Subgroups — C₁₃₉×#37120 #48031716

Order 35584.

1954 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2721×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2719×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2694×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2690×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2623×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2591×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	#2583×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2579×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2487×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2313×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#539×C₁₃₉	—	2	8	no	—
17	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#125×C₁₃₉	—	2	8	no	—
19	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	4	yes	—
37	#400×C₁₃₉	C₂²	1	4	yes	—
38	#399×C₁₃₉	C₂²	1	4	yes	—
39	#399×C₁₃₉	C₂²	1	4	yes	—
40	#398×C₁₃₉	C₂²	1	4	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	4	yes	—
43	#398×C₁₃₉	C₂²	1	4	yes	—
44	#397×C₁₃₉	C₂²	1	4	yes	—
45	#397×C₁₃₉	C₂²	1	4	yes	—
46	#396×C₁₃₉	C₂²	1	4	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#394×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	4	yes	—
52	#389×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#387×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	2	yes	—
62	#386×C₁₃₉	C₂²	1	2	yes	—
63	#386×C₁₃₉	C₂²	1	2	yes	—
64	#386×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	2	yes	—
66	#385×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	4	yes	—
68	#385×C₁₃₉	C₂²	1	2	yes	—
69	#385×C₁₃₉	C₂²	1	2	yes	—
70	#384×C₁₃₉	C₂²	1	2	yes	—
71	#382×C₁₃₉	C₂²	1	2	yes	—
72	#381×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	#126×C₁₃₉	—	2	8	no	—
89	#125×C₁₃₉	—	2	16	no	—
90	#125×C₁₃₉	—	2	16	no	—
91	#125×C₁₃₉	—	2	8	no	—
92	#123×C₁₃₉	—	2	8	no	—
93	#123×C₁₃₉	—	2	8	no	—
94	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
95	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
96	#121×C₁₃₉	—	2	4	no	—
97	C₄×D₄×C₁₃₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
99	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
100	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
101	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
102	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
103	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₉	—	2	4	no	—
136	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
140	#95×C₁₃₉	C₂³	1	2	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	4	yes	—
145	#95×C₁₃₉	C₂³	1	4	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂×Q₈×C₁₃₉	—	2	2	no	—
156	C₂×Q₈×C₁₃₉	—	4	2	no	—
157	C₂×D₄×C₁₃₉	—	2	4	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	2	no	—
160	C₂×D₄×C₁₃₉	—	4	2	no	—
161	C₂²×C₄×C₁₃₉	—	2	4	no	—
162	C₂²×C₄×C₁₃₉	—	2	2	no	—
163	C₂²×C₄×C₁₃₉	—	2	2	no	—
164	C₂²×C₄×C₁₃₉	—	2	2	no	—
165	C₂²×C₄×C₁₃₉	—	2	2	no	—
166	C₂²×C₄×C₁₃₉	—	2	4	no	—
167	C₂²×C₄×C₁₃₉	—	4	2	no	—
168	C₂²×C₄×C₁₃₉	—	4	2	no	—
169	C₂²×C₄×C₁₃₉	—	4	2	no	—
170	C₂²×C₄×C₁₃₉	—	4	2	no	—
171	C₂²×C₄×C₁₃₉	—	4	2	no	—
172	C₂²×C₄×C₁₃₉	—	4	2	no	—
173	C₂²×C₄×C₁₃₉	—	4	4	no	—
174	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
190	C₄⋊C₄×C₁₃₉	—	2	8	no	—
191	C₄⋊C₄×C₁₃₉	—	2	8	no	—
192	C₄⋊C₄×C₁₃₉	—	2	4	no	—
193	C₄⋊C₄×C₁₃₉	—	2	4	no	—
194	C₄⋊C₄×C₁₃₉	—	2	4	no	—
195	C₄⋊C₄×C₁₃₉	—	2	4	no	—
196	C₄⋊C₄×C₁₃₉	—	2	8	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	—	2	2	no	—
199	C₄⋊C₄×C₁₃₉	—	2	4	no	—
200	C₄⋊C₄×C₁₃₉	—	2	4	no	—
201	C₄⋊C₄×C₁₃₉	—	2	2	no	—
202	C₄⋊C₄×C₁₃₉	—	2	4	no	—
203	C₄⋊C₄×C₁₃₉	—	4	4	no	—
204	C₄⋊C₄×C₁₃₉	—	4	4	no	—
205	C₄⋊C₄×C₁₃₉	—	4	4	no	—
206	C₄⋊C₄×C₁₃₉	—	4	4	no	—
207	C₄⋊C₄×C₁₃₉	—	4	4	no	—
208	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
209	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
210	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
214	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
215	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
216	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
217	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
219	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
220	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
221	C₄²×C₁₃₉	—	2	8	no	—
222	C₄²×C₁₃₉	—	2	4	no	—
223	C₄²×C₁₃₉	—	4	2	no	—
224	C₄²×C₁₃₉	—	4	2	no	—
225	C₂³×C₁₃₉	—	2	2	no	—
226	C₂³×C₁₃₉	—	2	2	no	—
227	C₂³×C₁₃₉	—	2	2	no	—
228	C₂³×C₁₃₉	—	2	4	no	—
229	C₂³×C₁₃₉	—	2	4	no	—
230	C₂³×C₁₃₉	—	2	4	no	—
231	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
232	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
233	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
234	Q₈×C₁₃₉	—	8	2	no	—
235	D₄×C₁₃₉	—	4	8	no	—
236	D₄×C₁₃₉	—	8	2	no	—
237	C₂×C₄×C₁₃₉	—	2	8	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	4	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	2	no	—
244	C₂×C₄×C₁₃₉	—	2	2	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	2	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	4	no	—
250	C₂×C₄×C₁₃₉	—	2	4	no	—
251	C₂×C₄×C₁₃₉	—	2	4	no	—
252	C₂×C₄×C₁₃₉	—	2	4	no	—
253	C₂×C₄×C₁₃₉	—	2	4	no	—
254	C₂×C₄×C₁₃₉	—	2	4	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	4	no	—
257	C₂×C₄×C₁₃₉	—	2	4	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	4	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	4	no	—
263	C₂×C₄×C₁₃₉	—	4	4	no	—
264	C₂×C₄×C₁₃₉	—	4	4	no	—
265	C₂×C₄×C₁₃₉	—	4	4	no	—
266	C₂×C₄×C₁₃₉	—	4	4	no	—
267	C₂×C₄×C₁₃₉	—	4	4	no	—
268	C₂×C₄×C₁₃₉	—	4	4	no	—
269	C₂×C₄×C₁₃₉	—	8	4	no	—
270	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
272	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
274	C₂²×C₁₃₉	—	2	2	no	—
275	C₂²×C₁₃₉	—	2	2	no	—
276	C₂²×C₁₃₉	—	2	8	no	—
277	C₂²×C₁₃₉	—	4	2	no	—
278	C₂²×C₁₃₉	—	4	2	no	—
279	C₂²×C₁₃₉	—	4	2	no	—
280	C₂²×C₁₃₉	—	4	8	no	—
281	C₂²×C₁₃₉	#536	1	4	yes	—
282	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
283	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
284	C₂²×C₁₃₉	#585	1	2	yes	—
285	C₂²×C₁₃₉	#585	1	2	yes	—
286	C₄×C₁₃₉	—	2	4	no	—
287	C₄×C₁₃₉	—	2	4	no	—
288	C₄×C₁₃₉	—	2	2	no	—
289	C₄×C₁₃₉	—	2	2	no	—
290	C₄×C₁₃₉	—	4	2	no	—
291	C₄×C₁₃₉	—	4	2	no	—
292	C₄×C₁₃₉	—	4	2	no	—
293	C₄×C₁₃₉	—	4	2	no	—
294	C₄×C₁₃₉	—	4	2	no	—
295	C₄×C₁₃₉	—	4	2	no	—
296	C₄×C₁₃₉	—	4	2	no	—
297	C₄×C₁₃₉	—	4	4	no	—
298	C₄×C₁₃₉	—	4	4	no	—
299	C₂×C₁₃₉	—	2	4	no	—
300	C₂×C₁₃₉	—	8	2	no	—
301	C₂×C₁₃₉	C₂×#536	1	1	yes	characteristic
302	C₂×C₁₃₉	#3485	1	1	yes	characteristic
303	C₂×C₁₃₉	#3487	1	1	yes	characteristic
304	C₂×C₁₃₉	#3553	1	4	yes	—
305	#37120	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₁₃₉	#37120	1	1	yes	characteristic, direct product factor, Sylow
307	C₂×#539	C₂×C₁₃₉	1	1	yes	characteristic
308	C₂²×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
309	#2853	C₂×C₁₃₉	1	2	yes	complemented
310	#2721	C₂×C₁₃₉	1	4	yes	complemented
311	#2719	C₂×C₁₃₉	1	4	yes	complemented
312	#2694	C₂×C₁₃₉	1	4	yes	complemented
313	#2690	C₂×C₁₃₉	1	4	yes	complemented
314	#2623	C₂×C₁₃₉	1	2	yes	complemented
315	#2591	C₂×C₁₃₉	1	1	yes	characteristic
316	#2583	C₂×C₁₃₉	1	1	yes	characteristic, complemented
317	#2579	C₂×C₁₃₉	1	2	yes	complemented
318	#2504	C₂×C₁₃₉	1	1	yes	characteristic
319	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
320	#2487	C₂×C₁₃₉	1	2	yes	complemented
321	#2313	C₂×C₁₃₉	1	1	yes	characteristic, complemented
322	#539	—	2	8	no	—
323	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
324	C₂×#125	—	2	8	no	—
325	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
326	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
327	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
328	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
329	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
331	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
332	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
334	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
337	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
340	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
341	#400	C₂²×C₁₃₉	1	2	yes	—
342	#400	C₂²×C₁₃₉	1	4	yes	—
343	#400	C₂²×C₁₃₉	1	4	yes	—
344	#399	C₂²×C₁₃₉	1	4	yes	—
345	#399	C₂²×C₁₃₉	1	4	yes	—
346	#398	C₂²×C₁₃₉	1	4	yes	—
347	#398	C₂²×C₁₃₉	1	2	yes	—
348	#398	C₂²×C₁₃₉	1	4	yes	—
349	#398	C₂²×C₁₃₉	1	4	yes	—
350	#397	C₂²×C₁₃₉	1	4	yes	—
351	#397	C₂²×C₁₃₉	1	4	yes	—
352	#396	C₂²×C₁₃₉	1	4	yes	—
353	#395	C₂²×C₁₃₉	1	2	yes	—
354	#394	C₂²×C₁₃₉	1	2	yes	—
355	#391	C₂²×C₁₃₉	1	2	yes	—
356	#390	C₂²×C₁₃₉	1	2	yes	—
357	#389	C₂²×C₁₃₉	1	4	yes	—
358	#389	C₂²×C₁₃₉	1	4	yes	—
359	#388	C₂²×C₁₃₉	1	4	yes	—
360	#388	C₂²×C₁₃₉	1	4	yes	—
361	#388	C₂²×C₁₃₉	1	4	yes	—
362	#387	C₂²×C₁₃₉	1	4	yes	—
363	#387	C₂²×C₁₃₉	1	4	yes	—
364	#387	C₂²×C₁₃₉	1	4	yes	—
365	#387	C₂²×C₁₃₉	1	4	yes	—
366	#387	C₂²×C₁₃₉	1	4	yes	—
367	#386	C₂²×C₁₃₉	1	2	yes	—
368	#386	C₂²×C₁₃₉	1	2	yes	—
369	#386	C₂²×C₁₃₉	1	2	yes	—
370	#386	C₂²×C₁₃₉	1	2	yes	—
371	#385	C₂²×C₁₃₉	1	2	yes	—
372	#385	C₂²×C₁₃₉	1	2	yes	—
373	#385	C₂²×C₁₃₉	1	4	yes	—
374	#385	C₂²×C₁₃₉	1	2	yes	—
375	#385	C₂²×C₁₃₉	1	2	yes	—
376	#384	C₂²×C₁₃₉	1	2	yes	—
377	#382	C₂²×C₁₃₉	1	2	yes	—
378	#381	C₂²×C₁₃₉	1	2	yes	—
379	#380	C₂²×C₁₃₉	1	2	yes	—
380	#380	C₂²×C₁₃₉	1	4	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
394	#126	—	2	8	no	—
395	#125	—	2	16	no	—
396	#125	—	2	16	no	—
397	#125	—	2	8	no	—
398	#123	—	2	8	no	—
399	#123	—	2	8	no	—
400	C₂²⋊Q₈	—	2	4	no	—
401	C₂²⋊Q₈	—	2	8	no	—
402	#121	—	2	4	no	—
403	C₄×D₄	—	2	8	no	—
404	C₂×C₄⋊C₄	—	2	4	no	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	—	2	4	no	—
407	C₂×C₄⋊C₄	—	2	4	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
441	C₂×C₄²	—	2	4	no	—
442	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
443	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
444	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
445	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
446	#95	C₂³×C₁₃₉	1	2	yes	—
447	#95	C₂³×C₁₃₉	1	2	yes	—
448	#95	C₂³×C₁₃₉	1	4	yes	—
449	#95	C₂³×C₁₃₉	1	4	yes	—
450	#95	C₂³×C₁₃₉	1	4	yes	—
451	#95	C₂³×C₁₃₉	1	4	yes	—
452	#95	C₂³×C₁₃₉	1	4	yes	—
453	#95	C₂³×C₁₃₉	1	4	yes	—
454	#95	C₂³×C₁₃₉	1	4	yes	—
455	#95	C₂³×C₁₃₉	1	4	yes	—
456	#95	C₂³×C₁₃₉	1	4	yes	—
457	#95	C₂³×C₁₃₉	1	4	yes	—
458	#95	C₂³×C₁₃₉	1	4	yes	—
459	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
460	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	8	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
481	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
482	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
496	C₄⋊C₄	—	2	8	no	—
497	C₄⋊C₄	—	2	8	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	—	4	4	no	—
512	C₄⋊C₄	—	4	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
515	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₂²⋊C₄	—	4	4	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	4	no	—
527	C₄²	—	2	8	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	4	2	no	—
530	C₄²	—	4	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
538	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
539	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
540	Q₈	—	8	2	no	—
541	D₄	—	4	8	no	—
542	D₄	—	8	2	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	8	4	no	—
576	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
577	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	#536×C₁₃₉	1	4	yes	—
588	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
589	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
590	C₂²	#585×C₁₃₉	1	2	yes	—
591	C₂²	#585×C₁₃₉	1	2	yes	—
592	C₄	—	2	4	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	4	no	—
597	C₄	—	4	4	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₂	—	2	4	no	—
606	C₂	—	8	2	no	—
607	C₂	C₂×#536×C₁₃₉	1	1	yes	characteristic
608	C₂	#3485×C₁₃₉	1	1	yes	characteristic
609	C₂	#3487×C₁₃₉	1	1	yes	characteristic
610	C₂	#3553×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×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
2. C₂²×#125×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2721×C₁₃₉	C₂	semidirect
5. #2719×C₁₃₉	C₂	semidirect
6. #2694×C₁₃₉	C₂	semidirect
7. #2690×C₁₃₉	C₂	semidirect
8. #2623×C₁₃₉	C₂	semidirect
10. #2583×C₁₃₉	C₂	semidirect
11. #2579×C₁₃₉	C₂	semidirect
13. #2502×C₁₃₉	C₂	semidirect
14. #2487×C₁₃₉	C₂	semidirect
15. #2313×C₁₃₉	C₂	semidirect
305. #37120	C₁₃₉	direct (N × H)
306. C₁₃₉	#37120	direct (N × H)
308. C₂²×#125	C₂×C₁₃₉	semidirect
309. #2853	C₂×C₁₃₉	semidirect
310. #2721	C₂×C₁₃₉	semidirect
311. #2719	C₂×C₁₃₉	semidirect
312. #2694	C₂×C₁₃₉	semidirect
313. #2690	C₂×C₁₃₉	semidirect
314. #2623	C₂×C₁₃₉	semidirect
316. #2583	C₂×C₁₃₉	semidirect
317. #2579	C₂×C₁₃₉	semidirect
319. #2502	C₂×C₁₃₉	semidirect
320. #2487	C₂×C₁₃₉	semidirect
321. #2313	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×#539×C₁₃₉	2
C₂²×#125×C₁₃₉	2
#2853×C₁₃₉	2
#2721×C₁₃₉	2
#2719×C₁₃₉	2
#2694×C₁₃₉	2
#2690×C₁₃₉	2
#2623×C₁₃₉	2
#2591×C₁₃₉	2
#2583×C₁₃₉	2
#2579×C₁₃₉	2
#2504×C₁₃₉	2
#2502×C₁₃₉	2
#2487×C₁₃₉	2
#2313×C₁₃₉	2
#37120	139

Subgroups — C139×#37120 #48031716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37120 #48031716