Subgroups — C₂×#1823×C₁₃₉ #48015292

Order 35584.

1878 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×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	#1823×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₁₃₉	—	2	1	no	—
7	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₃₉	—	2	2	no	—
10	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
11	C₂²×C₄⋊C₄×C₁₃₉	—	2	4	no	—
12	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
17	C₂×C₂²⋊C₈×C₁₃₉	—	2	4	no	—
18	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
19	#380×C₁₃₉	—	2	2	no	—
20	#380×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#95×C₁₃₉	—	2	1	no	—
22	#340×C₁₃₉	C₂²	1	16	yes	complemented
23	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₉	—	2	8	no	—
25	C₂³×C₄×C₁₃₉	—	2	8	no	—
26	C₂³×C₄×C₁₃₉	—	2	4	no	—
27	C₂³×C₄×C₁₃₉	—	2	2	no	—
28	C₂³×C₄×C₁₃₉	—	2	2	no	—
29	C₂³×C₄×C₁₃₉	—	4	4	no	—
30	C₂³×C₄×C₁₃₉	—	4	4	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	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
52	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
54	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
55	#95×C₁₃₉	—	2	4	no	—
56	C₂⁴×C₁₃₉	—	2	4	no	—
57	C₂⁴×C₁₃₉	—	2	4	no	—
58	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
59	C₂⁴×C₁₃₉	D₈	1	4	yes	—
60	C₂⁴×C₁₃₉	SD₁₆	1	4	yes	—
61	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
62	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃₉	—	2	4	no	—
64	C₂²×C₄×C₁₃₉	—	2	16	no	—
65	C₂²×C₄×C₁₃₉	—	2	8	no	—
66	C₂²×C₄×C₁₃₉	—	2	16	no	—
67	C₂²×C₄×C₁₃₉	—	2	8	no	—
68	C₂²×C₄×C₁₃₉	—	2	8	no	—
69	C₂²×C₄×C₁₃₉	—	2	16	no	—
70	C₂²×C₄×C₁₃₉	—	2	4	no	—
71	C₂²×C₄×C₁₃₉	—	2	4	no	—
72	C₂²×C₄×C₁₃₉	—	4	32	no	—
73	C₂²×C₄×C₁₃₉	—	4	8	no	—
74	C₂²×C₄×C₁₃₉	—	4	4	no	—
75	C₂²×C₄×C₁₃₉	—	4	8	no	—
76	C₂²×C₄×C₁₃₉	—	4	4	no	—
77	C₂²×C₄×C₁₃₉	—	4	4	no	—
78	C₂²×C₄×C₁₃₉	—	4	4	no	—
79	C₂²×C₄×C₁₃₉	—	4	4	no	—
80	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
81	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
82	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
89	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₁₃₉	—	2	4	no	—
91	C₂×C₈×C₁₃₉	—	2	8	no	—
92	C₂×C₈×C₁₃₉	—	4	8	no	—
93	C₄⋊C₄×C₁₃₉	—	2	8	no	—
94	C₄⋊C₄×C₁₃₉	—	2	16	no	—
95	C₄⋊C₄×C₁₃₉	—	2	4	no	—
96	C₄⋊C₄×C₁₃₉	—	2	8	no	—
97	C₄⋊C₄×C₁₃₉	—	4	4	no	—
98	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
99	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
100	C₂³×C₁₃₉	—	2	4	no	—
101	C₂³×C₁₃₉	—	2	4	no	—
102	C₂³×C₁₃₉	—	2	8	no	—
103	C₂³×C₁₃₉	—	2	8	no	—
104	C₂³×C₁₃₉	—	2	16	no	—
105	C₂³×C₁₃₉	—	2	16	no	—
106	C₂³×C₁₃₉	#102	1	16	yes	—
107	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
108	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
109	C₂³×C₁₃₉	#123	1	4	yes	—
110	C₂³×C₁₃₉	C₂×D₈	1	4	yes	—
111	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
112	C₂³×C₁₃₉	C₂×SD₁₆	1	4	yes	—
113	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
114	C₂³×C₁₃₉	#137	1	4	yes	—
115	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₃₉	—	2	4	no	—
117	C₂×C₄×C₁₃₉	—	2	8	no	—
118	C₂×C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄×C₁₃₉	—	2	8	no	—
120	C₂×C₄×C₁₃₉	—	2	16	no	—
121	C₂×C₄×C₁₃₉	—	2	8	no	—
122	C₂×C₄×C₁₃₉	—	4	4	no	—
123	C₂×C₄×C₁₃₉	—	4	4	no	—
124	C₂×C₄×C₁₃₉	—	4	32	no	—
125	C₂×C₄×C₁₃₉	—	4	16	no	—
126	C₂×C₄×C₁₃₉	—	4	4	no	—
127	C₂×C₄×C₁₃₉	—	4	4	no	—
128	C₂×C₄×C₁₃₉	—	4	4	no	—
129	C₂×C₄×C₁₃₉	—	8	8	no	—
130	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
131	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂×C₄×C₁₃₉	#117	1	8	yes	—
133	C₂×C₄×C₁₃₉	#123	1	8	yes	—
134	C₂×C₄×C₁₃₉	#123	1	4	yes	—
135	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
138	C₈×C₁₃₉	—	4	4	no	—
139	C₂²×C₁₃₉	—	2	8	no	—
140	C₂²×C₁₃₉	—	2	8	no	—
141	C₂²×C₁₃₉	—	2	32	no	—
142	C₂²×C₁₃₉	—	2	4	no	—
143	C₂²×C₁₃₉	—	2	4	no	—
144	C₂²×C₁₃₉	#381	1	4	yes	—
145	C₂²×C₁₃₉	C₂×#102	1	8	yes	—
146	C₂²×C₁₃₉	C₂×#102	1	4	yes	—
147	C₂²×C₁₃₉	#419	1	4	yes	—
148	C₂²×C₁₃₉	#480	1	8	yes	—
149	C₂²×C₁₃₉	#483	1	8	yes	—
150	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₁₃₉	C₂×#123	1	2	yes	—
152	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
153	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
154	C₂²×C₁₃₉	C₂×#137	1	2	yes	—
155	C₄×C₁₃₉	—	2	4	no	—
156	C₄×C₁₃₉	—	4	8	no	—
157	C₄×C₁₃₉	—	8	4	no	—
158	C₄×C₁₃₉	#381	1	4	yes	—
159	C₄×C₁₃₉	C₂×#117	1	2	yes	—
160	C₄×C₁₃₉	C₂×#123	1	2	yes	—
161	C₂×C₁₃₉	—	2	8	no	—
162	C₂×C₁₃₉	#1823	1	8	yes	direct product factor
163	C₂×C₁₃₉	C₂×#381	1	1	yes	characteristic
164	C₂×C₁₃₉	C₂²×#102	1	1	yes	characteristic
165	C₂×C₁₃₉	C₂×#419	1	1	yes	characteristic
166	C₂×C₁₃₉	C₂×#480	1	2	yes	—
167	C₂×C₁₃₉	C₂×#483	1	2	yes	—
168	C₂×#1823	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₁₃₉	C₂×#1823	1	1	yes	characteristic, direct product factor, Sylow
170	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
171	C₂²×C₂²⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic
172	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
173	#1823	C₂×C₁₃₉	1	8	yes	direct product factor
174	C₂×#340	C₂×C₁₃₉	1	4	yes	complemented
175	C₂⁴×C₄	—	2	1	no	—
176	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
178	C₂²×C₄⋊C₄	—	2	1	no	—
179	C₂²×C₄⋊C₄	—	2	2	no	—
180	C₂²×C₄⋊C₄	—	2	4	no	—
181	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
182	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
185	C₂²×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₂²⋊C₈	—	2	4	no	—
187	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
188	#380	—	2	2	no	—
189	#380	C₂²×C₁₃₉	1	4	yes	—
190	C₂×#95	—	2	1	no	—
191	#340	C₂²×C₁₃₉	1	16	yes	complemented
192	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
193	C₂³×C₄	—	2	8	no	—
194	C₂³×C₄	—	2	8	no	—
195	C₂³×C₄	—	2	2	no	—
196	C₂³×C₄	—	2	4	no	—
197	C₂³×C₄	—	2	2	no	—
198	C₂³×C₄	—	4	4	no	—
199	C₂³×C₄	—	4	4	no	—
200	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
201	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
202	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
203	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
204	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	—	2	8	no	—
208	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
209	C₂×C₄⋊C₄	—	2	16	no	—
210	C₂×C₄⋊C₄	—	2	8	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	8	no	—
215	C₂×C₄⋊C₄	—	2	8	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
219	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
221	C₂×C₂²⋊C₄	—	2	4	no	—
222	C₂×C₂²⋊C₄	—	4	4	no	—
223	C₂²⋊C₈	—	2	8	no	—
224	#95	—	2	4	no	—
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	2	4	no	—
227	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
228	C₂⁴	D₈×C₁₃₉	1	4	yes	—
229	C₂⁴	SD₁₆×C₁₃₉	1	4	yes	—
230	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
231	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	16	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	16	no	—
236	C₂²×C₄	—	2	8	no	—
237	C₂²×C₄	—	2	8	no	—
238	C₂²×C₄	—	2	16	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	4	32	no	—
242	C₂²×C₄	—	4	8	no	—
243	C₂²×C₄	—	4	4	no	—
244	C₂²×C₄	—	4	8	no	—
245	C₂²×C₄	—	4	4	no	—
246	C₂²×C₄	—	4	4	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
250	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
255	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
257	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
258	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	8	no	—
261	C₂×C₈	—	4	8	no	—
262	C₄⋊C₄	—	2	8	no	—
263	C₄⋊C₄	—	2	16	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	4	4	no	—
267	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
268	C₂²⋊C₄	—	4	8	no	—
269	C₂³	—	2	8	no	—
270	C₂³	—	2	16	no	—
271	C₂³	—	2	16	no	—
272	C₂³	—	2	4	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	8	no	—
275	C₂³	#102×C₁₃₉	1	16	yes	—
276	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
277	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
278	C₂³	#123×C₁₃₉	1	4	yes	—
279	C₂³	C₂×D₈×C₁₃₉	1	4	yes	—
280	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
281	C₂³	C₂×SD₁₆×C₁₃₉	1	4	yes	—
282	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
283	C₂³	#137×C₁₃₉	1	4	yes	—
284	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	8	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	16	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	4	32	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	8	8	no	—
299	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
300	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
301	C₂×C₄	#117×C₁₃₉	1	8	yes	—
302	C₂×C₄	#123×C₁₃₉	1	8	yes	—
303	C₂×C₄	#123×C₁₃₉	1	4	yes	—
304	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
306	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
307	C₈	—	4	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	2	8	no	—
310	C₂²	—	2	8	no	—
311	C₂²	—	2	32	no	—
312	C₂²	—	2	4	no	—
313	C₂²	#381×C₁₃₉	1	4	yes	—
314	C₂²	C₂×#102×C₁₃₉	1	8	yes	—
315	C₂²	C₂×#102×C₁₃₉	1	4	yes	—
316	C₂²	#419×C₁₃₉	1	4	yes	—
317	C₂²	#480×C₁₃₉	1	8	yes	—
318	C₂²	#483×C₁₃₉	1	8	yes	—
319	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
320	C₂²	C₂×#123×C₁₃₉	1	2	yes	—
321	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
322	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
323	C₂²	C₂×#137×C₁₃₉	1	2	yes	—
324	C₄	—	2	4	no	—
325	C₄	—	4	8	no	—
326	C₄	—	8	4	no	—
327	C₄	#381×C₁₃₉	1	4	yes	—
328	C₄	C₂×#117×C₁₃₉	1	2	yes	—
329	C₄	C₂×#123×C₁₃₉	1	2	yes	—
330	C₂	—	2	8	no	—
331	C₂	#1823×C₁₃₉	1	8	yes	direct product factor
332	C₂	C₂×#381×C₁₃₉	1	1	yes	characteristic
333	C₂	C₂²×#102×C₁₃₉	1	1	yes	characteristic
334	C₂	C₂×#419×C₁₃₉	1	1	yes	characteristic
335	C₂	C₂×#480×C₁₃₉	1	2	yes	—
336	C₂	C₂×#483×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. #1823×C₁₃₉	C₂	direct (N × H)
5. C₂×#340×C₁₃₉	C₂	semidirect
12. C₂²×C₄⋊C₄×C₁₃₉	C₄	semidirect
22. #340×C₁₃₉	C₂²	semidirect
49. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
162. C₂×C₁₃₉	#1823	direct (N × H)
168. C₂×#1823	C₁₃₉	direct (N × H)
169. C₁₃₉	C₂×#1823	direct (N × H)
173. #1823	C₂×C₁₃₉	direct (N × H)
174. C₂×#340	C₂×C₁₃₉	semidirect
181. C₂²×C₄⋊C₄	C₄×C₁₃₉	semidirect
191. #340	C₂²×C₁₃₉	semidirect
218. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
331. C₂	#1823×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
C₂³×C₄⋊C₄×C₁₃₉	2
C₂²×C₂²⋊C₈×C₁₃₉	2
C₂×#380×C₁₃₉	2
#1823×C₁₃₉	2
C₂×#340×C₁₃₉	2
C₂×#1823	139

Subgroups — C2×#1823×C139 #48015292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1823×C₁₃₉ #48015292