Subgroups — C₁₃₉×#23609 #48018205

Order 35584.

1138 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#427×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#416×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#416×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2068×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2067×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2066×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2065×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#1735×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	#427×C₁₃₉	—	2	4	no	—
20	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₁₃₉	—	2	4	no	—
23	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
25	#416×C₁₃₉	—	2	4	no	—
26	#416×C₁₃₉	—	2	4	no	—
27	C₂×#103×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#103×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
33	#391×C₁₃₉	C₂²	1	2	yes	—
34	#390×C₁₃₉	C₂²	1	2	yes	—
35	#389×C₁₃₉	C₂²	1	2	yes	—
36	#389×C₁₃₉	C₂²	1	2	yes	—
37	#386×C₁₃₉	—	2	1	no	—
38	#386×C₁₃₉	—	2	1	no	—
39	#385×C₁₃₉	—	2	1	no	—
40	#385×C₁₃₉	—	2	1	no	—
41	C₄×C₄⋊C₄×C₁₃₉	—	2	2	no	—
42	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
43	#340×C₁₃₉	C₂²	1	2	yes	—
44	#340×C₁₃₉	C₂²	1	2	yes	—
45	C₂×#41×C₁₃₉	—	2	2	no	—
46	C₂×#41×C₁₃₉	—	2	2	no	—
47	C₂×#41×C₁₃₉	—	2	2	no	—
48	C₂×#41×C₁₃₉	—	2	2	no	—
49	C₂×#41×C₁₃₉	—	2	2	no	—
50	C₂×#41×C₁₃₉	Q₈	1	4	yes	—
51	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃₉	—	2	1	no	—
53	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃₉	—	2	1	no	—
55	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₉	—	2	2	no	—
59	C₂²×C₈×C₁₃₉	—	2	2	no	—
60	C₂²×C₈×C₁₃₉	—	2	2	no	—
61	C₂²×C₈×C₁₃₉	—	2	2	no	—
62	C₂²×C₈×C₁₃₉	—	2	2	no	—
63	C₂²×C₈×C₁₃₉	D₄	1	4	yes	—
64	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
67	#117×C₁₃₉	—	2	2	no	—
68	#117×C₁₃₉	—	2	2	no	—
69	#117×C₁₃₉	—	2	2	no	—
70	#117×C₁₃₉	—	2	2	no	—
71	#117×C₁₃₉	—	2	2	no	—
72	#117×C₁₃₉	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
84	C₂×C₄²×C₁₃₉	—	2	2	no	—
85	C₂×C₄²×C₁₃₉	—	2	1	no	—
86	C₂×C₄²×C₁₃₉	—	2	2	no	—
87	C₂×C₄²×C₁₃₉	—	2	1	no	—
88	C₂×C₄²×C₁₃₉	—	2	1	no	—
89	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
90	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
91	#107×C₁₃₉	—	2	4	no	—
92	#106×C₁₃₉	—	2	4	no	—
93	C₄⋊C₈×C₁₃₉	—	2	4	no	—
94	C₄⋊C₈×C₁₃₉	—	2	4	no	—
95	#103×C₁₃₉	—	2	2	no	—
96	#103×C₁₃₉	—	2	2	no	—
97	#103×C₁₃₉	—	2	4	no	—
98	#102×C₁₃₉	—	2	2	no	—
99	#102×C₁₃₉	—	2	2	no	—
100	#102×C₁₃₉	—	2	4	no	—
101	#95×C₁₃₉	—	2	2	no	—
102	#95×C₁₃₉	—	2	2	no	—
103	#95×C₁₃₉	—	2	2	no	—
104	#95×C₁₃₉	—	2	2	no	—
105	C₂⁴×C₁₃₉	—	2	1	no	—
106	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	#41×C₁₃₉	—	2	8	no	—
108	#41×C₁₃₉	—	2	8	no	—
109	#41×C₁₃₉	—	4	4	no	—
110	#41×C₁₃₉	—	4	4	no	—
111	C₂×Q₈×C₁₃₉	—	2	1	no	—
112	C₂×Q₈×C₁₃₉	—	2	1	no	—
113	C₂×Q₈×C₁₃₉	—	2	1	no	—
114	C₂×Q₈×C₁₃₉	—	2	1	no	—
115	C₂×Q₈×C₁₃₉	—	2	1	no	—
116	C₂×Q₈×C₁₃₉	C₂×Q₈	1	2	yes	—
117	C₂×D₄×C₁₃₉	—	2	4	no	—
118	C₂×D₄×C₁₃₉	—	2	1	no	—
119	C₂×D₄×C₁₃₉	—	2	1	no	—
120	C₂×D₄×C₁₃₉	—	2	1	no	—
121	C₂×D₄×C₁₃₉	—	2	1	no	—
122	C₂×D₄×C₁₃₉	—	2	1	no	—
123	C₂×D₄×C₁₃₉	—	4	2	no	—
124	C₂×D₄×C₁₃₉	—	4	2	no	—
125	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	4	no	—
128	C₂²×C₄×C₁₃₉	—	2	2	no	—
129	C₂²×C₄×C₁₃₉	—	2	1	no	—
130	C₂²×C₄×C₁₃₉	—	2	2	no	—
131	C₂²×C₄×C₁₃₉	—	2	4	no	—
132	C₂²×C₄×C₁₃₉	—	2	2	no	—
133	C₂²×C₄×C₁₃₉	—	2	1	no	—
134	C₂²×C₄×C₁₃₉	—	2	1	no	—
135	C₂²×C₄×C₁₃₉	—	4	2	no	—
136	C₂²×C₄×C₁₃₉	—	4	2	no	—
137	C₂²×C₄×C₁₃₉	—	4	2	no	—
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
145	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
146	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₃₉	—	2	8	no	—
149	C₂×C₈×C₁₃₉	—	2	1	no	—
150	C₂×C₈×C₁₃₉	—	2	1	no	—
151	C₂×C₈×C₁₃₉	—	2	1	no	—
152	C₂×C₈×C₁₃₉	—	2	1	no	—
153	C₂×C₈×C₁₃₉	—	2	2	no	—
154	C₂×C₈×C₁₃₉	—	2	2	no	—
155	C₂×C₈×C₁₃₉	—	2	2	no	—
156	C₂×C₈×C₁₃₉	—	4	4	no	—
157	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₁₃₉	—	2	2	no	—
160	C₄⋊C₄×C₁₃₉	—	2	1	no	—
161	C₄⋊C₄×C₁₃₉	—	2	1	no	—
162	C₄⋊C₄×C₁₃₉	—	2	2	no	—
163	C₄⋊C₄×C₁₃₉	—	2	1	no	—
164	C₄⋊C₄×C₁₃₉	—	2	1	no	—
165	C₄⋊C₄×C₁₃₉	—	2	2	no	—
166	C₄⋊C₄×C₁₃₉	—	4	4	no	—
167	C₄⋊C₄×C₁₃₉	—	4	4	no	—
168	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
169	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
171	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
172	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
173	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
174	C₄²×C₁₃₉	—	2	4	no	—
175	C₄²×C₁₃₉	—	2	4	no	—
176	C₄²×C₁₃₉	—	2	2	no	—
177	C₄²×C₁₃₉	—	2	2	no	—
178	C₄²×C₁₃₉	—	4	2	no	—
179	C₄²×C₁₃₉	—	4	2	no	—
180	C₂³×C₁₃₉	—	2	2	no	—
181	C₂³×C₁₃₉	—	2	2	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	4	1	no	—
184	C₂³×C₁₃₉	—	4	1	no	—
185	C₂³×C₁₃₉	—	4	2	no	—
186	C₂³×C₁₃₉	—	4	2	no	—
187	C₂³×C₁₃₉	#121	1	2	yes	—
188	C₂³×C₁₃₉	#121	1	2	yes	—
189	C₂³×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
190	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃₉	—	2	2	no	—
192	Q₈×C₁₃₉	—	2	2	no	—
193	Q₈×C₁₃₉	—	4	1	no	—
194	Q₈×C₁₃₉	—	4	1	no	—
195	D₄×C₁₃₉	—	2	2	no	—
196	D₄×C₁₃₉	—	2	2	no	—
197	D₄×C₁₃₉	—	4	8	no	—
198	D₄×C₁₃₉	—	4	1	no	—
199	D₄×C₁₃₉	—	4	1	no	—
200	C₂×C₄×C₁₃₉	—	2	8	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	2	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	4	4	no	—
209	C₂×C₄×C₁₃₉	—	4	1	no	—
210	C₂×C₄×C₁₃₉	—	4	1	no	—
211	C₂×C₄×C₁₃₉	—	4	2	no	—
212	C₂×C₄×C₁₃₉	—	4	2	no	—
213	C₂×C₄×C₁₃₉	—	4	8	no	—
214	C₂×C₄×C₁₃₉	—	4	2	no	—
215	C₂×C₄×C₁₃₉	—	4	1	no	—
216	C₂×C₄×C₁₃₉	—	4	1	no	—
217	C₂×C₄×C₁₃₉	—	4	2	no	—
218	C₂×C₄×C₁₃₉	—	4	2	no	—
219	C₂×C₄×C₁₃₉	—	4	2	no	—
220	C₂×C₄×C₁₃₉	—	4	2	no	—
221	C₂×C₄×C₁₃₉	#121	1	4	yes	—
222	C₂×C₄×C₁₃₉	#121	1	2	yes	—
223	C₂×C₄×C₁₃₉	#121	1	2	yes	—
224	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
225	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
226	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
227	C₂×C₄×C₁₃₉	#126	1	4	yes	—
228	C₂×C₄×C₁₃₉	#135	1	4	yes	—
229	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
235	C₈×C₁₃₉	—	2	2	no	—
236	C₈×C₁₃₉	—	2	2	no	—
237	C₈×C₁₃₉	—	4	2	no	—
238	C₂²×C₁₃₉	—	2	4	no	—
239	C₂²×C₁₃₉	—	2	4	no	—
240	C₂²×C₁₃₉	—	2	2	no	—
241	C₂²×C₁₃₉	—	2	2	no	—
242	C₂²×C₁₃₉	—	4	4	no	—
243	C₂²×C₁₃₉	—	4	2	no	—
244	C₂²×C₁₃₉	—	8	2	no	—
245	C₂²×C₁₃₉	—	8	1	no	—
246	C₂²×C₁₃₉	—	8	1	no	—
247	C₂²×C₁₃₉	#396	1	4	yes	—
248	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
249	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
250	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂²×C₁₃₉	C₂×#135	1	2	yes	—
252	C₂²×C₁₃₉	#575	1	2	yes	—
253	C₄×C₁₃₉	—	2	4	no	—
254	C₄×C₁₃₉	—	4	2	no	—
255	C₄×C₁₃₉	—	4	4	no	—
256	C₄×C₁₃₉	—	4	2	no	—
257	C₄×C₁₃₉	—	8	2	no	—
258	C₄×C₁₃₉	—	8	1	no	—
259	C₄×C₁₃₉	—	8	1	no	—
260	C₄×C₁₃₉	#396	1	4	yes	—
261	C₄×C₁₃₉	C₂×#121	1	1	yes	characteristic
262	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
263	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₄×C₁₃₉	C₂×#126	1	1	yes	characteristic
265	C₂×C₁₃₉	—	2	4	no	—
266	C₂×C₁₃₉	—	8	2	no	—
267	C₂×C₁₃₉	C₂×#396	1	1	yes	characteristic
268	C₂×C₁₃₉	#3035	1	2	yes	—
269	C₂×C₁₃₉	#3050	1	1	yes	characteristic
270	C₂×C₁₃₉	#3054	1	1	yes	characteristic
271	C₂×C₁₃₉	#3076	1	2	yes	—
272	#23609	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₁₃₉	#23609	1	1	yes	characteristic, direct product factor, Sylow
274	C₂×#427	C₂×C₁₃₉	1	1	yes	characteristic, complemented
275	C₂²×C₄⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	C₂×#416	C₂×C₁₃₉	1	1	yes	characteristic
277	C₂×#416	C₂×C₁₃₉	1	1	yes	characteristic
278	#2297	C₂×C₁₃₉	1	1	yes	characteristic
279	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
280	#2068	C₂×C₁₃₉	1	2	yes	complemented
281	#2067	C₂×C₁₃₉	1	2	yes	complemented
282	#2066	C₂×C₁₃₉	1	2	yes	complemented
283	#2065	C₂×C₁₃₉	1	2	yes	complemented
284	#1735	C₂×C₁₃₉	1	1	yes	characteristic, complemented
285	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
289	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
291	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
292	#427	—	2	4	no	—
293	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
294	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
295	C₂×C₄⋊C₈	—	2	4	no	—
296	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
297	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
298	#416	—	2	4	no	—
299	#416	—	2	4	no	—
300	C₂×#103	C₂²×C₁₃₉	1	1	yes	characteristic
301	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
302	C₂×#103	C₂²×C₁₃₉	1	1	yes	characteristic
303	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
304	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
305	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
306	#391	C₂²×C₁₃₉	1	2	yes	—
307	#390	C₂²×C₁₃₉	1	2	yes	—
308	#389	C₂²×C₁₃₉	1	2	yes	—
309	#389	C₂²×C₁₃₉	1	2	yes	—
310	#386	—	2	1	no	—
311	#386	—	2	1	no	—
312	#385	—	2	1	no	—
313	#385	—	2	1	no	—
314	C₄×C₄⋊C₄	—	2	2	no	—
315	C₄×C₂²⋊C₄	—	2	2	no	—
316	#340	C₂²×C₁₃₉	1	2	yes	—
317	#340	C₂²×C₁₃₉	1	2	yes	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	Q₈×C₁₃₉	1	4	yes	—
324	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
329	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	2	2	no	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	D₄×C₁₃₉	1	4	yes	—
337	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
338	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
340	#117	—	2	2	no	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	D₄×C₁₃₉	1	4	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
363	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
364	#107	—	2	4	no	—
365	#106	—	2	4	no	—
366	C₄⋊C₈	—	2	4	no	—
367	C₄⋊C₈	—	2	4	no	—
368	#103	—	2	2	no	—
369	#103	—	2	2	no	—
370	#103	—	2	4	no	—
371	#102	—	2	2	no	—
372	#102	—	2	2	no	—
373	#102	—	2	4	no	—
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	—	2	2	no	—
377	#95	—	2	2	no	—
378	C₂⁴	—	2	1	no	—
379	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
380	#41	—	2	8	no	—
381	#41	—	2	8	no	—
382	#41	—	4	4	no	—
383	#41	—	4	4	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	C₂×Q₈×C₁₃₉	1	2	yes	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
416	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
417	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
418	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
419	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
421	C₂×C₈	—	2	8	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	4	4	no	—
430	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
431	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	4	2	no	—
452	C₄²	—	4	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	#121×C₁₃₉	1	2	yes	—
461	C₂³	#121×C₁₃₉	1	2	yes	—
462	C₂³	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
463	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	#121×C₁₃₉	1	2	yes	—
495	C₂×C₄	#121×C₁₃₉	1	2	yes	—
496	C₂×C₄	#121×C₁₃₉	1	4	yes	—
497	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
498	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
499	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
500	C₂×C₄	#126×C₁₃₉	1	4	yes	—
501	C₂×C₄	#135×C₁₃₉	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	4	2	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	#396×C₁₃₉	1	4	yes	—
521	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
522	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
523	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
524	C₂²	C₂×#135×C₁₃₉	1	2	yes	—
525	C₂²	#575×C₁₃₉	1	2	yes	—
526	C₄	—	2	4	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	8	2	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	1	no	—
533	C₄	#396×C₁₃₉	1	4	yes	—
534	C₄	C₂×#121×C₁₃₉	1	1	yes	characteristic
535	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
536	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
537	C₄	C₂×#126×C₁₃₉	1	1	yes	characteristic
538	C₂	—	2	4	no	—
539	C₂	—	8	2	no	—
540	C₂	C₂×#396×C₁₃₉	1	1	yes	characteristic
541	C₂	#3035×C₁₃₉	1	2	yes	—
542	C₂	#3050×C₁₃₉	1	1	yes	characteristic
543	C₂	#3054×C₁₃₉	1	1	yes	characteristic
544	C₂	#3076×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂³×C₁₃₉	C₂²×D₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#427×C₁₃₉	C₂	semidirect
2. C₂²×C₄⋊C₈×C₁₃₉	C₂	semidirect
6. #2296×C₁₃₉	C₂	semidirect
7. #2068×C₁₃₉	C₂	semidirect
8. #2067×C₁₃₉	C₂	semidirect
9. #2066×C₁₃₉	C₂	semidirect
10. #2065×C₁₃₉	C₂	semidirect
11. #1735×C₁₃₉	C₂	semidirect
272. #23609	C₁₃₉	direct (N × H)
273. C₁₃₉	#23609	direct (N × H)
274. C₂×#427	C₂×C₁₃₉	semidirect
275. C₂²×C₄⋊C₈	C₂×C₁₃₉	semidirect
279. #2296	C₂×C₁₃₉	semidirect
280. #2068	C₂×C₁₃₉	semidirect
281. #2067	C₂×C₁₃₉	semidirect
282. #2066	C₂×C₁₃₉	semidirect
283. #2065	C₂×C₁₃₉	semidirect
284. #1735	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×#427×C₁₃₉	2
C₂²×C₄⋊C₈×C₁₃₉	2
C₂×#416×C₁₃₉	2
#2297×C₁₃₉	2
#2296×C₁₃₉	2
#2068×C₁₃₉	2
#2067×C₁₃₉	2
#2066×C₁₃₉	2
#2065×C₁₃₉	2
#1735×C₁₃₉	2
#23609	139

Subgroups — C139×#23609 #48018205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#23609 #48018205