Subgroups — C₁₃₉×#20634 #48015230

Order 35584.

1462 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#410×C₁₃₉	C₂	1	2	yes	maximal
3	#2316×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#1799×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#1740×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
7	#520×C₁₃₉	—	2	8	no	—
8	C₂×C₄×Q₈×C₁₃₉	C₄	1	2	yes	complemented
9	C₂×C₄×D₄×C₁₃₉	C₄	1	2	yes	complemented
10	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
11	C₂×#117×C₁₃₉	C₄	1	2	yes	complemented
12	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
13	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	2	yes	complemented
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	#410×C₁₃₉	—	2	8	no	—
17	C₂×#99×C₁₃₉	C₂²	1	8	yes	—
18	#389×C₁₃₉	—	2	8	no	—
19	#380×C₁₃₉	C₂²	1	8	yes	—
20	#342×C₁₃₉	C₂²	1	8	yes	—
21	C₂×#41×C₁₃₉	—	2	4	no	—
22	C₂×#41×C₁₃₉	—	2	4	no	—
23	C₂×#41×C₁₃₉	D₄	1	4	yes	—
24	C₂×#41×C₁₃₉	Q₈	1	4	yes	—
25	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
32	C₄×Q₈×C₁₃₉	—	2	8	no	—
33	C₄×D₄×C₁₃₉	—	2	16	no	—
34	C₄×D₄×C₁₃₉	—	2	8	no	—
35	#117×C₁₃₉	—	2	4	no	—
36	#117×C₁₃₉	—	2	8	no	—
37	#117×C₁₃₉	—	2	8	no	—
38	#117×C₁₃₉	—	2	8	no	—
39	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
42	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
48	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
50	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₃₉	—	2	4	no	—
52	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
54	#99×C₁₃₉	—	2	16	no	—
55	#95×C₁₃₉	—	2	8	no	—
56	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
57	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
58	#41×C₁₃₉	—	2	16	no	—
59	#41×C₁₃₉	—	2	16	no	—
60	C₂×Q₈×C₁₃₉	—	2	2	no	—
61	C₂×Q₈×C₁₃₉	—	2	2	no	—
62	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	4	yes	complemented
63	C₂×D₄×C₁₃₉	—	2	4	no	—
64	C₂×D₄×C₁₃₉	—	2	4	no	—
65	C₂×D₄×C₁₃₉	—	2	2	no	—
66	C₂×D₄×C₁₃₉	—	2	2	no	—
67	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	complemented
68	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
69	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
70	C₂²×C₄×C₁₃₉	—	2	4	no	—
71	C₂²×C₄×C₁₃₉	—	2	4	no	—
72	C₂²×C₄×C₁₃₉	—	2	8	no	—
73	C₂²×C₄×C₁₃₉	—	2	8	no	—
74	C₂²×C₄×C₁₃₉	—	8	2	no	—
75	C₂²×C₄×C₁₃₉	—	8	4	no	—
76	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	8	yes	complemented
77	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
85	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
88	C₄⋊C₄×C₁₃₉	—	2	2	no	—
89	C₄⋊C₄×C₁₃₉	—	2	8	no	—
90	C₄⋊C₄×C₁₃₉	—	2	2	no	—
91	C₄⋊C₄×C₁₃₉	—	4	8	no	—
92	C₄⋊C₄×C₁₃₉	—	8	8	no	—
93	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
94	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
95	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
96	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
97	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
98	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
99	C₄²×C₁₃₉	—	2	8	no	—
100	C₄²×C₁₃₉	—	2	4	no	—
101	C₄²×C₁₃₉	—	4	8	no	—
102	C₂³×C₁₃₉	—	2	2	no	—
103	C₂³×C₁₃₉	—	2	2	no	—
104	C₂³×C₁₃₉	—	4	1	no	—
105	C₂³×C₁₃₉	—	4	1	no	—
106	C₂³×C₁₃₉	—	4	2	no	—
107	C₂³×C₁₃₉	—	4	2	no	—
108	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
109	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
110	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
111	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
112	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
113	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
114	Q₈×C₁₃₉	—	2	8	no	—
115	D₄×C₁₃₉	—	2	8	no	—
116	D₄×C₁₃₉	—	2	8	no	—
117	D₄×C₁₃₉	—	2	8	no	—
118	C₂×C₄×C₁₃₉	—	2	2	no	—
119	C₂×C₄×C₁₃₉	—	2	2	no	—
120	C₂×C₄×C₁₃₉	—	2	16	no	—
121	C₂×C₄×C₁₃₉	—	2	2	no	—
122	C₂×C₄×C₁₃₉	—	2	2	no	—
123	C₂×C₄×C₁₃₉	—	4	8	no	—
124	C₂×C₄×C₁₃₉	—	4	4	no	—
125	C₂×C₄×C₁₃₉	—	4	2	no	—
126	C₂×C₄×C₁₃₉	—	4	2	no	—
127	C₂×C₄×C₁₃₉	—	4	8	no	—
128	C₂×C₄×C₁₃₉	—	4	8	no	—
129	C₂×C₄×C₁₃₉	—	4	8	no	—
130	C₂×C₄×C₁₃₉	—	8	8	no	—
131	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	—
132	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
135	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₃₉	#117	1	2	yes	—
138	C₂×C₄×C₁₃₉	#117	1	2	yes	—
139	C₂×C₄×C₁₃₉	#121	1	8	yes	—
140	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	8	yes	—
141	C₂²×C₁₃₉	—	2	2	no	—
142	C₂²×C₁₃₉	—	2	1	no	—
143	C₂²×C₁₃₉	—	2	2	no	—
144	C₂²×C₁₃₉	—	2	1	no	—
145	C₂²×C₁₃₉	—	2	4	no	—
146	C₂²×C₁₃₉	—	4	1	no	—
147	C₂²×C₁₃₉	—	4	1	no	—
148	C₂²×C₁₃₉	—	4	2	no	—
149	C₂²×C₁₃₉	—	4	4	no	—
150	C₂²×C₁₃₉	—	4	4	no	—
151	C₂²×C₁₃₉	—	4	2	no	—
152	C₂²×C₁₃₉	—	4	2	no	—
153	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×C₁₃₉	C₂×#117	1	1	yes	characteristic
156	C₂²×C₁₃₉	C₂×#121	1	2	yes	—
157	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	2	yes	—
158	C₄×C₁₃₉	—	2	8	no	—
159	C₄×C₁₃₉	—	2	4	no	—
160	C₄×C₁₃₉	—	4	2	no	—
161	C₄×C₁₃₉	—	4	2	no	—
162	C₄×C₁₃₉	—	8	8	no	—
163	C₄×C₁₃₉	#380	1	4	yes	—
164	C₄×C₁₃₉	#380	1	4	yes	—
165	C₂×C₁₃₉	—	2	2	no	—
166	C₂×C₁₃₉	—	2	1	no	—
167	C₂×C₁₃₉	—	2	1	no	—
168	C₂×C₁₃₉	—	2	2	no	—
169	C₂×C₁₃₉	—	4	4	no	—
170	C₂×C₁₃₉	C₂×#380	1	1	yes	characteristic
171	C₂×C₁₃₉	#2883	1	1	yes	characteristic
172	C₂×C₁₃₉	#2884	1	1	yes	characteristic
173	#20634	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₁₃₉	#20634	1	1	yes	characteristic, direct product factor, Sylow
175	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic
176	C₂×#410	C₂×C₁₃₉	1	2	yes	—
177	#2316	C₂×C₁₃₉	1	2	yes	complemented
178	#1799	C₂×C₁₃₉	1	8	yes	complemented
179	#1740	C₂×C₁₃₉	1	2	yes	complemented
180	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
181	#520	—	2	8	no	—
182	C₂×C₄×Q₈	C₄×C₁₃₉	1	2	yes	complemented
183	C₂×C₄×D₄	C₄×C₁₃₉	1	2	yes	complemented
184	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
185	C₂×#117	C₄×C₁₃₉	1	2	yes	complemented
186	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
187	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
188	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	2	yes	complemented
189	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
190	#410	—	2	8	no	—
191	C₂×#99	C₂²×C₁₃₉	1	8	yes	—
192	#389	—	2	8	no	—
193	#380	C₂²×C₁₃₉	1	8	yes	—
194	#342	C₂²×C₁₃₉	1	8	yes	—
195	C₂×#41	—	2	4	no	—
196	C₂×#41	—	2	4	no	—
197	C₂×#41	D₄×C₁₃₉	1	4	yes	—
198	C₂×#41	Q₈×C₁₃₉	1	4	yes	—
199	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
200	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
201	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
202	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
203	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
204	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
206	C₄×Q₈	—	2	8	no	—
207	C₄×D₄	—	2	16	no	—
208	C₄×D₄	—	2	8	no	—
209	#117	—	2	4	no	—
210	#117	—	2	8	no	—
211	#117	—	2	8	no	—
212	#117	—	2	8	no	—
213	C₂×C₄⋊C₄	—	2	8	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	8	no	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
221	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
225	C₂×C₄²	—	2	4	no	—
226	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
227	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
228	#99	—	2	16	no	—
229	#95	—	2	8	no	—
230	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
231	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
232	#41	—	2	16	no	—
233	#41	—	2	16	no	—
234	C₂×Q₈	—	2	2	no	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	4	yes	complemented
237	C₂×D₄	—	2	4	no	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	2	2	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	complemented
242	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
243	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	8	2	no	—
249	C₂²×C₄	—	8	4	no	—
250	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	8	yes	complemented
251	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
258	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
260	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
261	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	8	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	4	8	no	—
266	C₄⋊C₄	—	8	8	no	—
267	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
268	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	—	2	8	no	—
271	C₂²⋊C₄	—	2	8	no	—
272	C₂²⋊C₄	—	2	8	no	—
273	C₄²	—	2	8	no	—
274	C₄²	—	2	4	no	—
275	C₄²	—	4	8	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	4	1	no	—
279	C₂³	—	4	1	no	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	2	no	—
282	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
283	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
284	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
285	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
286	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
287	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
288	Q₈	—	2	8	no	—
289	D₄	—	2	8	no	—
290	D₄	—	2	8	no	—
291	D₄	—	2	8	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	16	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	8	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	8	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	8	8	no	—
305	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	—
306	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
307	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
308	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
309	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
310	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
311	C₂×C₄	#117×C₁₃₉	1	2	yes	—
312	C₂×C₄	#117×C₁₃₉	1	2	yes	—
313	C₂×C₄	#121×C₁₃₉	1	8	yes	—
314	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	8	yes	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	4	1	no	—
321	C₂²	—	4	1	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
328	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
329	C₂²	C₂×#117×C₁₃₉	1	1	yes	characteristic
330	C₂²	C₂×#121×C₁₃₉	1	2	yes	—
331	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	2	yes	—
332	C₄	—	2	4	no	—
333	C₄	—	2	8	no	—
334	C₄	—	4	2	no	—
335	C₄	—	4	2	no	—
336	C₄	—	8	8	no	—
337	C₄	#380×C₁₃₉	1	4	yes	—
338	C₄	#380×C₁₃₉	1	4	yes	—
339	C₂	—	2	2	no	—
340	C₂	—	2	1	no	—
341	C₂	—	2	1	no	—
342	C₂	—	2	2	no	—
343	C₂	—	4	4	no	—
344	C₂	C₂×#380×C₁₃₉	1	1	yes	characteristic
345	C₂	#2883×C₁₃₉	1	1	yes	characteristic
346	C₂	#2884×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂²×C₄⋊C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2316×C₁₃₉	C₂	semidirect
4. #1799×C₁₃₉	C₂	semidirect
5. #1740×C₁₃₉	C₂	semidirect
8. C₂×C₄×Q₈×C₁₃₉	C₄	semidirect
9. C₂×C₄×D₄×C₁₃₉	C₄	semidirect
11. C₂×#117×C₁₃₉	C₄	semidirect
14. C₂²×C₄⋊C₄×C₁₃₉	C₄	semidirect
62. C₂×Q₈×C₁₃₉	C₄⋊C₄	semidirect
67. C₂×D₄×C₁₃₉	C₄⋊C₄	semidirect
76. C₂²×C₄×C₁₃₉	C₄⋊C₄	semidirect
173. #20634	C₁₃₉	direct (N × H)
174. C₁₃₉	#20634	direct (N × H)
177. #2316	C₂×C₁₃₉	semidirect
178. #1799	C₂×C₁₃₉	semidirect
179. #1740	C₂×C₁₃₉	semidirect
182. C₂×C₄×Q₈	C₄×C₁₃₉	semidirect
183. C₂×C₄×D₄	C₄×C₁₃₉	semidirect
185. C₂×#117	C₄×C₁₃₉	semidirect
188. C₂²×C₄⋊C₄	C₄×C₁₃₉	semidirect
236. C₂×Q₈	C₄⋊C₄×C₁₃₉	semidirect
241. C₂×D₄	C₄⋊C₄×C₁₃₉	semidirect
250. C₂²×C₄	C₄⋊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×#520×C₁₃₉	2
C₂×#410×C₁₃₉	2
#2316×C₁₃₉	2
#1799×C₁₃₉	2
#1740×C₁₃₉	2
#20634	139

Subgroups — C139×#20634 #48015230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20634 #48015230