Subgroups — C₁₃₉×#29255 #48023851

Order 35584.

768 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	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2096×C₁₃₉	C₂	1	2	yes	maximal
4	#2024×C₁₃₉	C₂	1	2	yes	maximal
5	#1981×C₁₃₉	C₂	1	2	yes	maximal
6	#1948×C₁₃₉	C₂	1	2	yes	maximal
7	#1865×C₁₃₉	C₂	1	4	yes	maximal
8	#1831×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#106×C₁₃₉	C₂²	1	4	yes	—
14	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#103×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#103×C₁₃₉	C₂²	1	4	yes	—
17	#391×C₁₃₉	—	2	1	no	—
18	#391×C₁₃₉	C₂²	1	2	yes	—
19	#389×C₁₃₉	—	2	1	no	—
20	#389×C₁₃₉	—	2	1	no	—
21	#389×C₁₃₉	—	2	1	no	—
22	#389×C₁₃₉	C₂²	1	2	yes	—
23	#384×C₁₃₉	C₂²	1	1	yes	characteristic
24	#384×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
30	#340×C₁₃₉	C₂²	1	4	yes	—
31	#336×C₁₃₉	C₂²	1	2	yes	—
32	#336×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃₉	—	2	1	no	—
34	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
36	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
37	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
38	C₄⋊Q₈×C₁₃₉	Q₈	1	4	yes	complemented
39	C₄×Q₈×C₁₃₉	—	4	4	no	—
40	C₄×Q₈×C₁₃₉	—	4	4	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
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	1	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₃₉	—	2	2	no	—
54	C₂×C₄²×C₁₃₉	—	2	2	no	—
55	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
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	1	yes	characteristic
61	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
62	#106×C₁₃₉	—	4	4	no	—
63	C₄⋊C₈×C₁₃₉	—	2	4	no	—
64	#103×C₁₃₉	—	2	8	no	—
65	#103×C₁₃₉	—	4	4	no	—
66	#95×C₁₃₉	—	2	2	no	—
67	#95×C₁₃₉	—	2	2	no	—
68	#95×C₁₃₉	—	2	2	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	C₂×Q₈×C₁₃₉	—	2	4	no	—
71	C₂×Q₈×C₁₃₉	—	2	2	no	—
72	C₂×Q₈×C₁₃₉	—	2	4	no	—
73	C₂×Q₈×C₁₃₉	—	2	4	no	—
74	C₂×Q₈×C₁₃₉	—	4	2	no	—
75	C₂×Q₈×C₁₃₉	—	4	2	no	—
76	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	2	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₁₃₉	—	2	4	no	—
89	C₂×C₈×C₁₃₉	—	2	4	no	—
90	C₂×C₈×C₁₃₉	—	2	4	no	—
91	C₄⋊C₄×C₁₃₉	—	2	4	no	—
92	C₄⋊C₄×C₁₃₉	—	2	4	no	—
93	C₄⋊C₄×C₁₃₉	—	2	4	no	—
94	C₄⋊C₄×C₁₃₉	—	2	2	no	—
95	C₄⋊C₄×C₁₃₉	—	2	2	no	—
96	C₄⋊C₄×C₁₃₉	—	2	2	no	—
97	C₄⋊C₄×C₁₃₉	—	2	4	no	—
98	C₄⋊C₄×C₁₃₉	—	4	2	no	—
99	C₄⋊C₄×C₁₃₉	—	4	4	no	—
100	C₄⋊C₄×C₁₃₉	—	4	4	no	—
101	C₄⋊C₄×C₁₃₉	—	4	2	no	—
102	C₄⋊C₄×C₁₃₉	—	4	2	no	—
103	C₄⋊C₄×C₁₃₉	—	4	2	no	—
104	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
105	C₄²×C₁₃₉	—	2	2	no	—
106	C₄²×C₁₃₉	—	2	2	no	—
107	C₄²×C₁₃₉	—	2	2	no	—
108	C₄²×C₁₃₉	—	2	2	no	—
109	C₄²×C₁₃₉	—	4	1	no	—
110	C₄²×C₁₃₉	—	4	4	no	—
111	C₄²×C₁₃₉	—	4	4	no	—
112	C₄²×C₁₃₉	SD₁₆	1	4	yes	—
113	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
114	C₄²×C₁₃₉	#41	1	2	yes	—
115	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
116	Q₈×C₁₃₉	—	2	8	no	—
117	Q₈×C₁₃₉	—	4	8	no	—
118	Q₈×C₁₃₉	—	4	4	no	—
119	C₂×C₄×C₁₃₉	—	2	1	no	—
120	C₂×C₄×C₁₃₉	—	2	1	no	—
121	C₂×C₄×C₁₃₉	—	2	1	no	—
122	C₂×C₄×C₁₃₉	—	2	1	no	—
123	C₂×C₄×C₁₃₉	—	2	1	no	—
124	C₂×C₄×C₁₃₉	—	2	1	no	—
125	C₂×C₄×C₁₃₉	—	2	1	no	—
126	C₂×C₄×C₁₃₉	—	2	1	no	—
127	C₂×C₄×C₁₃₉	—	2	4	no	—
128	C₂×C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄×C₁₃₉	—	2	1	no	—
130	C₂×C₄×C₁₃₉	—	2	1	no	—
131	C₂×C₄×C₁₃₉	—	2	1	no	—
132	C₂×C₄×C₁₃₉	—	4	2	no	—
133	C₂×C₄×C₁₃₉	—	4	2	no	—
134	C₂×C₄×C₁₃₉	—	4	2	no	—
135	C₂×C₄×C₁₃₉	—	4	2	no	—
136	C₂×C₄×C₁₃₉	—	4	2	no	—
137	C₂×C₄×C₁₃₉	—	4	2	no	—
138	C₂×C₄×C₁₃₉	—	4	2	no	—
139	C₂×C₄×C₁₃₉	—	4	2	no	—
140	C₂×C₄×C₁₃₉	—	4	2	no	—
141	C₂×C₄×C₁₃₉	—	4	2	no	—
142	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
145	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
146	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
147	C₂×C₄×C₁₃₉	#137	1	2	yes	—
148	C₂×C₄×C₁₃₉	#137	1	2	yes	—
149	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
153	C₈×C₁₃₉	—	4	4	no	—
154	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
155	C₂²×C₁₃₉	#525	1	1	yes	characteristic
156	C₂²×C₁₃₉	#535	1	1	yes	characteristic
157	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
158	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
159	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
160	C₂²×C₁₃₉	#575	1	1	yes	characteristic
161	C₄×C₁₃₉	—	2	2	no	—
162	C₄×C₁₃₉	—	2	2	no	—
163	C₄×C₁₃₉	—	2	2	no	—
164	C₄×C₁₃₉	—	2	2	no	—
165	C₄×C₁₃₉	—	4	4	no	—
166	C₄×C₁₃₉	—	4	4	no	—
167	C₄×C₁₃₉	—	4	1	no	—
168	C₄×C₁₃₉	—	8	2	no	—
169	C₄×C₁₃₉	—	8	2	no	—
170	C₄×C₁₃₉	#475	1	4	yes	—
171	C₄×C₁₃₉	#554	1	2	yes	—
172	C₄×C₁₃₉	#559	1	2	yes	—
173	C₂×C₁₃₉	#2580	1	1	yes	characteristic
174	C₂×C₁₃₉	C₂×#475	1	1	yes	characteristic
175	C₂×C₁₃₉	#3078	1	1	yes	characteristic
176	C₂×C₁₃₉	#3101	1	1	yes	characteristic
177	C₂×C₁₃₉	#3113	1	1	yes	characteristic
178	C₂×C₁₃₉	#3206	1	1	yes	characteristic
179	C₂×C₁₃₉	#3216	1	1	yes	characteristic
180	#29255	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₉	#29255	1	1	yes	characteristic, direct product factor, Sylow
182	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
183	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
184	#2096	C₂×C₁₃₉	1	2	yes	—
185	#2024	C₂×C₁₃₉	1	2	yes	—
186	#1981	C₂×C₁₃₉	1	2	yes	—
187	#1948	C₂×C₁₃₉	1	2	yes	—
188	#1865	C₂×C₁₃₉	1	4	yes	—
189	#1831	C₂×C₁₃₉	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
191	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂×C₄×Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
194	C₂×#106	C₂²×C₁₃₉	1	4	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
196	C₂×#103	C₂²×C₁₃₉	1	4	yes	—
197	C₂×#103	C₂²×C₁₃₉	1	4	yes	—
198	#391	—	2	1	no	—
199	#391	C₂²×C₁₃₉	1	2	yes	—
200	#389	—	2	1	no	—
201	#389	—	2	1	no	—
202	#389	—	2	1	no	—
203	#389	C₂²×C₁₃₉	1	2	yes	—
204	#384	C₂²×C₁₃₉	1	1	yes	characteristic
205	#384	C₂²×C₁₃₉	1	1	yes	characteristic
206	C₄×C₄⋊C₄	—	2	1	no	—
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₄⋊C₄	—	2	1	no	—
209	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
210	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
211	#340	C₂²×C₁₃₉	1	4	yes	—
212	#336	C₂²×C₁₃₉	1	2	yes	—
213	#336	C₂²×C₁₃₉	1	2	yes	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
216	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
217	C₄⋊Q₈	—	2	4	no	—
218	C₄⋊Q₈	—	2	2	no	—
219	C₄⋊Q₈	Q₈×C₁₃₉	1	4	yes	complemented
220	C₄×Q₈	—	4	4	no	—
221	C₄×Q₈	—	4	4	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
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	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
243	#106	—	4	4	no	—
244	C₄⋊C₈	—	2	4	no	—
245	#103	—	2	8	no	—
246	#103	—	4	4	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	4	2	no	—
256	C₂×Q₈	—	4	2	no	—
257	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	4	1	no	—
291	C₄²	—	4	4	no	—
292	C₄²	—	4	4	no	—
293	C₄²	SD₁₆×C₁₃₉	1	4	yes	—
294	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
295	C₄²	#41×C₁₃₉	1	2	yes	—
296	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
297	Q₈	—	2	8	no	—
298	Q₈	—	4	8	no	—
299	Q₈	—	4	4	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
324	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
325	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
326	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
327	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
328	C₂×C₄	#137×C₁₃₉	1	2	yes	—
329	C₂×C₄	#137×C₁₃₉	1	2	yes	—
330	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
332	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
334	C₈	—	4	4	no	—
335	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
336	C₂²	#525×C₁₃₉	1	1	yes	characteristic
337	C₂²	#535×C₁₃₉	1	1	yes	characteristic
338	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
339	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
340	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
341	C₂²	#575×C₁₃₉	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	4	4	no	—
347	C₄	—	4	4	no	—
348	C₄	—	4	1	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	2	no	—
351	C₄	#475×C₁₃₉	1	4	yes	—
352	C₄	#554×C₁₃₉	1	2	yes	—
353	C₄	#559×C₁₃₉	1	2	yes	—
354	C₂	#2580×C₁₃₉	1	1	yes	characteristic
355	C₂	C₂×#475×C₁₃₉	1	1	yes	characteristic
356	C₂	#3078×C₁₃₉	1	1	yes	characteristic
357	C₂	#3101×C₁₃₉	1	1	yes	characteristic
358	C₂	#3113×C₁₃₉	1	1	yes	characteristic
359	C₂	#3206×C₁₃₉	1	1	yes	characteristic
360	C₂	#3216×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
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
38. C₄⋊Q₈×C₁₃₉	Q₈	semidirect
180. #29255	C₁₃₉	direct (N × H)
181. C₁₃₉	#29255	direct (N × H)
219. C₄⋊Q₈	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊Q₈×C₁₃₉	2
#2096×C₁₃₉	2
#2024×C₁₃₉	2
#1981×C₁₃₉	2
#1948×C₁₃₉	2
#1865×C₁₃₉	2
#1831×C₁₃₉	2
#29255	139

Subgroups — C139×#29255 #48023851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29255 #48023851