Subgroups — C₁₃₉×#29532 #48024128

Order 35584.

840 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2293×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2086×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2067×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2054×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1925×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1918×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1879×C₁₃₉	C₂	1	2	yes	maximal
8	#1862×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1831×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
12	C₂×#117×C₁₃₉	—	2	2	no	—
13	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
20	#390×C₁₃₉	C₂²	1	2	yes	—
21	#390×C₁₃₉	C₂²	1	2	yes	—
22	#389×C₁₃₉	C₂²	1	2	yes	—
23	#389×C₁₃₉	C₂²	1	2	yes	—
24	#388×C₁₃₉	—	2	2	no	—
25	#388×C₁₃₉	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
28	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
29	#340×C₁₃₉	C₂²	1	1	yes	characteristic
30	#340×C₁₃₉	C₂²	1	2	yes	—
31	#340×C₁₃₉	C₂²	1	1	yes	characteristic
32	#340×C₁₃₉	C₂²	1	2	yes	—
33	#336×C₁₃₉	C₂²	1	2	yes	—
34	#336×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	—	2	2	no	—
37	C₂×D₈×C₁₃₉	—	2	4	no	—
38	C₂×D₈×C₁₃₉	—	4	1	no	—
39	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₄×D₄×C₁₃₉	—	2	4	no	—
43	C₄×D₄×C₁₃₉	—	2	4	no	—
44	#117×C₁₃₉	—	4	8	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
55	C₂×C₄²×C₁₃₉	—	2	2	no	—
56	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
57	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
61	#107×C₁₃₉	—	2	4	no	—
62	#107×C₁₃₉	—	4	1	no	—
63	C₄⋊C₈×C₁₃₉	—	4	1	no	—
64	C₄⋊C₈×C₁₃₉	—	4	1	no	—
65	#102×C₁₃₉	—	2	4	no	—
66	#102×C₁₃₉	—	2	4	no	—
67	#102×C₁₃₉	—	4	2	no	—
68	#95×C₁₃₉	—	2	2	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	#95×C₁₃₉	—	2	2	no	—
71	C₂⁴×C₁₃₉	—	2	2	no	—
72	C₂×D₄×C₁₃₉	—	2	2	no	—
73	C₂×D₄×C₁₃₉	—	2	2	no	—
74	C₂×D₄×C₁₃₉	—	2	2	no	—
75	C₂×D₄×C₁₃₉	—	2	2	no	—
76	C₂×D₄×C₁₃₉	—	2	2	no	—
77	C₂×D₄×C₁₃₉	#41	1	4	yes	—
78	C₂²×C₄×C₁₃₉	—	2	8	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	4	4	no	—
83	C₂²×C₄×C₁₃₉	—	4	4	no	—
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
89	D₈×C₁₃₉	—	4	4	no	—
90	C₂×C₈×C₁₃₉	—	2	2	no	—
91	C₂×C₈×C₁₃₉	—	2	2	no	—
92	C₂×C₈×C₁₃₉	—	2	2	no	—
93	C₂×C₈×C₁₃₉	—	2	2	no	—
94	C₂×C₈×C₁₃₉	—	2	2	no	—
95	C₂×C₈×C₁₃₉	—	2	1	no	—
96	C₂×C₈×C₁₃₉	—	2	1	no	—
97	C₄⋊C₄×C₁₃₉	—	2	2	no	—
98	C₄⋊C₄×C₁₃₉	—	2	2	no	—
99	C₄⋊C₄×C₁₃₉	—	2	2	no	—
100	C₄⋊C₄×C₁₃₉	—	2	2	no	—
101	C₄⋊C₄×C₁₃₉	—	2	2	no	—
102	C₄⋊C₄×C₁₃₉	—	4	4	no	—
103	C₄⋊C₄×C₁₃₉	—	4	4	no	—
104	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
105	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
106	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
107	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
108	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
109	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
110	C₄²×C₁₃₉	—	2	2	no	—
111	C₄²×C₁₃₉	—	2	2	no	—
112	C₄²×C₁₃₉	—	2	1	no	—
113	C₄²×C₁₃₉	—	2	1	no	—
114	C₄²×C₁₃₉	—	4	2	no	—
115	C₄²×C₁₃₉	—	4	1	no	—
116	C₄²×C₁₃₉	—	4	4	no	—
117	C₄²×C₁₃₉	D₈	1	4	yes	complemented
118	C₂³×C₁₃₉	—	2	4	no	—
119	C₂³×C₁₃₉	—	4	2	no	—
120	C₂³×C₁₃₉	—	4	2	no	—
121	C₂³×C₁₃₉	—	4	2	no	—
122	C₂³×C₁₃₉	—	4	2	no	—
123	C₂³×C₁₃₉	—	4	2	no	—
124	C₂³×C₁₃₉	—	4	2	no	—
125	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
126	D₄×C₁₃₉	—	2	4	no	—
127	D₄×C₁₃₉	—	2	4	no	—
128	D₄×C₁₃₉	—	4	2	no	—
129	D₄×C₁₃₉	—	4	2	no	—
130	C₂×C₄×C₁₃₉	—	2	2	no	—
131	C₂×C₄×C₁₃₉	—	2	1	no	—
132	C₂×C₄×C₁₃₉	—	2	2	no	—
133	C₂×C₄×C₁₃₉	—	2	1	no	—
134	C₂×C₄×C₁₃₉	—	2	2	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	1	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	4	16	no	—
141	C₂×C₄×C₁₃₉	—	4	2	no	—
142	C₂×C₄×C₁₃₉	—	4	2	no	—
143	C₂×C₄×C₁₃₉	—	4	2	no	—
144	C₂×C₄×C₁₃₉	—	4	2	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	2	no	—
149	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
150	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
152	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
153	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
155	C₈×C₁₃₉	—	4	1	no	—
156	C₈×C₁₃₉	—	4	1	no	—
157	C₈×C₁₃₉	—	4	2	no	—
158	C₂²×C₁₃₉	—	4	4	no	—
159	C₂²×C₁₃₉	—	4	4	no	—
160	C₂²×C₁₃₉	—	4	4	no	—
161	C₂²×C₁₃₉	—	8	2	no	—
162	C₂²×C₁₃₉	—	8	2	no	—
163	C₂²×C₁₃₉	—	8	2	no	—
164	C₂²×C₁₃₉	—	8	2	no	—
165	C₂²×C₁₃₉	#525	1	2	yes	—
166	C₂²×C₁₃₉	#537	1	1	yes	characteristic
167	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
168	C₂²×C₁₃₉	#575	1	2	yes	—
169	C₂²×C₁₃₉	#575	1	1	yes	characteristic
170	C₄×C₁₃₉	—	2	4	no	—
171	C₄×C₁₃₉	—	2	2	no	—
172	C₄×C₁₃₉	—	4	4	no	—
173	C₄×C₁₃₉	—	4	2	no	—
174	C₄×C₁₃₉	—	4	1	no	—
175	C₄×C₁₃₉	—	8	2	no	—
176	C₄×C₁₃₉	—	8	2	no	—
177	C₄×C₁₃₉	#551	1	1	yes	characteristic
178	C₄×C₁₃₉	#552	1	2	yes	—
179	C₄×C₁₃₉	#555	1	1	yes	characteristic
180	C₂×C₁₃₉	—	8	4	no	—
181	C₂×C₁₃₉	#2609	1	1	yes	characteristic
182	C₂×C₁₃₉	#3100	1	2	yes	—
183	C₂×C₁₃₉	#3111	1	2	yes	—
184	C₂×C₁₃₉	#3245	1	1	yes	characteristic
185	C₂×C₁₃₉	#3256	1	1	yes	characteristic
186	#29532	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₁₃₉	#29532	1	1	yes	characteristic, direct product factor, Sylow
188	#2293	C₂×C₁₃₉	1	2	yes	complemented
189	#2086	C₂×C₁₃₉	1	1	yes	characteristic, complemented
190	#2067	C₂×C₁₃₉	1	2	yes	complemented
191	#2054	C₂×C₁₃₉	1	1	yes	characteristic
192	#1925	C₂×C₁₃₉	1	2	yes	complemented
193	#1918	C₂×C₁₃₉	1	2	yes	complemented
194	#1879	C₂×C₁₃₉	1	2	yes	—
195	#1862	C₂×C₁₃₉	1	2	yes	complemented
196	#1831	C₂×C₁₃₉	1	1	yes	characteristic, complemented
197	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
198	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
199	C₂×#117	—	2	2	no	—
200	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
201	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
204	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
205	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
206	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
207	#390	C₂²×C₁₃₉	1	2	yes	—
208	#390	C₂²×C₁₃₉	1	2	yes	—
209	#389	C₂²×C₁₃₉	1	2	yes	—
210	#389	C₂²×C₁₃₉	1	2	yes	—
211	#388	—	2	2	no	—
212	#388	—	2	2	no	—
213	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
214	C₄×C₂²⋊C₄	—	2	2	no	—
215	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
216	#340	C₂²×C₁₃₉	1	1	yes	characteristic
217	#340	C₂²×C₁₃₉	1	2	yes	—
218	#340	C₂²×C₁₃₉	1	1	yes	characteristic
219	#340	C₂²×C₁₃₉	1	2	yes	—
220	#336	C₂²×C₁₃₉	1	2	yes	—
221	#336	C₂²×C₁₃₉	1	2	yes	—
222	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂×D₈	—	2	4	no	—
225	C₂×D₈	—	4	1	no	—
226	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
229	C₄×D₄	—	2	4	no	—
230	C₄×D₄	—	2	4	no	—
231	#117	—	4	8	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
244	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
247	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
248	#107	—	2	4	no	—
249	#107	—	4	1	no	—
250	C₄⋊C₈	—	4	1	no	—
251	C₄⋊C₈	—	4	1	no	—
252	#102	—	2	4	no	—
253	#102	—	2	4	no	—
254	#102	—	4	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	C₂⁴	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	#41×C₁₃₉	1	4	yes	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
276	D₈	—	4	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	4	4	no	—
295	C₂²⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	4	2	no	—
302	C₄²	—	4	1	no	—
303	C₄²	—	4	4	no	—
304	C₄²	D₈×C₁₃₉	1	4	yes	complemented
305	C₂³	—	2	4	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
313	D₄	—	2	4	no	—
314	D₄	—	2	4	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	16	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
337	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
338	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
339	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
340	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
341	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
342	C₈	—	4	1	no	—
343	C₈	—	4	1	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	#525×C₁₃₉	1	2	yes	—
353	C₂²	#537×C₁₃₉	1	1	yes	characteristic
354	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
355	C₂²	#575×C₁₃₉	1	2	yes	—
356	C₂²	#575×C₁₃₉	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	2	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	1	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	2	no	—
364	C₄	#551×C₁₃₉	1	1	yes	characteristic
365	C₄	#552×C₁₃₉	1	2	yes	—
366	C₄	#555×C₁₃₉	1	1	yes	characteristic
367	C₂	—	8	4	no	—
368	C₂	#2609×C₁₃₉	1	1	yes	characteristic
369	C₂	#3100×C₁₃₉	1	2	yes	—
370	C₂	#3111×C₁₃₉	1	2	yes	—
371	C₂	#3245×C₁₃₉	1	1	yes	characteristic
372	C₂	#3256×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×D₈×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₄³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2293×C₁₃₉	C₂	semidirect
2. #2086×C₁₃₉	C₂	semidirect
3. #2067×C₁₃₉	C₂	semidirect
5. #1925×C₁₃₉	C₂	semidirect
6. #1918×C₁₃₉	C₂	semidirect
8. #1862×C₁₃₉	C₂	semidirect
9. #1831×C₁₃₉	C₂	semidirect
117. C₄²×C₁₃₉	D₈	semidirect
186. #29532	C₁₃₉	direct (N × H)
187. C₁₃₉	#29532	direct (N × H)
188. #2293	C₂×C₁₃₉	semidirect
189. #2086	C₂×C₁₃₉	semidirect
190. #2067	C₂×C₁₃₉	semidirect
192. #1925	C₂×C₁₃₉	semidirect
193. #1918	C₂×C₁₃₉	semidirect
195. #1862	C₂×C₁₃₉	semidirect
196. #1831	C₂×C₁₃₉	semidirect
304. C₄²	D₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2293×C₁₃₉	2
#2086×C₁₃₉	2
#2067×C₁₃₉	2
#2054×C₁₃₉	2
#1925×C₁₃₉	2
#1918×C₁₃₉	2
#1879×C₁₃₉	2
#1862×C₁₃₉	2
#1831×C₁₃₉	2
#29532	139

Subgroups — C139×#29532 #48024128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29532 #48024128