Subgroups — C₁₃₉×#29287 #48023883

Order 35584.

756 conjugacy classes of subgroups.

The subgroup lattice has 376 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	#2088×C₁₃₉	C₂	1	4	yes	maximal
4	#1988×C₁₃₉	C₂	1	2	yes	maximal
5	#1987×C₁₃₉	C₂	1	2	yes	maximal
6	#1948×C₁₃₉	C₂	1	2	yes	maximal
7	#1948×C₁₃₉	C₂	1	2	yes	maximal
8	#1842×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	—	2	1	no	—
13	C₂×#106×C₁₃₉	C₂²	1	4	yes	—
14	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
17	#391×C₁₃₉	—	2	1	no	—
18	#391×C₁₃₉	—	2	1	no	—
19	#389×C₁₃₉	—	2	1	no	—
20	#389×C₁₃₉	—	2	1	no	—
21	#389×C₁₃₉	C₂²	1	2	yes	—
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	C₂²	1	2	yes	—
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	#340×C₁₃₉	C₂²	1	4	yes	—
32	#340×C₁₃₉	C₂²	1	4	yes	—
33	C₂²×Q₈×C₁₃₉	—	2	1	no	—
34	C₂²×Q₈×C₁₃₉	—	2	1	no	—
35	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
36	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
37	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
38	C₄⋊Q₈×C₁₃₉	Q₈	1	4	yes	complemented
39	C₄⋊Q₈×C₁₃₉	Q₈	1	4	yes	complemented
40	C₄×Q₈×C₁₃₉	—	4	4	no	—
41	C₄×Q₈×C₁₃₉	—	4	4	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	1	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	2	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×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃₉	—	2	2	no	—
55	C₂×C₄²×C₁₃₉	—	2	2	no	—
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	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
63	#106×C₁₃₉	—	4	4	no	—
64	C₄⋊C₈×C₁₃₉	—	2	4	no	—
65	C₄⋊C₈×C₁₃₉	—	2	4	no	—
66	C₄⋊C₈×C₁₃₉	—	4	2	no	—
67	#95×C₁₃₉	—	2	2	no	—
68	#95×C₁₃₉	—	2	2	no	—
69	#95×C₁₃₉	—	2	2	no	—
70	#95×C₁₃₉	—	2	2	no	—
71	C₂×Q₈×C₁₃₉	—	2	4	no	—
72	C₂×Q₈×C₁₃₉	—	2	4	no	—
73	C₂×Q₈×C₁₃₉	—	4	2	no	—
74	C₂×Q₈×C₁₃₉	—	4	2	no	—
75	C₂×Q₈×C₁₃₉	—	4	2	no	—
76	C₂×Q₈×C₁₃₉	—	4	2	no	—
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	2	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	2	no	—
98	C₄⋊C₄×C₁₃₉	—	2	2	no	—
99	C₄⋊C₄×C₁₃₉	—	4	2	no	—
100	C₄⋊C₄×C₁₃₉	—	4	2	no	—
101	C₄⋊C₄×C₁₃₉	—	4	4	no	—
102	C₄⋊C₄×C₁₃₉	—	4	4	no	—
103	C₄⋊C₄×C₁₃₉	—	4	2	no	—
104	C₄⋊C₄×C₁₃₉	—	4	2	no	—
105	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
106	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
107	C₄²×C₁₃₉	—	2	2	no	—
108	C₄²×C₁₃₉	—	2	2	no	—
109	C₄²×C₁₃₉	—	2	1	no	—
110	C₄²×C₁₃₉	—	2	1	no	—
111	C₄²×C₁₃₉	—	4	1	no	—
112	C₄²×C₁₃₉	—	4	4	no	—
113	C₄²×C₁₃₉	—	4	4	no	—
114	C₄²×C₁₃₉	SD₁₆	1	4	yes	—
115	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
116	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
117	C₄²×C₁₃₉	#41	1	2	yes	—
118	C₄²×C₁₃₉	#41	1	2	yes	—
119	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₁₃₉	—	4	8	no	—
121	Q₈×C₁₃₉	—	4	8	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	1	no	—
128	C₂×C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄×C₁₃₉	—	2	1	no	—
131	C₂×C₄×C₁₃₉	—	2	1	no	—
132	C₂×C₄×C₁₃₉	—	2	1	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	—	4	2	no	—
143	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
148	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
149	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
150	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
151	C₂×C₄×C₁₃₉	#137	1	2	yes	—
152	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
158	C₈×C₁₃₉	—	4	4	no	—
159	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
160	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
161	C₂²×C₁₃₉	#537	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
163	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
165	C₂²×C₁₃₉	#575	1	1	yes	characteristic
166	C₄×C₁₃₉	—	2	2	no	—
167	C₄×C₁₃₉	—	2	2	no	—
168	C₄×C₁₃₉	—	2	2	no	—
169	C₄×C₁₃₉	—	4	4	no	—
170	C₄×C₁₃₉	—	4	1	no	—
171	C₄×C₁₃₉	—	4	4	no	—
172	C₄×C₁₃₉	—	8	2	no	—
173	C₄×C₁₃₉	—	8	2	no	—
174	C₄×C₁₃₉	#475	1	4	yes	—
175	C₄×C₁₃₉	#476	1	4	yes	—
176	C₄×C₁₃₉	#557	1	1	yes	characteristic
177	C₄×C₁₃₉	#557	1	1	yes	characteristic
178	C₄×C₁₃₉	Q₈²	1	1	yes	characteristic
179	C₄×C₁₃₉	#559	1	1	yes	characteristic
180	C₂×C₁₃₉	#2582	1	1	yes	characteristic
181	C₂×C₁₃₉	C₂×#476	1	1	yes	characteristic
182	C₂×C₁₃₉	C₂×#475	1	1	yes	characteristic
183	C₂×C₁₃₉	#3077	1	1	yes	characteristic
184	C₂×C₁₃₉	#3078	1	1	yes	characteristic
185	C₂×C₁₃₉	#3246	1	1	yes	characteristic
186	C₂×C₁₃₉	#3254	1	1	yes	characteristic
187	#29287	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₉	#29287	1	1	yes	characteristic, direct product factor, Sylow
189	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
190	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
191	#2088	C₂×C₁₃₉	1	4	yes	—
192	#1988	C₂×C₁₃₉	1	2	yes	—
193	#1987	C₂×C₁₃₉	1	2	yes	—
194	#1948	C₂×C₁₃₉	1	2	yes	—
195	#1948	C₂×C₁₃₉	1	2	yes	—
196	#1842	C₂×C₁₃₉	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×C₄×Q₈	—	2	1	no	—
201	C₂×#106	C₂²×C₁₃₉	1	4	yes	—
202	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
205	#391	—	2	1	no	—
206	#391	—	2	1	no	—
207	#389	—	2	1	no	—
208	#389	—	2	1	no	—
209	#389	C₂²×C₁₃₉	1	2	yes	—
210	#389	C₂²×C₁₃₉	1	2	yes	—
211	#384	C₂²×C₁₃₉	1	1	yes	characteristic
212	#384	C₂²×C₁₃₉	1	1	yes	characteristic
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	—	2	1	no	—
215	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
217	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
218	#340	C₂²×C₁₃₉	1	4	yes	—
219	#340	C₂²×C₁₃₉	1	4	yes	—
220	#340	C₂²×C₁₃₉	1	4	yes	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	Q₈×C₁₃₉	1	4	yes	complemented
227	C₄⋊Q₈	Q₈×C₁₃₉	1	4	yes	complemented
228	C₄×Q₈	—	4	4	no	—
229	C₄×Q₈	—	4	4	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
251	#106	—	4	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	4	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	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	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
294	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	4	1	no	—
300	C₄²	—	4	4	no	—
301	C₄²	—	4	4	no	—
302	C₄²	SD₁₆×C₁₃₉	1	4	yes	—
303	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
304	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
305	C₄²	#41×C₁₃₉	1	2	yes	—
306	C₄²	#41×C₁₃₉	1	2	yes	—
307	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
308	Q₈	—	4	8	no	—
309	Q₈	—	4	8	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
332	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
333	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
334	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
335	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
336	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
337	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
338	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
339	C₂×C₄	#137×C₁₃₉	1	2	yes	—
340	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
344	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
345	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
348	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
349	C₂²	#537×C₁₃₉	1	1	yes	characteristic
350	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
351	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
352	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
353	C₂²	#575×C₁₃₉	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	4	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	1	no	—
360	C₄	—	8	2	no	—
361	C₄	—	8	2	no	—
362	C₄	#475×C₁₃₉	1	4	yes	—
363	C₄	#476×C₁₃₉	1	4	yes	—
364	C₄	#557×C₁₃₉	1	1	yes	characteristic
365	C₄	#557×C₁₃₉	1	1	yes	characteristic
366	C₄	Q₈²×C₁₃₉	1	1	yes	characteristic
367	C₄	#559×C₁₃₉	1	1	yes	characteristic
368	C₂	#2582×C₁₃₉	1	1	yes	characteristic
369	C₂	C₂×#476×C₁₃₉	1	1	yes	characteristic
370	C₂	C₂×#475×C₁₃₉	1	1	yes	characteristic
371	C₂	#3077×C₁₃₉	1	1	yes	characteristic
372	C₂	#3078×C₁₃₉	1	1	yes	characteristic
373	C₂	#3246×C₁₃₉	1	1	yes	characteristic
374	C₂	#3254×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
39. C₄⋊Q₈×C₁₃₉	Q₈	semidirect
187. #29287	C₁₃₉	direct (N × H)
188. C₁₃₉	#29287	direct (N × H)
226. C₄⋊Q₈	Q₈×C₁₃₉	semidirect
227. 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
#2088×C₁₃₉	2
#1988×C₁₃₉	2
#1987×C₁₃₉	2
#1948×C₁₃₉	2
#1842×C₁₃₉	2
#29287	139

Subgroups — C139×#29287 #48023883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29287 #48023883