Subgroups — C₁₃₉×#20910 #48015506

Order 35584.

1954 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂×#407×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1875×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1873×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1736×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
11	#525×C₁₃₉	—	2	4	no	—
12	#525×C₁₃₉	C₄	1	8	yes	complemented
13	C₂×#123×C₁₃₉	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#120×C₁₃₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
18	C₂×#117×C₁₃₉	—	2	2	no	—
19	C₂×#117×C₁₃₉	—	2	8	no	—
20	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
24	C₂²×C₄²×C₁₃₉	—	2	1	no	—
25	#417×C₁₃₉	—	2	8	no	—
26	C₂×#103×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×#102×C₁₃₉	C₂²	1	4	yes	complemented
28	#407×C₁₃₉	—	2	4	no	—
29	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
30	#340×C₁₃₉	C₂²	1	8	yes	complemented
31	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
32	C₂×#41×C₁₃₉	—	2	2	no	—
33	C₂×#41×C₁₃₉	—	2	4	no	—
34	C₂×#41×C₁₃₉	—	2	4	no	—
35	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₃₉	—	2	2	no	—
38	C₂²×D₄×C₁₃₉	—	2	1	no	—
39	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	—	2	4	no	—
41	C₂³×C₄×C₁₃₉	—	2	4	no	—
42	C₂³×C₄×C₁₃₉	—	2	2	no	—
43	C₂³×C₄×C₁₃₉	—	2	1	no	—
44	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
47	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
48	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₃₉	—	2	4	no	—
51	C₂×M₁₆×C₁₃₉	—	2	4	no	—
52	C₂×M₁₆×C₁₃₉	—	2	4	no	—
53	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
54	#123×C₁₃₉	—	2	8	no	—
55	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
56	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	8	yes	complemented
57	#121×C₁₃₉	—	2	4	no	—
58	#121×C₁₃₉	C₂×C₄	1	8	yes	complemented
59	#120×C₁₃₉	—	2	8	no	—
60	C₄×D₄×C₁₃₉	—	2	16	no	—
61	#117×C₁₃₉	—	2	16	no	—
62	#117×C₁₃₉	—	2	2	no	—
63	#117×C₁₃₉	—	2	16	no	—
64	#117×C₁₃₉	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
76	C₂×C₄²×C₁₃₉	—	2	8	no	—
77	C₂×C₄²×C₁₃₉	—	2	4	no	—
78	C₂×C₄²×C₁₃₉	—	2	1	no	—
79	#103×C₁₃₉	—	2	8	no	—
80	#102×C₁₃₉	—	2	8	no	—
81	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
82	C₂⁴×C₁₃₉	—	2	2	no	—
83	C₂⁴×C₁₃₉	—	2	2	no	—
84	C₂⁴×C₁₃₉	—	2	1	no	—
85	C₂⁴×C₁₃₉	—	4	4	no	—
86	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
87	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
88	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
89	#41×C₁₃₉	—	2	16	no	—
90	#41×C₁₃₉	—	4	8	no	—
91	C₂×Q₈×C₁₃₉	—	2	1	no	—
92	C₂×Q₈×C₁₃₉	—	2	2	no	—
93	C₂×Q₈×C₁₃₉	—	2	2	no	—
94	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₁₃₉	—	2	8	no	—
96	C₂×D₄×C₁₃₉	—	2	4	no	—
97	C₂×D₄×C₁₃₉	—	2	2	no	—
98	C₂×D₄×C₁₃₉	—	2	1	no	—
99	C₂×D₄×C₁₃₉	—	2	2	no	—
100	C₂×D₄×C₁₃₉	—	4	8	no	—
101	C₂×D₄×C₁₃₉	—	4	2	no	—
102	C₂×D₄×C₁₃₉	—	4	2	no	—
103	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	16	no	—
107	C₂²×C₄×C₁₃₉	—	2	4	no	—
108	C₂²×C₄×C₁₃₉	—	2	16	no	—
109	C₂²×C₄×C₁₃₉	—	2	4	no	—
110	C₂²×C₄×C₁₃₉	—	2	4	no	—
111	C₂²×C₄×C₁₃₉	—	2	4	no	—
112	C₂²×C₄×C₁₃₉	—	2	8	no	—
113	C₂²×C₄×C₁₃₉	—	2	4	no	—
114	C₂²×C₄×C₁₃₉	—	2	2	no	—
115	C₂²×C₄×C₁₃₉	—	2	1	no	—
116	C₂²×C₄×C₁₃₉	—	2	4	no	—
117	C₂²×C₄×C₁₃₉	—	4	8	no	—
118	C₂²×C₄×C₁₃₉	—	4	2	no	—
119	C₂²×C₄×C₁₃₉	—	4	2	no	—
120	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
121	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
122	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₁₃₉	—	4	8	no	—
132	C₂×C₈×C₁₃₉	—	2	4	no	—
133	C₂×C₈×C₁₃₉	—	2	4	no	—
134	C₂×C₈×C₁₃₉	—	2	4	no	—
135	C₄⋊C₄×C₁₃₉	—	2	8	no	—
136	C₄⋊C₄×C₁₃₉	—	2	8	no	—
137	C₄⋊C₄×C₁₃₉	—	2	4	no	—
138	C₄⋊C₄×C₁₃₉	—	2	2	no	—
139	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
140	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
141	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
142	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
144	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
145	C₄²×C₁₃₉	—	2	16	no	—
146	C₄²×C₁₃₉	—	2	4	no	—
147	C₂³×C₁₃₉	—	2	4	no	—
148	C₂³×C₁₃₉	—	2	2	no	—
149	C₂³×C₁₃₉	—	2	2	no	—
150	C₂³×C₁₃₉	—	2	4	no	—
151	C₂³×C₁₃₉	—	2	4	no	—
152	C₂³×C₁₃₉	—	2	8	no	—
153	C₂³×C₁₃₉	—	2	2	no	—
154	C₂³×C₁₃₉	—	4	8	no	—
155	C₂³×C₁₃₉	—	4	8	no	—
156	C₂³×C₁₃₉	—	4	8	no	—
157	C₂³×C₁₃₉	—	4	1	no	—
158	C₂³×C₁₃₉	—	4	1	no	—
159	C₂³×C₁₃₉	—	4	4	no	—
160	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
161	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂³×C₁₃₉	#120	1	2	yes	—
163	C₂³×C₁₃₉	#123	1	2	yes	—
164	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃₉	—	2	4	no	—
166	Q₈×C₁₃₉	—	4	2	no	—
167	D₄×C₁₃₉	—	2	4	no	—
168	D₄×C₁₃₉	—	4	16	no	—
169	D₄×C₁₃₉	—	4	8	no	—
170	D₄×C₁₃₉	—	4	2	no	—
171	C₂×C₄×C₁₃₉	—	2	2	no	—
172	C₂×C₄×C₁₃₉	—	2	2	no	—
173	C₂×C₄×C₁₃₉	—	2	8	no	—
174	C₂×C₄×C₁₃₉	—	2	8	no	—
175	C₂×C₄×C₁₃₉	—	2	8	no	—
176	C₂×C₄×C₁₃₉	—	2	16	no	—
177	C₂×C₄×C₁₃₉	—	2	4	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	8	no	—
180	C₂×C₄×C₁₃₉	—	4	16	no	—
181	C₂×C₄×C₁₃₉	—	4	1	no	—
182	C₂×C₄×C₁₃₉	—	4	1	no	—
183	C₂×C₄×C₁₃₉	—	4	8	no	—
184	C₂×C₄×C₁₃₉	—	4	4	no	—
185	C₂×C₄×C₁₃₉	—	4	8	no	—
186	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
187	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
189	C₂×C₄×C₁₃₉	#120	1	2	yes	—
190	C₂×C₄×C₁₃₉	#121	1	8	yes	—
191	C₂×C₄×C₁₃₉	#123	1	2	yes	—
192	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
196	C₈×C₁₃₉	—	4	4	no	—
197	C₂²×C₁₃₉	—	2	4	no	—
198	C₂²×C₁₃₉	—	2	4	no	—
199	C₂²×C₁₃₉	—	2	4	no	—
200	C₂²×C₁₃₉	—	2	4	no	—
201	C₂²×C₁₃₉	—	2	4	no	—
202	C₂²×C₁₃₉	—	2	4	no	—
203	C₂²×C₁₃₉	—	4	16	no	—
204	C₂²×C₁₃₉	—	4	4	no	—
205	C₂²×C₁₃₉	—	4	4	no	—
206	C₂²×C₁₃₉	—	4	4	no	—
207	C₂²×C₁₃₉	—	4	2	no	—
208	C₂²×C₁₃₉	—	8	2	no	—
209	C₂²×C₁₃₉	—	8	2	no	—
210	C₂²×C₁₃₉	#386	1	4	yes	—
211	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
213	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
214	C₂²×C₁₃₉	#575	1	4	yes	—
215	C₄×C₁₃₉	—	2	4	no	—
216	C₄×C₁₃₉	—	4	4	no	—
217	C₄×C₁₃₉	—	4	8	no	—
218	C₄×C₁₃₉	—	4	2	no	—
219	C₄×C₁₃₉	#386	1	4	yes	—
220	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
221	C₄×C₁₃₉	C₂×#121	1	2	yes	—
222	C₂×C₁₃₉	—	2	4	no	—
223	C₂×C₁₃₉	—	4	4	no	—
224	C₂×C₁₃₉	—	8	2	no	—
225	C₂×C₁₃₉	C₂×#386	1	1	yes	characteristic
226	C₂×C₁₃₉	#2896	1	2	yes	—
227	C₂×C₁₃₉	#3005	1	2	yes	—
228	C₂×C₁₃₉	#3093	1	2	yes	—
229	#20910	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₃₉	#20910	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#525	C₂×C₁₃₉	1	1	yes	characteristic
232	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
233	C₂×#417	C₂×C₁₃₉	1	2	yes	complemented
234	C₂×#407	C₂×C₁₃₉	1	1	yes	characteristic, complemented
235	#1875	C₂×C₁₃₉	1	4	yes	complemented
236	#1873	C₂×C₁₃₉	1	4	yes	complemented
237	#1736	C₂×C₁₃₉	1	2	yes	complemented
238	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
241	#525	—	2	4	no	—
242	#525	C₄×C₁₃₉	1	8	yes	complemented
243	C₂×#123	—	2	1	no	—
244	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
245	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
246	C₂×#120	—	2	1	no	—
247	C₂×C₄×D₄	—	2	2	no	—
248	C₂×#117	—	2	2	no	—
249	C₂×#117	—	2	8	no	—
250	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
251	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
253	C₂²×C₂²⋊C₄	—	2	1	no	—
254	C₂²×C₄²	—	2	1	no	—
255	#417	—	2	8	no	—
256	C₂×#103	C₂²×C₁₃₉	1	4	yes	complemented
257	C₂×#102	C₂²×C₁₃₉	1	4	yes	complemented
258	#407	—	2	4	no	—
259	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
260	#340	C₂²×C₁₃₉	1	8	yes	complemented
261	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	4	no	—
264	C₂×#41	—	2	4	no	—
265	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
266	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
275	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
276	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
277	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
278	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	—	2	4	no	—
283	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
284	#123	—	2	8	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	8	yes	complemented
287	#121	—	2	4	no	—
288	#121	C₂×C₄×C₁₃₉	1	8	yes	complemented
289	#120	—	2	8	no	—
290	C₄×D₄	—	2	16	no	—
291	#117	—	2	16	no	—
292	#117	—	2	2	no	—
293	#117	—	2	16	no	—
294	#117	C₂×C₄×C₁₃₉	1	4	yes	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₄²	—	2	8	no	—
307	C₂×C₄²	—	2	4	no	—
308	C₂×C₄²	—	2	1	no	—
309	#103	—	2	8	no	—
310	#102	—	2	8	no	—
311	C₂²⋊C₈	—	2	8	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	—	4	4	no	—
316	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
317	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
318	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
319	#41	—	2	16	no	—
320	#41	—	4	8	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	8	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	16	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
351	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
359	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
361	M₁₆	—	4	8	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	4	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
370	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
371	C₂²⋊C₄	—	2	16	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₄²	—	2	16	no	—
376	C₄²	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	8	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	4	no	—
390	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
391	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
392	C₂³	#120×C₁₃₉	1	2	yes	—
393	C₂³	#123×C₁₃₉	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	4	2	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	16	no	—
399	D₄	—	4	8	no	—
400	D₄	—	4	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	4	16	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
418	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
419	C₂×C₄	#120×C₁₃₉	1	2	yes	—
420	C₂×C₄	#121×C₁₃₉	1	8	yes	—
421	C₂×C₄	#123×C₁₃₉	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
426	C₈	—	4	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	16	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	#386×C₁₃₉	1	4	yes	—
441	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
442	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
443	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
444	C₂²	#575×C₁₃₉	1	4	yes	—
445	C₄	—	2	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	8	no	—
449	C₄	#386×C₁₃₉	1	4	yes	—
450	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
451	C₄	C₂×#121×C₁₃₉	1	2	yes	—
452	C₂	—	2	4	no	—
453	C₂	—	4	4	no	—
454	C₂	—	8	2	no	—
455	C₂	C₂×#386×C₁₃₉	1	1	yes	characteristic
456	C₂	#2896×C₁₃₉	1	2	yes	—
457	C₂	#3005×C₁₃₉	1	2	yes	—
458	C₂	#3093×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#525×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₁₃₉	C₂	semidirect
3. C₂×#417×C₁₃₉	C₂	semidirect
4. C₂×#407×C₁₃₉	C₂	semidirect
5. #1875×C₁₃₉	C₂	semidirect
6. #1873×C₁₃₉	C₂	semidirect
7. #1736×C₁₃₉	C₂	semidirect
12. #525×C₁₃₉	C₄	semidirect
26. C₂×#103×C₁₃₉	C₂²	semidirect
27. C₂×#102×C₁₃₉	C₂²	semidirect
30. #340×C₁₃₉	C₂²	semidirect
56. C₂²⋊Q₈×C₁₃₉	C₂×C₄	semidirect
58. #121×C₁₃₉	C₂×C₄	semidirect
68. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
229. #20910	C₁₃₉	direct (N × H)
230. C₁₃₉	#20910	direct (N × H)
232. C₂²×#117	C₂×C₁₃₉	semidirect
233. C₂×#417	C₂×C₁₃₉	semidirect
234. C₂×#407	C₂×C₁₃₉	semidirect
235. #1875	C₂×C₁₃₉	semidirect
236. #1873	C₂×C₁₃₉	semidirect
237. #1736	C₂×C₁₃₉	semidirect
242. #525	C₄×C₁₃₉	semidirect
256. C₂×#103	C₂²×C₁₃₉	semidirect
257. C₂×#102	C₂²×C₁₃₉	semidirect
260. #340	C₂²×C₁₃₉	semidirect
286. C₂²⋊Q₈	C₂×C₄×C₁₃₉	semidirect
288. #121	C₂×C₄×C₁₃₉	semidirect
298. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₃₉	2
C₂²×#117×C₁₃₉	2
C₂×#417×C₁₃₉	2
C₂×#407×C₁₃₉	2
#1875×C₁₃₉	2
#1873×C₁₃₉	2
#1736×C₁₃₉	2
#20910	139

Subgroups — C139×#20910 #48015506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20910 #48015506