Subgroups — C₂×#1825×C₁₃₉ #48015293

Order 35584.

1574 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1825×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂×#340×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
9	C₂×#117×C₁₃₉	—	2	4	no	—
10	C₂×#117×C₁₃₉	—	2	2	no	—
11	C₂×#117×C₁₃₉	C₄	1	8	yes	complemented
12	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
18	C₂²×C₄²×C₁₃₉	—	2	1	no	—
19	C₂×C₂²⋊C₈×C₁₃₉	—	2	4	no	—
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
21	#380×C₁₃₉	—	2	2	no	—
22	#380×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#95×C₁₃₉	—	2	1	no	—
24	#340×C₁₃₉	C₂²	1	8	yes	complemented
25	#340×C₁₃₉	C₂²	1	8	yes	complemented
26	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃₉	—	2	8	no	—
28	C₂³×C₄×C₁₃₉	—	2	1	no	—
29	C₂³×C₄×C₁₃₉	—	2	1	no	—
30	C₂³×C₄×C₁₃₉	—	2	2	no	—
31	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃₉	—	2	4	no	—
38	C₂²×C₈×C₁₃₉	—	2	8	no	—
39	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
40	#117×C₁₃₉	—	2	16	no	—
41	#117×C₁₃₉	—	2	8	no	—
42	#117×C₁₃₉	C₂×C₄	1	16	yes	complemented
43	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
58	C₂×C₄²×C₁₃₉	—	2	8	no	—
59	C₂×C₄²×C₁₃₉	—	2	4	no	—
60	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
61	#95×C₁₃₉	—	2	4	no	—
62	C₂⁴×C₁₃₉	—	2	4	no	—
63	C₂⁴×C₁₃₉	—	2	4	no	—
64	C₂⁴×C₁₃₉	—	2	2	no	—
65	C₂⁴×C₁₃₉	—	2	2	no	—
66	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
67	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
68	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₉	—	2	4	no	—
70	C₂²×C₄×C₁₃₉	—	2	16	no	—
71	C₂²×C₄×C₁₃₉	—	2	8	no	—
72	C₂²×C₄×C₁₃₉	—	2	16	no	—
73	C₂²×C₄×C₁₃₉	—	2	8	no	—
74	C₂²×C₄×C₁₃₉	—	2	4	no	—
75	C₂²×C₄×C₁₃₉	—	2	4	no	—
76	C₂²×C₄×C₁₃₉	—	2	2	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	4	no	—
79	C₂²×C₄×C₁₃₉	—	4	4	no	—
80	C₂²×C₄×C₁₃₉	—	4	2	no	—
81	C₂²×C₄×C₁₃₉	—	4	2	no	—
82	C₂²×C₄×C₁₃₉	—	4	4	no	—
83	C₂²×C₄×C₁₃₉	—	4	4	no	—
84	C₂²×C₄×C₁₃₉	—	4	4	no	—
85	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
86	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
87	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
94	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₃₉	—	2	4	no	—
96	C₂×C₈×C₁₃₉	—	2	8	no	—
97	C₂×C₈×C₁₃₉	—	4	8	no	—
98	C₄⋊C₄×C₁₃₉	—	2	4	no	—
99	C₄⋊C₄×C₁₃₉	—	2	4	no	—
100	C₄⋊C₄×C₁₃₉	—	2	2	no	—
101	C₄⋊C₄×C₁₃₉	—	2	2	no	—
102	C₄⋊C₄×C₁₃₉	—	2	8	no	—
103	C₄⋊C₄×C₁₃₉	—	4	4	no	—
104	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
105	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
106	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
107	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
108	C₄²×C₁₃₉	—	2	16	no	—
109	C₂³×C₁₃₉	—	2	4	no	—
110	C₂³×C₁₃₉	—	2	4	no	—
111	C₂³×C₁₃₉	—	2	2	no	—
112	C₂³×C₁₃₉	—	2	2	no	—
113	C₂³×C₁₃₉	—	2	8	no	—
114	C₂³×C₁₃₉	—	2	8	no	—
115	C₂³×C₁₃₉	—	2	8	no	—
116	C₂³×C₁₃₉	—	4	8	no	—
117	C₂³×C₁₃₉	—	4	8	no	—
118	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
119	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
120	C₂³×C₁₃₉	#123	1	4	yes	—
121	C₂³×C₁₃₉	#135	1	4	yes	—
122	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₁₃₉	#137	1	2	yes	—
124	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₃₉	—	2	4	no	—
126	C₂×C₄×C₁₃₉	—	2	8	no	—
127	C₂×C₄×C₁₃₉	—	2	8	no	—
128	C₂×C₄×C₁₃₉	—	2	8	no	—
129	C₂×C₄×C₁₃₉	—	2	16	no	—
130	C₂×C₄×C₁₃₉	—	2	4	no	—
131	C₂×C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₄×C₁₃₉	—	4	4	no	—
133	C₂×C₄×C₁₃₉	—	4	2	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	—	4	8	no	—
136	C₂×C₄×C₁₃₉	—	4	8	no	—
137	C₂×C₄×C₁₃₉	—	4	4	no	—
138	C₂×C₄×C₁₃₉	—	4	4	no	—
139	C₂×C₄×C₁₃₉	—	4	4	no	—
140	C₂×C₄×C₁₃₉	—	8	8	no	—
141	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₃₉	#117	1	8	yes	—
144	C₂×C₄×C₁₃₉	#123	1	8	yes	—
145	C₂×C₄×C₁₃₉	#123	1	4	yes	—
146	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
149	C₈×C₁₃₉	—	4	4	no	—
150	C₂²×C₁₃₉	—	2	4	no	—
151	C₂²×C₁₃₉	—	2	4	no	—
152	C₂²×C₁₃₉	—	2	4	no	—
153	C₂²×C₁₃₉	—	4	4	no	—
154	C₂²×C₁₃₉	—	4	4	no	—
155	C₂²×C₁₃₉	—	4	16	no	—
156	C₂²×C₁₃₉	#381	1	4	yes	—
157	C₂²×C₁₃₉	#416	1	4	yes	—
158	C₂²×C₁₃₉	#417	1	4	yes	—
159	C₂²×C₁₃₉	#482	1	8	yes	—
160	C₂²×C₁₃₉	#485	1	8	yes	—
161	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
163	C₂²×C₁₃₉	C₂×#135	1	2	yes	—
164	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
166	C₄×C₁₃₉	—	2	4	no	—
167	C₄×C₁₃₉	—	4	4	no	—
168	C₄×C₁₃₉	—	4	4	no	—
169	C₄×C₁₃₉	—	8	4	no	—
170	C₄×C₁₃₉	#381	1	4	yes	—
171	C₄×C₁₃₉	C₂×#117	1	2	yes	—
172	C₄×C₁₃₉	C₂×#123	1	2	yes	—
173	C₂×C₁₃₉	—	4	4	no	—
174	C₂×C₁₃₉	#1825	1	8	yes	direct product factor
175	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
176	C₂×C₁₃₉	C₂×#416	1	1	yes	characteristic
177	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
178	C₂×C₁₃₉	C₂×#482	1	2	yes	—
179	C₂×C₁₃₉	C₂×#485	1	2	yes	—
180	C₂×#1825	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₉	C₂×#1825	1	1	yes	characteristic, direct product factor, Sylow
182	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic
183	C₂²×C₂²⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic
184	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
185	#1825	C₂×C₁₃₉	1	8	yes	direct product factor
186	C₂×#340	C₂×C₁₃₉	1	2	yes	complemented
187	C₂×#340	C₂×C₁₃₉	1	2	yes	complemented
188	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
189	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
190	C₂×#117	—	2	4	no	—
191	C₂×#117	—	2	2	no	—
192	C₂×#117	C₄×C₁₃₉	1	8	yes	complemented
193	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
197	C₂²×C₂²⋊C₄	—	2	1	no	—
198	C₂²×C₂²⋊C₄	—	2	1	no	—
199	C₂²×C₄²	—	2	1	no	—
200	C₂×C₂²⋊C₈	—	2	4	no	—
201	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
202	#380	—	2	2	no	—
203	#380	C₂²×C₁₃₉	1	4	yes	—
204	C₂×#95	—	2	1	no	—
205	#340	C₂²×C₁₃₉	1	8	yes	complemented
206	#340	C₂²×C₁₃₉	1	8	yes	complemented
207	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
208	C₂³×C₄	—	2	8	no	—
209	C₂³×C₄	—	2	1	no	—
210	C₂³×C₄	—	2	1	no	—
211	C₂³×C₄	—	2	2	no	—
212	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
213	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
214	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
216	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	8	no	—
220	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
221	#117	—	2	16	no	—
222	#117	—	2	8	no	—
223	#117	C₂×C₄×C₁₃₉	1	16	yes	complemented
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
233	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
235	C₂×C₂²⋊C₄	—	2	8	no	—
236	C₂×C₂²⋊C₄	—	2	4	no	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₂²⋊C₄	—	4	4	no	—
239	C₂×C₄²	—	2	8	no	—
240	C₂×C₄²	—	2	4	no	—
241	C₂²⋊C₈	—	2	8	no	—
242	#95	—	2	4	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	2	no	—
246	C₂⁴	—	2	2	no	—
247	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
248	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
249	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	16	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
267	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
271	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
274	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
275	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	—	4	8	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
286	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
287	C₂²⋊C₄	—	2	16	no	—
288	C₂²⋊C₄	—	4	8	no	—
289	C₄²	—	2	16	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	8	no	—
297	C₂³	—	4	8	no	—
298	C₂³	—	4	8	no	—
299	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
300	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
301	C₂³	#123×C₁₃₉	1	4	yes	—
302	C₂³	#135×C₁₃₉	1	4	yes	—
303	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
304	C₂³	#137×C₁₃₉	1	2	yes	—
305	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	16	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	8	8	no	—
322	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
324	C₂×C₄	#117×C₁₃₉	1	8	yes	—
325	C₂×C₄	#123×C₁₃₉	1	8	yes	—
326	C₂×C₄	#123×C₁₃₉	1	4	yes	—
327	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
330	C₈	—	4	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	16	no	—
337	C₂²	#381×C₁₃₉	1	4	yes	—
338	C₂²	#416×C₁₃₉	1	4	yes	—
339	C₂²	#417×C₁₃₉	1	4	yes	—
340	C₂²	#482×C₁₃₉	1	8	yes	—
341	C₂²	#485×C₁₃₉	1	8	yes	—
342	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
343	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
344	C₂²	C₂×#135×C₁₃₉	1	2	yes	—
345	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
346	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	4	4	no	—
349	C₄	—	4	4	no	—
350	C₄	—	8	4	no	—
351	C₄	#381×C₁₃₉	1	4	yes	—
352	C₄	C₂×#117×C₁₃₉	1	2	yes	—
353	C₄	C₂×#123×C₁₃₉	1	2	yes	—
354	C₂	—	4	4	no	—
355	C₂	#1825×C₁₃₉	1	8	yes	direct product factor
356	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
357	C₂	C₂×#416×C₁₃₉	1	1	yes	characteristic
358	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
359	C₂	C₂×#482×C₁₃₉	1	2	yes	—
360	C₂	C₂×#485×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁵×C₁₃₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1825×C₁₃₉	C₂	direct (N × H)
5. C₂×#340×C₁₃₉	C₂	semidirect
6. C₂×#340×C₁₃₉	C₂	semidirect
11. C₂×#117×C₁₃₉	C₄	semidirect
24. #340×C₁₃₉	C₂²	semidirect
25. #340×C₁₃₉	C₂²	semidirect
42. #117×C₁₃₉	C₂×C₄	semidirect
174. C₂×C₁₃₉	#1825	direct (N × H)
180. C₂×#1825	C₁₃₉	direct (N × H)
181. C₁₃₉	C₂×#1825	direct (N × H)
185. #1825	C₂×C₁₃₉	direct (N × H)
186. C₂×#340	C₂×C₁₃₉	semidirect
187. C₂×#340	C₂×C₁₃₉	semidirect
192. C₂×#117	C₄×C₁₃₉	semidirect
205. #340	C₂²×C₁₃₉	semidirect
206. #340	C₂²×C₁₃₉	semidirect
223. #117	C₂×C₄×C₁₃₉	semidirect
355. C₂	#1825×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×#117×C₁₃₉	2
C₂²×C₂²⋊C₈×C₁₃₉	2
C₂×#380×C₁₃₉	2
#1825×C₁₃₉	2
C₂×#340×C₁₃₉	2
C₂×#1825	139

Subgroups — C2×#1825×C139 #48015293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1825×C₁₃₉ #48015293