Subgroups — C₁₃₉×#36181 #48030777

Order 35584.

2238 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	2	yes	maximal
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2565×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2506×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2503×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2499×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2496×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2486×C₁₃₉	C₂	1	4	yes	maximal
11	#2344×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#552×C₁₃₉	—	2	16	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
33	#400×C₁₃₉	C₂²	1	8	yes	—
34	#398×C₁₃₉	C₂²	1	8	yes	—
35	#397×C₁₃₉	C₂²	1	8	yes	—
36	#391×C₁₃₉	C₂²	1	2	yes	—
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#389×C₁₃₉	C₂²	1	4	yes	—
40	#389×C₁₃₉	C₂²	1	4	yes	—
41	#389×C₁₃₉	C₂²	1	4	yes	—
42	#389×C₁₃₉	C₂²	1	4	yes	—
43	#389×C₁₃₉	C₂²	1	4	yes	—
44	#387×C₁₃₉	C₂²	1	8	yes	—
45	#387×C₁₃₉	C₂²	1	8	yes	—
46	#384×C₁₃₉	C₂²	1	1	yes	characteristic
47	#384×C₁₃₉	C₂²	1	2	yes	—
48	#384×C₁₃₉	C₂²	1	1	yes	characteristic
49	#384×C₁₃₉	C₂²	1	4	yes	—
50	#384×C₁₃₉	C₂²	1	1	yes	characteristic
51	#382×C₁₃₉	C₂²	1	2	yes	—
52	#382×C₁₃₉	C₂²	1	2	yes	—
53	#381×C₁₃₉	C₂²	1	8	yes	—
54	#380×C₁₃₉	C₂²	1	4	yes	—
55	#380×C₁₃₉	C₂²	1	4	yes	—
56	#380×C₁₃₉	C₂²	1	4	yes	—
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
74	#126×C₁₃₉	—	2	16	no	—
75	#125×C₁₃₉	—	2	16	no	—
76	#125×C₁₃₉	—	2	8	no	—
77	#123×C₁₃₉	—	2	16	no	—
78	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
79	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
80	C₄×Q₈×C₁₃₉	—	2	8	no	—
81	C₄×D₄×C₁₃₉	—	2	8	no	—
82	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
83	#117×C₁₃₉	—	2	8	no	—
84	#117×C₁₃₉	—	2	16	no	—
85	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
86	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃₉	—	2	4	no	—
111	C₂×C₄²×C₁₃₉	—	2	4	no	—
112	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	#95×C₁₃₉	C₂³	1	8	yes	—
124	#95×C₁₃₉	C₂³	1	8	yes	—
125	#95×C₁₃₉	C₂³	1	8	yes	—
126	#95×C₁₃₉	C₂³	1	8	yes	—
127	#95×C₁₃₉	C₂³	1	8	yes	—
128	#95×C₁₃₉	C₂³	1	2	yes	—
129	#95×C₁₃₉	C₂³	1	2	yes	—
130	#95×C₁₃₉	C₂³	1	2	yes	—
131	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
132	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
133	C₂×Q₈×C₁₃₉	—	2	4	no	—
134	C₂×Q₈×C₁₃₉	—	2	4	no	—
135	C₂×Q₈×C₁₃₉	—	2	4	no	—
136	C₂×D₄×C₁₃₉	—	2	4	no	—
137	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃₉	—	2	2	no	—
139	C₂²×C₄×C₁₃₉	—	2	2	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	—	2	2	no	—
142	C₂²×C₄×C₁₃₉	—	2	2	no	—
143	C₂²×C₄×C₁₃₉	—	2	4	no	—
144	C₂²×C₄×C₁₃₉	—	2	8	no	—
145	C₂²×C₄×C₁₃₉	—	2	16	no	—
146	C₂²×C₄×C₁₃₉	—	2	4	no	—
147	C₂²×C₄×C₁₃₉	—	2	4	no	—
148	C₂²×C₄×C₁₃₉	—	2	4	no	—
149	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₄⋊C₄×C₁₃₉	—	2	8	no	—
168	C₄⋊C₄×C₁₃₉	—	2	4	no	—
169	C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₄⋊C₄×C₁₃₉	—	2	8	no	—
171	C₄⋊C₄×C₁₃₉	—	2	8	no	—
172	C₄⋊C₄×C₁₃₉	—	2	8	no	—
173	C₄⋊C₄×C₁₃₉	—	2	8	no	—
174	C₄⋊C₄×C₁₃₉	—	2	16	no	—
175	C₄⋊C₄×C₁₃₉	—	2	8	no	—
176	C₄⋊C₄×C₁₃₉	—	2	8	no	—
177	C₄⋊C₄×C₁₃₉	—	2	4	no	—
178	C₄⋊C₄×C₁₃₉	—	2	8	no	—
179	C₄⋊C₄×C₁₃₉	—	2	8	no	—
180	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
181	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
182	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
187	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
188	C₄²×C₁₃₉	—	2	8	no	—
189	C₄²×C₁₃₉	—	2	8	no	—
190	C₄²×C₁₃₉	—	2	2	no	—
191	C₄²×C₁₃₉	—	2	4	no	—
192	C₄²×C₁₃₉	—	2	4	no	—
193	C₄²×C₁₃₉	—	2	2	no	—
194	C₄²×C₁₃₉	—	2	4	no	—
195	C₄²×C₁₃₉	—	2	4	no	—
196	C₄²×C₁₃₉	—	2	2	no	—
197	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
198	C₄²×C₁₃₉	#41	1	4	yes	—
199	C₂³×C₁₃₉	—	2	1	no	—
200	C₂³×C₁₃₉	—	2	1	no	—
201	C₂³×C₁₃₉	—	2	2	no	—
202	C₂³×C₁₃₉	—	2	2	no	—
203	C₂³×C₁₃₉	—	2	1	no	—
204	C₂³×C₁₃₉	—	2	1	no	—
205	C₂³×C₁₃₉	—	2	2	no	—
206	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
208	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
209	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
210	Q₈×C₁₃₉	—	4	8	no	—
211	D₄×C₁₃₉	—	2	8	no	—
212	C₂×C₄×C₁₃₉	—	2	1	no	—
213	C₂×C₄×C₁₃₉	—	2	1	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	1	no	—
218	C₂×C₄×C₁₃₉	—	2	1	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	8	no	—
221	C₂×C₄×C₁₃₉	—	2	8	no	—
222	C₂×C₄×C₁₃₉	—	2	16	no	—
223	C₂×C₄×C₁₃₉	—	2	4	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	4	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	8	no	—
231	C₂×C₄×C₁₃₉	—	2	8	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	2	no	—
235	C₂×C₄×C₁₃₉	—	2	8	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	4	no	—
238	C₂×C₄×C₁₃₉	—	4	16	no	—
239	C₂×C₄×C₁₃₉	—	4	8	no	—
240	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
246	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
247	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
250	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
251	C₂²×C₁₃₉	—	2	2	no	—
252	C₂²×C₁₃₉	—	2	4	no	—
253	C₂²×C₁₃₉	—	2	2	no	—
254	C₂²×C₁₃₉	—	2	4	no	—
255	C₂²×C₁₃₉	—	2	2	no	—
256	C₂²×C₁₃₉	—	2	2	no	—
257	C₂²×C₁₃₉	—	2	2	no	—
258	C₂²×C₁₃₉	—	4	2	no	—
259	C₂²×C₁₃₉	—	4	2	no	—
260	C₂²×C₁₃₉	#532	1	4	yes	—
261	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
262	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
263	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
264	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
265	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
266	C₄×C₁₃₉	—	2	2	no	—
267	C₄×C₁₃₉	—	2	2	no	—
268	C₄×C₁₃₉	—	2	2	no	—
269	C₄×C₁₃₉	—	2	4	no	—
270	C₄×C₁₃₉	—	2	2	no	—
271	C₄×C₁₃₉	—	4	4	no	—
272	C₄×C₁₃₉	—	4	4	no	—
273	C₄×C₁₃₉	—	4	4	no	—
274	C₄×C₁₃₉	—	4	2	no	—
275	C₄×C₁₃₉	—	4	4	no	—
276	C₄×C₁₃₉	—	4	2	no	—
277	C₄×C₁₃₉	#547	1	4	yes	—
278	C₄×C₁₃₉	#552	1	8	yes	complemented
279	C₂×C₁₃₉	—	2	4	no	—
280	C₂×C₁₃₉	—	4	2	no	—
281	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
282	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
283	C₂×C₁₃₉	C₂×#552	1	2	yes	—
284	C₂×C₁₃₉	#3499	1	1	yes	characteristic
285	C₂×C₁₃₉	#3509	1	2	yes	—
286	#36181	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₁₃₉	#36181	1	1	yes	characteristic, direct product factor, Sylow
288	C₂×#552	C₂×C₁₃₉	1	2	yes	—
289	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
291	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
292	#2565	C₂×C₁₃₉	1	2	yes	complemented
293	#2506	C₂×C₁₃₉	1	4	yes	complemented
294	#2503	C₂×C₁₃₉	1	2	yes	complemented
295	#2499	C₂×C₁₃₉	1	2	yes	complemented
296	#2496	C₂×C₁₃₉	1	4	yes	complemented
297	#2486	C₂×C₁₃₉	1	4	yes	—
298	#2344	C₂×C₁₃₉	1	4	yes	complemented
299	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
300	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
301	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic, complemented
302	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
303	#552	—	2	16	no	—
304	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
306	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
307	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
308	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
309	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
311	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
312	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
313	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
314	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
315	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
316	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
317	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
318	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
319	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
320	#400	C₂²×C₁₃₉	1	8	yes	—
321	#398	C₂²×C₁₃₉	1	8	yes	—
322	#397	C₂²×C₁₃₉	1	8	yes	—
323	#391	C₂²×C₁₃₉	1	2	yes	—
324	#391	C₂²×C₁₃₉	1	2	yes	—
325	#391	C₂²×C₁₃₉	1	2	yes	—
326	#389	C₂²×C₁₃₉	1	4	yes	—
327	#389	C₂²×C₁₃₉	1	4	yes	—
328	#389	C₂²×C₁₃₉	1	4	yes	—
329	#389	C₂²×C₁₃₉	1	4	yes	—
330	#389	C₂²×C₁₃₉	1	4	yes	—
331	#387	C₂²×C₁₃₉	1	8	yes	—
332	#387	C₂²×C₁₃₉	1	8	yes	—
333	#384	C₂²×C₁₃₉	1	1	yes	characteristic
334	#384	C₂²×C₁₃₉	1	2	yes	—
335	#384	C₂²×C₁₃₉	1	1	yes	characteristic
336	#384	C₂²×C₁₃₉	1	1	yes	characteristic
337	#384	C₂²×C₁₃₉	1	4	yes	—
338	#382	C₂²×C₁₃₉	1	2	yes	—
339	#382	C₂²×C₁₃₉	1	2	yes	—
340	#381	C₂²×C₁₃₉	1	8	yes	—
341	#380	C₂²×C₁₃₉	1	4	yes	—
342	#380	C₂²×C₁₃₉	1	4	yes	—
343	#380	C₂²×C₁₃₉	1	4	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	4	yes	—
347	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
352	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
353	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
354	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
356	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
360	C₄⋊Q₈	—	2	4	no	—
361	#126	—	2	16	no	—
362	#125	—	2	16	no	—
363	#125	—	2	8	no	—
364	#123	—	2	16	no	—
365	C₂²⋊Q₈	—	2	8	no	—
366	C₂²⋊Q₈	—	2	8	no	—
367	C₄×Q₈	—	2	8	no	—
368	C₄×D₄	—	2	8	no	—
369	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
370	#117	—	2	8	no	—
371	#117	—	2	16	no	—
372	C₂×C₄⋊C₄	—	2	8	no	—
373	C₂×C₄⋊C₄	—	2	16	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
397	C₂×C₄²	—	2	4	no	—
398	C₂×C₄²	—	2	4	no	—
399	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
400	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
401	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
410	#95	C₂³×C₁₃₉	1	2	yes	—
411	#95	C₂³×C₁₃₉	1	2	yes	—
412	#95	C₂³×C₁₃₉	1	2	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	8	yes	—
417	#95	C₂³×C₁₃₉	1	8	yes	—
418	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
419	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	16	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
437	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
438	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
439	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	16	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
474	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
475	C₄²	—	2	8	no	—
476	C₄²	—	2	8	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	4	no	—
482	C₄²	—	2	4	no	—
483	C₄²	—	2	2	no	—
484	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
485	C₄²	#41×C₁₃₉	1	4	yes	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	2	no	—
493	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
494	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
495	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
496	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
497	Q₈	—	4	8	no	—
498	D₄	—	2	8	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	16	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	8	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	4	16	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
532	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
533	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
534	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
535	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
536	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
537	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	#532×C₁₃₉	1	4	yes	—
548	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
549	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
550	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
551	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
552	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	2	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₄	#547×C₁₃₉	1	4	yes	—
565	C₄	#552×C₁₃₉	1	8	yes	complemented
566	C₂	—	2	4	no	—
567	C₂	—	4	2	no	—
568	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
569	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
570	C₂	C₂×#552×C₁₃₉	1	2	yes	—
571	C₂	#3499×C₁₃₉	1	1	yes	characteristic
572	C₂	#3509×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
2. #2859×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2565×C₁₃₉	C₂	semidirect
6. #2506×C₁₃₉	C₂	semidirect
7. #2503×C₁₃₉	C₂	semidirect
8. #2499×C₁₃₉	C₂	semidirect
9. #2496×C₁₃₉	C₂	semidirect
11. #2344×C₁₃₉	C₂	semidirect
12. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
13. #2285×C₁₃₉	C₂	semidirect
14. C₂×#384×C₁₃₉	C₂	semidirect
278. C₄×C₁₃₉	#552	semidirect
286. #36181	C₁₃₉	direct (N × H)
287. C₁₃₉	#36181	direct (N × H)
289. #2859	C₂×C₁₃₉	semidirect
290. #2857	C₂×C₁₃₉	semidirect
291. #2857	C₂×C₁₃₉	semidirect
292. #2565	C₂×C₁₃₉	semidirect
293. #2506	C₂×C₁₃₉	semidirect
294. #2503	C₂×C₁₃₉	semidirect
295. #2499	C₂×C₁₃₉	semidirect
296. #2496	C₂×C₁₃₉	semidirect
298. #2344	C₂×C₁₃₉	semidirect
299. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
300. #2285	C₂×C₁₃₉	semidirect
301. C₂×#384	C₂×C₁₃₉	semidirect
565. C₄	#552×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
#2859×C₁₃₉	2
#2857×C₁₃₉	2
#2565×C₁₃₉	2
#2506×C₁₃₉	2
#2503×C₁₃₉	2
#2499×C₁₃₉	2
#2496×C₁₃₉	2
#2486×C₁₃₉	2
#2344×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2285×C₁₃₉	2
C₂×#384×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36181	139

Subgroups — C139×#36181 #48030777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36181 #48030777