃₉	—	2	4	no	—
64	C₂⁴×C₁₃₉	—	2	2	no	—
65	C₂⁴×C₁₃₉	—	2	2	no	—
66	C₂⁴×C₁₃₉	—	4	4	no	—
67	C₂⁴×C₁₃₉	C₄⋊C₄	1	4	yes	—
68	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
69	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₉	—	2	2	no	—
71	C₂²×C₄×C₁₃₉	—	2	2	no	—
72	C₂²×C₄×C₁₃₉	—	2	16	no	—
73	C₂²×C₄×C₁₃₉	—	2	4	no	—
74	C₂²×C₄×C₁₃₉	—	2	16	no	—
75	C₂²×C₄×C₁₃₉	—	2	4	no	—
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	8	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	4	8	no	—
83	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
85	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
93	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₁₃₉	—	2	16	no	—
95	C₂×C₈×C₁₃₉	—	2	4	no	—
96	C₂×C₈×C₁₃₉	—	2	4	no	—
97	C₂×C₈×C₁₃₉	C₂²×C₄	1	8	yes	—
98	C₄⋊C₄×C₁₃₉	—	2	8	no	—
99	C₄⋊C₄×C₁₃₉	—	2	4	no	—
100	C₄⋊C₄×C₁₃₉	—	2	2	no	—
101	C₄⋊C₄×C₁₃₉	—	2	2	no	—
102	C₄⋊C₄×C₁₃₉	—	2	4	no	—
103	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
104	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
105	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
106	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
107	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
108	C₄²×C₁₃₉	—	2	16	no	—
109	C₄²×C₁₃₉	—	4	2	no	—
110	C₄²×C₁₃₉	—	4	2	no	—
111	C₂³×C₁₃₉	—	2	4	no	—
112	C₂³×C₁₃₉	—	2	2	no	—
113	C₂³×C₁₃₉	—	2	2	no	—
114	C₂³×C₁₃₉	—	2	4	no	—
115	C₂³×C₁₃₉	—	2	4	no	—
116	C₂³×C₁₃₉	—	2	8	no	—
117	C₂³×C₁₃₉	—	4	8	no	—
118	C₂³×C₁₃₉	—	4	8	no	—
119	C₂³×C₁₃₉	—	4	8	no	—
120	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
121	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
122	C₂³×C₁₃₉	#120	1	2	yes	—
123	C₂³×C₁₃₉	#123	1	2	yes	—
124	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₃₉	—	2	2	no	—
126	C₂×C₄×C₁₃₉	—	2	2	no	—
127	C₂×C₄×C₁₃₉	—	2	8	no	—
128	C₂×C₄×C₁₃₉	—	2	8	no	—
129	C₂×C₄×C₁₃₉	—	2	8	no	—
130	C₂×C₄×C₁₃₉	—	2	16	no	—
131	C₂×C₄×C₁₃₉	—	2	8	no	—
132	C₂×C₄×C₁₃₉	—	4	16	no	—
133	C₂×C₄×C₁₃₉	—	4	8	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	—	4	4	no	—
137	C₂×C₄×C₁₃₉	—	4	4	no	—
138	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
139	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
141	C₂×C₄×C₁₃₉	#120	1	2	yes	—
142	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	8	yes	—
143	C₂×C₄×C₁₃₉	#123	1	2	yes	—
144	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
146	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
148	C₈×C₁₃₉	—	2	8	no	—
149	C₂²×C₁₃₉	—	2	4	no	—
150	C₂²×C₁₃₉	—	2	4	no	—
151	C₂²×C₁₃₉	—	2	4	no	—
152	C₂²×C₁₃₉	—	2	4	no	—
153	C₂²×C₁₃₉	—	2	4	no	—
154	C₂²×C₁₃₉	—	2	4	no	—
155	C₂²×C₁₃₉	—	4	16	no	—
156	C₂²×C₁₃₉	—	4	4	no	—
157	C₂²×C₁₃₉	—	4	4	no	—
158	C₂²×C₁₃₉	#385	1	4	yes	—
159	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
160	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
161	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
162	C₂²×C₁₃₉	#575	1	4	yes	—
163	C₄×C₁₃₉	—	2	4	no	—
164	C₄×C₁₃₉	—	4	8	no	—
165	C₄×C₁₃₉	—	8	2	no	—
166	C₄×C₁₃₉	—	8	2	no	—
167	C₄×C₁₃₉	#385	1	4	yes	—
168	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
169	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	2	yes	—
170	C₂×C₁₃₉	—	2	4	no	—
171	C₂×C₁₃₉	—	4	4	no	—
172	C₂×C₁₃₉	C₂×#385	1	1	yes	characteristic
173	C₂×C₁₃₉	#2911	1	2	yes	—
174	C₂×C₁₃₉	#3005	1	2	yes	—
175	C₂×C₁₃₉	#3093	1	2	yes	—
176	#20845	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃₉	#20845	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic
179	C₂×#428	C₂×C₁₃₉	1	2	yes	complemented
180	C₂×#407	C₂×C₁₃₉	1	1	yes	characteristic
181	#2280	C₂×C₁₃₉	1	1	yes	characteristic
182	#1854	C₂×C₁₃₉	1	8	yes	complemented
183	#1736	C₂×C₁₃₉	1	2	yes	complemented
184	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
185	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
186	C₂×#117	—	2	2	no	—
187	C₂×#117	—	2	8	no	—
188	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
189	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
190	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
191	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
192	C₂²×C₂²⋊C₄	—	2	1	no	—
193	C₂²×C₄²	—	2	1	no	—
194	#428	—	2	8	no	—
195	C₂×#107	C₂²×C₁₃₉	1	4	yes	complemented
196	C₂×#106	C₂²×C₁₃₉	1	4	yes	complemented
197	#407	C₄×C₁₃₉	1	8	yes	complemented
198	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
199	#381	—	2	1	no	—
200	#380	C₂²×C₁₃₉	1	4	yes	—
201	#379	—	2	1	no	—
202	C₄×C₂²⋊C₄	—	2	2	no	—
203	#340	C₂²×C₁₃₉	1	8	yes	complemented
204	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
205	C₂³×C₄	—	2	4	no	—
206	C₂³×C₄	—	2	4	no	—
207	C₂³×C₄	—	2	2	no	—
208	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
209	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
210	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
211	C₂³×C₄	Q₈×C₁₃₉	1	4	yes	—
212	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
213	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	C₂×C₄×C₁₃₉	1	8	yes	—
217	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
218	#117	—	2	16	no	—
219	#117	—	2	16	no	—
220	#117	—	2	4	no	—
221	#117	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
228	C₂×C₂²⋊C₄	—	2	8	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₄²	—	2	8	no	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	#107	—	2	8	no	—
238	#106	—	2	8	no	—
239	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	16	yes	complemented
240	#95	—	2	4	no	—
241	C₂⁴	—	2	2	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	4	4	no	—
244	C₂⁴	C₄⋊C₄×C₁₃₉	1	4	yes	—
245	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
246	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	4	8	no	—
260	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
261	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
267	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
268	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
269	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
271	M₁₆	—	2	16	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	C₂²×C₄×C₁₃₉	1	8	yes	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
281	C₂²⋊C₄	—	2	16	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₂²⋊C₄	—	4	2	no	—
285	C₄²	—	2	16	no	—
286	C₄²	—	4	2	no	—
287	C₄²	—	4	2	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	4	8	no	—
295	C₂³	—	4	8	no	—
296	C₂³	—	4	8	no	—
297	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
298	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
299	C₂³	#120×C₁₃₉	1	2	yes	—
300	C₂³	#123×C₁₃₉	1	2	yes	—
301	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	16	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	4	16	no	—
310	C₂×C₄	—	4	8	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
316	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
317	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
318	C₂×C₄	#120×C₁₃₉	1	2	yes	—
319	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	8	yes	—
320	C₂×C₄	#123×C₁₃₉	1	2	yes	—
321	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
322	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
323	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
325	C₈	—	2	8	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	16	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	4	no	—
335	C₂²	#385×C₁₃₉	1	4	yes	—
336	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
337	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
338	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
339	C₂²	#575×C₁₃₉	1	4	yes	—
340	C₄	—	2	4	no	—
341	C₄	—	4	8	no	—
342	C₄	—	8	2	no	—
343	C₄	—	8	2	no	—
344	C₄	#385×C₁₃₉	1	4	yes	—
345	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
346	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	2	yes	—
347	C₂	—	2	4	no	—
348	C₂	—	4	4	no	—
349	C₂	C₂×#385×C₁₃₉	1	1	yes	characteristic
350	C₂	#2911×C₁₃₉	1	2	yes	—
351	C₂	#3005×C₁₃₉	1	2	yes	—
352	C₂	#3093×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁵×C₁₃₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#428×C₁₃₉	C₂	semidirect
5. #1854×C₁₃₉	C₂	semidirect
6. #1736×C₁₃₉	C₂	semidirect
18. C₂×#107×C₁₃₉	C₂²	semidirect
19. C₂×#106×C₁₃₉	C₂²	semidirect
20. #407×C₁₃₉	C₄	semidirect
26. #340×C₁₃₉	C₂²	semidirect
62. C₂²⋊C₈×C₁₃₉	C₂×C₄	semidirect
176. #20845	C₁₃₉	direct (N × H)
177. C₁₃₉	#20845	direct (N × H)
179. C₂×#428	C₂×C₁₃₉	semidirect
182. #1854	C₂×C₁₃₉	semidirect
183. #1736	C₂×C₁₃₉	semidirect
195. C₂×#107	C₂²×C₁₃₉	semidirect
196. C₂×#106	C₂²×C₁₃₉	semidirect
197. #407	C₄×C₁₃₉	semidirect
203. #340	C₂²×C₁₃₉	semidirect
239. C₂²⋊C₈	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×#428×C₁₃₉	2
C₂×#407×C₁₃₉	2
#2280×C₁₃₉	2
#1854×C₁₃₉	2
#1736×C₁₃₉	2
#20845	139

Subgroups — C139×#20845 #48015441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20845 #48015441