Subgroups — C₁₃₉×#36955 #48031551

Order 35584.

2610 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2717×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2709×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2708×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2622×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2484×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2412×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2406×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2308×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	#535×C₁₃₉	—	2	8	no	—
16	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#123×C₁₃₉	—	2	8	no	—
19	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#123×C₁₃₉	C₂²	1	4	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	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	4	yes	complemented
31	#398×C₁₃₉	C₂²	1	4	yes	complemented
32	#397×C₁₃₉	C₂²	1	8	yes	complemented
33	#397×C₁₃₉	C₂²	1	8	yes	complemented
34	#395×C₁₃₉	C₂²	1	4	yes	complemented
35	#394×C₁₃₉	C₂²	1	8	yes	complemented
36	#394×C₁₃₉	C₂²	1	4	yes	complemented
37	#394×C₁₃₉	C₂²	1	8	yes	complemented
38	#387×C₁₃₉	C₂²	1	8	yes	complemented
39	#386×C₁₃₉	C₂²	1	4	yes	—
40	#386×C₁₃₉	C₂²	1	4	yes	—
41	#386×C₁₃₉	C₂²	1	4	yes	—
42	#386×C₁₃₉	C₂²	1	8	yes	complemented
43	#386×C₁₃₉	C₂²	1	8	yes	complemented
44	#385×C₁₃₉	C₂²	1	4	yes	—
45	#385×C₁₃₉	C₂²	1	8	yes	complemented
46	#385×C₁₃₉	C₂²	1	8	yes	complemented
47	#381×C₁₃₉	C₂²	1	2	yes	—
48	#381×C₁₃₉	C₂²	1	4	yes	—
49	#380×C₁₃₉	C₂²	1	8	yes	complemented
50	#379×C₁₃₉	C₂²	1	2	yes	—
51	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂×#41×C₁₃₉	—	2	4	no	—
54	C₂×#41×C₁₃₉	—	4	4	no	—
55	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₃₉	—	4	4	no	—
57	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃₉	—	2	4	no	—
65	C₂³×C₄×C₁₃₉	—	4	4	no	—
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	4	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
72	#127×C₁₃₉	—	2	8	no	—
73	#124×C₁₃₉	—	2	8	no	—
74	#123×C₁₃₉	—	2	16	no	—
75	#123×C₁₃₉	—	2	16	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	#117×C₁₃₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
89	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	8	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
100	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
101	#95×C₁₃₉	C₂³	1	8	yes	—
102	#95×C₁₃₉	C₂³	1	4	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	4	yes	—
106	#95×C₁₃₉	C₂³	1	8	yes	—
107	C₂⁴×C₁₃₉	—	2	4	no	—
108	C₂⁴×C₁₃₉	—	2	4	no	—
109	C₂⁴×C₁₃₉	—	4	4	no	—
110	C₂⁴×C₁₃₉	—	4	4	no	—
111	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
112	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
113	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
114	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
115	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
116	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
117	#41×C₁₃₉	—	4	16	no	—
118	C₂×Q₈×C₁₃₉	—	2	2	no	—
119	C₂×Q₈×C₁₃₉	—	4	2	no	—
120	C₂×D₄×C₁₃₉	—	2	4	no	—
121	C₂×D₄×C₁₃₉	—	2	8	no	—
122	C₂×D₄×C₁₃₉	—	2	8	no	—
123	C₂×D₄×C₁₃₉	—	2	8	no	—
124	C₂×D₄×C₁₃₉	—	2	2	no	—
125	C₂×D₄×C₁₃₉	—	4	16	no	—
126	C₂×D₄×C₁₃₉	—	4	2	no	—
127	C₂×D₄×C₁₃₉	—	4	2	no	—
128	C₂×D₄×C₁₃₉	—	4	2	no	—
129	C₂×D₄×C₁₃₉	—	4	2	no	—
130	C₂×D₄×C₁₃₉	—	4	2	no	—
131	C₂×D₄×C₁₃₉	—	4	8	no	—
132	C₂×D₄×C₁₃₉	—	4	8	no	—
133	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
134	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
135	C₂²×C₄×C₁₃₉	—	2	4	no	—
136	C₂²×C₄×C₁₃₉	—	2	4	no	—
137	C₂²×C₄×C₁₃₉	—	2	4	no	—
138	C₂²×C₄×C₁₃₉	—	2	8	no	—
139	C₂²×C₄×C₁₃₉	—	2	8	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	—	4	4	no	—
142	C₂²×C₄×C₁₃₉	—	4	4	no	—
143	C₂²×C₄×C₁₃₉	—	4	4	no	—
144	C₂²×C₄×C₁₃₉	—	4	4	no	—
145	C₂²×C₄×C₁₃₉	—	4	4	no	—
146	C₂²×C₄×C₁₃₉	—	4	8	no	—
147	C₂²×C₄×C₁₃₉	—	4	16	no	—
148	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₁₃₉	—	2	8	no	—
157	C₄⋊C₄×C₁₃₉	—	2	8	no	—
158	C₄⋊C₄×C₁₃₉	—	2	4	no	—
159	C₄⋊C₄×C₁₃₉	—	4	8	no	—
160	C₄⋊C₄×C₁₃₉	—	4	8	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	4	4	no	—
168	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
171	C₄²×C₁₃₉	—	2	4	no	—
172	C₂³×C₁₃₉	—	2	4	no	—
173	C₂³×C₁₃₉	—	2	8	no	—
174	C₂³×C₁₃₉	—	2	2	no	—
175	C₂³×C₁₃₉	—	2	2	no	—
176	C₂³×C₁₃₉	—	2	2	no	—
177	C₂³×C₁₃₉	—	2	2	no	—
178	C₂³×C₁₃₉	—	2	8	no	—
179	C₂³×C₁₃₉	—	2	8	no	—
180	C₂³×C₁₃₉	—	2	8	no	—
181	C₂³×C₁₃₉	—	2	2	no	—
182	C₂³×C₁₃₉	—	2	4	no	—
183	C₂³×C₁₃₉	—	2	8	no	—
184	C₂³×C₁₃₉	—	4	8	no	—
185	C₂³×C₁₃₉	—	4	8	no	—
186	C₂³×C₁₃₉	—	4	16	no	—
187	C₂³×C₁₃₉	—	8	8	no	—
188	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
189	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
190	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
192	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
193	Q₈×C₁₃₉	—	4	4	no	—
194	D₄×C₁₃₉	—	4	8	no	—
195	D₄×C₁₃₉	—	4	8	no	—
196	D₄×C₁₃₉	—	4	4	no	—
197	D₄×C₁₃₉	—	4	8	no	—
198	D₄×C₁₃₉	—	8	8	no	—
199	D₄×C₁₃₉	—	8	8	no	—
200	C₂×C₄×C₁₃₉	—	2	8	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	4	no	—
207	C₂×C₄×C₁₃₉	—	2	8	no	—
208	C₂×C₄×C₁₃₉	—	2	8	no	—
209	C₂×C₄×C₁₃₉	—	2	4	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	8	no	—
212	C₂×C₄×C₁₃₉	—	2	8	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	4	8	no	—
216	C₂×C₄×C₁₃₉	—	4	8	no	—
217	C₂×C₄×C₁₃₉	—	4	16	no	—
218	C₂×C₄×C₁₃₉	—	4	8	no	—
219	C₂×C₄×C₁₃₉	—	8	8	no	—
220	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
222	C₂²×C₁₃₉	—	2	4	no	—
223	C₂²×C₁₃₉	—	2	8	no	—
224	C₂²×C₁₃₉	—	2	4	no	—
225	C₂²×C₁₃₉	—	2	4	no	—
226	C₂²×C₁₃₉	—	2	8	no	—
227	C₂²×C₁₃₉	—	2	8	no	—
228	C₂²×C₁₃₉	—	4	16	no	—
229	C₂²×C₁₃₉	—	4	4	no	—
230	C₂²×C₁₃₉	—	4	4	no	—
231	C₂²×C₁₃₉	—	4	4	no	—
232	C₂²×C₁₃₉	—	4	4	no	—
233	C₂²×C₁₃₉	—	4	2	no	—
234	C₂²×C₁₃₉	—	4	4	no	—
235	C₂²×C₁₃₉	—	4	8	no	—
236	C₂²×C₁₃₉	—	8	8	no	—
237	C₂²×C₁₃₉	#534	1	4	yes	—
238	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
239	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
240	C₂²×C₁₃₉	#585	1	4	yes	—
241	C₄×C₁₃₉	—	2	2	no	—
242	C₄×C₁₃₉	—	2	2	no	—
243	C₄×C₁₃₉	—	4	4	no	—
244	C₄×C₁₃₉	—	4	2	no	—
245	C₄×C₁₃₉	—	4	4	no	—
246	C₄×C₁₃₉	—	4	4	no	—
247	C₄×C₁₃₉	—	4	8	no	—
248	C₂×C₁₃₉	—	2	4	no	—
249	C₂×C₁₃₉	—	4	4	no	—
250	C₂×C₁₃₉	—	4	4	no	—
251	C₂×C₁₃₉	—	8	2	no	—
252	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
253	C₂×C₁₃₉	#3485	1	2	yes	—
254	C₂×C₁₃₉	#3533	1	4	yes	—
255	#36955	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₁₃₉	#36955	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#535	C₂×C₁₃₉	1	1	yes	characteristic
258	C₂²×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
259	#2849	C₂×C₁₃₉	1	2	yes	complemented
260	#2717	C₂×C₁₃₉	1	4	yes	complemented
261	#2709	C₂×C₁₃₉	1	4	yes	complemented
262	#2708	C₂×C₁₃₉	1	8	yes	complemented
263	#2622	C₂×C₁₃₉	1	2	yes	complemented
264	#2484	C₂×C₁₃₉	1	2	yes	complemented
265	#2412	C₂×C₁₃₉	1	4	yes	complemented
266	#2406	C₂×C₁₃₉	1	2	yes	complemented
267	#2308	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
271	#535	—	2	8	no	—
272	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
273	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
274	C₂×#123	—	2	8	no	—
275	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
276	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
277	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
278	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
279	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
280	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
281	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
286	#400	C₂²×C₁₃₉	1	4	yes	complemented
287	#398	C₂²×C₁₃₉	1	4	yes	complemented
288	#397	C₂²×C₁₃₉	1	8	yes	complemented
289	#397	C₂²×C₁₃₉	1	8	yes	complemented
290	#395	C₂²×C₁₃₉	1	4	yes	complemented
291	#394	C₂²×C₁₃₉	1	8	yes	complemented
292	#394	C₂²×C₁₃₉	1	4	yes	complemented
293	#394	C₂²×C₁₃₉	1	8	yes	complemented
294	#387	C₂²×C₁₃₉	1	8	yes	complemented
295	#386	C₂²×C₁₃₉	1	4	yes	—
296	#386	C₂²×C₁₃₉	1	4	yes	—
297	#386	C₂²×C₁₃₉	1	4	yes	—
298	#386	C₂²×C₁₃₉	1	8	yes	complemented
299	#386	C₂²×C₁₃₉	1	8	yes	complemented
300	#385	C₂²×C₁₃₉	1	4	yes	—
301	#385	C₂²×C₁₃₉	1	8	yes	complemented
302	#385	C₂²×C₁₃₉	1	8	yes	complemented
303	#381	C₂²×C₁₃₉	1	2	yes	—
304	#381	C₂²×C₁₃₉	1	4	yes	—
305	#380	C₂²×C₁₃₉	1	8	yes	complemented
306	#379	C₂²×C₁₃₉	1	2	yes	—
307	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
308	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	4	4	no	—
311	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
312	C₂²×D₄	—	4	4	no	—
313	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
314	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
315	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
316	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
317	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
319	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
320	C₂³×C₄	—	2	4	no	—
321	C₂³×C₄	—	4	4	no	—
322	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
327	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
328	#127	—	2	8	no	—
329	#124	—	2	8	no	—
330	#123	—	2	16	no	—
331	#123	—	2	16	no	—
332	#123	—	4	8	no	—
333	#121	—	2	16	no	—
334	#120	—	2	8	no	—
335	#120	—	2	8	no	—
336	#117	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	8	no	—
338	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	2	8	no	—
345	C₂×C₂²⋊C₄	—	4	4	no	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
356	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
357	#95	C₂³×C₁₃₉	1	8	yes	—
358	#95	C₂³×C₁₃₉	1	8	yes	—
359	#95	C₂³×C₁₃₉	1	4	yes	—
360	#95	C₂³×C₁₃₉	1	8	yes	—
361	#95	C₂³×C₁₃₉	1	4	yes	—
362	#95	C₂³×C₁₃₉	1	8	yes	—
363	C₂⁴	—	2	4	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	4	4	no	—
366	C₂⁴	—	4	4	no	—
367	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
368	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
369	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
370	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
371	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
372	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
373	#41	—	4	16	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	16	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
390	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	16	no	—
404	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
407	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	4	8	no	—
416	C₄⋊C₄	—	4	8	no	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	16	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	8	no	—
425	C₂²⋊C₄	—	4	8	no	—
426	C₂²⋊C₄	—	4	8	no	—
427	C₄²	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	16	no	—
443	C₂³	—	8	8	no	—
444	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
445	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
446	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
447	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
448	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
449	Q₈	—	4	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	8	no	—
454	D₄	—	8	8	no	—
455	D₄	—	8	8	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	—	4	16	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	8	8	no	—
476	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	8	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	2	8	no	—
484	C₂²	—	4	16	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	8	8	no	—
493	C₂²	#534×C₁₃₉	1	4	yes	—
494	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
495	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
496	C₂²	#585×C₁₃₉	1	4	yes	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	8	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	4	no	—
506	C₂	—	4	4	no	—
507	C₂	—	8	2	no	—
508	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
509	C₂	#3485×C₁₃₉	1	2	yes	—
510	C₂	#3533×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#535×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×#123×C₁₃₉	C₂	semidirect
3. #2849×C₁₃₉	C₂	semidirect
4. #2717×C₁₃₉	C₂	semidirect
5. #2709×C₁₃₉	C₂	semidirect
6. #2708×C₁₃₉	C₂	semidirect
7. #2622×C₁₃₉	C₂	semidirect
8. #2484×C₁₃₉	C₂	semidirect
9. #2412×C₁₃₉	C₂	semidirect
10. #2406×C₁₃₉	C₂	semidirect
11. #2308×C₁₃₉	C₂	semidirect
30. #400×C₁₃₉	C₂²	semidirect
31. #398×C₁₃₉	C₂²	semidirect
32. #397×C₁₃₉	C₂²	semidirect
33. #397×C₁₃₉	C₂²	semidirect
34. #395×C₁₃₉	C₂²	semidirect
35. #394×C₁₃₉	C₂²	semidirect
36. #394×C₁₃₉	C₂²	semidirect
37. #394×C₁₃₉	C₂²	semidirect
38. #387×C₁₃₉	C₂²	semidirect
42. #386×C₁₃₉	C₂²	semidirect
43. #386×C₁₃₉	C₂²	semidirect
45. #385×C₁₃₉	C₂²	semidirect
46. #385×C₁₃₉	C₂²	semidirect
49. #380×C₁₃₉	C₂²	semidirect
255. #36955	C₁₃₉	direct (N × H)
256. C₁₃₉	#36955	direct (N × H)
258. C₂²×#123	C₂×C₁₃₉	semidirect
259. #2849	C₂×C₁₃₉	semidirect
260. #2717	C₂×C₁₃₉	semidirect
261. #2709	C₂×C₁₃₉	semidirect
262. #2708	C₂×C₁₃₉	semidirect
263. #2622	C₂×C₁₃₉	semidirect
264. #2484	C₂×C₁₃₉	semidirect
265. #2412	C₂×C₁₃₉	semidirect
266. #2406	C₂×C₁₃₉	semidirect
267. #2308	C₂×C₁₃₉	semidirect
286. #400	C₂²×C₁₃₉	semidirect
287. #398	C₂²×C₁₃₉	semidirect
288. #397	C₂²×C₁₃₉	semidirect
289. #397	C₂²×C₁₃₉	semidirect
290. #395	C₂²×C₁₃₉	semidirect
291. #394	C₂²×C₁₃₉	semidirect
292. #394	C₂²×C₁₃₉	semidirect
293. #394	C₂²×C₁₃₉	semidirect
294. #387	C₂²×C₁₃₉	semidirect
298. #386	C₂²×C₁₃₉	semidirect
299. #386	C₂²×C₁₃₉	semidirect
301. #385	C₂²×C₁₃₉	semidirect
302. #385	C₂²×C₁₃₉	semidirect
305. #380	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×#535×C₁₃₉	2
C₂²×#123×C₁₃₉	2
#2849×C₁₃₉	2
#2717×C₁₃₉	2
#2709×C₁₃₉	2
#2708×C₁₃₉	2
#2622×C₁₃₉	2
#2484×C₁₃₉	2
#2412×C₁₃₉	2
#2406×C₁₃₉	2
#2308×C₁₃₉	2
#36955	139

Subgroups — C139×#36955 #48031551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36955 #48031551