Subgroups — C₄×#392×C₁₃₉ #48008453

Order 35584.

3502 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃₉	C₂	1	3	yes	maximal, complemented
2	C₂×#392×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#1444×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1439×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#1438×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	C₄×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₃₉	C₂²	1	3	yes	—
9	C₂⁴×C₄×C₁₃₉	C₂²	1	3	yes	—
10	C₂×C₄×D₄×C₁₃₉	—	2	24	no	—
11	C₂×C₄×D₄×C₁₃₉	—	2	12	no	—
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
13	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
14	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
15	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
16	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃₉	C₂²	1	3	yes	—
18	#392×C₁₃₉	C₄	1	8	yes	direct product factor
19	C₄×C₂²⋊C₄×C₁₃₉	—	2	12	no	—
20	C₂×#95×C₁₃₉	C₂²	1	3	yes	—
21	C₂×#95×C₁₃₉	C₂²	1	3	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	3	yes	—
23	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂⁵×C₁₃₉	C₂³	1	3	yes	—
25	C₂²×D₄×C₁₃₉	—	2	12	no	—
26	C₂²×D₄×C₁₃₉	—	2	12	no	—
27	C₂²×D₄×C₁₃₉	—	2	6	no	—
28	C₂²×D₄×C₁₃₉	—	2	6	no	—
29	C₂²×D₄×C₁₃₉	C₂×C₄	1	12	yes	complemented
30	C₂³×C₄×C₁₃₉	—	2	12	no	—
31	C₂³×C₄×C₁₃₉	—	2	12	no	—
32	C₂³×C₄×C₁₃₉	—	2	6	no	—
33	C₂³×C₄×C₁₃₉	—	2	6	no	—
34	C₂³×C₄×C₁₃₉	D₄	1	12	yes	complemented
35	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₄×D₄×C₁₃₉	—	2	96	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	12	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	6	no	—
44	C₂×C₂²⋊C₄×C₁₃₉	—	2	12	no	—
45	C₂×C₂²⋊C₄×C₁₃₉	—	2	6	no	—
46	C₂×C₂²⋊C₄×C₁₃₉	—	2	12	no	—
47	C₂×C₂²⋊C₄×C₁₃₉	—	2	12	no	—
48	C₂×C₂²⋊C₄×C₁₃₉	—	2	6	no	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	2	6	no	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	6	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	6	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	12	yes	complemented
53	C₂×C₄²×C₁₃₉	—	2	12	no	—
54	C₂×C₄²×C₁₃₉	—	2	6	no	—
55	C₂×C₄²×C₁₃₉	D₄	1	12	yes	complemented
56	#95×C₁₃₉	—	2	6	no	—
57	#95×C₁₃₉	—	2	6	no	—
58	#95×C₁₃₉	—	2	6	no	—
59	#95×C₁₃₉	C₂×C₄	1	4	yes	complemented
60	C₂⁴×C₁₃₉	—	2	3	no	—
61	C₂⁴×C₁₃₉	—	2	6	no	—
62	C₂⁴×C₁₃₉	—	2	6	no	—
63	C₂⁴×C₁₃₉	—	2	3	no	—
64	C₂⁴×C₁₃₉	—	2	3	no	—
65	C₂⁴×C₁₃₉	—	2	3	no	—
66	C₂⁴×C₁₃₉	—	2	6	no	—
67	C₂⁴×C₁₃₉	—	2	6	no	—
68	C₂⁴×C₁₃₉	C₂²×C₄	1	6	yes	—
69	C₂⁴×C₁₃₉	C₂×D₄	1	6	yes	—
70	C₂⁴×C₁₃₉	#41	1	6	yes	—
71	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
72	C₂×D₄×C₁₃₉	—	2	24	no	—
73	C₂×D₄×C₁₃₉	—	2	24	no	—
74	C₂×D₄×C₁₃₉	—	2	48	no	—
75	C₂×D₄×C₁₃₉	—	2	48	no	—
76	C₂×D₄×C₁₃₉	—	2	24	no	—
77	C₂²×C₄×C₁₃₉	—	2	6	no	—
78	C₂²×C₄×C₁₃₉	—	2	6	no	—
79	C₂²×C₄×C₁₃₉	—	2	3	no	—
80	C₂²×C₄×C₁₃₉	—	2	3	no	—
81	C₂²×C₄×C₁₃₉	—	2	3	no	—
82	C₂²×C₄×C₁₃₉	—	2	6	no	—
83	C₂²×C₄×C₁₃₉	—	2	6	no	—
84	C₂²×C₄×C₁₃₉	—	2	6	no	—
85	C₂²×C₄×C₁₃₉	—	2	6	no	—
86	C₂²×C₄×C₁₃₉	—	2	3	no	—
87	C₂²×C₄×C₁₃₉	—	2	3	no	—
88	C₂²×C₄×C₁₃₉	—	2	3	no	—
89	C₂²×C₄×C₁₃₉	—	2	3	no	—
90	C₂²×C₄×C₁₃₉	—	2	3	no	—
91	C₂²×C₄×C₁₃₉	—	2	48	no	—
92	C₂²×C₄×C₁₃₉	—	2	24	no	—
93	C₂²×C₄×C₁₃₉	—	4	12	no	—
94	C₂²×C₄×C₁₃₉	—	4	24	no	—
95	C₂²×C₄×C₁₃₉	—	4	12	no	—
96	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂²×C₄	1	6	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	6	yes	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	6	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	6	yes	—
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	6	yes	—
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	6	yes	—
103	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
104	C₂²×C₄×C₁₃₉	#41	1	6	yes	—
105	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
106	C₄⋊C₄×C₁₃₉	—	2	24	no	—
107	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
108	C₂²⋊C₄×C₁₃₉	—	2	48	no	—
109	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
110	C₄²×C₁₃₉	—	2	24	no	—
111	C₄²×C₁₃₉	—	4	4	no	—
112	C₂³×C₁₃₉	—	2	6	no	—
113	C₂³×C₁₃₉	—	2	12	no	—
114	C₂³×C₁₃₉	—	2	12	no	—
115	C₂³×C₁₃₉	—	2	6	no	—
116	C₂³×C₁₃₉	—	2	12	no	—
117	C₂³×C₁₃₉	—	2	6	no	—
118	C₂³×C₁₃₉	—	2	6	no	—
119	C₂³×C₁₃₉	—	2	12	no	—
120	C₂³×C₁₃₉	—	2	12	no	—
121	C₂³×C₁₃₉	—	2	12	no	—
122	C₂³×C₁₃₉	—	2	6	no	—
123	C₂³×C₁₃₉	—	2	6	no	—
124	C₂³×C₁₃₉	—	4	3	no	—
125	C₂³×C₁₃₉	—	4	6	no	—
126	C₂³×C₁₃₉	—	4	6	no	—
127	C₂³×C₁₃₉	—	4	6	no	—
128	C₂³×C₁₃₉	—	4	3	no	—
129	C₂³×C₁₃₉	—	4	6	no	—
130	C₂³×C₁₃₉	—	4	3	no	—
131	C₂³×C₁₃₉	—	4	3	no	—
132	C₂³×C₁₃₉	—	4	6	no	—
133	C₂³×C₁₃₉	—	4	6	no	—
134	C₂³×C₁₃₉	C₄×D₄	1	12	yes	complemented
135	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
136	C₂³×C₁₃₉	C₂²×D₄	1	3	yes	—
137	C₂³×C₁₃₉	C₂²×D₄	1	3	yes	—
138	C₂³×C₁₃₉	C₂×#41	1	3	yes	—
139	C₂³×C₁₃₉	C₂×#41	1	3	yes	—
140	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
141	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
142	D₄×C₁₃₉	—	2	96	no	—
143	C₂×C₄×C₁₃₉	—	2	12	no	—
144	C₂×C₄×C₁₃₉	—	2	6	no	—
145	C₂×C₄×C₁₃₉	—	2	6	no	—
146	C₂×C₄×C₁₃₉	—	2	12	no	—
147	C₂×C₄×C₁₃₉	—	2	6	no	—
148	C₂×C₄×C₁₃₉	—	2	6	no	—
149	C₂×C₄×C₁₃₉	—	2	12	no	—
150	C₂×C₄×C₁₃₉	—	2	6	no	—
151	C₂×C₄×C₁₃₉	—	2	6	no	—
152	C₂×C₄×C₁₃₉	—	2	6	no	—
153	C₂×C₄×C₁₃₉	—	2	6	no	—
154	C₂×C₄×C₁₃₉	—	4	3	no	—
155	C₂×C₄×C₁₃₉	—	4	6	no	—
156	C₂×C₄×C₁₃₉	—	4	6	no	—
157	C₂×C₄×C₁₃₉	—	4	3	no	—
158	C₂×C₄×C₁₃₉	—	4	1	no	—
159	C₂×C₄×C₁₃₉	—	4	1	no	—
160	C₂×C₄×C₁₃₉	—	4	3	no	—
161	C₂×C₄×C₁₃₉	—	4	3	no	—
162	C₂×C₄×C₁₃₉	—	4	6	no	—
163	C₂×C₄×C₁₃₉	—	4	48	no	—
164	C₂×C₄×C₁₃₉	C₄×D₄	1	12	yes	complemented
165	C₂×C₄×C₁₃₉	#120	1	12	yes	—
166	C₂×C₄×C₁₃₉	#121	1	12	yes	—
167	C₂×C₄×C₁₃₉	#127	1	4	yes	—
168	C₂²×C₁₃₉	—	2	24	no	—
169	C₂²×C₁₃₉	—	2	12	no	—
170	C₂²×C₁₃₉	—	4	6	no	—
171	C₂²×C₁₃₉	—	4	6	no	—
172	C₂²×C₁₃₉	—	4	12	no	—
173	C₂²×C₁₃₉	—	4	6	no	—
174	C₂²×C₁₃₉	—	4	6	no	—
175	C₂²×C₁₃₉	—	4	12	no	—
176	C₂²×C₁₃₉	—	4	6	no	—
177	C₂²×C₁₃₉	—	4	6	no	—
178	C₂²×C₁₃₉	—	4	12	no	—
179	C₂²×C₁₃₉	C₂×C₄×D₄	1	3	yes	—
180	C₂²×C₁₃₉	C₂×C₄×D₄	1	3	yes	—
181	C₂²×C₁₃₉	C₄×#41	1	1	yes	characteristic
182	C₂²×C₁₃₉	C₂×#120	1	3	yes	—
183	C₂²×C₁₃₉	C₂×#121	1	3	yes	—
184	C₂²×C₁₃₉	#525	1	6	yes	—
185	C₂²×C₁₃₉	#525	1	3	yes	—
186	C₂²×C₁₃₉	#525	1	3	yes	—
187	C₂²×C₁₃₉	#529	1	3	yes	—
188	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
189	C₂²×C₁₃₉	#532	1	3	yes	—
190	C₂²×C₁₃₉	#532	1	3	yes	—
191	C₄×C₁₃₉	—	2	12	no	—
192	C₄×C₁₃₉	—	4	2	no	—
193	C₄×C₁₃₉	—	4	6	no	—
194	C₄×C₁₃₉	—	4	6	no	—
195	C₄×C₁₃₉	—	4	2	no	—
196	C₄×C₁₃₉	#392	1	8	yes	direct product factor
197	C₂×C₁₃₉	—	4	12	no	—
198	C₂×C₁₃₉	C₄×#120	1	3	yes	—
199	C₂×C₁₃₉	C₄×#121	1	3	yes	—
200	C₂×C₁₃₉	C₄×#127	1	1	yes	characteristic
201	C₂×C₁₃₉	C₂×#392	1	1	yes	characteristic
202	C₂×C₁₃₉	#2388	1	3	yes	—
203	C₂×C₁₃₉	#2392	1	3	yes	—
204	C₂×C₁₃₉	#2397	1	1	yes	characteristic
205	C₄×#392	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₁₃₉	C₄×#392	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²×C₄×D₄	C₂×C₁₃₉	1	3	yes	complemented
208	C₂×#392	C₂×C₁₃₉	1	1	yes	characteristic
209	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	3	yes	complemented
210	#1444	C₂×C₁₃₉	1	1	yes	characteristic, complemented
211	#1439	C₂×C₁₃₉	1	3	yes	complemented
212	#1438	C₂×C₁₃₉	1	3	yes	complemented
213	C₄×#95	C₂×C₁₃₉	1	1	yes	characteristic, complemented
214	C₂³×D₄	C₂²×C₁₃₉	1	3	yes	—
215	C₂⁴×C₄	C₂²×C₁₃₉	1	3	yes	—
216	C₂×C₄×D₄	—	2	24	no	—
217	C₂×C₄×D₄	—	2	12	no	—
218	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
222	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₁₃₉	1	3	yes	—
224	#392	C₄×C₁₃₉	1	8	yes	direct product factor
225	C₄×C₂²⋊C₄	—	2	12	no	—
226	C₂×#95	C₂²×C₁₃₉	1	3	yes	—
227	C₂×#95	C₂²×C₁₃₉	1	3	yes	—
228	C₂×#95	C₂²×C₁₃₉	1	3	yes	—
229	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
230	C₂⁵	C₂³×C₁₃₉	1	3	yes	—
231	C₂²×D₄	—	2	12	no	—
232	C₂²×D₄	—	2	12	no	—
233	C₂²×D₄	—	2	6	no	—
234	C₂²×D₄	—	2	6	no	—
235	C₂²×D₄	C₂×C₄×C₁₃₉	1	12	yes	complemented
236	C₂³×C₄	—	2	12	no	—
237	C₂³×C₄	—	2	12	no	—
238	C₂³×C₄	—	2	6	no	—
239	C₂³×C₄	—	2	6	no	—
240	C₂³×C₄	D₄×C₁₃₉	1	12	yes	complemented
241	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
243	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
244	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
246	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
247	C₄×D₄	—	2	96	no	—
248	C₂×C₄⋊C₄	—	2	12	no	—
249	C₂×C₄⋊C₄	—	2	6	no	—
250	C₂×C₂²⋊C₄	—	2	12	no	—
251	C₂×C₂²⋊C₄	—	2	6	no	—
252	C₂×C₂²⋊C₄	—	2	12	no	—
253	C₂×C₂²⋊C₄	—	2	12	no	—
254	C₂×C₂²⋊C₄	—	2	6	no	—
255	C₂×C₂²⋊C₄	—	2	6	no	—
256	C₂×C₂²⋊C₄	—	2	6	no	—
257	C₂×C₂²⋊C₄	—	2	6	no	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	12	yes	complemented
259	C₂×C₄²	—	2	12	no	—
260	C₂×C₄²	—	2	6	no	—
261	C₂×C₄²	D₄×C₁₃₉	1	12	yes	complemented
262	#95	—	2	6	no	—
263	#95	—	2	6	no	—
264	#95	—	2	6	no	—
265	#95	C₂×C₄×C₁₃₉	1	4	yes	complemented
266	C₂⁴	—	2	3	no	—
267	C₂⁴	—	2	6	no	—
268	C₂⁴	—	2	6	no	—
269	C₂⁴	—	2	3	no	—
270	C₂⁴	—	2	3	no	—
271	C₂⁴	—	2	3	no	—
272	C₂⁴	—	2	6	no	—
273	C₂⁴	—	2	6	no	—
274	C₂⁴	C₂²×C₄×C₁₃₉	1	6	yes	—
275	C₂⁴	C₂×D₄×C₁₃₉	1	6	yes	—
276	C₂⁴	#41×C₁₃₉	1	6	yes	—
277	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
278	C₂×D₄	—	2	24	no	—
279	C₂×D₄	—	2	24	no	—
280	C₂×D₄	—	2	48	no	—
281	C₂×D₄	—	2	48	no	—
282	C₂×D₄	—	2	24	no	—
283	C₂²×C₄	—	2	6	no	—
284	C₂²×C₄	—	2	6	no	—
285	C₂²×C₄	—	2	3	no	—
286	C₂²×C₄	—	2	3	no	—
287	C₂²×C₄	—	2	3	no	—
288	C₂²×C₄	—	2	6	no	—
289	C₂²×C₄	—	2	6	no	—
290	C₂²×C₄	—	2	6	no	—
291	C₂²×C₄	—	2	6	no	—
292	C₂²×C₄	—	2	3	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	3	no	—
295	C₂²×C₄	—	2	3	no	—
296	C₂²×C₄	—	2	3	no	—
297	C₂²×C₄	—	2	48	no	—
298	C₂²×C₄	—	2	24	no	—
299	C₂²×C₄	—	4	12	no	—
300	C₂²×C₄	—	4	24	no	—
301	C₂²×C₄	—	4	12	no	—
302	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃₉	1	6	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃₉	1	6	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃₉	1	6	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	6	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	6	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	6	yes	—
309	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
310	C₂²×C₄	#41×C₁₃₉	1	6	yes	—
311	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
312	C₄⋊C₄	—	2	24	no	—
313	C₂²⋊C₄	—	2	24	no	—
314	C₂²⋊C₄	—	2	48	no	—
315	C₂²⋊C₄	—	2	24	no	—
316	C₄²	—	2	24	no	—
317	C₄²	—	4	4	no	—
318	C₂³	—	2	6	no	—
319	C₂³	—	2	12	no	—
320	C₂³	—	2	12	no	—
321	C₂³	—	2	6	no	—
322	C₂³	—	2	12	no	—
323	C₂³	—	2	6	no	—
324	C₂³	—	2	6	no	—
325	C₂³	—	2	12	no	—
326	C₂³	—	2	12	no	—
327	C₂³	—	2	12	no	—
328	C₂³	—	2	6	no	—
329	C₂³	—	2	6	no	—
330	C₂³	—	4	3	no	—
331	C₂³	—	4	6	no	—
332	C₂³	—	4	6	no	—
333	C₂³	—	4	3	no	—
334	C₂³	—	4	6	no	—
335	C₂³	—	4	6	no	—
336	C₂³	—	4	3	no	—
337	C₂³	—	4	6	no	—
338	C₂³	—	4	3	no	—
339	C₂³	—	4	6	no	—
340	C₂³	C₄×D₄×C₁₃₉	1	12	yes	complemented
341	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
342	C₂³	C₂²×D₄×C₁₃₉	1	3	yes	—
343	C₂³	C₂²×D₄×C₁₃₉	1	3	yes	—
344	C₂³	C₂×#41×C₁₃₉	1	3	yes	—
345	C₂³	C₂×#41×C₁₃₉	1	3	yes	—
346	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
347	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
348	D₄	—	2	96	no	—
349	C₂×C₄	—	2	12	no	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	2	12	no	—
353	C₂×C₄	—	2	6	no	—
354	C₂×C₄	—	2	6	no	—
355	C₂×C₄	—	2	12	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	6	no	—
359	C₂×C₄	—	2	6	no	—
360	C₂×C₄	—	4	3	no	—
361	C₂×C₄	—	4	6	no	—
362	C₂×C₄	—	4	6	no	—
363	C₂×C₄	—	4	3	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	3	no	—
367	C₂×C₄	—	4	3	no	—
368	C₂×C₄	—	4	6	no	—
369	C₂×C₄	—	4	48	no	—
370	C₂×C₄	C₄×D₄×C₁₃₉	1	12	yes	complemented
371	C₂×C₄	#120×C₁₃₉	1	12	yes	—
372	C₂×C₄	#121×C₁₃₉	1	12	yes	—
373	C₂×C₄	#127×C₁₃₉	1	4	yes	—
374	C₂²	—	2	24	no	—
375	C₂²	—	2	12	no	—
376	C₂²	—	4	6	no	—
377	C₂²	—	4	12	no	—
378	C₂²	—	4	6	no	—
379	C₂²	—	4	6	no	—
380	C₂²	—	4	12	no	—
381	C₂²	—	4	6	no	—
382	C₂²	—	4	6	no	—
383	C₂²	—	4	12	no	—
384	C₂²	—	4	6	no	—
385	C₂²	C₂×C₄×D₄×C₁₃₉	1	3	yes	—
386	C₂²	C₂×C₄×D₄×C₁₃₉	1	3	yes	—
387	C₂²	C₄×#41×C₁₃₉	1	1	yes	characteristic
388	C₂²	C₂×#120×C₁₃₉	1	3	yes	—
389	C₂²	C₂×#121×C₁₃₉	1	3	yes	—
390	C₂²	#525×C₁₃₉	1	6	yes	—
391	C₂²	#525×C₁₃₉	1	3	yes	—
392	C₂²	#525×C₁₃₉	1	3	yes	—
393	C₂²	#529×C₁₃₉	1	3	yes	—
394	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
395	C₂²	#532×C₁₃₉	1	3	yes	—
396	C₂²	#532×C₁₃₉	1	3	yes	—
397	C₄	—	2	12	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	6	no	—
400	C₄	—	4	6	no	—
401	C₄	—	4	2	no	—
402	C₄	#392×C₁₃₉	1	8	yes	direct product factor
403	C₂	—	4	12	no	—
404	C₂	C₄×#120×C₁₃₉	1	3	yes	—
405	C₂	C₄×#121×C₁₃₉	1	3	yes	—
406	C₂	C₄×#127×C₁₃₉	1	1	yes	characteristic
407	C₂	C₂×#392×C₁₃₉	1	1	yes	characteristic
408	C₂	#2388×C₁₃₉	1	3	yes	—
409	C₂	#2392×C₁₃₉	1	3	yes	—
410	C₂	#2397×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₃₉	C₂³
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
socle	C₂⁴×C₁₃₉	C₂⁴
prime radical	C₂×#392×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
4. #1444×C₁₃₉	C₂	semidirect
5. #1439×C₁₃₉	C₂	semidirect
6. #1438×C₁₃₉	C₂	semidirect
7. C₄×#95×C₁₃₉	C₂	semidirect
18. #392×C₁₃₉	C₄	direct (N × H)
29. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
34. C₂³×C₄×C₁₃₉	D₄	semidirect
52. C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	semidirect
55. C₂×C₄²×C₁₃₉	D₄	semidirect
59. #95×C₁₃₉	C₂×C₄	semidirect
134. C₂³×C₁₃₉	C₄×D₄	semidirect
164. C₂×C₄×C₁₃₉	C₄×D₄	semidirect
196. C₄×C₁₃₉	#392	direct (N × H)
205. C₄×#392	C₁₃₉	direct (N × H)
206. C₁₃₉	C₄×#392	direct (N × H)
207. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
209. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
210. #1444	C₂×C₁₃₉	semidirect
211. #1439	C₂×C₁₃₉	semidirect
212. #1438	C₂×C₁₃₉	semidirect
213. C₄×#95	C₂×C₁₃₉	semidirect
224. #392	C₄×C₁₃₉	direct (N × H)
235. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
240. C₂³×C₄	D₄×C₁₃₉	semidirect
258. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	semidirect
261. C₂×C₄²	D₄×C₁₃₉	semidirect
265. #95	C₂×C₄×C₁₃₉	semidirect
340. C₂³	C₄×D₄×C₁₃₉	semidirect
370. C₂×C₄	C₄×D₄×C₁₃₉	semidirect
402. C₄	#392×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
C₂²×C₄×D₄×C₁₃₉	2
C₂×#392×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
#1444×C₁₃₉	2
#1439×C₁₃₉	2
#1438×C₁₃₉	2
C₄×#95×C₁₃₉	2
C₄×#392	139

Subgroups — C4×#392×C139 #48008453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#392×C₁₃₉ #48008453