Subgroups — C₁₃₉×#37119 #48031715

Order 35584.

2610 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2717×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2686×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2684×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2614×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2483×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2412×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2405×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2308×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	#534×C₁₃₉	—	2	8	no	—
16	C₂×#124×C₁₃₉	—	2	8	no	—
17	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
19	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	#397×C₁₃₉	C₂²	1	8	yes	complemented
31	#397×C₁₃₉	C₂²	1	8	yes	complemented
32	#395×C₁₃₉	C₂²	1	8	yes	complemented
33	#394×C₁₃₉	C₂²	1	8	yes	complemented
34	#394×C₁₃₉	C₂²	1	8	yes	complemented
35	#393×C₁₃₉	C₂²	1	8	yes	complemented
36	#388×C₁₃₉	C₂²	1	8	yes	complemented
37	#387×C₁₃₉	C₂²	1	8	yes	complemented
38	#386×C₁₃₉	C₂²	1	4	yes	—
39	#386×C₁₃₉	C₂²	1	4	yes	—
40	#386×C₁₃₉	C₂²	1	4	yes	complemented
41	#386×C₁₃₉	C₂²	1	8	yes	complemented
42	#385×C₁₃₉	C₂²	1	4	yes	complemented
43	#385×C₁₃₉	C₂²	1	4	yes	complemented
44	#385×C₁₃₉	C₂²	1	4	yes	complemented
45	#381×C₁₃₉	C₂²	1	2	yes	complemented
46	#381×C₁₃₉	C₂²	1	4	yes	complemented
47	#381×C₁₃₉	C₂²	1	4	yes	complemented
48	#380×C₁₃₉	C₂²	1	8	yes	complemented
49	#379×C₁₃₉	C₂²	1	2	yes	—
50	#379×C₁₃₉	C₂²	1	4	yes	complemented
51	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃₉	—	2	4	no	—
55	C₂²×Q₈×C₁₃₉	—	4	4	no	—
56	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃₉	—	2	4	no	—
58	C₂²×D₄×C₁₃₉	—	4	4	no	—
59	C₂²×D₄×C₁₃₉	—	4	4	no	—
60	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
61	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
72	#124×C₁₃₉	—	2	16	no	—
73	#124×C₁₃₉	—	2	16	no	—
74	#123×C₁₃₉	—	2	8	no	—
75	#123×C₁₃₉	—	2	8	no	—
76	#123×C₁₃₉	—	4	8	no	—
77	#121×C₁₃₉	—	2	16	no	—
78	#120×C₁₃₉	—	2	8	no	—
79	#120×C₁₃₉	—	2	8	no	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
100	C₂×C₄²×C₁₃₉	—	2	4	no	—
101	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	8	yes	—
106	#95×C₁₃₉	C₂³	1	8	yes	—
107	C₂⁴×C₁₃₉	—	2	4	no	—
108	C₂⁴×C₁₃₉	—	2	4	no	—
109	C₂⁴×C₁₃₉	—	2	2	no	—
110	C₂⁴×C₁₃₉	—	4	2	no	—
111	C₂⁴×C₁₃₉	—	4	4	no	—
112	C₂⁴×C₁₃₉	—	4	4	no	—
113	C₂⁴×C₁₃₉	—	4	4	no	—
114	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
115	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
116	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
117	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
119	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
120	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
121	C₂×Q₈×C₁₃₉	—	2	8	no	—
122	C₂×Q₈×C₁₃₉	—	4	4	no	—
123	C₂×Q₈×C₁₃₉	—	4	4	no	—
124	C₂×Q₈×C₁₃₉	—	4	16	no	—
125	C₂×D₄×C₁₃₉	—	2	4	no	—
126	C₂×D₄×C₁₃₉	—	2	4	no	—
127	C₂×D₄×C₁₃₉	—	2	8	no	—
128	C₂×D₄×C₁₃₉	—	2	8	no	—
129	C₂×D₄×C₁₃₉	—	4	16	no	—
130	C₂×D₄×C₁₃₉	—	4	2	no	—
131	C₂×D₄×C₁₃₉	—	4	2	no	—
132	C₂×D₄×C₁₃₉	—	4	2	no	—
133	C₂×D₄×C₁₃₉	—	4	2	no	—
134	C₂×D₄×C₁₃₉	—	4	4	no	—
135	C₂×D₄×C₁₃₉	—	4	8	no	—
136	C₂×D₄×C₁₃₉	—	4	16	no	—
137	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
138	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
139	C₂²×C₄×C₁₃₉	—	2	4	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	—	2	4	no	—
142	C₂²×C₄×C₁₃₉	—	2	2	no	—
143	C₂²×C₄×C₁₃₉	—	2	8	no	—
144	C₂²×C₄×C₁₃₉	—	2	4	no	—
145	C₂²×C₄×C₁₃₉	—	4	4	no	—
146	C₂²×C₄×C₁₃₉	—	4	2	no	—
147	C₂²×C₄×C₁₃₉	—	4	4	no	—
148	C₂²×C₄×C₁₃₉	—	4	8	no	—
149	C₂²×C₄×C₁₃₉	—	4	4	no	—
150	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₄⋊C₄×C₁₃₉	—	2	8	no	—
158	C₄⋊C₄×C₁₃₉	—	4	8	no	—
159	C₄⋊C₄×C₁₃₉	—	4	8	no	—
160	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
168	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
171	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
173	C₄²×C₁₃₉	—	2	8	no	—
174	C₂³×C₁₃₉	—	2	4	no	—
175	C₂³×C₁₃₉	—	2	2	no	—
176	C₂³×C₁₃₉	—	2	2	no	—
177	C₂³×C₁₃₉	—	2	2	no	—
178	C₂³×C₁₃₉	—	2	2	no	—
179	C₂³×C₁₃₉	—	2	4	no	—
180	C₂³×C₁₃₉	—	2	4	no	—
181	C₂³×C₁₃₉	—	2	8	no	—
182	C₂³×C₁₃₉	—	2	8	no	—
183	C₂³×C₁₃₉	—	2	8	no	—
184	C₂³×C₁₃₉	—	2	2	no	—
185	C₂³×C₁₃₉	—	2	4	no	—
186	C₂³×C₁₃₉	—	2	8	no	—
187	C₂³×C₁₃₉	—	4	8	no	—
188	C₂³×C₁₃₉	—	4	8	no	—
189	C₂³×C₁₃₉	—	4	4	no	—
190	C₂³×C₁₃₉	—	8	8	no	—
191	C₂³×C₁₃₉	—	8	8	no	—
192	C₂³×C₁₃₉	—	8	4	no	—
193	C₂³×C₁₃₉	—	8	8	no	—
194	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
195	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
196	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
197	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
198	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
199	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
200	Q₈×C₁₃₉	—	4	16	no	—
201	D₄×C₁₃₉	—	4	8	no	—
202	D₄×C₁₃₉	—	4	8	no	—
203	D₄×C₁₃₉	—	4	8	no	—
204	D₄×C₁₃₉	—	4	8	no	—
205	D₄×C₁₃₉	—	8	8	no	—
206	C₂×C₄×C₁₃₉	—	2	8	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	2	2	no	—
209	C₂×C₄×C₁₃₉	—	2	4	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	4	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	8	no	—
214	C₂×C₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	8	no	—
217	C₂×C₄×C₁₃₉	—	2	8	no	—
218	C₂×C₄×C₁₃₉	—	2	8	no	—
219	C₂×C₄×C₁₃₉	—	2	8	no	—
220	C₂×C₄×C₁₃₉	—	4	8	no	—
221	C₂×C₄×C₁₃₉	—	4	4	no	—
222	C₂×C₄×C₁₃₉	—	4	8	no	—
223	C₂×C₄×C₁₃₉	—	8	4	no	—
224	C₂×C₄×C₁₃₉	—	8	8	no	—
225	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
226	C₂²×C₁₃₉	—	2	4	no	—
227	C₂²×C₁₃₉	—	2	8	no	—
228	C₂²×C₁₃₉	—	2	2	no	—
229	C₂²×C₁₃₉	—	2	2	no	—
230	C₂²×C₁₃₉	—	2	4	no	—
231	C₂²×C₁₃₉	—	2	4	no	—
232	C₂²×C₁₃₉	—	2	8	no	—
233	C₂²×C₁₃₉	—	2	4	no	—
234	C₂²×C₁₃₉	—	4	4	no	—
235	C₂²×C₁₃₉	—	4	4	no	—
236	C₂²×C₁₃₉	—	4	4	no	—
237	C₂²×C₁₃₉	—	4	4	no	—
238	C₂²×C₁₃₉	—	4	2	no	—
239	C₂²×C₁₃₉	—	4	4	no	—
240	C₂²×C₁₃₉	—	4	8	no	—
241	C₂²×C₁₃₉	—	8	8	no	—
242	C₂²×C₁₃₉	—	8	8	no	—
243	C₂²×C₁₃₉	—	8	8	no	—
244	C₂²×C₁₃₉	#534	1	4	yes	—
245	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
246	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
247	C₂²×C₁₃₉	#585	1	4	yes	—
248	C₄×C₁₃₉	—	2	4	no	—
249	C₄×C₁₃₉	—	4	2	no	—
250	C₄×C₁₃₉	—	4	4	no	—
251	C₄×C₁₃₉	—	4	4	no	—
252	C₄×C₁₃₉	—	4	4	no	—
253	C₄×C₁₃₉	—	4	8	no	—
254	C₂×C₁₃₉	—	2	4	no	—
255	C₂×C₁₃₉	—	4	2	no	—
256	C₂×C₁₃₉	—	4	4	no	—
257	C₂×C₁₃₉	—	4	2	no	—
258	C₂×C₁₃₉	—	8	2	no	—
259	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
260	C₂×C₁₃₉	#3485	1	2	yes	—
261	C₂×C₁₃₉	#3545	1	4	yes	—
262	#37119	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₁₃₉	#37119	1	1	yes	characteristic, direct product factor, Sylow
264	C₂×#534	C₂×C₁₃₉	1	1	yes	characteristic
265	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
266	#2853	C₂×C₁₃₉	1	2	yes	complemented
267	#2717	C₂×C₁₃₉	1	4	yes	complemented
268	#2686	C₂×C₁₃₉	1	8	yes	complemented
269	#2684	C₂×C₁₃₉	1	4	yes	complemented
270	#2614	C₂×C₁₃₉	1	2	yes	complemented
271	#2483	C₂×C₁₃₉	1	2	yes	complemented
272	#2412	C₂×C₁₃₉	1	4	yes	complemented
273	#2405	C₂×C₁₃₉	1	2	yes	complemented
274	#2308	C₂×C₁₃₉	1	1	yes	characteristic, complemented
275	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
276	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
277	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
278	#534	—	2	8	no	—
279	C₂×#124	—	2	8	no	—
280	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
281	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
282	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
283	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
284	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
285	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
286	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
287	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
289	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
291	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
292	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
293	#397	C₂²×C₁₃₉	1	8	yes	complemented
294	#397	C₂²×C₁₃₉	1	8	yes	complemented
295	#395	C₂²×C₁₃₉	1	8	yes	complemented
296	#394	C₂²×C₁₃₉	1	8	yes	complemented
297	#394	C₂²×C₁₃₉	1	8	yes	complemented
298	#393	C₂²×C₁₃₉	1	8	yes	complemented
299	#388	C₂²×C₁₃₉	1	8	yes	complemented
300	#387	C₂²×C₁₃₉	1	8	yes	complemented
301	#386	C₂²×C₁₃₉	1	4	yes	—
302	#386	C₂²×C₁₃₉	1	4	yes	—
303	#386	C₂²×C₁₃₉	1	4	yes	complemented
304	#386	C₂²×C₁₃₉	1	8	yes	complemented
305	#385	C₂²×C₁₃₉	1	4	yes	complemented
306	#385	C₂²×C₁₃₉	1	4	yes	complemented
307	#385	C₂²×C₁₃₉	1	4	yes	complemented
308	#381	C₂²×C₁₃₉	1	2	yes	complemented
309	#381	C₂²×C₁₃₉	1	4	yes	complemented
310	#381	C₂²×C₁₃₉	1	4	yes	complemented
311	#380	C₂²×C₁₃₉	1	8	yes	complemented
312	#379	C₂²×C₁₃₉	1	2	yes	—
313	#379	C₂²×C₁₃₉	1	4	yes	complemented
314	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
315	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
317	C₂²×Q₈	—	2	4	no	—
318	C₂²×Q₈	—	4	4	no	—
319	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	—	4	4	no	—
322	C₂²×D₄	—	4	4	no	—
323	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
324	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
325	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
326	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
327	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
328	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
329	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
332	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
333	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
335	#124	—	2	16	no	—
336	#124	—	2	16	no	—
337	#123	—	2	8	no	—
338	#123	—	2	8	no	—
339	#123	—	4	8	no	—
340	#121	—	2	16	no	—
341	#120	—	2	8	no	—
342	#120	—	2	8	no	—
343	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	—	4	4	no	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
363	C₂×C₄²	—	2	4	no	—
364	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
365	#95	C₂³×C₁₃₉	1	8	yes	—
366	#95	C₂³×C₁₃₉	1	8	yes	—
367	#95	C₂³×C₁₃₉	1	8	yes	—
368	#95	C₂³×C₁₃₉	1	8	yes	—
369	#95	C₂³×C₁₃₉	1	8	yes	—
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	2	4	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	4	2	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	—	4	4	no	—
376	C₂⁴	—	4	4	no	—
377	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
378	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
379	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
380	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
381	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
382	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
383	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
384	C₂×Q₈	—	2	8	no	—
385	C₂×Q₈	—	4	4	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×Q₈	—	4	16	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	4	16	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	8	no	—
399	C₂×D₄	—	4	16	no	—
400	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
401	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
415	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	4	8	no	—
422	C₄⋊C₄	—	4	8	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	8	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	8	no	—
436	C₄²	—	2	8	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	8	8	no	—
454	C₂³	—	8	8	no	—
455	C₂³	—	8	4	no	—
456	C₂³	—	8	8	no	—
457	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
458	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
459	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
460	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
461	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
462	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
463	Q₈	—	4	16	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	8	no	—
466	D₄	—	4	8	no	—
467	D₄	—	4	8	no	—
468	D₄	—	8	8	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	8	4	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
489	C₂²	—	2	8	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	8	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	8	8	no	—
505	C₂²	—	8	8	no	—
506	C₂²	—	8	8	no	—
507	C₂²	#534×C₁₃₉	1	4	yes	—
508	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
509	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
510	C₂²	#585×C₁₃₉	1	4	yes	—
511	C₄	—	2	4	no	—
512	C₄	—	4	8	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	4	no	—
516	C₄	—	4	4	no	—
517	C₂	—	2	4	no	—
518	C₂	—	4	2	no	—
519	C₂	—	4	2	no	—
520	C₂	—	4	4	no	—
521	C₂	—	8	2	no	—
522	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
523	C₂	#3485×C₁₃₉	1	2	yes	—
524	C₂	#3545×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#534×C₁₃₉	C₂
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×#124×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2717×C₁₃₉	C₂	semidirect
5. #2686×C₁₃₉	C₂	semidirect
6. #2684×C₁₃₉	C₂	semidirect
7. #2614×C₁₃₉	C₂	semidirect
8. #2483×C₁₃₉	C₂	semidirect
9. #2412×C₁₃₉	C₂	semidirect
10. #2405×C₁₃₉	C₂	semidirect
11. #2308×C₁₃₉	C₂	semidirect
12. C₂³×Q₈×C₁₃₉	C₂²	semidirect
18. C₂×#124×C₁₃₉	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
28. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
29. C₂²×C₄²×C₁₃₉	C₂²	semidirect
30. #397×C₁₃₉	C₂²	semidirect
31. #397×C₁₃₉	C₂²	semidirect
32. #395×C₁₃₉	C₂²	semidirect
33. #394×C₁₃₉	C₂²	semidirect
34. #394×C₁₃₉	C₂²	semidirect
35. #393×C₁₃₉	C₂²	semidirect
36. #388×C₁₃₉	C₂²	semidirect
37. #387×C₁₃₉	C₂²	semidirect
40. #386×C₁₃₉	C₂²	semidirect
41. #386×C₁₃₉	C₂²	semidirect
42. #385×C₁₃₉	C₂²	semidirect
43. #385×C₁₃₉	C₂²	semidirect
44. #385×C₁₃₉	C₂²	semidirect
45. #381×C₁₃₉	C₂²	semidirect
46. #381×C₁₃₉	C₂²	semidirect
47. #381×C₁₃₉	C₂²	semidirect
48. #380×C₁₃₉	C₂²	semidirect
50. #379×C₁₃₉	C₂²	semidirect
262. #37119	C₁₃₉	direct (N × H)
263. C₁₃₉	#37119	direct (N × H)
265. C₂²×#124	C₂×C₁₃₉	semidirect
266. #2853	C₂×C₁₃₉	semidirect
267. #2717	C₂×C₁₃₉	semidirect
268. #2686	C₂×C₁₃₉	semidirect
269. #2684	C₂×C₁₃₉	semidirect
270. #2614	C₂×C₁₃₉	semidirect
271. #2483	C₂×C₁₃₉	semidirect
272. #2412	C₂×C₁₃₉	semidirect
273. #2405	C₂×C₁₃₉	semidirect
274. #2308	C₂×C₁₃₉	semidirect
275. C₂³×Q₈	C₂²×C₁₃₉	semidirect
281. C₂×#124	C₂²×C₁₃₉	semidirect
290. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
291. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
292. C₂²×C₄²	C₂²×C₁₃₉	semidirect
293. #397	C₂²×C₁₃₉	semidirect
294. #397	C₂²×C₁₃₉	semidirect
295. #395	C₂²×C₁₃₉	semidirect
296. #394	C₂²×C₁₃₉	semidirect
297. #394	C₂²×C₁₃₉	semidirect
298. #393	C₂²×C₁₃₉	semidirect
299. #388	C₂²×C₁₃₉	semidirect
300. #387	C₂²×C₁₃₉	semidirect
303. #386	C₂²×C₁₃₉	semidirect
304. #386	C₂²×C₁₃₉	semidirect
305. #385	C₂²×C₁₃₉	semidirect
306. #385	C₂²×C₁₃₉	semidirect
307. #385	C₂²×C₁₃₉	semidirect
308. #381	C₂²×C₁₃₉	semidirect
309. #381	C₂²×C₁₃₉	semidirect
310. #381	C₂²×C₁₃₉	semidirect
311. #380	C₂²×C₁₃₉	semidirect
313. #379	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₁₃₉	2
C₂²×#124×C₁₃₉	2
#2853×C₁₃₉	2
#2717×C₁₃₉	2
#2686×C₁₃₉	2
#2684×C₁₃₉	2
#2614×C₁₃₉	2
#2483×C₁₃₉	2
#2412×C₁₃₉	2
#2405×C₁₃₉	2
#2308×C₁₃₉	2
#37119	139

Subgroups — C139×#37119 #48031715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37119 #48031715