Subgroups — C₁₃₉×#37232 #48031828

Order 35584.

3426 conjugacy classes of subgroups.

The subgroup lattice has 598 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, complemented
2	C₂²×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2709×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2673×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2669×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2613×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2410×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2405×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2403×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2308×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	complemented
17	#534×C₁₃₉	—	2	8	no	—
18	C₂×#127×C₁₃₉	—	2	8	no	—
19	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#127×C₁₃₉	C₂²	1	4	yes	complemented
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	8	yes	complemented
26	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
28	C₂×#120×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#120×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	#394×C₁₃₉	C₂²	1	8	yes	complemented
34	#394×C₁₃₉	C₂²	1	8	yes	complemented
35	#394×C₁₃₉	C₂²	1	8	yes	complemented
36	#392×C₁₃₉	C₂²	1	8	yes	complemented
37	#392×C₁₃₉	C₂²	1	8	yes	complemented
38	#392×C₁₃₉	C₂²	1	8	yes	complemented
39	#388×C₁₃₉	C₂²	1	8	yes	complemented
40	#387×C₁₃₉	C₂²	1	8	yes	complemented
41	#386×C₁₃₉	C₂²	1	4	yes	—
42	#386×C₁₃₉	C₂²	1	4	yes	complemented
43	#386×C₁₃₉	C₂²	1	4	yes	complemented
44	#386×C₁₃₉	C₂²	1	4	yes	complemented
45	#386×C₁₃₉	C₂²	1	4	yes	complemented
46	#386×C₁₃₉	C₂²	1	8	yes	complemented
47	#385×C₁₃₉	C₂²	1	4	yes	complemented
48	#381×C₁₃₉	C₂²	1	2	yes	complemented
49	#379×C₁₃₉	C₂²	1	2	yes	—
50	#379×C₁₃₉	C₂²	1	4	yes	complemented
51	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
52	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃₉	—	2	8	no	—
56	C₂²×D₄×C₁₃₉	—	2	8	no	—
57	C₂²×D₄×C₁₃₉	—	2	4	no	—
58	C₂²×D₄×C₁₃₉	—	2	4	no	—
59	C₂²×D₄×C₁₃₉	—	4	8	no	—
60	C₂²×D₄×C₁₃₉	—	4	8	no	—
61	C₂²×D₄×C₁₃₉	—	4	4	no	—
62	C₂²×D₄×C₁₃₉	—	4	4	no	—
63	C₂²×D₄×C₁₃₉	—	4	4	no	—
64	C₂²×D₄×C₁₃₉	D₄	1	8	yes	complemented
65	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
80	#127×C₁₃₉	—	2	16	no	—
81	#127×C₁₃₉	—	2	16	no	—
82	#123×C₁₃₉	—	2	8	no	—
83	#123×C₁₃₉	—	2	8	no	—
84	#123×C₁₃₉	—	4	8	no	—
85	#121×C₁₃₉	—	2	16	no	—
86	#121×C₁₃₉	—	4	16	no	—
87	#120×C₁₃₉	—	2	8	no	—
88	#120×C₁₃₉	—	2	8	no	—
89	#120×C₁₃₉	—	4	8	no	—
90	#120×C₁₃₉	—	4	8	no	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
107	C₂×C₄²×C₁₃₉	—	2	4	no	—
108	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
109	#95×C₁₃₉	C₂³	1	8	yes	—
110	#95×C₁₃₉	C₂³	1	8	yes	—
111	#95×C₁₃₉	C₂³	1	8	yes	—
112	C₂⁴×C₁₃₉	—	2	4	no	—
113	C₂⁴×C₁₃₉	—	2	4	no	—
114	C₂⁴×C₁₃₉	—	2	4	no	—
115	C₂⁴×C₁₃₉	—	2	2	no	—
116	C₂⁴×C₁₃₉	—	2	8	no	—
117	C₂⁴×C₁₃₉	—	4	4	no	—
118	C₂⁴×C₁₃₉	—	4	4	no	—
119	C₂⁴×C₁₃₉	—	4	4	no	—
120	C₂⁴×C₁₃₉	—	4	4	no	—
121	C₂⁴×C₁₃₉	—	4	2	no	—
122	C₂⁴×C₁₃₉	—	4	4	no	—
123	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
124	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
125	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
126	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
127	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
128	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
129	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
130	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
131	C₂×D₄×C₁₃₉	—	2	4	no	—
132	C₂×D₄×C₁₃₉	—	2	4	no	—
133	C₂×D₄×C₁₃₉	—	2	8	no	—
134	C₂×D₄×C₁₃₉	—	2	16	no	—
135	C₂×D₄×C₁₃₉	—	2	8	no	—
136	C₂×D₄×C₁₃₉	—	2	8	no	—
137	C₂×D₄×C₁₃₉	—	2	8	no	—
138	C₂×D₄×C₁₃₉	—	2	8	no	—
139	C₂×D₄×C₁₃₉	—	2	8	no	—
140	C₂×D₄×C₁₃₉	—	2	16	no	—
141	C₂×D₄×C₁₃₉	—	2	8	no	—
142	C₂×D₄×C₁₃₉	—	4	16	no	—
143	C₂×D₄×C₁₃₉	—	4	2	no	—
144	C₂×D₄×C₁₃₉	—	4	2	no	—
145	C₂×D₄×C₁₃₉	—	4	2	no	—
146	C₂×D₄×C₁₃₉	—	4	2	no	—
147	C₂×D₄×C₁₃₉	—	4	4	no	—
148	C₂×D₄×C₁₃₉	—	4	4	no	—
149	C₂×D₄×C₁₃₉	—	4	8	no	—
150	C₂×D₄×C₁₃₉	—	4	4	no	—
151	C₂×D₄×C₁₃₉	—	4	4	no	—
152	C₂×D₄×C₁₃₉	—	4	4	no	—
153	C₂×D₄×C₁₃₉	—	4	32	no	—
154	C₂×D₄×C₁₃₉	—	4	32	no	—
155	C₂×D₄×C₁₃₉	—	4	16	no	—
156	C₂×D₄×C₁₃₉	—	4	8	no	—
157	C₂×D₄×C₁₃₉	—	4	8	no	—
158	C₂×D₄×C₁₃₉	—	4	8	no	—
159	C₂×D₄×C₁₃₉	—	4	8	no	—
160	C₂×D₄×C₁₃₉	—	4	16	no	—
161	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
162	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
163	C₂²×C₄×C₁₃₉	—	2	4	no	—
164	C₂²×C₄×C₁₃₉	—	2	4	no	—
165	C₂²×C₄×C₁₃₉	—	2	8	no	—
166	C₂²×C₄×C₁₃₉	—	2	2	no	—
167	C₂²×C₄×C₁₃₉	—	2	4	no	—
168	C₂²×C₄×C₁₃₉	—	4	2	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	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
178	C₄⋊C₄×C₁₃₉	—	2	8	no	—
179	C₄⋊C₄×C₁₃₉	—	2	16	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
191	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
192	C₄²×C₁₃₉	—	2	8	no	—
193	C₂³×C₁₃₉	—	2	4	no	—
194	C₂³×C₁₃₉	—	2	2	no	—
195	C₂³×C₁₃₉	—	2	4	no	—
196	C₂³×C₁₃₉	—	2	4	no	—
197	C₂³×C₁₃₉	—	2	2	no	—
198	C₂³×C₁₃₉	—	2	8	no	—
199	C₂³×C₁₃₉	—	2	2	no	—
200	C₂³×C₁₃₉	—	2	2	no	—
201	C₂³×C₁₃₉	—	2	8	no	—
202	C₂³×C₁₃₉	—	2	8	no	—
203	C₂³×C₁₃₉	—	2	2	no	—
204	C₂³×C₁₃₉	—	2	4	no	—
205	C₂³×C₁₃₉	—	2	8	no	—
206	C₂³×C₁₃₉	—	2	4	no	—
207	C₂³×C₁₃₉	—	2	8	no	—
208	C₂³×C₁₃₉	—	2	8	no	—
209	C₂³×C₁₃₉	—	2	4	no	—
210	C₂³×C₁₃₉	—	2	4	no	—
211	C₂³×C₁₃₉	—	4	8	no	—
212	C₂³×C₁₃₉	—	4	8	no	—
213	C₂³×C₁₃₉	—	4	8	no	—
214	C₂³×C₁₃₉	—	4	8	no	—
215	C₂³×C₁₃₉	—	4	4	no	—
216	C₂³×C₁₃₉	—	4	8	no	—
217	C₂³×C₁₃₉	—	8	8	no	—
218	C₂³×C₁₃₉	—	8	8	no	—
219	C₂³×C₁₃₉	—	8	16	no	—
220	C₂³×C₁₃₉	—	8	4	no	—
221	C₂³×C₁₃₉	—	8	8	no	—
222	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
224	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
225	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
226	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
227	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
228	D₄×C₁₃₉	—	4	8	no	—
229	D₄×C₁₃₉	—	4	8	no	—
230	D₄×C₁₃₉	—	4	16	no	—
231	D₄×C₁₃₉	—	4	32	no	—
232	D₄×C₁₃₉	—	4	16	no	—
233	D₄×C₁₃₉	—	4	16	no	—
234	D₄×C₁₃₉	—	4	8	no	—
235	D₄×C₁₃₉	—	4	8	no	—
236	D₄×C₁₃₉	—	8	8	no	—
237	D₄×C₁₃₉	—	8	16	no	—
238	C₂×C₄×C₁₃₉	—	2	16	no	—
239	C₂×C₄×C₁₃₉	—	2	8	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	8	no	—
247	C₂×C₄×C₁₃₉	—	2	8	no	—
248	C₂×C₄×C₁₃₉	—	2	8	no	—
249	C₂×C₄×C₁₃₉	—	2	8	no	—
250	C₂×C₄×C₁₃₉	—	2	4	no	—
251	C₂×C₄×C₁₃₉	—	4	4	no	—
252	C₂×C₄×C₁₃₉	—	8	4	no	—
253	C₂×C₄×C₁₃₉	—	8	8	no	—
254	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	8	yes	—
256	C₂²×C₁₃₉	—	2	4	no	—
257	C₂²×C₁₃₉	—	2	8	no	—
258	C₂²×C₁₃₉	—	2	2	no	—
259	C₂²×C₁₃₉	—	2	2	no	—
260	C₂²×C₁₃₉	—	2	4	no	—
261	C₂²×C₁₃₉	—	2	4	no	—
262	C₂²×C₁₃₉	—	2	8	no	—
263	C₂²×C₁₃₉	—	2	4	no	—
264	C₂²×C₁₃₉	—	4	4	no	—
265	C₂²×C₁₃₉	—	4	4	no	—
266	C₂²×C₁₃₉	—	4	4	no	—
267	C₂²×C₁₃₉	—	4	4	no	—
268	C₂²×C₁₃₉	—	4	4	no	—
269	C₂²×C₁₃₉	—	4	2	no	—
270	C₂²×C₁₃₉	—	4	4	no	—
271	C₂²×C₁₃₉	—	4	4	no	—
272	C₂²×C₁₃₉	—	4	4	no	—
273	C₂²×C₁₃₉	—	4	8	no	—
274	C₂²×C₁₃₉	—	4	8	no	—
275	C₂²×C₁₃₉	—	4	8	no	—
276	C₂²×C₁₃₉	—	8	8	no	—
277	C₂²×C₁₃₉	—	8	8	no	—
278	C₂²×C₁₃₉	—	8	16	no	—
279	C₂²×C₁₃₉	—	8	8	no	—
280	C₂²×C₁₃₉	#534	1	4	yes	—
281	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
282	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
283	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	4	yes	—
284	C₄×C₁₃₉	—	2	4	no	—
285	C₄×C₁₃₉	—	2	8	no	—
286	C₄×C₁₃₉	—	4	2	no	—
287	C₄×C₁₃₉	—	4	4	no	—
288	C₄×C₁₃₉	—	4	8	no	—
289	C₂×C₁₃₉	—	2	4	no	—
290	C₂×C₁₃₉	—	4	2	no	—
291	C₂×C₁₃₉	—	4	4	no	—
292	C₂×C₁₃₉	—	4	2	no	—
293	C₂×C₁₃₉	—	8	4	no	—
294	C₂×C₁₃₉	—	8	2	no	—
295	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
296	C₂×C₁₃₉	#3484	1	2	yes	—
297	C₂×C₁₃₉	#3543	1	4	yes	—
298	#37232	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₁₃₉	#37232	1	1	yes	characteristic, direct product factor, Sylow
300	C₂×#534	C₂×C₁₃₉	1	1	yes	characteristic, complemented
301	C₂²×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
302	#2853	C₂×C₁₃₉	1	2	yes	complemented
303	#2709	C₂×C₁₃₉	1	4	yes	complemented
304	#2673	C₂×C₁₃₉	1	8	yes	complemented
305	#2669	C₂×C₁₃₉	1	4	yes	complemented
306	#2613	C₂×C₁₃₉	1	2	yes	complemented
307	#2410	C₂×C₁₃₉	1	4	yes	complemented
308	#2405	C₂×C₁₃₉	1	2	yes	complemented
309	#2403	C₂×C₁₃₉	1	2	yes	complemented
310	#2308	C₂×C₁₃₉	1	1	yes	characteristic, complemented
311	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
312	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
313	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
314	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
315	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	complemented
316	#534	—	2	8	no	—
317	C₂×#127	—	2	8	no	—
318	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
319	C₂×#127	C₂²×C₁₃₉	1	4	yes	complemented
320	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
321	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
322	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
323	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
324	C₂×#121	C₂²×C₁₃₉	1	8	yes	complemented
325	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
326	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
327	C₂×#120	C₂²×C₁₃₉	1	2	yes	complemented
328	C₂×#120	C₂²×C₁₃₉	1	4	yes	complemented
329	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
331	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
332	#394	C₂²×C₁₃₉	1	8	yes	complemented
333	#394	C₂²×C₁₃₉	1	8	yes	complemented
334	#394	C₂²×C₁₃₉	1	8	yes	complemented
335	#392	C₂²×C₁₃₉	1	8	yes	complemented
336	#392	C₂²×C₁₃₉	1	8	yes	complemented
337	#392	C₂²×C₁₃₉	1	8	yes	complemented
338	#388	C₂²×C₁₃₉	1	8	yes	complemented
339	#387	C₂²×C₁₃₉	1	8	yes	complemented
340	#386	C₂²×C₁₃₉	1	4	yes	—
341	#386	C₂²×C₁₃₉	1	4	yes	complemented
342	#386	C₂²×C₁₃₉	1	4	yes	complemented
343	#386	C₂²×C₁₃₉	1	4	yes	complemented
344	#386	C₂²×C₁₃₉	1	4	yes	complemented
345	#386	C₂²×C₁₃₉	1	8	yes	complemented
346	#385	C₂²×C₁₃₉	1	4	yes	complemented
347	#381	C₂²×C₁₃₉	1	2	yes	complemented
348	#379	C₂²×C₁₃₉	1	2	yes	—
349	#379	C₂²×C₁₃₉	1	4	yes	complemented
350	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
351	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
352	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
353	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
354	C₂²×D₄	—	2	8	no	—
355	C₂²×D₄	—	2	8	no	—
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	—	2	4	no	—
358	C₂²×D₄	—	4	8	no	—
359	C₂²×D₄	—	4	8	no	—
360	C₂²×D₄	—	4	4	no	—
361	C₂²×D₄	—	4	4	no	—
362	C₂²×D₄	—	4	4	no	—
363	C₂²×D₄	D₄×C₁₃₉	1	8	yes	complemented
364	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
365	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
366	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
367	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
368	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
369	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
370	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
371	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
372	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
373	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
375	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
377	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
379	#127	—	2	16	no	—
380	#127	—	2	16	no	—
381	#123	—	2	8	no	—
382	#123	—	2	8	no	—
383	#123	—	4	8	no	—
384	#121	—	2	16	no	—
385	#121	—	4	16	no	—
386	#120	—	2	8	no	—
387	#120	—	2	8	no	—
388	#120	—	4	8	no	—
389	#120	—	4	8	no	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
392	C₂×C₂²⋊C₄	—	2	4	no	—
393	C₂×C₂²⋊C₄	—	4	4	no	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
406	C₂×C₄²	—	2	4	no	—
407	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
408	#95	C₂³×C₁₃₉	1	8	yes	—
409	#95	C₂³×C₁₃₉	1	8	yes	—
410	#95	C₂³×C₁₃₉	1	8	yes	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	8	no	—
416	C₂⁴	—	4	4	no	—
417	C₂⁴	—	4	4	no	—
418	C₂⁴	—	4	4	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	4	2	no	—
421	C₂⁴	—	4	4	no	—
422	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
423	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
424	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
425	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
426	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
427	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
428	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
429	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	16	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	4	16	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	8	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	32	no	—
453	C₂×D₄	—	4	32	no	—
454	C₂×D₄	—	4	16	no	—
455	C₂×D₄	—	4	8	no	—
456	C₂×D₄	—	4	8	no	—
457	C₂×D₄	—	4	8	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	—	4	16	no	—
460	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
461	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	—	4	8	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
473	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	16	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	16	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	8	no	—
488	C₂²⋊C₄	—	4	8	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	4	8	no	—
491	C₄²	—	2	8	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	8	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	8	no	—
507	C₂³	—	2	8	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	8	no	—
516	C₂³	—	8	8	no	—
517	C₂³	—	8	8	no	—
518	C₂³	—	8	16	no	—
519	C₂³	—	8	4	no	—
520	C₂³	—	8	8	no	—
521	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
522	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
523	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
524	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
525	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
526	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
527	D₄	—	4	8	no	—
528	D₄	—	4	8	no	—
529	D₄	—	4	16	no	—
530	D₄	—	4	32	no	—
531	D₄	—	4	16	no	—
532	D₄	—	4	16	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	8	no	—
535	D₄	—	8	8	no	—
536	D₄	—	8	16	no	—
537	C₂×C₄	—	2	16	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	8	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	8	4	no	—
552	C₂×C₄	—	8	8	no	—
553	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
554	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	8	yes	—
555	C₂²	—	2	8	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	4	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	8	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	4	8	no	—
569	C₂²	—	4	8	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	8	8	no	—
576	C₂²	—	8	8	no	—
577	C₂²	—	8	16	no	—
578	C₂²	—	8	8	no	—
579	C₂²	#534×C₁₃₉	1	4	yes	—
580	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
581	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
582	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	4	yes	—
583	C₄	—	2	4	no	—
584	C₄	—	2	8	no	—
585	C₄	—	4	8	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	4	no	—
588	C₂	—	2	4	no	—
589	C₂	—	4	2	no	—
590	C₂	—	4	2	no	—
591	C₂	—	4	4	no	—
592	C₂	—	8	2	no	—
593	C₂	—	8	4	no	—
594	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
595	C₂	#3484×C₁₃₉	1	2	yes	—
596	C₂	#3543×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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
1. C₂×#534×C₁₃₉	C₂	semidirect
2. C₂²×#127×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2709×C₁₃₉	C₂	semidirect
5. #2673×C₁₃₉	C₂	semidirect
6. #2669×C₁₃₉	C₂	semidirect
7. #2613×C₁₃₉	C₂	semidirect
8. #2410×C₁₃₉	C₂	semidirect
9. #2405×C₁₃₉	C₂	semidirect
10. #2403×C₁₃₉	C₂	semidirect
11. #2308×C₁₃₉	C₂	semidirect
15. C₂³×D₄×C₁₃₉	C₂²	semidirect
16. C₂³×D₄×C₁₃₉	C₂²	semidirect
20. C₂×#127×C₁₃₉	C₂²	semidirect
22. C₂×#123×C₁₃₉	C₂²	semidirect
23. C₂×#123×C₁₃₉	C₂²	semidirect
24. C₂×#121×C₁₃₉	C₂²	semidirect
25. C₂×#121×C₁₃₉	C₂²	semidirect
28. C₂×#120×C₁₃₉	C₂²	semidirect
29. C₂×#120×C₁₃₉	C₂²	semidirect
31. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
32. C₂²×C₄²×C₁₃₉	C₂²	semidirect
33. #394×C₁₃₉	C₂²	semidirect
34. #394×C₁₃₉	C₂²	semidirect
35. #394×C₁₃₉	C₂²	semidirect
36. #392×C₁₃₉	C₂²	semidirect
37. #392×C₁₃₉	C₂²	semidirect
38. #392×C₁₃₉	C₂²	semidirect
39. #388×C₁₃₉	C₂²	semidirect
40. #387×C₁₃₉	C₂²	semidirect
42. #386×C₁₃₉	C₂²	semidirect
43. #386×C₁₃₉	C₂²	semidirect
44. #386×C₁₃₉	C₂²	semidirect
45. #386×C₁₃₉	C₂²	semidirect
46. #386×C₁₃₉	C₂²	semidirect
47. #385×C₁₃₉	C₂²	semidirect
48. #381×C₁₃₉	C₂²	semidirect
50. #379×C₁₃₉	C₂²	semidirect
64. C₂²×D₄×C₁₃₉	D₄	semidirect
298. #37232	C₁₃₉	direct (N × H)
299. C₁₃₉	#37232	direct (N × H)
300. C₂×#534	C₂×C₁₃₉	semidirect
301. C₂²×#127	C₂×C₁₃₉	semidirect
302. #2853	C₂×C₁₃₉	semidirect
303. #2709	C₂×C₁₃₉	semidirect
304. #2673	C₂×C₁₃₉	semidirect
305. #2669	C₂×C₁₃₉	semidirect
306. #2613	C₂×C₁₃₉	semidirect
307. #2410	C₂×C₁₃₉	semidirect
308. #2405	C₂×C₁₃₉	semidirect
309. #2403	C₂×C₁₃₉	semidirect
310. #2308	C₂×C₁₃₉	semidirect
314. C₂³×D₄	C₂²×C₁₃₉	semidirect
315. C₂³×D₄	C₂²×C₁₃₉	semidirect
319. C₂×#127	C₂²×C₁₃₉	semidirect
321. C₂×#123	C₂²×C₁₃₉	semidirect
322. C₂×#123	C₂²×C₁₃₉	semidirect
323. C₂×#121	C₂²×C₁₃₉	semidirect
324. C₂×#121	C₂²×C₁₃₉	semidirect
327. C₂×#120	C₂²×C₁₃₉	semidirect
328. C₂×#120	C₂²×C₁₃₉	semidirect
330. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
331. C₂²×C₄²	C₂²×C₁₃₉	semidirect
332. #394	C₂²×C₁₃₉	semidirect
333. #394	C₂²×C₁₃₉	semidirect
334. #394	C₂²×C₁₃₉	semidirect
335. #392	C₂²×C₁₃₉	semidirect
336. #392	C₂²×C₁₃₉	semidirect
337. #392	C₂²×C₁₃₉	semidirect
338. #388	C₂²×C₁₃₉	semidirect
339. #387	C₂²×C₁₃₉	semidirect
341. #386	C₂²×C₁₃₉	semidirect
342. #386	C₂²×C₁₃₉	semidirect
343. #386	C₂²×C₁₃₉	semidirect
344. #386	C₂²×C₁₃₉	semidirect
345. #386	C₂²×C₁₃₉	semidirect
346. #385	C₂²×C₁₃₉	semidirect
347. #381	C₂²×C₁₃₉	semidirect
349. #379	C₂²×C₁₃₉	semidirect
363. C₂²×D₄	D₄×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×#127×C₁₃₉	2
#2853×C₁₃₉	2
#2709×C₁₃₉	2
#2673×C₁₃₉	2
#2669×C₁₃₉	2
#2613×C₁₃₉	2
#2410×C₁₃₉	2
#2405×C₁₃₉	2
#2403×C₁₃₉	2
#2308×C₁₃₉	2
#37232	139

Subgroups — C139×#37232 #48031828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37232 #48031828