Subgroups — C₁₃₉×#21937 #48016533

Order 35584.

1030 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#408×C₁₃₉	C₂	1	2	yes	maximal
2	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#1851×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#1850×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#1798×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1797×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
9	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
10	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	—
13	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	—
14	#408×C₁₃₉	—	2	8	no	—
15	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
17	#391×C₁₃₉	C₄	1	2	yes	—
18	#390×C₁₃₉	C₄	1	2	yes	—
19	#386×C₁₃₉	C₄	1	2	yes	—
20	#386×C₁₃₉	C₄	1	2	yes	—
21	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
22	#336×C₁₃₉	C₂²	1	2	yes	—
23	#336×C₁₃₉	C₂²	1	2	yes	—
24	#336×C₁₃₉	C₂²	1	2	yes	—
25	#336×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#41×C₁₃₉	—	4	2	no	—
27	C₂×#41×C₁₃₉	—	4	2	no	—
28	C₂×#41×C₁₃₉	D₄	1	4	yes	—
29	C₂×#41×C₁₃₉	Q₈	1	4	yes	—
30	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂×M₁₆×C₁₃₉	—	2	4	no	—
38	C₂×M₁₆×C₁₃₉	—	4	2	no	—
39	C₂×M₁₆×C₁₃₉	—	4	2	no	—
40	C₂²×C₈×C₁₃₉	—	2	4	no	—
41	C₂²×C₈×C₁₃₉	—	4	2	no	—
42	C₂²×C₈×C₁₃₉	—	4	2	no	—
43	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
45	#117×C₁₃₉	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
48	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₃₉	—	4	2	no	—
51	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
54	C₄⋊C₈×C₁₃₉	—	4	4	no	—
55	C₄⋊C₈×C₁₃₉	—	4	4	no	—
56	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
57	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
58	#95×C₁₃₉	C₂×C₄	1	4	yes	—
59	#95×C₁₃₉	C₂×C₄	1	4	yes	—
60	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
61	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
62	#41×C₁₃₉	—	4	8	no	—
63	#41×C₁₃₉	—	4	8	no	—
64	C₂×Q₈×C₁₃₉	—	4	1	no	—
65	C₂×Q₈×C₁₃₉	—	4	1	no	—
66	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	4	yes	—
67	C₂×D₄×C₁₃₉	—	4	1	no	—
68	C₂×D₄×C₁₃₉	—	4	1	no	—
69	C₂×D₄×C₁₃₉	—	4	2	no	—
70	C₂×D₄×C₁₃₉	—	4	2	no	—
71	C₂×D₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
72	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
73	C₂²×C₄×C₁₃₉	—	2	2	no	—
74	C₂²×C₄×C₁₃₉	—	2	2	no	—
75	C₂²×C₄×C₁₃₉	—	2	2	no	—
76	C₂²×C₄×C₁₃₉	—	2	2	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	—	4	1	no	—
81	C₂²×C₄×C₁₃₉	—	4	1	no	—
82	C₂²×C₄×C₁₃₉	—	4	2	no	—
83	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
92	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
93	M₁₆×C₁₃₉	—	4	8	no	—
94	C₂×C₈×C₁₃₉	—	2	4	no	—
95	C₂×C₈×C₁₃₉	—	2	4	no	—
96	C₂×C₈×C₁₃₉	—	2	4	no	—
97	C₂×C₈×C₁₃₉	—	2	4	no	—
98	C₂×C₈×C₁₃₉	—	2	4	no	—
99	C₂×C₈×C₁₃₉	—	2	4	no	—
100	C₂×C₈×C₁₃₉	—	4	8	no	—
101	C₄⋊C₄×C₁₃₉	—	4	2	no	—
102	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
103	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
104	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
105	C₄²×C₁₃₉	—	2	4	no	—
106	C₄²×C₁₃₉	—	2	4	no	—
107	C₄²×C₁₃₉	—	4	2	no	—
108	C₂³×C₁₃₉	—	2	1	no	—
109	C₂³×C₁₃₉	—	2	1	no	—
110	C₂³×C₁₃₉	—	2	2	no	—
111	C₂³×C₁₃₉	—	2	2	no	—
112	C₂³×C₁₃₉	—	2	4	no	—
113	C₂³×C₁₃₉	—	2	2	no	—
114	C₂³×C₁₃₉	—	2	4	no	—
115	C₂³×C₁₃₉	—	2	2	no	—
116	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
117	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
118	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
119	Q₈×C₁₃₉	—	4	4	no	—
120	D₄×C₁₃₉	—	4	4	no	—
121	D₄×C₁₃₉	—	4	8	no	—
122	C₂×C₄×C₁₃₉	—	2	2	no	—
123	C₂×C₄×C₁₃₉	—	2	1	no	—
124	C₂×C₄×C₁₃₉	—	2	1	no	—
125	C₂×C₄×C₁₃₉	—	2	2	no	—
126	C₂×C₄×C₁₃₉	—	2	2	no	—
127	C₂×C₄×C₁₃₉	—	2	2	no	—
128	C₂×C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄×C₁₃₉	—	2	4	no	—
131	C₂×C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	2	2	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	4	4	no	—
141	C₂×C₄×C₁₃₉	—	4	4	no	—
142	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₁₃₉	#131	1	4	yes	—
145	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
148	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
149	C₈×C₁₃₉	—	4	4	no	—
150	C₈×C₁₃₉	—	4	4	no	—
151	C₂²×C₁₃₉	—	2	4	no	—
152	C₂²×C₁₃₉	—	2	2	no	—
153	C₂²×C₁₃₉	—	2	8	no	—
154	C₂²×C₁₃₉	—	2	4	no	—
155	C₂²×C₁₃₉	—	4	1	no	—
156	C₂²×C₁₃₉	—	4	2	no	—
157	C₂²×C₁₃₉	—	4	1	no	—
158	C₂²×C₁₃₉	—	4	2	no	—
159	C₂²×C₁₃₉	—	4	2	no	—
160	C₂²×C₁₃₉	—	4	4	no	—
161	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₃₉	#518	1	1	yes	characteristic
163	C₂²×C₁₃₉	#518	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#131	1	2	yes	—
165	C₂²×C₁₃₉	#568	1	2	yes	—
166	C₄×C₁₃₉	—	2	2	no	—
167	C₄×C₁₃₉	—	2	4	no	—
168	C₄×C₁₃₉	—	2	4	no	—
169	C₄×C₁₃₉	—	4	2	no	—
170	C₄×C₁₃₉	—	4	4	no	—
171	C₄×C₁₃₉	#534	1	2	yes	—
172	C₄×C₁₃₉	#543	1	2	yes	—
173	C₂×C₁₃₉	—	4	2	no	—
174	C₂×C₁₃₉	—	4	4	no	—
175	C₂×C₁₃₉	#2315	1	1	yes	characteristic
176	C₂×C₁₃₉	#2906	1	2	yes	—
177	C₂×C₁₃₉	#2977	1	1	yes	characteristic
178	C₂×C₁₃₉	#2978	1	1	yes	characteristic
179	C₂×C₁₃₉	#2981	1	2	yes	—
180	#21937	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₉	#21937	1	1	yes	characteristic, direct product factor, Sylow
182	C₂×#408	C₂×C₁₃₉	1	2	yes	—
183	#2297	C₂×C₁₃₉	1	1	yes	characteristic
184	#1851	C₂×C₁₃₉	1	4	yes	complemented
185	#1850	C₂×C₁₃₉	1	4	yes	complemented
186	#1798	C₂×C₁₃₉	1	2	yes	complemented
187	#1797	C₂×C₁₃₉	1	2	yes	complemented
188	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
189	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
190	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
191	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	—
195	#408	—	2	8	no	—
196	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
197	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
198	#391	C₄×C₁₃₉	1	2	yes	—
199	#390	C₄×C₁₃₉	1	2	yes	—
200	#386	C₄×C₁₃₉	1	2	yes	—
201	#386	C₄×C₁₃₉	1	2	yes	—
202	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
203	#336	C₂²×C₁₃₉	1	2	yes	—
204	#336	C₂²×C₁₃₉	1	2	yes	—
205	#336	C₂²×C₁₃₉	1	2	yes	—
206	#336	C₂²×C₁₃₉	1	2	yes	—
207	C₂×#41	—	4	2	no	—
208	C₂×#41	—	4	2	no	—
209	C₂×#41	D₄×C₁₃₉	1	4	yes	—
210	C₂×#41	Q₈×C₁₃₉	1	4	yes	—
211	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
212	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
213	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
214	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
218	C₂×M₁₆	—	2	4	no	—
219	C₂×M₁₆	—	4	2	no	—
220	C₂×M₁₆	—	4	2	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	—	4	2	no	—
223	C₂²×C₈	—	4	2	no	—
224	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
225	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
226	#117	—	4	2	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
231	C₂×C₄²	—	4	2	no	—
232	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
233	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
234	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
235	C₄⋊C₈	—	4	4	no	—
236	C₄⋊C₈	—	4	4	no	—
237	C₂²⋊C₈	—	2	8	no	—
238	C₂²⋊C₈	—	2	8	no	—
239	#95	C₂×C₄×C₁₃₉	1	4	yes	—
240	#95	C₂×C₄×C₁₃₉	1	4	yes	—
241	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
242	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
243	#41	—	4	8	no	—
244	#41	—	4	8	no	—
245	C₂×Q₈	—	4	1	no	—
246	C₂×Q₈	—	4	1	no	—
247	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	4	yes	—
248	C₂×D₄	—	4	1	no	—
249	C₂×D₄	—	4	1	no	—
250	C₂×D₄	—	4	2	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
253	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	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	4	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
271	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
272	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
274	M₁₆	—	4	8	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	8	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	—	2	8	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₂²⋊C₄	—	4	2	no	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	4	no	—
288	C₄²	—	4	2	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	2	no	—
297	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
298	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
299	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
300	Q₈	—	4	4	no	—
301	D₄	—	4	4	no	—
302	D₄	—	4	8	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
324	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
325	C₂×C₄	#131×C₁₃₉	1	4	yes	—
326	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
327	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
329	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
330	C₈	—	4	4	no	—
331	C₈	—	4	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	8	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	4	no	—
342	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
343	C₂²	#518×C₁₃₉	1	1	yes	characteristic
344	C₂²	#518×C₁₃₉	1	1	yes	characteristic
345	C₂²	C₂×#131×C₁₃₉	1	2	yes	—
346	C₂²	#568×C₁₃₉	1	2	yes	—
347	C₄	—	2	2	no	—
348	C₄	—	2	4	no	—
349	C₄	—	2	4	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	4	no	—
352	C₄	#534×C₁₃₉	1	2	yes	—
353	C₄	#543×C₁₃₉	1	2	yes	—
354	C₂	—	4	2	no	—
355	C₂	—	4	4	no	—
356	C₂	#2315×C₁₃₉	1	1	yes	characteristic
357	C₂	#2906×C₁₃₉	1	2	yes	—
358	C₂	#2977×C₁₃₉	1	1	yes	characteristic
359	C₂	#2978×C₁₃₉	1	1	yes	characteristic
360	C₂	#2981×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #1851×C₁₃₉	C₂	semidirect
4. #1850×C₁₃₉	C₂	semidirect
5. #1798×C₁₃₉	C₂	semidirect
6. #1797×C₁₃₉	C₂	semidirect
180. #21937	C₁₃₉	direct (N × H)
181. C₁₃₉	#21937	direct (N × H)
184. #1851	C₂×C₁₃₉	semidirect
185. #1850	C₂×C₁₃₉	semidirect
186. #1798	C₂×C₁₃₉	semidirect
187. #1797	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#408×C₁₃₉	2
#2297×C₁₃₉	2
#1851×C₁₃₉	2
#1850×C₁₃₉	2
#1798×C₁₃₉	2
#1797×C₁₃₉	2
#21937	139

Subgroups — C139×#21937 #48016533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21937 #48016533