Subgroups — C₂×#1781×C₁₃₉ #48015178

Order 35584.

6254 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#99×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	C₂×#379×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#1781×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂⁶×C₁₃₉	C₄	1	1	yes	characteristic, complemented
6	C₂⁶×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂³×D₄×C₁₃₉	—	2	4	no	—
8	C₂³×D₄×C₁₃₉	—	2	4	no	—
9	C₂³×D₄×C₁₃₉	—	2	16	no	—
10	C₂³×D₄×C₁₃₉	C₄	1	2	yes	complemented
11	C₂³×D₄×C₁₃₉	C₄	1	4	yes	complemented
12	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	—
14	C₂⁴×C₄×C₁₃₉	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
16	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
17	C₂×#99×C₁₃₉	—	2	16	no	—
18	C₂×#99×C₁₃₉	C₂²	1	16	yes	complemented
19	#379×C₁₃₉	—	2	4	no	—
20	#379×C₁₃₉	C₂²	1	8	yes	complemented
21	C₂⁵×C₁₃₉	—	2	2	no	—
22	C₂⁵×C₁₃₉	—	2	2	no	—
23	C₂⁵×C₁₃₉	—	2	8	no	—
24	C₂⁵×C₁₃₉	—	2	8	no	—
25	C₂⁵×C₁₃₉	—	4	8	no	—
26	C₂⁵×C₁₃₉	—	4	8	no	—
27	C₂⁵×C₁₃₉	C₂×C₄	1	1	yes	characteristic
28	C₂⁵×C₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂⁵×C₁₃₉	C₂×C₄	1	2	yes	—
30	C₂⁵×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₂⁵×C₁₃₉	C₂×C₄	1	4	yes	complemented
32	C₂⁵×C₁₃₉	D₄	1	4	yes	—
33	C₂⁵×C₁₃₉	D₄	1	4	yes	—
34	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
35	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₃₉	—	2	64	no	—
37	C₂²×D₄×C₁₃₉	—	2	64	no	—
38	C₂²×D₄×C₁₃₉	—	2	4	no	—
39	C₂²×D₄×C₁₃₉	—	2	16	no	—
40	C₂²×D₄×C₁₃₉	—	2	4	no	—
41	C₂²×D₄×C₁₃₉	—	2	8	no	—
42	C₂²×D₄×C₁₃₉	—	2	4	no	—
43	C₂²×D₄×C₁₃₉	—	2	8	no	—
44	C₂²×D₄×C₁₃₉	—	2	16	no	—
45	C₂²×D₄×C₁₃₉	—	2	4	no	—
46	C₂²×D₄×C₁₃₉	—	2	32	no	—
47	C₂²×D₄×C₁₃₉	—	2	32	no	—
48	C₂²×D₄×C₁₃₉	—	2	8	no	—
49	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
50	C₂²×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
51	C₂²×D₄×C₁₃₉	D₄	1	16	yes	—
52	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃₉	—	2	2	no	—
54	C₂³×C₄×C₁₃₉	—	2	2	no	—
55	C₂³×C₄×C₁₃₉	—	2	8	no	—
56	C₂³×C₄×C₁₃₉	—	2	4	no	—
57	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
58	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	4	16	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	complemented
64	#99×C₁₃₉	—	2	32	no	—
65	C₂⁴×C₁₃₉	—	2	8	no	—
66	C₂⁴×C₁₃₉	—	2	4	no	—
67	C₂⁴×C₁₃₉	—	2	16	no	—
68	C₂⁴×C₁₃₉	—	2	16	no	—
69	C₂⁴×C₁₃₉	—	2	16	no	—
70	C₂⁴×C₁₃₉	—	2	8	no	—
71	C₂⁴×C₁₃₉	—	2	4	no	—
72	C₂⁴×C₁₃₉	—	2	2	no	—
73	C₂⁴×C₁₃₉	—	2	4	no	—
74	C₂⁴×C₁₃₉	—	2	8	no	—
75	C₂⁴×C₁₃₉	—	2	2	no	—
76	C₂⁴×C₁₃₉	—	2	16	no	—
77	C₂⁴×C₁₃₉	—	2	16	no	—
78	C₂⁴×C₁₃₉	—	2	16	no	—
79	C₂⁴×C₁₃₉	—	2	8	no	—
80	C₂⁴×C₁₃₉	—	4	4	no	—
81	C₂⁴×C₁₃₉	—	4	8	no	—
82	C₂⁴×C₁₃₉	—	4	8	no	—
83	C₂⁴×C₁₃₉	—	4	16	no	—
84	C₂⁴×C₁₃₉	—	4	4	no	—
85	C₂⁴×C₁₃₉	—	4	8	no	—
86	C₂⁴×C₁₃₉	—	4	8	no	—
87	C₂⁴×C₁₃₉	—	4	16	no	—
88	C₂⁴×C₁₃₉	—	4	64	no	—
89	C₂⁴×C₁₃₉	—	4	64	no	—
90	C₂⁴×C₁₃₉	—	4	8	no	—
91	C₂⁴×C₁₃₉	—	4	16	no	—
92	C₂⁴×C₁₃₉	—	4	8	no	—
93	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
94	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
95	C₂⁴×C₁₃₉	C₂²⋊C₄	1	8	yes	—
96	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
97	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
98	C₂⁴×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
99	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
100	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
101	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₁₃₉	C₂²×C₄	1	4	yes	—
103	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
105	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
106	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
108	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
109	C₂×D₄×C₁₃₉	—	2	128	no	—
110	C₂×D₄×C₁₃₉	—	2	128	no	—
111	C₂×D₄×C₁₃₉	—	2	32	no	—
112	C₂×D₄×C₁₃₉	—	2	32	no	—
113	C₂×D₄×C₁₃₉	—	2	8	no	—
114	C₂×D₄×C₁₃₉	—	2	8	no	—
115	C₂×D₄×C₁₃₉	—	2	16	no	—
116	C₂×D₄×C₁₃₉	—	2	16	no	—
117	C₂×D₄×C₁₃₉	—	2	32	no	—
118	C₂×D₄×C₁₃₉	—	2	32	no	—
119	C₂×D₄×C₁₃₉	—	2	8	no	—
120	C₂×D₄×C₁₃₉	—	2	8	no	—
121	C₂×D₄×C₁₃₉	—	2	16	no	—
122	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	16	yes	complemented
123	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
124	C₂²×C₄×C₁₃₉	—	2	16	no	—
125	C₂²×C₄×C₁₃₉	—	2	16	no	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	4	no	—
128	C₂²×C₄×C₁₃₉	—	2	8	no	—
129	C₂²×C₄×C₁₃₉	—	2	2	no	—
130	C₂²×C₄×C₁₃₉	—	2	16	no	—
131	C₂²×C₄×C₁₃₉	—	2	8	no	—
132	C₂²×C₄×C₁₃₉	—	4	16	no	—
133	C₂²×C₄×C₁₃₉	—	4	8	no	—
134	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
135	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
136	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
137	C₂²⋊C₄×C₁₃₉	—	4	32	no	—
138	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
139	C₂³×C₁₃₉	—	2	32	no	—
140	C₂³×C₁₃₉	—	2	4	no	—
141	C₂³×C₁₃₉	—	2	4	no	—
142	C₂³×C₁₃₉	—	2	4	no	—
143	C₂³×C₁₃₉	—	2	8	no	—
144	C₂³×C₁₃₉	—	2	4	no	—
145	C₂³×C₁₃₉	—	2	4	no	—
146	C₂³×C₁₃₉	—	2	8	no	—
147	C₂³×C₁₃₉	—	2	8	no	—
148	C₂³×C₁₃₉	—	2	32	no	—
149	C₂³×C₁₃₉	—	2	4	no	—
150	C₂³×C₁₃₉	—	2	4	no	—
151	C₂³×C₁₃₉	—	2	4	no	—
152	C₂³×C₁₃₉	—	2	16	no	—
153	C₂³×C₁₃₉	—	2	16	no	—
154	C₂³×C₁₃₉	—	2	4	no	—
155	C₂³×C₁₃₉	—	2	4	no	—
156	C₂³×C₁₃₉	—	2	8	no	—
157	C₂³×C₁₃₉	—	2	8	no	—
158	C₂³×C₁₃₉	—	2	8	no	—
159	C₂³×C₁₃₉	—	2	16	no	—
160	C₂³×C₁₃₉	—	2	16	no	—
161	C₂³×C₁₃₉	—	4	8	no	—
162	C₂³×C₁₃₉	—	4	4	no	—
163	C₂³×C₁₃₉	—	4	2	no	—
164	C₂³×C₁₃₉	—	4	4	no	—
165	C₂³×C₁₃₉	—	4	4	no	—
166	C₂³×C₁₃₉	—	4	8	no	—
167	C₂³×C₁₃₉	—	4	16	no	—
168	C₂³×C₁₃₉	—	4	2	no	—
169	C₂³×C₁₃₉	—	4	64	no	—
170	C₂³×C₁₃₉	—	4	16	no	—
171	C₂³×C₁₃₉	—	4	8	no	—
172	C₂³×C₁₃₉	—	4	32	no	—
173	C₂³×C₁₃₉	—	4	64	no	—
174	C₂³×C₁₃₉	—	4	32	no	—
175	C₂³×C₁₃₉	—	4	64	no	—
176	C₂³×C₁₃₉	—	4	64	no	—
177	C₂³×C₁₃₉	—	4	8	no	—
178	C₂³×C₁₃₉	—	4	16	no	—
179	C₂³×C₁₃₉	—	4	64	no	—
180	C₂³×C₁₃₉	—	4	16	no	—
181	C₂³×C₁₃₉	—	4	16	no	—
182	C₂³×C₁₃₉	—	4	8	no	—
183	C₂³×C₁₃₉	—	4	16	no	—
184	C₂³×C₁₃₉	#99	1	8	yes	complemented
185	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
190	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	complemented
193	C₂³×C₁₃₉	#120	1	8	yes	—
194	C₂³×C₁₃₉	#120	1	8	yes	—
195	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
196	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
197	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
198	D₄×C₁₃₉	—	2	64	no	—
199	D₄×C₁₃₉	—	2	32	no	—
200	D₄×C₁₃₉	—	2	32	no	—
201	C₂×C₄×C₁₃₉	—	2	32	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	8	no	—
205	C₂×C₄×C₁₃₉	—	2	8	no	—
206	C₂×C₄×C₁₃₉	—	4	16	no	—
207	C₂×C₄×C₁₃₉	—	4	8	no	—
208	C₂×C₄×C₁₃₉	—	8	16	no	—
209	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	complemented
210	C₂²×C₁₃₉	—	2	16	no	—
211	C₂²×C₁₃₉	—	2	16	no	—
212	C₂²×C₁₃₉	—	2	4	no	—
213	C₂²×C₁₃₉	—	2	2	no	—
214	C₂²×C₁₃₉	—	2	4	no	—
215	C₂²×C₁₃₉	—	2	2	no	—
216	C₂²×C₁₃₉	—	2	4	no	—
217	C₂²×C₁₃₉	—	2	4	no	—
218	C₂²×C₁₃₉	—	2	16	no	—
219	C₂²×C₁₃₉	—	2	16	no	—
220	C₂²×C₁₃₉	—	2	8	no	—
221	C₂²×C₁₃₉	—	2	8	no	—
222	C₂²×C₁₃₉	—	2	4	no	—
223	C₂²×C₁₃₉	—	2	8	no	—
224	C₂²×C₁₃₉	—	4	4	no	—
225	C₂²×C₁₃₉	—	4	8	no	—
226	C₂²×C₁₃₉	—	4	4	no	—
227	C₂²×C₁₃₉	—	4	32	no	—
228	C₂²×C₁₃₉	—	4	32	no	—
229	C₂²×C₁₃₉	—	4	8	no	—
230	C₂²×C₁₃₉	—	4	8	no	—
231	C₂²×C₁₃₉	—	4	8	no	—
232	C₂²×C₁₃₉	—	4	8	no	—
233	C₂²×C₁₃₉	—	4	16	no	—
234	C₂²×C₁₃₉	—	4	64	no	—
235	C₂²×C₁₃₉	—	4	8	no	—
236	C₂²×C₁₃₉	—	4	8	no	—
237	C₂²×C₁₃₉	—	4	16	no	—
238	C₂²×C₁₃₉	#379	1	2	yes	—
239	C₂²×C₁₃₉	#379	1	4	yes	—
240	C₂²×C₁₃₉	#379	1	2	yes	—
241	C₂²×C₁₃₉	C₂×#99	1	4	yes	—
242	C₂²×C₁₃₉	C₂×#99	1	8	yes	complemented
243	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	2	yes	—
244	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₁₃₉	C₂×#120	1	4	yes	—
246	C₄×C₁₃₉	—	2	8	no	—
247	C₄×C₁₃₉	—	8	8	no	—
248	C₂×C₁₃₉	—	2	4	no	—
249	C₂×C₁₃₉	—	2	2	no	—
250	C₂×C₁₃₉	—	2	2	no	—
251	C₂×C₁₃₉	—	2	8	no	—
252	C₂×C₁₃₉	—	2	4	no	—
253	C₂×C₁₃₉	—	4	4	no	—
254	C₂×C₁₃₉	—	4	8	no	—
255	C₂×C₁₃₉	#1781	1	4	yes	direct product factor
256	C₂×C₁₃₉	C₂×#379	1	1	yes	characteristic
257	C₂×C₁₃₉	C₂²×#99	1	2	yes	—
258	C₂×#1781	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₁₃₉	C₂×#1781	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴×D₄	C₂×C₁₃₉	1	1	yes	characteristic
261	C₂²×#99	C₂×C₁₃₉	1	4	yes	complemented
262	C₂×#379	C₂×C₁₃₉	1	2	yes	complemented
263	#1781	C₂×C₁₃₉	1	8	yes	direct product factor
264	C₂⁶	C₄×C₁₃₉	1	1	yes	characteristic, complemented
265	C₂⁶	C₂²×C₁₃₉	1	1	yes	characteristic
266	C₂³×D₄	—	2	4	no	—
267	C₂³×D₄	—	2	4	no	—
268	C₂³×D₄	—	2	16	no	—
269	C₂³×D₄	C₄×C₁₃₉	1	2	yes	complemented
270	C₂³×D₄	C₄×C₁₃₉	1	4	yes	complemented
271	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
272	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	—
273	C₂⁴×C₄	C₄×C₁₃₉	1	1	yes	characteristic, complemented
274	C₂²×C₂²⋊C₄	—	2	4	no	—
275	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
276	C₂×#99	—	2	16	no	—
277	C₂×#99	C₂²×C₁₃₉	1	16	yes	complemented
278	#379	—	2	4	no	—
279	#379	C₂²×C₁₃₉	1	8	yes	complemented
280	C₂⁵	—	2	2	no	—
281	C₂⁵	—	2	2	no	—
282	C₂⁵	—	2	8	no	—
283	C₂⁵	—	2	8	no	—
284	C₂⁵	—	4	8	no	—
285	C₂⁵	—	4	8	no	—
286	C₂⁵	C₂×C₄×C₁₃₉	1	1	yes	characteristic
287	C₂⁵	C₂×C₄×C₁₃₉	1	1	yes	characteristic
288	C₂⁵	C₂×C₄×C₁₃₉	1	2	yes	—
289	C₂⁵	C₂×C₄×C₁₃₉	1	2	yes	—
290	C₂⁵	C₂×C₄×C₁₃₉	1	4	yes	complemented
291	C₂⁵	D₄×C₁₃₉	1	4	yes	—
292	C₂⁵	D₄×C₁₃₉	1	4	yes	—
293	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
294	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
295	C₂²×D₄	—	2	64	no	—
296	C₂²×D₄	—	2	64	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	—	2	16	no	—
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	—	2	4	no	—
303	C₂²×D₄	—	2	8	no	—
304	C₂²×D₄	—	2	16	no	—
305	C₂²×D₄	—	2	32	no	—
306	C₂²×D₄	—	2	32	no	—
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
309	C₂²×D₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
310	C₂²×D₄	D₄×C₁₃₉	1	16	yes	—
311	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	—	2	2	no	—
314	C₂³×C₄	—	2	8	no	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
317	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
318	C₂×C₂²⋊C₄	—	2	16	no	—
319	C₂×C₂²⋊C₄	—	2	16	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	4	16	no	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	complemented
323	#99	—	2	32	no	—
324	C₂⁴	—	2	8	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	2	16	no	—
327	C₂⁴	—	2	16	no	—
328	C₂⁴	—	2	16	no	—
329	C₂⁴	—	2	8	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	2	8	no	—
335	C₂⁴	—	2	16	no	—
336	C₂⁴	—	2	16	no	—
337	C₂⁴	—	2	16	no	—
338	C₂⁴	—	2	8	no	—
339	C₂⁴	—	4	4	no	—
340	C₂⁴	—	4	8	no	—
341	C₂⁴	—	4	8	no	—
342	C₂⁴	—	4	16	no	—
343	C₂⁴	—	4	4	no	—
344	C₂⁴	—	4	8	no	—
345	C₂⁴	—	4	8	no	—
346	C₂⁴	—	4	16	no	—
347	C₂⁴	—	4	64	no	—
348	C₂⁴	—	4	64	no	—
349	C₂⁴	—	4	8	no	—
350	C₂⁴	—	4	16	no	—
351	C₂⁴	—	4	8	no	—
352	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
353	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
354	C₂⁴	C₂²⋊C₄×C₁₃₉	1	8	yes	—
355	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
356	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
357	C₂⁴	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
358	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
359	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
360	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
361	C₂⁴	C₂²×C₄×C₁₃₉	1	4	yes	—
362	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
363	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
364	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
365	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
366	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
367	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
368	C₂×D₄	—	2	128	no	—
369	C₂×D₄	—	2	128	no	—
370	C₂×D₄	—	2	32	no	—
371	C₂×D₄	—	2	32	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	16	no	—
375	C₂×D₄	—	2	16	no	—
376	C₂×D₄	—	2	32	no	—
377	C₂×D₄	—	2	32	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	16	no	—
381	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	16	yes	complemented
382	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
383	C₂²×C₄	—	2	16	no	—
384	C₂²×C₄	—	2	16	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	16	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	4	16	no	—
392	C₂²×C₄	—	4	8	no	—
393	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
394	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
395	C₂²⋊C₄	—	2	16	no	—
396	C₂²⋊C₄	—	4	32	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₂³	—	2	32	no	—
399	C₂³	—	2	8	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	8	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	32	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	16	no	—
410	C₂³	—	2	16	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	16	no	—
415	C₂³	—	2	16	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	8	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	4	8	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	16	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	64	no	—
429	C₂³	—	4	16	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	32	no	—
432	C₂³	—	4	64	no	—
433	C₂³	—	4	32	no	—
434	C₂³	—	4	64	no	—
435	C₂³	—	4	64	no	—
436	C₂³	—	4	64	no	—
437	C₂³	—	4	16	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	16	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	16	no	—
443	C₂³	#99×C₁₃₉	1	8	yes	complemented
444	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
445	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
446	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
447	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
448	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
449	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
450	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
451	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
452	C₂³	#120×C₁₃₉	1	8	yes	—
453	C₂³	#120×C₁₃₉	1	8	yes	—
454	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
455	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
456	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
457	D₄	—	2	64	no	—
458	D₄	—	2	32	no	—
459	D₄	—	2	32	no	—
460	C₂×C₄	—	2	32	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	4	16	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	8	16	no	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
469	C₂²	—	2	16	no	—
470	C₂²	—	2	16	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	16	no	—
473	C₂²	—	2	16	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	32	no	—
487	C₂²	—	4	32	no	—
488	C₂²	—	4	8	no	—
489	C₂²	—	4	64	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	16	no	—
494	C₂²	—	4	8	no	—
495	C₂²	—	4	16	no	—
496	C₂²	—	4	8	no	—
497	C₂²	#379×C₁₃₉	1	2	yes	—
498	C₂²	#379×C₁₃₉	1	4	yes	—
499	C₂²	#379×C₁₃₉	1	2	yes	—
500	C₂²	C₂×#99×C₁₃₉	1	4	yes	—
501	C₂²	C₂×#99×C₁₃₉	1	8	yes	complemented
502	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	2	yes	—
503	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
504	C₂²	C₂×#120×C₁₃₉	1	4	yes	—
505	C₄	—	2	8	no	—
506	C₄	—	8	8	no	—
507	C₂	—	2	4	no	—
508	C₂	—	2	8	no	—
509	C₂	—	2	2	no	—
510	C₂	—	2	2	no	—
511	C₂	—	2	4	no	—
512	C₂	—	4	4	no	—
513	C₂	—	4	8	no	—
514	C₂	#1781×C₁₃₉	1	4	yes	direct product factor
515	C₂	C₂×#379×C₁₃₉	1	1	yes	characteristic
516	C₂	C₂²×#99×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
prime radical	C₂⁴×D₄×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁶×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×#99×C₁₃₉	C₂	semidirect
3. C₂×#379×C₁₃₉	C₂	semidirect
4. #1781×C₁₃₉	C₂	direct (N × H)
5. C₂⁶×C₁₃₉	C₄	semidirect
10. C₂³×D₄×C₁₃₉	C₄	semidirect
11. C₂³×D₄×C₁₃₉	C₄	semidirect
14. C₂⁴×C₄×C₁₃₉	C₄	semidirect
16. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
18. C₂×#99×C₁₃₉	C₂²	semidirect
20. #379×C₁₃₉	C₂²	semidirect
31. C₂⁵×C₁₃₉	C₂×C₄	semidirect
50. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
58. C₂³×C₄×C₁₃₉	C₂×C₄	semidirect
63. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
98. C₂⁴×C₁₃₉	C₂²⋊C₄	semidirect
122. C₂×D₄×C₁₃₉	C₂²⋊C₄	semidirect
134. C₂²×C₄×C₁₃₉	C₂²⋊C₄	semidirect
184. C₂³×C₁₃₉	#99	semidirect
192. C₂³×C₁₃₉	C₂×C₂²⋊C₄	semidirect
209. C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	semidirect
242. C₂²×C₁₃₉	C₂×#99	semidirect
255. C₂×C₁₃₉	#1781	direct (N × H)
258. C₂×#1781	C₁₃₉	direct (N × H)
259. C₁₃₉	C₂×#1781	direct (N × H)
261. C₂²×#99	C₂×C₁₃₉	semidirect
262. C₂×#379	C₂×C₁₃₉	semidirect
263. #1781	C₂×C₁₃₉	direct (N × H)
264. C₂⁶	C₄×C₁₃₉	semidirect
269. C₂³×D₄	C₄×C₁₃₉	semidirect
270. C₂³×D₄	C₄×C₁₃₉	semidirect
273. C₂⁴×C₄	C₄×C₁₃₉	semidirect
275. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
277. C₂×#99	C₂²×C₁₃₉	semidirect
279. #379	C₂²×C₁₃₉	semidirect
290. C₂⁵	C₂×C₄×C₁₃₉	semidirect
309. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
317. C₂³×C₄	C₂×C₄×C₁₃₉	semidirect
322. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
357. C₂⁴	C₂²⋊C₄×C₁₃₉	semidirect
381. C₂×D₄	C₂²⋊C₄×C₁₃₉	semidirect
393. C₂²×C₄	C₂²⋊C₄×C₁₃₉	semidirect
443. C₂³	#99×C₁₃₉	semidirect
451. C₂³	C₂×C₂²⋊C₄×C₁₃₉	semidirect
468. C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	semidirect
501. C₂²	C₂×#99×C₁₃₉	semidirect
514. C₂	#1781×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₃₉	2
C₂²×#99×C₁₃₉	2
C₂×#379×C₁₃₉	2
#1781×C₁₃₉	2
C₂×#1781	139

Subgroups — C2×#1781×C139 #48015178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1781×C₁₃₉ #48015178