Subgroups — C₁₃₉×#35700 #48030296

Order 35584.

2882 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, complemented
2	C₂×D₄×Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2621×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2546×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2536×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#2429×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2415×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2392×C₁₃₉	C₂	1	3	yes	maximal
10	#2351×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₁₃₉	—	2	16	no	—
15	D₄×Q₈×C₁₃₉	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
21	#519×C₁₃₉	—	2	8	no	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	3	yes	—
30	C₂×#117×C₁₃₉	C₂²	1	3	yes	—
31	#398×C₁₃₉	C₂²	1	6	yes	—
32	#398×C₁₃₉	C₂²	1	3	yes	—
33	#398×C₁₃₉	C₂²	1	6	yes	—
34	#397×C₁₃₉	C₂²	1	3	yes	—
35	#397×C₁₃₉	C₂²	1	6	yes	—
36	#396×C₁₃₉	C₂²	1	6	yes	—
37	#394×C₁₃₉	C₂²	1	3	yes	—
38	#394×C₁₃₉	C₂²	1	6	yes	—
39	#392×C₁₃₉	C₂²	1	1	yes	characteristic
40	#391×C₁₃₉	C₂²	1	6	yes	—
41	#391×C₁₃₉	C₂²	1	6	yes	—
42	#389×C₁₃₉	C₂²	1	12	yes	—
43	#389×C₁₃₉	C₂²	1	6	yes	—
44	#388×C₁₃₉	C₂²	1	12	yes	—
45	#382×C₁₃₉	C₂²	1	3	yes	—
46	#380×C₁₃₉	C₂²	1	6	yes	—
47	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
49	C₂²×Q₈×C₁₃₉	—	2	4	no	—
50	C₂²×Q₈×C₁₃₉	—	2	4	no	—
51	C₂²×Q₈×C₁₃₉	—	2	8	no	—
52	C₂²×Q₈×C₁₃₉	—	2	8	no	—
53	C₂²×Q₈×C₁₃₉	—	2	8	no	—
54	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	complemented
55	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
56	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
57	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
62	C₄⋊Q₈×C₁₃₉	—	2	24	no	—
63	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
64	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
65	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
66	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
67	C₄×Q₈×C₁₃₉	—	2	4	no	—
68	C₄×Q₈×C₁₃₉	—	2	8	no	—
69	C₄×Q₈×C₁₃₉	—	2	12	no	—
70	C₄×Q₈×C₁₃₉	—	2	12	no	—
71	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
72	C₄×D₄×C₁₃₉	—	2	24	no	—
73	C₄×D₄×C₁₃₉	—	2	12	no	—
74	#117×C₁₃₉	—	2	12	no	—
75	#117×C₁₃₉	—	2	12	no	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	12	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
93	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
94	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
97	#95×C₁₃₉	C₂³	1	6	yes	—
98	#95×C₁₃₉	C₂³	1	3	yes	—
99	#95×C₁₃₉	C₂³	1	12	yes	—
100	#95×C₁₃₉	C₂³	1	6	yes	—
101	#95×C₁₃₉	C₂³	1	1	yes	characteristic
102	#95×C₁₃₉	C₂³	1	6	yes	—
103	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
104	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
105	C₂×Q₈×C₁₃₉	—	2	32	no	—
106	C₂×Q₈×C₁₃₉	—	2	6	no	—
107	C₂×Q₈×C₁₃₉	—	2	12	no	—
108	C₂×Q₈×C₁₃₉	—	2	12	no	—
109	C₂×Q₈×C₁₃₉	—	2	6	no	—
110	C₂×Q₈×C₁₃₉	—	2	12	no	—
111	C₂×Q₈×C₁₃₉	—	4	32	no	—
112	C₂×Q₈×C₁₃₉	C₂×D₄	1	12	yes	—
113	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
114	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
115	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
116	C₂×D₄×C₁₃₉	—	2	4	no	—
117	C₂×D₄×C₁₃₉	—	2	4	no	—
118	C₂×D₄×C₁₃₉	—	2	4	no	—
119	C₂×D₄×C₁₃₉	—	2	2	no	—
120	C₂×D₄×C₁₃₉	—	2	4	no	—
121	C₂²×C₄×C₁₃₉	—	2	6	no	—
122	C₂²×C₄×C₁₃₉	—	2	6	no	—
123	C₂²×C₄×C₁₃₉	—	2	12	no	—
124	C₂²×C₄×C₁₃₉	—	2	12	no	—
125	C₂²×C₄×C₁₃₉	—	2	12	no	—
126	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
127	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
133	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
136	C₄⋊C₄×C₁₃₉	—	2	6	no	—
137	C₄⋊C₄×C₁₃₉	—	2	6	no	—
138	C₄⋊C₄×C₁₃₉	—	2	6	no	—
139	C₄⋊C₄×C₁₃₉	—	2	12	no	—
140	C₄⋊C₄×C₁₃₉	—	2	6	no	—
141	C₄⋊C₄×C₁₃₉	—	2	12	no	—
142	C₄⋊C₄×C₁₃₉	—	2	24	no	—
143	C₄⋊C₄×C₁₃₉	—	2	12	no	—
144	C₄⋊C₄×C₁₃₉	—	2	12	no	—
145	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
146	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
147	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
148	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
149	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
152	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
153	C₄²×C₁₃₉	—	2	12	no	—
154	C₄²×C₁₃₉	—	2	6	no	—
155	C₄²×C₁₃₉	—	2	12	no	—
156	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
157	C₂³×C₁₃₉	—	2	1	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	2	2	no	—
160	C₂³×C₁₃₉	—	2	1	no	—
161	C₂³×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	2	no	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	2	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
168	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
169	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
170	Q₈×C₁₃₉	—	2	24	no	—
171	Q₈×C₁₃₉	—	4	24	no	—
172	Q₈×C₁₃₉	#121	1	16	yes	—
173	D₄×C₁₃₉	—	2	8	no	—
174	D₄×C₁₃₉	—	2	16	no	—
175	C₂×C₄×C₁₃₉	—	2	2	no	—
176	C₂×C₄×C₁₃₉	—	2	3	no	—
177	C₂×C₄×C₁₃₉	—	2	3	no	—
178	C₂×C₄×C₁₃₉	—	2	6	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	24	no	—
182	C₂×C₄×C₁₃₉	—	2	3	no	—
183	C₂×C₄×C₁₃₉	—	2	1	no	—
184	C₂×C₄×C₁₃₉	—	2	6	no	—
185	C₂×C₄×C₁₃₉	—	2	6	no	—
186	C₂×C₄×C₁₃₉	—	2	6	no	—
187	C₂×C₄×C₁₃₉	—	2	6	no	—
188	C₂×C₄×C₁₃₉	—	2	6	no	—
189	C₂×C₄×C₁₃₉	—	2	6	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	6	no	—
192	C₂×C₄×C₁₃₉	—	4	24	no	—
193	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
194	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
196	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
197	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
198	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
199	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
200	C₂²×C₁₃₉	—	2	2	no	—
201	C₂²×C₁₃₉	—	2	4	no	—
202	C₂²×C₁₃₉	—	2	4	no	—
203	C₂²×C₁₃₉	—	2	4	no	—
204	C₂²×C₁₃₉	—	2	4	no	—
205	C₂²×C₁₃₉	—	4	2	no	—
206	C₂²×C₁₃₉	—	4	1	no	—
207	C₂²×C₁₃₉	—	4	2	no	—
208	C₂²×C₁₃₉	—	4	1	no	—
209	C₂²×C₁₃₉	—	4	2	no	—
210	C₂²×C₁₃₉	—	4	2	no	—
211	C₂²×C₁₃₉	—	4	2	no	—
212	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
213	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
214	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
215	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
216	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
217	C₄×C₁₃₉	—	2	6	no	—
218	C₄×C₁₃₉	—	2	2	no	—
219	C₄×C₁₃₉	—	2	4	no	—
220	C₄×C₁₃₉	—	2	6	no	—
221	C₄×C₁₃₉	—	4	6	no	—
222	C₄×C₁₃₉	—	4	3	no	—
223	C₄×C₁₃₉	—	4	6	no	—
224	C₄×C₁₃₉	—	4	1	no	—
225	C₄×C₁₃₉	C₂×#121	1	12	yes	—
226	C₂×C₁₃₉	—	4	2	no	—
227	C₂×C₁₃₉	—	4	4	no	—
228	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
229	C₂×C₁₃₉	#3486	1	1	yes	characteristic
230	C₂×C₁₃₉	#3486	1	2	yes	—
231	C₂×C₁₃₉	#3499	1	1	yes	characteristic
232	C₂×C₁₃₉	#3523	1	2	yes	—
233	#35700	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₁₃₉	#35700	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×D₄×Q₈	C₂×C₁₃₉	1	2	yes	complemented
236	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
237	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
238	#2621	C₂×C₁₃₉	1	3	yes	complemented
239	#2546	C₂×C₁₃₉	1	3	yes	complemented
240	#2536	C₂×C₁₃₉	1	3	yes	complemented
241	#2429	C₂×C₁₃₉	1	6	yes	complemented
242	#2415	C₂×C₁₃₉	1	6	yes	complemented
243	#2392	C₂×C₁₃₉	1	3	yes	—
244	#2351	C₂×C₁₃₉	1	1	yes	characteristic, complemented
245	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
246	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
247	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
248	D₄×Q₈	—	2	16	no	—
249	D₄×Q₈	—	2	8	no	—
250	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
251	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
254	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
255	#519	—	2	8	no	—
256	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
258	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
259	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
260	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	—
262	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
263	C₂×#117	C₂²×C₁₃₉	1	3	yes	—
264	C₂×#117	C₂²×C₁₃₉	1	3	yes	—
265	#398	C₂²×C₁₃₉	1	6	yes	—
266	#398	C₂²×C₁₃₉	1	6	yes	—
267	#398	C₂²×C₁₃₉	1	3	yes	—
268	#397	C₂²×C₁₃₉	1	3	yes	—
269	#397	C₂²×C₁₃₉	1	6	yes	—
270	#396	C₂²×C₁₃₉	1	6	yes	—
271	#394	C₂²×C₁₃₉	1	6	yes	—
272	#394	C₂²×C₁₃₉	1	3	yes	—
273	#392	C₂²×C₁₃₉	1	1	yes	characteristic
274	#391	C₂²×C₁₃₉	1	6	yes	—
275	#391	C₂²×C₁₃₉	1	6	yes	—
276	#389	C₂²×C₁₃₉	1	6	yes	—
277	#389	C₂²×C₁₃₉	1	12	yes	—
278	#388	C₂²×C₁₃₉	1	12	yes	—
279	#382	C₂²×C₁₃₉	1	3	yes	—
280	#380	C₂²×C₁₃₉	1	6	yes	—
281	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	2	8	no	—
286	C₂²×Q₈	—	2	8	no	—
287	C₂²×Q₈	—	2	8	no	—
288	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	complemented
289	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
290	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
291	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
295	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
296	C₄⋊Q₈	—	2	24	no	—
297	C₄⋊Q₈	—	2	12	no	—
298	C₂²⋊Q₈	—	2	24	no	—
299	C₂²⋊Q₈	—	2	24	no	—
300	C₂²⋊Q₈	—	2	24	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	2	8	no	—
303	C₄×Q₈	—	2	12	no	—
304	C₄×Q₈	—	2	12	no	—
305	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
306	C₄×D₄	—	2	24	no	—
307	C₄×D₄	—	2	12	no	—
308	#117	—	2	12	no	—
309	#117	—	2	12	no	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	12	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
327	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
328	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
329	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
330	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
331	#95	C₂³×C₁₃₉	1	6	yes	—
332	#95	C₂³×C₁₃₉	1	6	yes	—
333	#95	C₂³×C₁₃₉	1	1	yes	characteristic
334	#95	C₂³×C₁₃₉	1	3	yes	—
335	#95	C₂³×C₁₃₉	1	12	yes	—
336	#95	C₂³×C₁₃₉	1	6	yes	—
337	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
338	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
339	C₂×Q₈	—	2	32	no	—
340	C₂×Q₈	—	2	6	no	—
341	C₂×Q₈	—	2	12	no	—
342	C₂×Q₈	—	2	12	no	—
343	C₂×Q₈	—	2	6	no	—
344	C₂×Q₈	—	2	12	no	—
345	C₂×Q₈	—	4	32	no	—
346	C₂×Q₈	C₂×D₄×C₁₃₉	1	12	yes	—
347	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
348	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
349	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂²×C₄	—	2	6	no	—
356	C₂²×C₄	—	2	6	no	—
357	C₂²×C₄	—	2	12	no	—
358	C₂²×C₄	—	2	12	no	—
359	C₂²×C₄	—	2	12	no	—
360	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
361	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
362	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
364	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
365	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
367	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
368	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
369	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
370	C₄⋊C₄	—	2	6	no	—
371	C₄⋊C₄	—	2	6	no	—
372	C₄⋊C₄	—	2	6	no	—
373	C₄⋊C₄	—	2	12	no	—
374	C₄⋊C₄	—	2	6	no	—
375	C₄⋊C₄	—	2	12	no	—
376	C₄⋊C₄	—	2	24	no	—
377	C₄⋊C₄	—	2	12	no	—
378	C₄⋊C₄	—	2	12	no	—
379	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
380	C₂²⋊C₄	—	2	12	no	—
381	C₂²⋊C₄	—	2	12	no	—
382	C₂²⋊C₄	—	2	6	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	12	no	—
385	C₂²⋊C₄	—	2	12	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₄²	—	2	12	no	—
388	C₄²	—	2	6	no	—
389	C₄²	—	2	12	no	—
390	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
402	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
403	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
404	Q₈	—	2	24	no	—
405	Q₈	—	4	24	no	—
406	Q₈	#121×C₁₃₉	1	16	yes	—
407	D₄	—	2	8	no	—
408	D₄	—	2	16	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	3	no	—
411	C₂×C₄	—	2	3	no	—
412	C₂×C₄	—	2	6	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	24	no	—
416	C₂×C₄	—	2	3	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	6	no	—
419	C₂×C₄	—	2	6	no	—
420	C₂×C₄	—	2	6	no	—
421	C₂×C₄	—	2	6	no	—
422	C₂×C₄	—	2	6	no	—
423	C₂×C₄	—	2	6	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	6	no	—
426	C₂×C₄	—	4	24	no	—
427	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
432	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
433	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
447	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
448	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
449	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
450	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
451	C₄	—	2	6	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	4	no	—
454	C₄	—	2	6	no	—
455	C₄	—	4	6	no	—
456	C₄	—	4	3	no	—
457	C₄	—	4	6	no	—
458	C₄	—	4	1	no	—
459	C₄	C₂×#121×C₁₃₉	1	12	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	4	4	no	—
462	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
463	C₂	#3486×C₁₃₉	1	1	yes	characteristic
464	C₂	#3486×C₁₃₉	1	2	yes	—
465	C₂	#3499×C₁₃₉	1	1	yes	characteristic
466	C₂	#3523×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#392×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₁₃₉	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃₉	C₂	semidirect
3. C₂×#519×C₁₃₉	C₂	semidirect
4. #2621×C₁₃₉	C₂	semidirect
5. #2546×C₁₃₉	C₂	semidirect
6. #2536×C₁₃₉	C₂	semidirect
7. #2429×C₁₃₉	C₂	semidirect
8. #2415×C₁₃₉	C₂	semidirect
10. #2351×C₁₃₉	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
54. C₂²×Q₈×C₁₃₉	D₄	semidirect
71. C₄×Q₈×C₁₃₉	D₄	semidirect
233. #35700	C₁₃₉	direct (N × H)
234. C₁₃₉	#35700	direct (N × H)
235. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
236. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
237. C₂×#519	C₂×C₁₃₉	semidirect
238. #2621	C₂×C₁₃₉	semidirect
239. #2546	C₂×C₁₃₉	semidirect
240. #2536	C₂×C₁₃₉	semidirect
241. #2429	C₂×C₁₃₉	semidirect
242. #2415	C₂×C₁₃₉	semidirect
244. #2351	C₂×C₁₃₉	semidirect
245. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
288. C₂²×Q₈	D₄×C₁₃₉	semidirect
305. C₄×Q₈	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×D₄×Q₈×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2621×C₁₃₉	2
#2546×C₁₃₉	2
#2536×C₁₃₉	2
#2429×C₁₃₉	2
#2415×C₁₃₉	2
#2392×C₁₃₉	2
#2351×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
#35700	139

Subgroups — C139×#35700 #48030296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35700 #48030296