Subgroups — C₁₃₉×#25844 #48020440

Order 35584.

1224 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#478×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2058×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2057×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1987×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1985×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1864×C₁₃₉	C₂	1	2	yes	maximal
10	#1862×C₁₃₉	C₂	1	2	yes	maximal
11	#1762×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃₉	—	2	1	no	—
13	D₄×Q₈×C₁₃₉	—	2	4	no	—
14	D₄×Q₈×C₁₃₉	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	#501×C₁₃₉	—	2	4	no	—
24	#478×C₁₃₉	—	2	4	no	—
25	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#106×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
34	#398×C₁₃₉	—	2	1	no	—
35	#395×C₁₃₉	—	2	1	no	—
36	#389×C₁₃₉	—	2	2	no	—
37	#389×C₁₃₉	C₂²	1	2	yes	—
38	#389×C₁₃₉	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	#340×C₁₃₉	C₂²	1	2	yes	—
41	#340×C₁₃₉	C₂²	1	2	yes	—
42	#340×C₁₃₉	C₂²	1	2	yes	—
43	#336×C₁₃₉	C₂²	1	2	yes	—
44	#336×C₁₃₉	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₉	—	2	8	no	—
46	C₂²×Q₈×C₁₃₉	—	2	1	no	—
47	C₂²×Q₈×C₁₃₉	—	2	2	no	—
48	C₂²×Q₈×C₁₃₉	—	4	8	no	—
49	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃₉	—	2	2	no	—
52	C₂³×C₄×C₁₃₉	—	2	1	no	—
53	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
57	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
58	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
59	C₄⋊Q₈×C₁₃₉	D₄	1	4	yes	—
60	#125×C₁₃₉	—	2	2	no	—
61	#125×C₁₃₉	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
63	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
64	C₄×Q₈×C₁₃₉	—	2	2	no	—
65	C₄×Q₈×C₁₃₉	—	2	2	no	—
66	C₄×D₄×C₁₃₉	—	2	4	no	—
67	C₄×D₄×C₁₃₉	—	2	4	no	—
68	C₄×D₄×C₁₃₉	—	2	2	no	—
69	C₄×D₄×C₁₃₉	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
85	C₂×C₄²×C₁₃₉	—	2	1	no	—
86	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
88	#107×C₁₃₉	—	2	2	no	—
89	#107×C₁₃₉	—	2	4	no	—
90	#106×C₁₃₉	—	2	2	no	—
91	#106×C₁₃₉	—	2	4	no	—
92	C₄⋊C₈×C₁₃₉	—	2	2	no	—
93	#102×C₁₃₉	—	2	2	no	—
94	#102×C₁₃₉	—	2	2	no	—
95	#102×C₁₃₉	Q₈	1	8	yes	complemented
96	#97×C₁₃₉	—	2	2	no	—
97	#95×C₁₃₉	—	2	1	no	—
98	#95×C₁₃₉	—	2	2	no	—
99	#95×C₁₃₉	—	2	2	no	—
100	C₂⁴×C₁₃₉	—	2	1	no	—
101	C₂×Q₈×C₁₃₉	—	2	8	no	—
102	C₂×Q₈×C₁₃₉	—	2	2	no	—
103	C₂×Q₈×C₁₃₉	—	2	4	no	—
104	C₂×Q₈×C₁₃₉	—	2	4	no	—
105	C₂×Q₈×C₁₃₉	—	4	4	no	—
106	C₂×Q₈×C₁₃₉	—	4	4	no	—
107	C₂×Q₈×C₁₃₉	—	4	32	no	—
108	C₂×Q₈×C₁₃₉	—	4	4	no	—
109	C₂×D₄×C₁₃₉	—	2	1	no	—
110	C₂×D₄×C₁₃₉	—	2	2	no	—
111	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₁₃₉	—	2	8	no	—
114	C₂²×C₄×C₁₃₉	—	2	2	no	—
115	C₂²×C₄×C₁₃₉	—	2	2	no	—
116	C₂²×C₄×C₁₃₉	—	2	1	no	—
117	C₂²×C₄×C₁₃₉	—	2	4	no	—
118	C₂²×C₄×C₁₃₉	—	2	1	no	—
119	C₂²×C₄×C₁₃₉	—	2	1	no	—
120	C₂²×C₄×C₁₃₉	—	4	4	no	—
121	C₂²×C₄×C₁₃₉	—	4	4	no	—
122	C₂²×C₄×C₁₃₉	—	4	4	no	—
123	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₃₉	—	2	2	no	—
129	C₂×C₈×C₁₃₉	—	2	2	no	—
130	C₂×C₈×C₁₃₉	—	2	1	no	—
131	C₂×C₈×C₁₃₉	—	2	1	no	—
132	C₂×C₈×C₁₃₉	—	2	2	no	—
133	C₂×C₈×C₁₃₉	—	2	2	no	—
134	C₂×C₈×C₁₃₉	C₂×Q₈	1	4	yes	complemented
135	C₄⋊C₄×C₁₃₉	—	2	8	no	—
136	C₄⋊C₄×C₁₃₉	—	2	4	no	—
137	C₄⋊C₄×C₁₃₉	—	2	4	no	—
138	C₄⋊C₄×C₁₃₉	—	2	2	no	—
139	C₄⋊C₄×C₁₃₉	—	2	2	no	—
140	C₄⋊C₄×C₁₃₉	—	2	1	no	—
141	C₄⋊C₄×C₁₃₉	—	2	2	no	—
142	C₄⋊C₄×C₁₃₉	—	2	1	no	—
143	C₄⋊C₄×C₁₃₉	—	2	1	no	—
144	C₄⋊C₄×C₁₃₉	—	2	1	no	—
145	C₄⋊C₄×C₁₃₉	—	2	1	no	—
146	C₄⋊C₄×C₁₃₉	—	4	2	no	—
147	C₄⋊C₄×C₁₃₉	—	4	2	no	—
148	C₄⋊C₄×C₁₃₉	—	4	4	no	—
149	C₄⋊C₄×C₁₃₉	—	8	2	no	—
150	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
153	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
155	C₄²×C₁₃₉	—	2	2	no	—
156	C₄²×C₁₃₉	—	2	2	no	—
157	C₄²×C₁₃₉	—	8	1	no	—
158	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
160	C₂³×C₁₃₉	—	2	2	no	—
161	C₂³×C₁₃₉	—	2	4	no	—
162	C₂³×C₁₃₉	—	4	2	no	—
163	C₂³×C₁₃₉	—	4	1	no	—
164	C₂³×C₁₃₉	—	4	1	no	—
165	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃₉	—	2	8	no	—
167	Q₈×C₁₃₉	—	4	8	no	—
168	Q₈×C₁₃₉	—	4	16	no	—
169	D₄×C₁₃₉	—	2	2	no	—
170	D₄×C₁₃₉	—	2	4	no	—
171	D₄×C₁₃₉	C₄⋊Q₈	1	4	yes	—
172	C₂×C₄×C₁₃₉	—	2	2	no	—
173	C₂×C₄×C₁₃₉	—	2	2	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	2	1	no	—
176	C₂×C₄×C₁₃₉	—	2	1	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	4	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	4	8	no	—
184	C₂×C₄×C₁₃₉	—	4	16	no	—
185	C₂×C₄×C₁₃₉	—	4	2	no	—
186	C₂×C₄×C₁₃₉	—	4	2	no	—
187	C₂×C₄×C₁₃₉	—	4	2	no	—
188	C₂×C₄×C₁₃₉	—	4	2	no	—
189	C₂×C₄×C₁₃₉	—	4	2	no	—
190	C₂×C₄×C₁₃₉	—	4	1	no	—
191	C₂×C₄×C₁₃₉	—	4	1	no	—
192	C₂×C₄×C₁₃₉	—	4	2	no	—
193	C₂×C₄×C₁₃₉	—	4	1	no	—
194	C₂×C₄×C₁₃₉	—	4	1	no	—
195	C₂×C₄×C₁₃₉	#120	1	2	yes	—
196	C₂×C₄×C₁₃₉	#120	1	2	yes	—
197	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
198	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
201	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
202	C₈×C₁₃₉	—	2	4	no	—
203	C₈×C₁₃₉	—	4	1	no	—
204	C₈×C₁₃₉	—	4	1	no	—
205	C₂²×C₁₃₉	—	2	4	no	—
206	C₂²×C₁₃₉	—	4	4	no	—
207	C₂²×C₁₃₉	—	4	4	no	—
208	C₂²×C₁₃₉	—	4	2	no	—
209	C₂²×C₁₃₉	—	4	2	no	—
210	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
211	C₂²×C₁₃₉	D₄×Q₈	1	2	yes	—
212	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
213	C₂²×C₁₃₉	#577	1	1	yes	characteristic
214	C₂²×C₁₃₉	#578	1	1	yes	characteristic
215	C₄×C₁₃₉	—	2	2	no	—
216	C₄×C₁₃₉	—	2	4	no	—
217	C₄×C₁₃₉	—	2	2	no	—
218	C₄×C₁₃₉	—	4	4	no	—
219	C₄×C₁₃₉	—	4	4	no	—
220	C₄×C₁₃₉	—	4	2	no	—
221	C₄×C₁₃₉	—	4	2	no	—
222	C₄×C₁₃₉	—	8	1	no	—
223	C₄×C₁₃₉	—	8	1	no	—
224	C₄×C₁₃₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
225	C₄×C₁₃₉	#536	1	1	yes	characteristic
226	C₄×C₁₃₉	D₄×Q₈	1	2	yes	—
227	C₂×C₁₃₉	—	4	4	no	—
228	C₂×C₁₃₉	#2434	1	1	yes	characteristic
229	C₂×C₁₃₉	#3003	1	1	yes	characteristic
230	C₂×C₁₃₉	#3013	1	1	yes	characteristic
231	C₂×C₁₃₉	#3384	1	2	yes	—
232	C₂×C₁₃₉	#3386	1	2	yes	—
233	#25844	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₁₃₉	#25844	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic
236	C₂×#501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
237	C₂×#478	C₂×C₁₃₉	1	1	yes	characteristic
238	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
239	#2058	C₂×C₁₃₉	1	2	yes	complemented
240	#2057	C₂×C₁₃₉	1	2	yes	complemented
241	#1987	C₂×C₁₃₉	1	1	yes	characteristic, complemented
242	#1985	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	#1864	C₂×C₁₃₉	1	2	yes	—
244	#1862	C₂×C₁₃₉	1	2	yes	—
245	#1762	C₂×C₁₃₉	1	1	yes	characteristic
246	C₂³×Q₈	—	2	1	no	—
247	D₄×Q₈	—	2	4	no	—
248	D₄×Q₈	—	2	4	no	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
250	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
251	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂×C₂²⋊Q₈	—	2	2	no	—
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
256	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
257	#501	—	2	4	no	—
258	#478	—	2	4	no	—
259	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
260	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
261	C₂×#106	C₂²×C₁₃₉	1	1	yes	characteristic
262	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
264	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
266	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
267	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
268	#398	—	2	1	no	—
269	#395	—	2	1	no	—
270	#389	—	2	2	no	—
271	#389	C₂²×C₁₃₉	1	2	yes	—
272	#389	C₂²×C₁₃₉	1	2	yes	—
273	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
274	#340	C₂²×C₁₃₉	1	2	yes	—
275	#340	C₂²×C₁₃₉	1	2	yes	—
276	#340	C₂²×C₁₃₉	1	2	yes	—
277	#336	C₂²×C₁₃₉	1	2	yes	—
278	#336	C₂²×C₁₃₉	1	2	yes	—
279	C₂²×Q₈	—	2	8	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	—	2	2	no	—
282	C₂²×Q₈	—	4	8	no	—
283	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	1	no	—
287	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	2	4	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	D₄×C₁₃₉	1	4	yes	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₂²⋊Q₈	—	2	16	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	D₄×C₁₃₉	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
311	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
321	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
322	#107	—	2	2	no	—
323	#107	—	2	4	no	—
324	#106	—	2	2	no	—
325	#106	—	2	4	no	—
326	C₄⋊C₈	—	2	2	no	—
327	#102	—	2	2	no	—
328	#102	—	2	2	no	—
329	#102	Q₈×C₁₃₉	1	8	yes	complemented
330	#97	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	C₂⁴	—	2	1	no	—
335	C₂×Q₈	—	2	8	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×Q₈	—	4	4	no	—
341	C₂×Q₈	—	4	32	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
346	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	C₂×Q₈×C₁₃₉	1	4	yes	complemented
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	8	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
386	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	8	1	no	—
392	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
393	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
400	Q₈	—	2	8	no	—
401	Q₈	—	4	8	no	—
402	Q₈	—	4	16	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	4	no	—
405	D₄	C₄⋊Q₈×C₁₃₉	1	4	yes	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	16	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	#120×C₁₃₉	1	2	yes	—
430	C₂×C₄	#120×C₁₃₉	1	2	yes	—
431	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
435	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
436	C₈	—	2	4	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
445	C₂²	D₄×Q₈×C₁₃₉	1	2	yes	—
446	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
447	C₂²	#577×C₁₃₉	1	1	yes	characteristic
448	C₂²	#578×C₁₃₉	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	C₂×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
459	C₄	#536×C₁₃₉	1	1	yes	characteristic
460	C₄	D₄×Q₈×C₁₃₉	1	2	yes	—
461	C₂	—	4	4	no	—
462	C₂	#2434×C₁₃₉	1	1	yes	characteristic
463	C₂	#3003×C₁₃₉	1	1	yes	characteristic
464	C₂	#3013×C₁₃₉	1	1	yes	characteristic
465	C₂	#3384×C₁₃₉	1	2	yes	—
466	C₂	#3386×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×C₄×Q₈×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₁₃₉	C₂	semidirect
4. #2584×C₁₃₉	C₂	semidirect
5. #2058×C₁₃₉	C₂	semidirect
6. #2057×C₁₃₉	C₂	semidirect
7. #1987×C₁₃₉	C₂	semidirect
8. #1985×C₁₃₉	C₂	semidirect
95. #102×C₁₃₉	Q₈	semidirect
134. C₂×C₈×C₁₃₉	C₂×Q₈	semidirect
152. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
233. #25844	C₁₃₉	direct (N × H)
234. C₁₃₉	#25844	direct (N × H)
236. C₂×#501	C₂×C₁₃₉	semidirect
238. #2584	C₂×C₁₃₉	semidirect
239. #2058	C₂×C₁₃₉	semidirect
240. #2057	C₂×C₁₃₉	semidirect
241. #1987	C₂×C₁₃₉	semidirect
242. #1985	C₂×C₁₃₉	semidirect
329. #102	Q₈×C₁₃₉	semidirect
368. C₂×C₈	C₂×Q₈×C₁₃₉	semidirect
386. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃₉	2
C₂×#501×C₁₃₉	2
C₂×#478×C₁₃₉	2
#2584×C₁₃₉	2
#2058×C₁₃₉	2
#2057×C₁₃₉	2
#1987×C₁₃₉	2
#1985×C₁₃₉	2
#1864×C₁₃₉	2
#1862×C₁₃₉	2
#1762×C₁₃₉	2
#25844	139

Subgroups — C139×#25844 #48020440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#25844 #48020440