Subgroups — C₁₃₉×#10856 #48005452

Order 35584.

810 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#423×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×C₁₃₉	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
6	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
7	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
9	#423×C₁₃₉	—	2	2	no	—
10	#423×C₁₃₉	—	2	2	no	—
11	#423×C₁₃₉	—	2	1	no	—
12	#423×C₁₃₉	—	2	1	no	—
13	#423×C₁₃₉	C₄	1	2	yes	complemented
14	#423×C₁₃₉	C₄	1	2	yes	complemented
15	C₂×C₄⋊C₈×C₁₃₉	—	2	2	no	—
16	C₂×C₄⋊C₈×C₁₃₉	C₄	1	4	yes	complemented
17	C₄×C₄⋊C₄×C₁₃₉	—	2	2	no	—
18	C₄×C₂²⋊C₄×C₁₃₉	C₄	1	4	yes	—
19	#376×C₁₃₉	—	2	1	no	—
20	C₄³×C₁₃₉	—	2	1	no	—
21	#344×C₁₃₉	—	2	8	no	—
22	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₁₃₉	—	2	2	no	—
25	C₂×M₁₆×C₁₃₉	—	2	2	no	—
26	C₂×M₁₆×C₁₃₉	—	2	2	no	—
27	C₂×M₁₆×C₁₃₉	—	2	4	no	—
28	C₂×M₁₆×C₁₃₉	—	2	4	no	—
29	C₂×M₁₆×C₁₃₉	—	2	4	no	—
30	C₂×M₁₆×C₁₃₉	—	2	4	no	—
31	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₃₉	—	2	2	no	—
33	C₂²×C₈×C₁₃₉	C₂×C₄	1	4	yes	—
34	#117×C₁₃₉	—	2	2	no	—
35	#117×C₁₃₉	—	2	2	no	—
36	#117×C₁₃₉	D₄	1	4	yes	—
37	#117×C₁₃₉	Q₈	1	4	yes	—
38	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
40	C₂×C₄²×C₁₃₉	—	2	2	no	—
41	C₂×C₄²×C₁₃₉	—	2	4	no	—
42	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
46	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
49	C₂×C₄²×C₁₃₉	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₁₃₉	Q₈	1	1	yes	characteristic
51	C₄⋊C₈×C₁₃₉	—	2	4	no	—
52	C₄⋊C₈×C₁₃₉	—	2	4	no	—
53	C₄⋊C₈×C₁₃₉	—	2	4	no	—
54	C₄⋊C₈×C₁₃₉	—	2	4	no	—
55	#95×C₁₃₉	—	2	4	no	—
56	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃₉	—	2	4	no	—
58	C₂²×C₄×C₁₃₉	—	4	4	no	—
59	C₂²×C₄×C₁₃₉	C₄²	1	2	yes	—
60	C₂²×C₄×C₁₃₉	C₄²	1	2	yes	—
61	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
73	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
74	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
75	M₁₆×C₁₃₉	—	2	8	no	—
76	M₁₆×C₁₃₉	—	4	4	no	—
77	M₁₆×C₁₃₉	—	4	4	no	—
78	M₁₆×C₁₃₉	—	4	2	no	—
79	M₁₆×C₁₃₉	—	4	2	no	—
80	C₂×C₈×C₁₃₉	—	2	4	no	—
81	C₂×C₈×C₁₃₉	—	2	4	no	—
82	C₂×C₈×C₁₃₉	—	2	8	no	—
83	C₂×C₈×C₁₃₉	—	4	2	no	—
84	C₂×C₈×C₁₃₉	—	4	2	no	—
85	C₄⋊C₄×C₁₃₉	—	2	4	no	—
86	C₄⋊C₄×C₁₃₉	—	2	4	no	—
87	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
88	C₂²⋊C₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
89	C₄²×C₁₃₉	—	2	4	no	—
90	C₄²×C₁₃₉	—	2	4	no	—
91	C₄²×C₁₃₉	—	4	8	no	—
92	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₁₃₉	C₄⋊C₄	1	2	yes	—
97	C₄²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃₉	C₄⋊C₄	1	2	yes	—
101	C₄²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂³×C₁₃₉	—	4	2	no	—
103	C₂³×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
104	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
107	C₂³×C₁₃₉	#117	1	2	yes	—
108	C₂×C₄×C₁₃₉	—	2	4	no	—
109	C₂×C₄×C₁₃₉	—	2	4	no	—
110	C₂×C₄×C₁₃₉	—	2	4	no	—
111	C₂×C₄×C₁₃₉	—	2	8	no	—
112	C₂×C₄×C₁₃₉	—	4	2	no	—
113	C₂×C₄×C₁₃₉	—	4	2	no	—
114	C₂×C₄×C₁₃₉	—	4	2	no	—
115	C₂×C₄×C₁₃₉	—	4	8	no	—
116	C₂×C₄×C₁₃₉	#95	1	2	yes	—
117	C₂×C₄×C₁₃₉	#95	1	2	yes	—
118	C₂×C₄×C₁₃₉	#95	1	2	yes	—
119	C₂×C₄×C₁₃₉	#95	1	2	yes	—
120	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
126	C₂×C₄×C₁₃₉	C₄×Q₈	1	2	yes	—
127	C₂×C₄×C₁₃₉	C₄×Q₈	1	2	yes	—
128	C₂×C₄×C₁₃₉	#121	1	2	yes	—
129	C₂×C₄×C₁₃₉	#121	1	2	yes	—
130	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
132	C₂×C₄×C₁₃₉	#124	1	1	yes	characteristic
133	C₂×C₄×C₁₃₉	#124	1	1	yes	characteristic
134	C₂×C₄×C₁₃₉	#125	1	2	yes	—
135	C₂×C₄×C₁₃₉	#127	1	1	yes	characteristic
136	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	2	yes	—
137	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	1	yes	characteristic
138	C₈×C₁₃₉	—	4	4	no	—
139	C₈×C₁₃₉	—	4	4	no	—
140	C₂²×C₁₃₉	—	2	2	no	—
141	C₂²×C₁₃₉	—	2	2	no	—
142	C₂²×C₁₃₉	—	2	2	no	—
143	C₂²×C₁₃₉	—	4	2	no	—
144	C₂²×C₁₃₉	—	4	2	no	—
145	C₂²×C₁₃₉	C₂×#95	1	1	yes	characteristic
146	C₂²×C₁₃₉	C₄×C₄⋊C₄	1	2	yes	—
147	C₂²×C₁₃₉	#380	1	2	yes	—
148	C₂²×C₁₃₉	#382	1	1	yes	characteristic
149	C₂²×C₁₃₉	#384	1	1	yes	characteristic
150	C₄×C₁₃₉	—	2	2	no	—
151	C₄×C₁₃₉	—	2	2	no	—
152	C₄×C₁₃₉	—	2	2	no	—
153	C₄×C₁₃₉	—	4	8	no	—
154	C₄×C₁₃₉	#344	1	4	yes	complemented
155	C₄×C₁₃₉	#389	1	2	yes	—
156	C₄×C₁₃₉	#389	1	2	yes	—
157	C₄×C₁₃₉	#390	1	1	yes	characteristic
158	C₄×C₁₃₉	#390	1	1	yes	characteristic
159	C₄×C₁₃₉	#391	1	1	yes	characteristic
160	C₄×C₁₃₉	#391	1	1	yes	characteristic
161	C₂×C₁₃₉	—	2	2	no	—
162	C₂×C₁₃₉	—	2	2	no	—
163	C₂×C₁₃₉	—	2	1	no	—
164	C₂×C₁₃₉	—	2	1	no	—
165	C₂×C₁₃₉	C₄⋊#95	1	1	yes	characteristic
166	C₂×C₁₃₉	C₂×#344	1	2	yes	—
167	#10856	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₁₃₉	#10856	1	1	yes	characteristic, direct product factor, Sylow
169	C₂×#423	C₂×C₁₃₉	1	1	yes	characteristic
170	C₂×#423	C₂×C₁₃₉	1	1	yes	characteristic
171	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic
172	C₂×#344	C₂×C₁₃₉	1	4	yes	—
173	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
174	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
175	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
176	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
177	#423	—	2	2	no	—
178	#423	—	2	2	no	—
179	#423	—	2	1	no	—
180	#423	—	2	1	no	—
181	#423	C₄×C₁₃₉	1	2	yes	complemented
182	#423	C₄×C₁₃₉	1	2	yes	complemented
183	C₂×C₄⋊C₈	—	2	2	no	—
184	C₂×C₄⋊C₈	C₄×C₁₃₉	1	4	yes	complemented
185	C₄×C₄⋊C₄	—	2	2	no	—
186	C₄×C₂²⋊C₄	C₄×C₁₃₉	1	4	yes	—
187	#376	—	2	1	no	—
188	C₄³	—	2	1	no	—
189	#344	—	2	8	no	—
190	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
191	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
192	C₂×M₁₆	—	2	4	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	2	2	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	4	no	—
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	—	2	4	no	—
199	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	C₂×C₄×C₁₃₉	1	4	yes	—
202	#117	—	2	2	no	—
203	#117	—	2	2	no	—
204	#117	D₄×C₁₃₉	1	4	yes	—
205	#117	Q₈×C₁₃₉	1	4	yes	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
208	C₂×C₄²	—	2	2	no	—
209	C₂×C₄²	—	2	4	no	—
210	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
211	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
212	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
213	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
214	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
215	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
216	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
217	C₂×C₄²	Q₈×C₁₃₉	1	1	yes	characteristic
218	C₂×C₄²	Q₈×C₁₃₉	1	1	yes	characteristic
219	C₄⋊C₈	—	2	4	no	—
220	C₄⋊C₈	—	2	4	no	—
221	C₄⋊C₈	—	2	4	no	—
222	C₄⋊C₈	—	2	4	no	—
223	#95	—	2	4	no	—
224	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	4	4	no	—
227	C₂²×C₄	C₄²×C₁₃₉	1	2	yes	—
228	C₂²×C₄	C₄²×C₁₃₉	1	2	yes	—
229	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
230	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
231	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
232	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
233	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
234	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
235	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
236	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
237	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
238	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
239	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
240	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
241	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
242	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
243	M₁₆	—	2	8	no	—
244	M₁₆	—	4	4	no	—
245	M₁₆	—	4	4	no	—
246	M₁₆	—	4	2	no	—
247	M₁₆	—	4	2	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	8	no	—
251	C₂×C₈	—	4	2	no	—
252	C₂×C₈	—	4	2	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₂²⋊C₄	—	2	4	no	—
256	C₂²⋊C₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
257	C₄²	—	2	4	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	4	8	no	—
260	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
261	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
262	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
263	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
264	C₄²	C₄⋊C₄×C₁₃₉	1	2	yes	—
265	C₄²	C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
266	C₄²	C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
267	C₄²	C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
268	C₄²	C₄⋊C₄×C₁₃₉	1	2	yes	—
269	C₄²	C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
270	C₂³	—	4	2	no	—
271	C₂³	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
272	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
273	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
274	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
275	C₂³	#117×C₁₃₉	1	2	yes	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	4	8	no	—
284	C₂×C₄	#95×C₁₃₉	1	2	yes	—
285	C₂×C₄	#95×C₁₃₉	1	2	yes	—
286	C₂×C₄	#95×C₁₃₉	1	2	yes	—
287	C₂×C₄	#95×C₁₃₉	1	2	yes	—
288	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
289	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
290	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
291	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
292	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
293	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
294	C₂×C₄	C₄×Q₈×C₁₃₉	1	2	yes	—
295	C₂×C₄	C₄×Q₈×C₁₃₉	1	2	yes	—
296	C₂×C₄	#121×C₁₃₉	1	2	yes	—
297	C₂×C₄	#121×C₁₃₉	1	2	yes	—
298	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
299	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
300	C₂×C₄	#124×C₁₃₉	1	1	yes	characteristic
301	C₂×C₄	#124×C₁₃₉	1	1	yes	characteristic
302	C₂×C₄	#125×C₁₃₉	1	2	yes	—
303	C₂×C₄	#127×C₁₃₉	1	1	yes	characteristic
304	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	2	yes	—
305	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
306	C₈	—	4	4	no	—
307	C₈	—	4	4	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	C₂×#95×C₁₃₉	1	1	yes	characteristic
314	C₂²	C₄×C₄⋊C₄×C₁₃₉	1	2	yes	—
315	C₂²	#380×C₁₃₉	1	2	yes	—
316	C₂²	#382×C₁₃₉	1	1	yes	characteristic
317	C₂²	#384×C₁₃₉	1	1	yes	characteristic
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	4	8	no	—
322	C₄	#344×C₁₃₉	1	4	yes	complemented
323	C₄	#389×C₁₃₉	1	2	yes	—
324	C₄	#389×C₁₃₉	1	2	yes	—
325	C₄	#390×C₁₃₉	1	1	yes	characteristic
326	C₄	#390×C₁₃₉	1	1	yes	characteristic
327	C₄	#391×C₁₃₉	1	1	yes	characteristic
328	C₄	#391×C₁₃₉	1	1	yes	characteristic
329	C₂	—	2	2	no	—
330	C₂	—	2	2	no	—
331	C₂	—	2	1	no	—
332	C₂	—	2	1	no	—
333	C₂	C₄⋊#95×C₁₃₉	1	1	yes	characteristic
334	C₂	C₂×#344×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	C₂×#95
prime radical	C₂⁴×C₁₃₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
13. #423×C₁₃₉	C₄	semidirect
14. #423×C₁₃₉	C₄	semidirect
16. C₂×C₄⋊C₈×C₁₃₉	C₄	semidirect
154. C₄×C₁₃₉	#344	semidirect
167. #10856	C₁₃₉	direct (N × H)
168. C₁₃₉	#10856	direct (N × H)
181. #423	C₄×C₁₃₉	semidirect
182. #423	C₄×C₁₃₉	semidirect
184. C₂×C₄⋊C₈	C₄×C₁₃₉	semidirect
322. C₄	#344×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#423×C₁₃₉	2
C₄×#117×C₁₃₉	2
C₂×#344×C₁₃₉	2
#10856	139

Subgroups — C139×#10856 #48005452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10856 #48005452