Subgroups — C₁₃₉×#7664 #48002260

Order 35584.

708 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1797×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1270×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₁₃₉	—	2	1	no	—
6	C₂×#127×C₁₃₉	C₄	1	1	yes	characteristic
7	C₂×#121×C₁₃₉	—	2	1	no	—
8	C₂×#121×C₁₃₉	—	2	1	no	—
9	C₂×#121×C₁₃₉	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
12	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
13	#390×C₁₃₉	—	2	1	no	—
14	#390×C₁₃₉	—	2	1	no	—
15	#390×C₁₃₉	C₂²	1	2	yes	—
16	#384×C₁₃₉	C₄	1	1	yes	characteristic
17	#336×C₁₃₉	—	2	1	no	—
18	#336×C₁₃₉	C₂²	1	2	yes	—
19	#336×C₁₃₉	C₂²	1	2	yes	—
20	C₂²×D₄×C₁₃₉	—	2	2	no	—
21	C₂²×D₄×C₁₃₉	—	2	1	no	—
22	C₂²×D₄×C₁₃₉	—	2	1	no	—
23	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃₉	—	2	4	no	—
28	C₂²×C₈×C₁₃₉	—	2	2	no	—
29	C₂²×C₈×C₁₃₉	—	2	2	no	—
30	C₂²×C₈×C₁₃₉	—	4	2	no	—
31	C₂²×C₈×C₁₃₉	—	4	2	no	—
32	#127×C₁₃₉	—	4	2	no	—
33	#121×C₁₃₉	—	4	4	no	—
34	#121×C₁₃₉	—	4	2	no	—
35	#121×C₁₃₉	—	4	2	no	—
36	#121×C₁₃₉	—	4	2	no	—
37	#121×C₁₃₉	—	4	2	no	—
38	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
44	C₂×C₄²×C₁₃₉	—	4	2	no	—
45	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₁₃₉	—	4	2	no	—
50	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
51	C₂⁴×C₁₃₉	—	2	2	no	—
52	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×D₄×C₁₃₉	—	2	4	no	—
54	C₂×D₄×C₁₃₉	—	4	2	no	—
55	C₂×D₄×C₁₃₉	—	4	2	no	—
56	C₂×D₄×C₁₃₉	—	4	2	no	—
57	C₂×D₄×C₁₃₉	—	4	2	no	—
58	C₂×D₄×C₁₃₉	—	4	4	no	—
59	C₂×D₄×C₁₃₉	—	4	4	no	—
60	C₂×D₄×C₁₃₉	—	4	4	no	—
61	C₂×D₄×C₁₃₉	—	4	2	no	—
62	C₂×D₄×C₁₃₉	—	4	2	no	—
63	C₂×D₄×C₁₃₉	—	4	2	no	—
64	C₂×D₄×C₁₃₉	—	4	2	no	—
65	C₂²×C₄×C₁₃₉	—	2	2	no	—
66	C₂²×C₄×C₁₃₉	—	2	2	no	—
67	C₂²×C₄×C₁₃₉	—	2	2	no	—
68	C₂²×C₄×C₁₃₉	—	2	2	no	—
69	C₂²×C₄×C₁₃₉	—	2	2	no	—
70	C₂²×C₄×C₁₃₉	—	4	1	no	—
71	C₂²×C₄×C₁₃₉	—	4	1	no	—
72	C₂²×C₄×C₁₃₉	—	4	1	no	—
73	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₉	D₈	1	2	yes	—
77	C₂²×C₄×C₁₃₉	D₈	1	2	yes	—
78	C₂²×C₄×C₁₃₉	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₁₃₉	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₃₉	—	2	4	no	—
84	C₂×C₈×C₁₃₉	—	4	2	no	—
85	C₂×C₈×C₁₃₉	—	4	8	no	—
86	C₂×C₈×C₁₃₉	—	4	2	no	—
87	C₂×C₈×C₁₃₉	—	4	2	no	—
88	C₂×C₈×C₁₃₉	—	4	2	no	—
89	C₂×C₈×C₁₃₉	—	4	2	no	—
90	C₄⋊C₄×C₁₃₉	—	4	2	no	—
91	C₄⋊C₄×C₁₃₉	—	4	2	no	—
92	C₄⋊C₄×C₁₃₉	—	4	2	no	—
93	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
94	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
95	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
96	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
97	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
98	C₄²×C₁₃₉	—	2	2	no	—
99	C₄²×C₁₃₉	—	2	2	no	—
100	C₄²×C₁₃₉	—	4	1	no	—
101	C₄²×C₁₃₉	—	4	1	no	—
102	C₂³×C₁₃₉	—	2	1	no	—
103	C₂³×C₁₃₉	—	2	1	no	—
104	C₂³×C₁₃₉	—	2	1	no	—
105	C₂³×C₁₃₉	—	2	1	no	—
106	C₂³×C₁₃₉	—	4	2	no	—
107	C₂³×C₁₃₉	—	4	2	no	—
108	C₂³×C₁₃₉	—	4	2	no	—
109	C₂³×C₁₃₉	—	4	2	no	—
110	C₂³×C₁₃₉	—	4	2	no	—
111	C₂³×C₁₃₉	—	4	2	no	—
112	C₂³×C₁₃₉	—	4	2	no	—
113	C₂³×C₁₃₉	#100	1	2	yes	—
114	C₂³×C₁₃₉	#102	1	2	yes	—
115	C₂³×C₁₃₉	#102	1	2	yes	—
116	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	D₄×C₁₃₉	—	8	4	no	—
118	D₄×C₁₃₉	—	8	4	no	—
119	D₄×C₁₃₉	—	8	8	no	—
120	D₄×C₁₃₉	—	8	4	no	—
121	C₂×C₄×C₁₃₉	—	2	1	no	—
122	C₂×C₄×C₁₃₉	—	2	1	no	—
123	C₂×C₄×C₁₃₉	—	2	1	no	—
124	C₂×C₄×C₁₃₉	—	2	1	no	—
125	C₂×C₄×C₁₃₉	—	2	1	no	—
126	C₂×C₄×C₁₃₉	—	2	1	no	—
127	C₂×C₄×C₁₃₉	—	2	1	no	—
128	C₂×C₄×C₁₃₉	—	2	1	no	—
129	C₂×C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄×C₁₃₉	—	2	4	no	—
131	C₂×C₄×C₁₃₉	—	2	1	no	—
132	C₂×C₄×C₁₃₉	—	2	1	no	—
133	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
138	C₂×C₄×C₁₃₉	—	4	2	no	—
139	C₂×C₄×C₁₃₉	—	4	2	no	—
140	C₂×C₄×C₁₃₉	#99	1	2	yes	—
141	C₂×C₄×C₁₃₉	#102	1	2	yes	—
142	C₂×C₄×C₁₃₉	#102	1	2	yes	—
143	C₂×C₄×C₁₃₉	#104	1	2	yes	—
144	C₂×C₄×C₁₃₉	#131	1	2	yes	—
145	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₈×C₁₃₉	—	4	4	no	—
150	C₈×C₁₃₉	—	8	2	no	—
151	C₂²×C₁₃₉	—	2	2	no	—
152	C₂²×C₁₃₉	—	2	2	no	—
153	C₂²×C₁₃₉	—	2	2	no	—
154	C₂²×C₁₃₉	—	2	2	no	—
155	C₂²×C₁₃₉	—	2	2	no	—
156	C₂²×C₁₃₉	—	2	2	no	—
157	C₂²×C₁₃₉	—	8	2	no	—
158	C₂²×C₁₃₉	—	8	2	no	—
159	C₂²×C₁₃₉	—	8	2	no	—
160	C₂²×C₁₃₉	—	8	2	no	—
161	C₂²×C₁₃₉	—	8	2	no	—
162	C₂²×C₁₃₉	—	8	2	no	—
163	C₂²×C₁₃₉	—	8	2	no	—
164	C₂²×C₁₃₉	#331	1	4	yes	—
165	C₂²×C₁₃₉	#408	1	1	yes	characteristic
166	C₂²×C₁₃₉	C₂×#99	1	1	yes	characteristic
167	C₂²×C₁₃₉	C₂×#100	1	1	yes	characteristic
168	C₂²×C₁₃₉	C₂×#102	1	1	yes	characteristic
169	C₂²×C₁₃₉	C₂×#102	1	1	yes	characteristic
170	C₂²×C₁₃₉	C₂×#104	1	1	yes	characteristic
171	C₂²×C₁₃₉	#421	1	1	yes	characteristic
172	C₄×C₁₃₉	—	2	2	no	—
173	C₄×C₁₃₉	—	2	1	no	—
174	C₄×C₁₃₉	—	2	1	no	—
175	C₄×C₁₃₉	—	2	1	no	—
176	C₄×C₁₃₉	—	2	2	no	—
177	C₄×C₁₃₉	—	2	1	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	—	8	2	no	—
180	C₄×C₁₃₉	#327	1	4	yes	—
181	C₂×C₁₃₉	—	2	4	no	—
182	C₂×C₁₃₉	—	16	2	no	—
183	C₂×C₁₃₉	#1471	1	1	yes	characteristic
184	C₂×C₁₃₉	#1480	1	1	yes	characteristic
185	C₂×C₁₃₉	#1492	1	1	yes	characteristic
186	C₂×C₁₃₉	C₂×#327	1	1	yes	characteristic
187	C₂×C₁₃₉	#1519	1	1	yes	characteristic
188	C₂×C₁₃₉	#1530	1	1	yes	characteristic
189	C₂×C₁₃₉	C₂×#331	1	1	yes	characteristic
190	#7664	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₉	#7664	1	1	yes	characteristic, direct product factor, Sylow
192	#2856	C₂×C₁₃₉	1	1	yes	characteristic
193	#1797	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	C₂×#336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	#1270	C₂×C₁₃₉	1	4	yes	complemented
196	C₂³×C₈	—	2	1	no	—
197	C₂×#127	C₄×C₁₃₉	1	1	yes	characteristic
198	C₂×#121	—	2	1	no	—
199	C₂×#121	—	2	1	no	—
200	C₂×#121	C₄×C₁₃₉	1	2	yes	—
201	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₂²⋊C₈	—	2	1	no	—
204	#390	—	2	1	no	—
205	#390	—	2	1	no	—
206	#390	C₂²×C₁₃₉	1	2	yes	—
207	#384	C₄×C₁₃₉	1	1	yes	characteristic
208	#336	—	2	1	no	—
209	#336	C₂²×C₁₃₉	1	2	yes	—
210	#336	C₂²×C₁₃₉	1	2	yes	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	1	no	—
214	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
215	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
216	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	4	2	no	—
222	C₂²×C₈	—	4	2	no	—
223	#127	—	4	2	no	—
224	#121	—	4	4	no	—
225	#121	—	4	2	no	—
226	#121	—	4	2	no	—
227	#121	—	4	2	no	—
228	#121	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²	—	4	2	no	—
236	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
240	C₄⋊C₈	—	4	2	no	—
241	C₂²⋊C₈	—	4	2	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	2	no	—
248	C₂×D₄	—	4	2	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂×D₄	—	4	4	no	—
252	C₂×D₄	—	4	2	no	—
253	C₂×D₄	—	4	2	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
267	C₂²×C₄	D₈×C₁₃₉	1	2	yes	—
268	C₂²×C₄	D₈×C₁₃₉	1	2	yes	—
269	C₂²×C₄	SD₁₆×C₁₃₉	1	2	yes	—
270	C₂²×C₄	SD₁₆×C₁₃₉	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	4	2	no	—
276	C₂×C₈	—	4	8	no	—
277	C₂×C₈	—	4	2	no	—
278	C₂×C₈	—	4	2	no	—
279	C₂×C₈	—	4	2	no	—
280	C₂×C₈	—	4	2	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₂²⋊C₄	—	4	2	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	#100×C₁₃₉	1	2	yes	—
305	C₂³	#102×C₁₃₉	1	2	yes	—
306	C₂³	#102×C₁₃₉	1	2	yes	—
307	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
308	D₄	—	8	4	no	—
309	D₄	—	8	4	no	—
310	D₄	—	8	8	no	—
311	D₄	—	8	4	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	#99×C₁₃₉	1	2	yes	—
332	C₂×C₄	#102×C₁₃₉	1	2	yes	—
333	C₂×C₄	#102×C₁₃₉	1	2	yes	—
334	C₂×C₄	#104×C₁₃₉	1	2	yes	—
335	C₂×C₄	#131×C₁₃₉	1	2	yes	—
336	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
338	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
340	C₈	—	4	4	no	—
341	C₈	—	8	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	#331×C₁₃₉	1	4	yes	—
356	C₂²	#408×C₁₃₉	1	1	yes	characteristic
357	C₂²	C₂×#99×C₁₃₉	1	1	yes	characteristic
358	C₂²	C₂×#100×C₁₃₉	1	1	yes	characteristic
359	C₂²	C₂×#102×C₁₃₉	1	1	yes	characteristic
360	C₂²	C₂×#102×C₁₃₉	1	1	yes	characteristic
361	C₂²	C₂×#104×C₁₃₉	1	1	yes	characteristic
362	C₂²	#421×C₁₃₉	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	#327×C₁₃₉	1	4	yes	—
372	C₂	—	2	4	no	—
373	C₂	—	16	2	no	—
374	C₂	#1471×C₁₃₉	1	1	yes	characteristic
375	C₂	#1480×C₁₃₉	1	1	yes	characteristic
376	C₂	#1492×C₁₃₉	1	1	yes	characteristic
377	C₂	C₂×#327×C₁₃₉	1	1	yes	characteristic
378	C₂	#1519×C₁₃₉	1	1	yes	characteristic
379	C₂	#1530×C₁₃₉	1	1	yes	characteristic
380	C₂	C₂×#331×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
prime radical	#2856×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #1797×C₁₃₉	C₂	semidirect
3. C₂×#336×C₁₃₉	C₂	semidirect
4. #1270×C₁₃₉	C₂	semidirect
190. #7664	C₁₃₉	direct (N × H)
191. C₁₃₉	#7664	direct (N × H)
193. #1797	C₂×C₁₃₉	semidirect
194. C₂×#336	C₂×C₁₃₉	semidirect
195. #1270	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2856×C₁₃₉	2
#1797×C₁₃₉	2
C₂×#336×C₁₃₉	2
#1270×C₁₃₉	2
#7664	139

Subgroups — C139×#7664 #48002260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#7664 #48002260