Subgroups — C₁₃₉×#32966 #48027562

Order 35584.

1414 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#478×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1864×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1862×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1854×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1802×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1798×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1786×C₁₃₉	C₂	1	2	yes	maximal
10	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
12	#518×C₁₃₉	—	2	8	no	—
13	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
19	#478×C₁₃₉	—	2	8	no	—
20	C₂×#107×C₁₃₉	C₂²	1	2	yes	complemented
21	C₂×#106×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
28	#398×C₁₃₉	—	2	2	no	—
29	#396×C₁₃₉	—	2	2	no	—
30	#389×C₁₃₉	C₂²	1	2	yes	complemented
31	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
32	#380×C₁₃₉	C₂²	1	2	yes	—
33	#340×C₁₃₉	C₂²	1	2	yes	complemented
34	#340×C₁₃₉	C₂²	1	2	yes	complemented
35	#336×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	#336×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
37	C₂⁵×C₁₃₉	—	2	1	no	—
38	C₂²×D₄×C₁₃₉	—	2	4	no	—
39	C₂²×D₄×C₁₃₉	—	2	4	no	—
40	C₂²×D₄×C₁₃₉	—	2	1	no	—
41	C₂²×D₄×C₁₃₉	—	2	2	no	—
42	C₂²×D₄×C₁₃₉	Q₈	1	4	yes	—
43	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₉	—	2	2	no	—
45	C₂³×C₄×C₁₃₉	—	2	2	no	—
46	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
49	#125×C₁₃₉	—	2	4	no	—
50	C₄×D₄×C₁₃₉	—	2	16	no	—
51	C₄×D₄×C₁₃₉	—	2	4	no	—
52	C₄×D₄×C₁₃₉	—	2	4	no	—
53	C₄×D₄×C₁₃₉	—	2	4	no	—
54	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
55	#117×C₁₃₉	—	2	4	no	—
56	#117×C₁₃₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃₉	—	2	1	no	—
71	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
73	#107×C₁₃₉	—	2	4	no	—
74	#106×C₁₃₉	—	2	4	no	—
75	C₄⋊C₈×C₁₃₉	—	2	4	no	—
76	#102×C₁₃₉	—	2	4	no	—
77	#102×C₁₃₉	—	2	4	no	—
78	#102×C₁₃₉	—	2	4	no	—
79	#102×C₁₃₉	—	2	4	no	—
80	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
81	#95×C₁₃₉	—	2	2	no	—
82	#95×C₁₃₉	—	2	2	no	—
83	C₂⁴×C₁₃₉	—	2	4	no	—
84	C₂⁴×C₁₃₉	—	2	4	no	—
85	C₂⁴×C₁₃₉	—	2	2	no	—
86	C₂⁴×C₁₃₉	—	2	4	no	—
87	C₂⁴×C₁₃₉	—	8	2	no	—
88	C₂⁴×C₁₃₉	—	8	2	no	—
89	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₃₉	—	2	4	no	—
91	C₂×D₄×C₁₃₉	—	2	4	no	—
92	C₂×D₄×C₁₃₉	—	2	16	no	—
93	C₂×D₄×C₁₃₉	—	2	16	no	—
94	C₂×D₄×C₁₃₉	—	2	4	no	—
95	C₂×D₄×C₁₃₉	—	2	2	no	—
96	C₂×D₄×C₁₃₉	—	2	2	no	—
97	C₂×D₄×C₁₃₉	—	2	2	no	—
98	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
100	C₂×D₄×C₁₃₉	#41	1	4	yes	—
101	C₂²×C₄×C₁₃₉	—	2	2	no	—
102	C₂²×C₄×C₁₃₉	—	2	2	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	8	no	—
105	C₂²×C₄×C₁₃₉	—	2	8	no	—
106	C₂²×C₄×C₁₃₉	—	2	2	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	8	2	no	—
109	C₂²×C₄×C₁₃₉	—	8	2	no	—
110	C₂²×C₄×C₁₃₉	—	8	2	no	—
111	C₂²×C₄×C₁₃₉	—	8	2	no	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₁₃₉	—	2	2	no	—
119	C₂×C₈×C₁₃₉	—	2	2	no	—
120	C₂×C₈×C₁₃₉	—	2	2	no	—
121	C₂×C₈×C₁₃₉	—	2	2	no	—
122	C₂×C₈×C₁₃₉	—	2	2	no	—
123	C₂×C₈×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₄⋊C₄×C₁₃₉	—	2	2	no	—
126	C₄⋊C₄×C₁₃₉	—	2	2	no	—
127	C₄⋊C₄×C₁₃₉	—	2	2	no	—
128	C₄⋊C₄×C₁₃₉	—	2	2	no	—
129	C₄⋊C₄×C₁₃₉	—	2	2	no	—
130	C₄⋊C₄×C₁₃₉	—	4	4	no	—
131	C₄⋊C₄×C₁₃₉	—	8	2	no	—
132	C₄⋊C₄×C₁₃₉	—	8	2	no	—
133	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
134	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
136	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
138	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
139	C₄²×C₁₃₉	—	2	4	no	—
140	C₄²×C₁₃₉	—	2	2	no	—
141	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
142	C₂³×C₁₃₉	—	2	16	no	—
143	C₂³×C₁₃₉	—	2	1	no	—
144	C₂³×C₁₃₉	—	2	4	no	—
145	C₂³×C₁₃₉	—	2	4	no	—
146	C₂³×C₁₃₉	—	2	1	no	—
147	C₂³×C₁₃₉	—	2	4	no	—
148	C₂³×C₁₃₉	—	2	2	no	—
149	C₂³×C₁₃₉	—	2	2	no	—
150	C₂³×C₁₃₉	—	4	2	no	—
151	C₂³×C₁₃₉	—	4	2	no	—
152	C₂³×C₁₃₉	—	4	2	no	—
153	C₂³×C₁₃₉	—	4	2	no	—
154	C₂³×C₁₃₉	—	8	8	no	—
155	C₂³×C₁₃₉	—	8	4	no	—
156	C₂³×C₁₃₉	—	8	4	no	—
157	C₂³×C₁₃₉	—	8	8	no	—
158	C₂³×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
159	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₁₃₉	—	2	16	no	—
161	D₄×C₁₃₉	—	2	4	no	—
162	D₄×C₁₃₉	—	2	4	no	—
163	D₄×C₁₃₉	—	2	4	no	—
164	D₄×C₁₃₉	C₂²⋊Q₈	1	8	yes	—
165	C₂×C₄×C₁₃₉	—	2	1	no	—
166	C₂×C₄×C₁₃₉	—	2	1	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	4	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	—	2	2	no	—
172	C₂×C₄×C₁₃₉	—	2	4	no	—
173	C₂×C₄×C₁₃₉	—	2	2	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	4	2	no	—
176	C₂×C₄×C₁₃₉	—	4	2	no	—
177	C₂×C₄×C₁₃₉	—	4	2	no	—
178	C₂×C₄×C₁₃₉	—	4	2	no	—
179	C₂×C₄×C₁₃₉	—	4	2	no	—
180	C₂×C₄×C₁₃₉	—	4	2	no	—
181	C₂×C₄×C₁₃₉	—	4	2	no	—
182	C₂×C₄×C₁₃₉	—	4	2	no	—
183	C₂×C₄×C₁₃₉	—	8	8	no	—
184	C₂×C₄×C₁₃₉	—	8	8	no	—
185	C₂×C₄×C₁₃₉	#120	1	4	yes	—
186	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃₉	—	4	2	no	—
192	C₈×C₁₃₉	—	4	2	no	—
193	C₂²×C₁₃₉	—	2	4	no	—
194	C₂²×C₁₃₉	—	2	2	no	—
195	C₂²×C₁₃₉	—	2	8	no	—
196	C₂²×C₁₃₉	—	4	4	no	—
197	C₂²×C₁₃₉	—	4	4	no	—
198	C₂²×C₁₃₉	—	4	1	no	—
199	C₂²×C₁₃₉	—	4	4	no	—
200	C₂²×C₁₃₉	—	4	1	no	—
201	C₂²×C₁₃₉	—	4	4	no	—
202	C₂²×C₁₃₉	—	4	4	no	—
203	C₂²×C₁₃₉	—	4	4	no	—
204	C₂²×C₁₃₉	—	4	2	no	—
205	C₂²×C₁₃₉	—	8	16	no	—
206	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
207	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
208	C₂²×C₁₃₉	#525	1	1	yes	characteristic
209	C₂²×C₁₃₉	#576	1	2	yes	—
210	C₂²×C₁₃₉	#577	1	2	yes	—
211	C₄×C₁₃₉	—	2	2	no	—
212	C₄×C₁₃₉	—	2	4	no	—
213	C₄×C₁₃₉	—	4	2	no	—
214	C₄×C₁₃₉	—	4	4	no	—
215	C₄×C₁₃₉	—	8	2	no	—
216	C₄×C₁₃₉	—	8	2	no	—
217	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	2	yes	—
218	C₄×C₁₃₉	#525	1	2	yes	—
219	C₂×C₁₃₉	—	4	2	no	—
220	C₂×C₁₃₉	—	4	8	no	—
221	C₂×C₁₃₉	#2848	1	1	yes	characteristic
222	C₂×C₁₃₉	#3012	1	2	yes	—
223	C₂×C₁₃₉	#3081	1	2	yes	—
224	C₂×C₁₃₉	#3122	1	1	yes	characteristic
225	C₂×C₁₃₉	#3123	1	1	yes	characteristic
226	#32966	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₃₉	#32966	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic
229	C₂×#478	C₂×C₁₃₉	1	2	yes	complemented
230	#2629	C₂×C₁₃₉	1	1	yes	characteristic, complemented
231	#1864	C₂×C₁₃₉	1	2	yes	complemented
232	#1862	C₂×C₁₃₉	1	2	yes	complemented
233	#1854	C₂×C₁₃₉	1	2	yes	complemented
234	#1802	C₂×C₁₃₉	1	2	yes	complemented
235	#1798	C₂×C₁₃₉	1	1	yes	characteristic, complemented
236	#1786	C₂×C₁₃₉	1	2	yes	—
237	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
239	#518	—	2	8	no	—
240	C₂×C₄×D₄	—	2	2	no	—
241	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
243	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	—	2	2	no	—
246	#478	—	2	8	no	—
247	C₂×#107	C₂²×C₁₃₉	1	2	yes	complemented
248	C₂×#106	C₂²×C₁₃₉	1	2	yes	complemented
249	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	complemented
250	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
251	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
252	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
253	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
255	#398	—	2	2	no	—
256	#396	—	2	2	no	—
257	#389	C₂²×C₁₃₉	1	2	yes	complemented
258	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
259	#380	C₂²×C₁₃₉	1	2	yes	—
260	#340	C₂²×C₁₃₉	1	2	yes	complemented
261	#340	C₂²×C₁₃₉	1	2	yes	complemented
262	#336	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
263	#336	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
264	C₂⁵	—	2	1	no	—
265	C₂²×D₄	—	2	4	no	—
266	C₂²×D₄	—	2	4	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	Q₈×C₁₃₉	1	4	yes	—
270	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
276	#125	—	2	4	no	—
277	C₄×D₄	—	2	16	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
282	#117	—	2	4	no	—
283	#117	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	16	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
300	#107	—	2	4	no	—
301	#106	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	4	no	—
307	C₂²⋊C₈	—	2	4	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	8	2	no	—
315	C₂⁴	—	8	2	no	—
316	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
326	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
327	C₂×D₄	#41×C₁₃₉	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	8	2	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
343	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	—	8	2	no	—
360	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
369	C₂³	—	2	16	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	8	8	no	—
382	C₂³	—	8	4	no	—
383	C₂³	—	8	4	no	—
384	C₂³	—	8	8	no	—
385	C₂³	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
386	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
387	D₄	—	2	16	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	C₂²⋊Q₈×C₁₃₉	1	8	yes	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	8	no	—
411	C₂×C₄	—	8	8	no	—
412	C₂×C₄	#120×C₁₃₉	1	4	yes	—
413	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
415	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
417	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	16	no	—
433	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
434	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
435	C₂²	#525×C₁₃₉	1	1	yes	characteristic
436	C₂²	#576×C₁₃₉	1	2	yes	—
437	C₂²	#577×C₁₃₉	1	2	yes	—
438	C₄	—	2	2	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	2	no	—
444	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	2	yes	—
445	C₄	#525×C₁₃₉	1	2	yes	—
446	C₂	—	4	2	no	—
447	C₂	—	4	8	no	—
448	C₂	#2848×C₁₃₉	1	1	yes	characteristic
449	C₂	#3012×C₁₃₉	1	2	yes	—
450	C₂	#3081×C₁₃₉	1	2	yes	—
451	C₂	#3122×C₁₃₉	1	1	yes	characteristic
452	C₂	#3123×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#478×C₁₃₉	C₂	semidirect
3. #2629×C₁₃₉	C₂	semidirect
4. #1864×C₁₃₉	C₂	semidirect
5. #1862×C₁₃₉	C₂	semidirect
6. #1854×C₁₃₉	C₂	semidirect
7. #1802×C₁₃₉	C₂	semidirect
8. #1798×C₁₃₉	C₂	semidirect
11. C₂×#125×C₁₃₉	C₂²	semidirect
20. C₂×#107×C₁₃₉	C₂²	semidirect
21. C₂×#106×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
30. #389×C₁₃₉	C₂²	semidirect
31. #384×C₁₃₉	C₂²	semidirect
33. #340×C₁₃₉	C₂²	semidirect
34. #340×C₁₃₉	C₂²	semidirect
35. #336×C₁₃₉	C₂²	semidirect
36. #336×C₁₃₉	C₂²	semidirect
226. #32966	C₁₃₉	direct (N × H)
227. C₁₃₉	#32966	direct (N × H)
229. C₂×#478	C₂×C₁₃₉	semidirect
230. #2629	C₂×C₁₃₉	semidirect
231. #1864	C₂×C₁₃₉	semidirect
232. #1862	C₂×C₁₃₉	semidirect
233. #1854	C₂×C₁₃₉	semidirect
234. #1802	C₂×C₁₃₉	semidirect
235. #1798	C₂×C₁₃₉	semidirect
238. C₂×#125	C₂²×C₁₃₉	semidirect
247. C₂×#107	C₂²×C₁₃₉	semidirect
248. C₂×#106	C₂²×C₁₃₉	semidirect
249. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
257. #389	C₂²×C₁₃₉	semidirect
258. #384	C₂²×C₁₃₉	semidirect
260. #340	C₂²×C₁₃₉	semidirect
261. #340	C₂²×C₁₃₉	semidirect
262. #336	C₂²×C₁₃₉	semidirect
263. #336	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518×C₁₃₉	2
C₂×#478×C₁₃₉	2
#2629×C₁₃₉	2
#1864×C₁₃₉	2
#1862×C₁₃₉	2
#1854×C₁₃₉	2
#1802×C₁₃₉	2
#1798×C₁₃₉	2
#1786×C₁₃₉	2
#32966	139

Subgroups — C139×#32966 #48027562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#32966 #48027562