Subgroups — C₁₃₉×#36276 #48030872

Order 35584.

2462 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2550×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2549×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2502×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2434×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2349×C₁₃₉	C₂	1	4	yes	maximal
12	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#391×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
16	#554×C₁₃₉	—	2	8	no	—
17	D₄×Q₈×C₁₃₉	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	4	yes	—
37	#398×C₁₃₉	C₂²	1	8	yes	—
38	#395×C₁₃₉	C₂²	1	4	yes	—
39	#395×C₁₃₉	C₂²	1	8	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	8	yes	—
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#391×C₁₃₉	C₂²	1	2	yes	—
46	#391×C₁₃₉	C₂²	1	1	yes	characteristic
47	#391×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	4	yes	—
49	#389×C₁₃₉	C₂²	1	4	yes	—
50	#389×C₁₃₉	C₂²	1	8	yes	—
51	#389×C₁₃₉	C₂²	1	4	yes	—
52	#385×C₁₃₉	C₂²	1	8	yes	—
53	#385×C₁₃₉	C₂²	1	8	yes	—
54	#384×C₁₃₉	C₂²	1	1	yes	characteristic
55	#384×C₁₃₉	C₂²	1	2	yes	—
56	#382×C₁₃₉	C₂²	1	4	yes	—
57	#380×C₁₃₉	C₂²	1	8	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃₉	—	2	8	no	—
66	C₂²×Q₈×C₁₃₉	—	2	8	no	—
67	C₂²×Q₈×C₁₃₉	—	4	4	no	—
68	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
71	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
79	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
80	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
81	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
82	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
83	#125×C₁₃₉	—	2	8	no	—
84	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
85	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
86	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
87	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
88	C₄×Q₈×C₁₃₉	—	2	4	no	—
89	C₄×Q₈×C₁₃₉	—	2	4	no	—
90	C₄×D₄×C₁₃₉	—	2	8	no	—
91	C₄×D₄×C₁₃₉	—	2	8	no	—
92	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
93	C₄×D₄×C₁₃₉	Q₈	1	16	yes	complemented
94	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃₉	—	4	4	no	—
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	2	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	8	yes	—
129	#95×C₁₃₉	C₂³	1	8	yes	—
130	#95×C₁₃₉	C₂³	1	8	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	8	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
135	C₂×Q₈×C₁₃₉	—	2	2	no	—
136	C₂×Q₈×C₁₃₉	—	2	2	no	—
137	C₂×Q₈×C₁₃₉	—	2	8	no	—
138	C₂×Q₈×C₁₃₉	—	2	4	no	—
139	C₂×Q₈×C₁₃₉	—	2	4	no	—
140	C₂×Q₈×C₁₃₉	—	2	2	no	—
141	C₂×Q₈×C₁₃₉	—	2	8	no	—
142	C₂×Q₈×C₁₃₉	—	2	4	no	—
143	C₂×Q₈×C₁₃₉	—	2	2	no	—
144	C₂×Q₈×C₁₃₉	—	2	2	no	—
145	C₂×Q₈×C₁₃₉	—	2	4	no	—
146	C₂×Q₈×C₁₃₉	—	4	4	no	—
147	C₂×Q₈×C₁₃₉	—	4	4	no	—
148	C₂×Q₈×C₁₃₉	—	4	32	no	—
149	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
150	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
151	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
152	C₂²×C₄×C₁₃₉	—	2	4	no	—
153	C₂²×C₄×C₁₃₉	—	2	4	no	—
154	C₂²×C₄×C₁₃₉	—	2	8	no	—
155	C₂²×C₄×C₁₃₉	—	2	8	no	—
156	C₂²×C₄×C₁₃₉	—	2	8	no	—
157	C₂²×C₄×C₁₃₉	—	4	4	no	—
158	C₂²×C₄×C₁₃₉	—	4	4	no	—
159	C₂²×C₄×C₁₃₉	—	4	4	no	—
160	C₂²×C₄×C₁₃₉	—	4	8	no	—
161	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
162	C₂²×C₄×C₁₃₉	C₂×Q₈	1	16	yes	complemented
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₄⋊C₄×C₁₃₉	—	2	2	no	—
177	C₄⋊C₄×C₁₃₉	—	2	8	no	—
178	C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₄⋊C₄×C₁₃₉	—	2	4	no	—
180	C₄⋊C₄×C₁₃₉	—	2	4	no	—
181	C₄⋊C₄×C₁₃₉	—	2	4	no	—
182	C₄⋊C₄×C₁₃₉	—	2	2	no	—
183	C₄⋊C₄×C₁₃₉	—	2	4	no	—
184	C₄⋊C₄×C₁₃₉	—	2	8	no	—
185	C₄⋊C₄×C₁₃₉	—	2	8	no	—
186	C₄⋊C₄×C₁₃₉	—	2	4	no	—
187	C₄⋊C₄×C₁₃₉	—	2	8	no	—
188	C₄⋊C₄×C₁₃₉	—	4	4	no	—
189	C₄⋊C₄×C₁₃₉	—	4	8	no	—
190	C₄⋊C₄×C₁₃₉	—	4	8	no	—
191	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
192	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
193	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
195	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
196	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	16	yes	complemented
197	C₄²×C₁₃₉	—	2	4	no	—
198	C₄²×C₁₃₉	—	2	4	no	—
199	C₄²×C₁₃₉	—	2	2	no	—
200	C₄²×C₁₃₉	—	2	2	no	—
201	C₄²×C₁₃₉	—	2	4	no	—
202	C₄²×C₁₃₉	—	4	4	no	—
203	C₄²×C₁₃₉	—	4	2	no	—
204	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
205	C₄²×C₁₃₉	C₂×Q₈	1	8	yes	complemented
206	C₂³×C₁₃₉	—	2	2	no	—
207	C₂³×C₁₃₉	—	2	2	no	—
208	C₂³×C₁₃₉	—	2	4	no	—
209	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₃₉	C₂²×Q₈	1	8	yes	—
211	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃₉	—	2	8	no	—
213	Q₈×C₁₃₉	—	4	16	no	—
214	Q₈×C₁₃₉	—	4	4	no	—
215	Q₈×C₁₃₉	—	4	8	no	—
216	Q₈×C₁₃₉	—	8	4	no	—
217	D₄×C₁₃₉	C₄⋊Q₈	1	16	yes	complemented
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	4	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	2	16	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	2	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	4	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	4	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	8	no	—
242	C₂×C₄×C₁₃₉	—	4	16	no	—
243	C₂×C₄×C₁₃₉	—	4	16	no	—
244	C₂×C₄×C₁₃₉	—	8	8	no	—
245	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
250	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
251	C₂×C₄×C₁₃₉	C₂²×Q₈	1	8	yes	—
252	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
253	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
254	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
256	C₂²×C₁₃₉	—	2	4	no	—
257	C₂²×C₁₃₉	—	2	8	no	—
258	C₂²×C₁₃₉	—	2	4	no	—
259	C₂²×C₁₃₉	—	2	8	no	—
260	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	8	yes	—
261	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
262	C₂²×C₁₃₉	C₂³×Q₈	1	2	yes	—
263	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
264	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
265	C₂²×C₁₃₉	#585	1	2	yes	—
266	C₄×C₁₃₉	—	2	4	no	—
267	C₄×C₁₃₉	—	2	4	no	—
268	C₄×C₁₃₉	—	2	4	no	—
269	C₄×C₁₃₉	—	2	2	no	—
270	C₄×C₁₃₉	—	2	4	no	—
271	C₄×C₁₃₉	—	2	8	no	—
272	C₄×C₁₃₉	—	4	4	no	—
273	C₄×C₁₃₉	—	4	2	no	—
274	C₄×C₁₃₉	—	4	2	no	—
275	C₄×C₁₃₉	—	4	2	no	—
276	C₄×C₁₃₉	—	4	4	no	—
277	C₄×C₁₃₉	C₂×C₄⋊Q₈	1	4	yes	—
278	C₄×C₁₃₉	#546	1	4	yes	—
279	C₂×C₁₃₉	—	2	8	no	—
280	C₂×C₁₃₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
281	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
282	C₂×C₁₃₉	Q₈×#41	1	2	yes	—
283	C₂×C₁₃₉	#3500	1	1	yes	characteristic
284	C₂×C₁₃₉	#3501	1	2	yes	—
285	#36276	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₁₃₉	#36276	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
288	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic
289	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	#2857	C₂×C₁₃₉	1	2	yes	complemented
291	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
292	#2550	C₂×C₁₃₉	1	4	yes	complemented
293	#2549	C₂×C₁₃₉	1	8	yes	complemented
294	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
295	#2502	C₂×C₁₃₉	1	2	yes	complemented
296	#2434	C₂×C₁₃₉	1	2	yes	complemented
297	#2349	C₂×C₁₃₉	1	4	yes	—
298	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
299	C₂×#391	C₂×C₁₃₉	1	2	yes	complemented
300	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
301	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
302	#554	—	2	8	no	—
303	D₄×Q₈	—	2	8	no	—
304	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
307	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
308	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
309	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
311	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
312	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
313	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
314	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
317	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
321	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
322	#398	C₂²×C₁₃₉	1	8	yes	—
323	#398	C₂²×C₁₃₉	1	4	yes	—
324	#395	C₂²×C₁₃₉	1	4	yes	—
325	#395	C₂²×C₁₃₉	1	8	yes	—
326	#391	C₂²×C₁₃₉	1	1	yes	characteristic
327	#391	C₂²×C₁₃₉	1	1	yes	characteristic
328	#391	C₂²×C₁₃₉	1	2	yes	—
329	#391	C₂²×C₁₃₉	1	2	yes	—
330	#391	C₂²×C₁₃₉	1	2	yes	—
331	#391	C₂²×C₁₃₉	1	4	yes	—
332	#391	C₂²×C₁₃₉	1	2	yes	—
333	#391	C₂²×C₁₃₉	1	8	yes	—
334	#389	C₂²×C₁₃₉	1	4	yes	—
335	#389	C₂²×C₁₃₉	1	4	yes	—
336	#389	C₂²×C₁₃₉	1	8	yes	—
337	#389	C₂²×C₁₃₉	1	4	yes	—
338	#385	C₂²×C₁₃₉	1	8	yes	—
339	#385	C₂²×C₁₃₉	1	8	yes	—
340	#384	C₂²×C₁₃₉	1	1	yes	characteristic
341	#384	C₂²×C₁₃₉	1	2	yes	—
342	#382	C₂²×C₁₃₉	1	4	yes	—
343	#380	C₂²×C₁₃₉	1	8	yes	—
344	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
345	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
349	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
350	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
351	C₂²×Q₈	—	2	8	no	—
352	C₂²×Q₈	—	2	8	no	—
353	C₂²×Q₈	—	4	4	no	—
354	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
355	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
356	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
357	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
359	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
361	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
363	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
364	C₄⋊Q₈	—	2	4	no	—
365	C₄⋊Q₈	—	2	8	no	—
366	C₄⋊Q₈	—	2	4	no	—
367	C₄⋊Q₈	—	2	4	no	—
368	C₄⋊Q₈	—	4	4	no	—
369	#125	—	2	8	no	—
370	C₂²⋊Q₈	—	2	8	no	—
371	C₂²⋊Q₈	—	2	8	no	—
372	C₂²⋊Q₈	—	2	16	no	—
373	C₂²⋊Q₈	—	2	16	no	—
374	C₄×Q₈	—	2	4	no	—
375	C₄×Q₈	—	2	4	no	—
376	C₄×D₄	—	2	8	no	—
377	C₄×D₄	—	2	8	no	—
378	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
379	C₄×D₄	Q₈×C₁₃₉	1	16	yes	complemented
380	C₂×C₄⋊C₄	—	2	8	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
402	C₂×C₄²	—	4	4	no	—
403	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
407	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
412	#95	C₂³×C₁₃₉	1	4	yes	—
413	#95	C₂³×C₁₃₉	1	8	yes	—
414	#95	C₂³×C₁₃₉	1	8	yes	—
415	#95	C₂³×C₁₃₉	1	8	yes	—
416	#95	C₂³×C₁₃₉	1	2	yes	—
417	#95	C₂³×C₁₃₉	1	4	yes	—
418	#95	C₂³×C₁₃₉	1	4	yes	—
419	#95	C₂³×C₁₃₉	1	8	yes	—
420	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	8	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	8	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×Q₈	—	4	32	no	—
435	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
436	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
437	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	8	no	—
442	C₂²×C₄	—	2	8	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
448	C₂²×C₄	C₂×Q₈×C₁₃₉	1	16	yes	complemented
449	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	8	no	—
476	C₄⋊C₄	—	4	8	no	—
477	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
478	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
482	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	16	yes	complemented
483	C₄²	—	2	4	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	4	4	no	—
489	C₄²	—	4	2	no	—
490	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
491	C₄²	C₂×Q₈×C₁₃₉	1	8	yes	complemented
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
496	C₂³	C₂²×Q₈×C₁₃₉	1	8	yes	—
497	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
498	Q₈	—	2	8	no	—
499	Q₈	—	4	16	no	—
500	Q₈	—	4	8	no	—
501	Q₈	—	4	4	no	—
502	Q₈	—	8	4	no	—
503	D₄	C₄⋊Q₈×C₁₃₉	1	16	yes	complemented
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	16	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	4	16	no	—
529	C₂×C₄	—	4	16	no	—
530	C₂×C₄	—	8	8	no	—
531	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
532	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
533	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
535	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
536	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
537	C₂×C₄	C₂²×Q₈×C₁₃₉	1	8	yes	—
538	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
539	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
540	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
541	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	8	no	—
546	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	8	yes	—
547	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
548	C₂²	C₂³×Q₈×C₁₃₉	1	2	yes	—
549	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
550	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
551	C₂²	#585×C₁₃₉	1	2	yes	—
552	C₄	—	2	4	no	—
553	C₄	—	2	4	no	—
554	C₄	—	2	4	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	8	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	2	no	—
563	C₄	C₂×C₄⋊Q₈×C₁₃₉	1	4	yes	—
564	C₄	#546×C₁₃₉	1	4	yes	—
565	C₂	—	2	8	no	—
566	C₂	C₂²×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
567	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
568	C₂	Q₈×#41×C₁₃₉	1	2	yes	—
569	C₂	#3500×C₁₃₉	1	1	yes	characteristic
570	C₂	#3501×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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
3. #2862×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2567×C₁₃₉	C₂	semidirect
6. #2550×C₁₃₉	C₂	semidirect
7. #2549×C₁₃₉	C₂	semidirect
8. #2546×C₁₃₉	C₂	semidirect
9. #2502×C₁₃₉	C₂	semidirect
10. #2434×C₁₃₉	C₂	semidirect
12. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
13. C₂×#391×C₁₃₉	C₂	semidirect
93. C₄×D₄×C₁₃₉	Q₈	semidirect
162. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
192. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
196. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
205. C₄²×C₁₃₉	C₂×Q₈	semidirect
217. D₄×C₁₃₉	C₄⋊Q₈	semidirect
285. #36276	C₁₃₉	direct (N × H)
286. C₁₃₉	#36276	direct (N × H)
289. #2862	C₂×C₁₃₉	semidirect
290. #2857	C₂×C₁₃₉	semidirect
291. #2567	C₂×C₁₃₉	semidirect
292. #2550	C₂×C₁₃₉	semidirect
293. #2549	C₂×C₁₃₉	semidirect
294. #2546	C₂×C₁₃₉	semidirect
295. #2502	C₂×C₁₃₉	semidirect
296. #2434	C₂×C₁₃₉	semidirect
298. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
299. C₂×#391	C₂×C₁₃₉	semidirect
379. C₄×D₄	Q₈×C₁₃₉	semidirect
448. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
478. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect
482. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect
491. C₄²	C₂×Q₈×C₁₃₉	semidirect
503. D₄	C₄⋊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×#554×C₁₃₉	2
C₂×D₄×Q₈×C₁₃₉	2
#2862×C₁₃₉	2
#2857×C₁₃₉	2
#2567×C₁₃₉	2
#2550×C₁₃₉	2
#2549×C₁₃₉	2
#2546×C₁₃₉	2
#2502×C₁₃₉	2
#2434×C₁₃₉	2
#2349×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36276	139

Subgroups — C139×#36276 #48030872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36276 #48030872