Subgroups — C₁₃₉×#33455 #48028051

Order 35584.

660 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#510×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2951×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2950×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2176×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2175×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₄×Q₃₂×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₄×SD₃₂×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2159×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2138×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#358×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2108×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
14	#520×C₁₃₉	—	2	1	no	—
15	#519×C₁₃₉	—	2	1	no	—
16	#510×C₁₃₉	C₄	1	8	yes	complemented
17	C₂×Q₃₂×C₁₃₉	C₂²	1	2	yes	—
18	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	—
19	C₂×M₃₂×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
21	#441×C₁₃₉	—	2	2	no	—
22	#440×C₁₃₉	—	2	2	no	—
23	C₄×Q₁₆×C₁₃₉	C₂²	1	2	yes	—
24	C₄×Q₁₆×C₁₃₉	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₁₃₉	C₂²	1	2	yes	—
26	C₄×D₈×C₁₃₉	C₂²	1	2	yes	—
27	#427×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
29	#419×C₁₃₉	—	2	1	no	—
30	#417×C₁₃₉	—	2	1	no	—
31	#405×C₁₃₉	C₂²	1	1	yes	characteristic
32	#367×C₁₃₉	C₂²	1	2	yes	—
33	#366×C₁₃₉	C₂²	1	2	yes	—
34	#358×C₁₃₉	C₂²	1	2	yes	—
35	#358×C₁₃₉	C₂²	1	2	yes	—
36	#358×C₁₃₉	C₂²	1	1	yes	characteristic
37	#358×C₁₃₉	C₂²	1	1	yes	characteristic
38	#357×C₁₃₉	C₂²	1	1	yes	characteristic
39	#357×C₁₃₉	C₂²	1	1	yes	characteristic
40	#346×C₁₃₉	C₂²	1	2	yes	—
41	C₄×C₁₆×C₁₃₉	C₂²	1	2	yes	—
42	C₂×#41×C₁₃₉	—	2	1	no	—
43	C₂²×Q₈×C₁₃₉	—	2	1	no	—
44	#135×C₁₃₉	—	2	2	no	—
45	#135×C₁₃₉	C₂×C₄	1	4	yes	—
46	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
47	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
48	C₂×Q₁₆×C₁₃₉	C₂×C₄	1	4	yes	complemented
49	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂×SD₁₆×C₁₃₉	—	2	1	no	—
52	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₁₃₉	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₄×Q₈×C₁₃₉	—	2	2	no	—
56	C₄×Q₈×C₁₃₉	—	2	2	no	—
57	C₄×Q₈×C₁₃₉	—	2	2	no	—
58	C₄×Q₈×C₁₃₉	—	4	1	no	—
59	C₄×Q₈×C₁₃₉	—	4	1	no	—
60	C₄×D₄×C₁₃₉	—	2	2	no	—
61	C₄×D₄×C₁₃₉	—	4	2	no	—
62	#117×C₁₃₉	—	2	1	no	—
63	#117×C₁₃₉	—	4	1	no	—
64	#117×C₁₃₉	—	4	2	no	—
65	#117×C₁₃₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
68	Q₃₂×C₁₃₉	C₂×C₄	1	8	yes	complemented
69	SD₃₂×C₁₃₉	C₂×C₄	1	8	yes	complemented
70	M₃₂×C₁₃₉	C₂×C₄	1	4	yes	complemented
71	C₂×C₁₆×C₁₃₉	—	2	2	no	—
72	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
75	#107×C₁₃₉	—	2	1	no	—
76	#107×C₁₃₉	C₂³	1	2	yes	—
77	#107×C₁₃₉	C₂³	1	1	yes	characteristic
78	#107×C₁₃₉	C₂³	1	1	yes	characteristic
79	#106×C₁₃₉	—	2	1	no	—
80	#103×C₁₃₉	—	2	2	no	—
81	#103×C₁₃₉	—	2	2	no	—
82	#103×C₁₃₉	—	2	2	no	—
83	#102×C₁₃₉	—	2	2	no	—
84	#97×C₁₃₉	D₄	1	2	yes	—
85	C₄×C₈×C₁₃₉	C₂³	1	2	yes	—
86	#41×C₁₃₉	—	2	4	no	—
87	#41×C₁₃₉	—	4	2	no	—
88	C₂×Q₈×C₁₃₉	—	2	4	no	—
89	C₂×Q₈×C₁₃₉	—	2	1	no	—
90	C₂×Q₈×C₁₃₉	—	2	2	no	—
91	C₂×Q₈×C₁₃₉	—	4	1	no	—
92	C₂×Q₈×C₁₃₉	—	4	2	no	—
93	C₂×D₄×C₁₃₉	—	2	1	no	—
94	C₂×D₄×C₁₃₉	—	4	1	no	—
95	C₂²×C₄×C₁₃₉	—	4	1	no	—
96	C₂²×C₄×C₁₃₉	—	4	1	no	—
97	C₂²×C₄×C₁₃₉	—	4	1	no	—
98	C₂²×C₄×C₁₃₉	—	4	2	no	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
100	Q₁₆×C₁₃₉	—	2	4	no	—
101	Q₁₆×C₁₃₉	—	2	2	no	—
102	Q₁₆×C₁₃₉	—	2	1	no	—
103	Q₁₆×C₁₃₉	C₂²×C₄	1	4	yes	—
104	Q₁₆×C₁₃₉	C₂²×C₄	1	2	yes	—
105	SD₁₆×C₁₃₉	—	2	4	no	—
106	D₈×C₁₃₉	—	2	1	no	—
107	D₈×C₁₃₉	C₂²×C₄	1	2	yes	—
108	M₁₆×C₁₃₉	—	2	2	no	—
109	C₂×C₈×C₁₃₉	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₉	#41	1	2	yes	—
113	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₁₃₉	—	2	2	no	—
115	C₄⋊C₄×C₁₃₉	—	2	1	no	—
116	C₄⋊C₄×C₁₃₉	—	2	1	no	—
117	C₄⋊C₄×C₁₃₉	—	4	1	no	—
118	C₄⋊C₄×C₁₃₉	—	4	2	no	—
119	C₄⋊C₄×C₁₃₉	—	4	2	no	—
120	C₄⋊C₄×C₁₃₉	—	4	2	no	—
121	C₄⋊C₄×C₁₃₉	D₈	1	1	yes	characteristic
122	C₄⋊C₄×C₁₃₉	D₈	1	1	yes	characteristic
123	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
125	C₂²⋊C₄×C₁₃₉	D₈	1	2	yes	—
126	C₄²×C₁₃₉	—	4	1	no	—
127	C₄²×C₁₃₉	—	4	2	no	—
128	C₄²×C₁₃₉	—	4	2	no	—
129	C₄²×C₁₃₉	—	4	2	no	—
130	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
131	C₁₆×C₁₃₉	—	2	1	no	—
132	C₁₆×C₁₃₉	—	2	1	no	—
133	C₁₆×C₁₃₉	C₂²×C₄	1	4	yes	—
134	C₂³×C₁₃₉	—	4	1	no	—
135	C₂³×C₁₃₉	C₂×D₈	1	1	yes	characteristic
136	Q₈×C₁₃₉	—	2	2	no	—
137	Q₈×C₁₃₉	—	2	4	no	—
138	Q₈×C₁₃₉	—	4	2	no	—
139	Q₈×C₁₃₉	—	4	1	no	—
140	Q₈×C₁₃₉	—	4	4	no	—
141	D₄×C₁₃₉	—	2	2	no	—
142	D₄×C₁₃₉	—	4	4	no	—
143	D₄×C₁₃₉	—	4	1	no	—
144	C₂×C₄×C₁₃₉	—	4	1	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	4	no	—
147	C₂×C₄×C₁₃₉	—	4	4	no	—
148	C₂×C₄×C₁₃₉	—	4	1	no	—
149	C₂×C₄×C₁₃₉	—	4	1	no	—
150	C₂×C₄×C₁₃₉	—	4	2	no	—
151	C₂×C₄×C₁₃₉	—	16	2	no	—
152	C₂×C₄×C₁₃₉	—	16	1	no	—
153	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	#135	1	2	yes	—
158	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₁₃₉	—	2	2	no	—
160	C₈×C₁₃₉	C₄×D₄	1	2	yes	—
161	C₈×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
162	C₈×C₁₃₉	C₂×#41	1	1	yes	characteristic
163	C₂²×C₁₃₉	—	2	1	no	—
164	C₂²×C₁₃₉	—	2	1	no	—
165	C₂²×C₁₃₉	—	4	2	no	—
166	C₂²×C₁₃₉	—	8	1	no	—
167	C₂²×C₁₃₉	—	8	1	no	—
168	C₂²×C₁₃₉	C₄×D₈	1	2	yes	—
169	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
170	C₄×C₁₃₉	—	2	2	no	—
171	C₄×C₁₃₉	—	2	2	no	—
172	C₄×C₁₃₉	—	4	2	no	—
173	C₄×C₁₃₉	—	4	4	no	—
174	C₄×C₁₃₉	—	8	1	no	—
175	C₄×C₁₃₉	—	8	2	no	—
176	C₄×C₁₃₉	—	8	1	no	—
177	C₄×C₁₃₉	C₄×D₈	1	2	yes	—
178	C₄×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₁₃₉	C₂×#135	1	1	yes	characteristic
180	C₂×C₁₃₉	—	2	2	no	—
181	C₂×C₁₃₉	—	8	2	no	—
182	C₂×C₁₃₉	C₂×C₄×D₈	1	1	yes	characteristic
183	C₂×C₁₃₉	#3416	1	1	yes	characteristic
184	C₂×C₁₃₉	#3417	1	1	yes	characteristic
185	#33455	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₉	#33455	1	1	yes	characteristic, direct product factor, Sylow
187	C₂×#510	C₂×C₁₃₉	1	1	yes	characteristic
188	#2951	C₂×C₁₃₉	1	1	yes	characteristic
189	#2950	C₂×C₁₃₉	1	1	yes	characteristic, complemented
190	#2176	C₂×C₁₃₉	1	2	yes	complemented
191	#2175	C₂×C₁₃₉	1	2	yes	complemented
192	C₄×Q₃₂	C₂×C₁₃₉	1	2	yes	complemented
193	C₄×SD₃₂	C₂×C₁₃₉	1	2	yes	complemented
194	#2159	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	#2138	C₂×C₁₃₉	1	1	yes	characteristic
196	C₂×#358	C₂×C₁₃₉	1	1	yes	characteristic, complemented
197	#2108	C₂×C₁₃₉	1	1	yes	characteristic, complemented
198	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic
199	C₂²×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
200	#520	—	2	1	no	—
201	#519	—	2	1	no	—
202	#510	C₄×C₁₃₉	1	8	yes	complemented
203	C₂×Q₃₂	C₂²×C₁₃₉	1	2	yes	—
204	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	—
205	C₂×M₃₂	C₂²×C₁₃₉	1	1	yes	characteristic
206	C₂²×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
207	#441	—	2	2	no	—
208	#440	—	2	2	no	—
209	C₄×Q₁₆	C₂²×C₁₃₉	1	2	yes	—
210	C₄×Q₁₆	C₂²×C₁₃₉	1	2	yes	—
211	C₄×Q₁₆	C₂²×C₁₃₉	1	2	yes	—
212	C₄×D₈	C₂²×C₁₃₉	1	2	yes	—
213	#427	C₂²×C₁₃₉	1	1	yes	characteristic
214	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
215	#419	—	2	1	no	—
216	#417	—	2	1	no	—
217	#405	C₂²×C₁₃₉	1	1	yes	characteristic
218	#367	C₂²×C₁₃₉	1	2	yes	—
219	#366	C₂²×C₁₃₉	1	2	yes	—
220	#358	C₂²×C₁₃₉	1	2	yes	—
221	#358	C₂²×C₁₃₉	1	2	yes	—
222	#358	C₂²×C₁₃₉	1	1	yes	characteristic
223	#358	C₂²×C₁₃₉	1	1	yes	characteristic
224	#357	C₂²×C₁₃₉	1	1	yes	characteristic
225	#357	C₂²×C₁₃₉	1	1	yes	characteristic
226	#346	C₂²×C₁₃₉	1	2	yes	—
227	C₄×C₁₆	C₂²×C₁₃₉	1	2	yes	—
228	C₂×#41	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	#135	—	2	2	no	—
231	#135	C₂×C₄×C₁₃₉	1	4	yes	—
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	C₂×C₄×C₁₃₉	1	4	yes	complemented
235	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
236	C₂×Q₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
237	C₂×SD₁₆	—	2	1	no	—
238	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
239	C₂×M₁₆	D₄×C₁₃₉	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
241	C₄×Q₈	—	2	2	no	—
242	C₄×Q₈	—	2	2	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×Q₈	—	4	1	no	—
245	C₄×Q₈	—	4	1	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	4	2	no	—
248	#117	—	2	1	no	—
249	#117	—	4	1	no	—
250	#117	—	4	2	no	—
251	#117	D₄×C₁₃₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	4	1	no	—
254	Q₃₂	C₂×C₄×C₁₃₉	1	8	yes	complemented
255	SD₃₂	C₂×C₄×C₁₃₉	1	8	yes	complemented
256	M₃₂	C₂×C₄×C₁₃₉	1	4	yes	complemented
257	C₂×C₁₆	—	2	2	no	—
258	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
260	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
261	#107	—	2	1	no	—
262	#107	C₂³×C₁₃₉	1	1	yes	characteristic
263	#107	C₂³×C₁₃₉	1	1	yes	characteristic
264	#107	C₂³×C₁₃₉	1	2	yes	—
265	#106	—	2	1	no	—
266	#103	—	2	2	no	—
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#102	—	2	2	no	—
270	#97	D₄×C₁₃₉	1	2	yes	—
271	C₄×C₈	C₂³×C₁₃₉	1	2	yes	—
272	#41	—	2	4	no	—
273	#41	—	4	2	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
286	Q₁₆	—	2	4	no	—
287	Q₁₆	—	2	2	no	—
288	Q₁₆	—	2	1	no	—
289	Q₁₆	C₂²×C₄×C₁₃₉	1	4	yes	—
290	Q₁₆	C₂²×C₄×C₁₃₉	1	2	yes	—
291	SD₁₆	—	2	4	no	—
292	D₈	—	2	1	no	—
293	D₈	C₂²×C₄×C₁₃₉	1	2	yes	—
294	M₁₆	—	2	2	no	—
295	C₂×C₈	C₂²×C₄×C₁₃₉	1	2	yes	—
296	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
298	C₂×C₈	#41×C₁₃₉	1	2	yes	—
299	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	D₈×C₁₃₉	1	1	yes	characteristic
308	C₄⋊C₄	D₈×C₁₃₉	1	1	yes	characteristic
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	D₈×C₁₃₉	1	2	yes	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	2	no	—
314	C₄²	—	4	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	C₂²×C₄×C₁₃₉	1	4	yes	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×D₈×C₁₃₉	1	1	yes	characteristic
322	Q₈	—	2	2	no	—
323	Q₈	—	2	4	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	1	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	1	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	16	2	no	—
338	C₂×C₄	—	16	1	no	—
339	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
340	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
343	C₂×C₄	#135×C₁₃₉	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	C₄×D₄×C₁₃₉	1	2	yes	—
347	C₈	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
348	C₈	C₂×#41×C₁₃₉	1	1	yes	characteristic
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	1	no	—
354	C₂²	C₄×D₈×C₁₃₉	1	2	yes	—
355	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	4	no	—
360	C₄	—	8	2	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	1	no	—
363	C₄	C₄×D₈×C₁₃₉	1	2	yes	—
364	C₄	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
365	C₄	C₂×#135×C₁₃₉	1	1	yes	characteristic
366	C₂	—	2	2	no	—
367	C₂	—	8	2	no	—
368	C₂	C₂×C₄×D₈×C₁₃₉	1	1	yes	characteristic
369	C₂	#3416×C₁₃₉	1	1	yes	characteristic
370	C₂	#3417×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×D₈
commutator	C₈	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
prime radical	C₂×#135×C₁₃₉	C₂²
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ #117×C₁₃₉ ◁ #405×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2950×C₁₃₉	C₂	semidirect
4. #2176×C₁₃₉	C₂	semidirect
5. #2175×C₁₃₉	C₂	semidirect
6. C₄×Q₃₂×C₁₃₉	C₂	semidirect
7. C₄×SD₃₂×C₁₃₉	C₂	semidirect
8. #2159×C₁₃₉	C₂	semidirect
10. C₂×#358×C₁₃₉	C₂	semidirect
11. #2108×C₁₃₉	C₂	semidirect
16. #510×C₁₃₉	C₄	semidirect
48. C₂×Q₁₆×C₁₃₉	C₂×C₄	semidirect
68. Q₃₂×C₁₃₉	C₂×C₄	semidirect
69. SD₃₂×C₁₃₉	C₂×C₄	semidirect
70. M₃₂×C₁₃₉	C₂×C₄	semidirect
185. #33455	C₁₃₉	direct (N × H)
186. C₁₃₉	#33455	direct (N × H)
189. #2950	C₂×C₁₃₉	semidirect
190. #2176	C₂×C₁₃₉	semidirect
191. #2175	C₂×C₁₃₉	semidirect
192. C₄×Q₃₂	C₂×C₁₃₉	semidirect
193. C₄×SD₃₂	C₂×C₁₃₉	semidirect
194. #2159	C₂×C₁₃₉	semidirect
196. C₂×#358	C₂×C₁₃₉	semidirect
197. #2108	C₂×C₁₃₉	semidirect
202. #510	C₄×C₁₃₉	semidirect
234. C₂×Q₁₆	C₂×C₄×C₁₃₉	semidirect
254. Q₃₂	C₂×C₄×C₁₃₉	semidirect
255. SD₃₂	C₂×C₄×C₁₃₉	semidirect
256. M₃₂	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
C₂×#510×C₁₃₉	2
#2951×C₁₃₉	2
#2950×C₁₃₉	2
#2176×C₁₃₉	2
#2175×C₁₃₉	2
C₄×Q₃₂×C₁₃₉	2
C₄×SD₃₂×C₁₃₉	2
#2159×C₁₃₉	2
#2138×C₁₃₉	2
C₂×#358×C₁₃₉	2
#2108×C₁₃₉	2
#33455	139

Subgroups — C139×#33455 #48028051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33455 #48028051