Subgroups — C₁₃₉×#21833 #48016429

Order 35584.

1302 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1990×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#1988×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1823×C₁₃₉	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₁₃₉	—	2	1	no	—
8	C₂×C₄⋊Q₈×C₁₃₉	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₁₃₉	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₁₃₉	—	2	4	no	—
11	C₂×C₄⋊Q₈×C₁₃₉	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#117×C₁₃₉	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
18	#431×C₁₃₉	—	2	4	no	—
19	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
22	#384×C₁₃₉	C₂²	1	2	yes	—
23	#382×C₁₃₉	—	2	1	no	—
24	#380×C₁₃₉	—	2	1	no	—
25	#380×C₁₃₉	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	#340×C₁₃₉	C₂²	1	16	yes	—
29	C₂²×Q₈×C₁₃₉	—	2	8	no	—
30	C₂²×Q₈×C₁₃₉	—	2	2	no	—
31	C₂²×Q₈×C₁₃₉	—	2	2	no	—
32	C₂²×Q₈×C₁₃₉	—	4	4	no	—
33	C₂²×Q₈×C₁₃₉	—	4	4	no	—
34	C₂³×C₄×C₁₃₉	—	2	2	no	—
35	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
40	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
41	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
42	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
43	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	8	yes	—
44	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	8	yes	—
45	#117×C₁₃₉	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₄²×C₁₃₉	—	2	2	no	—
58	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
62	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₁₃₉	—	2	4	no	—
65	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
66	C₄×C₈×C₁₃₉	—	2	4	no	—
67	#95×C₁₃₉	—	2	2	no	—
68	#95×C₁₃₉	—	2	2	no	—
69	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
70	C₂×Q₈×C₁₃₉	—	2	8	no	—
71	C₂×Q₈×C₁₃₉	—	2	8	no	—
72	C₂×Q₈×C₁₃₉	—	4	32	no	—
73	C₂×Q₈×C₁₃₉	—	4	4	no	—
74	C₂×Q₈×C₁₃₉	—	4	4	no	—
75	C₂×Q₈×C₁₃₉	—	4	4	no	—
76	C₂×Q₈×C₁₃₉	—	4	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	4	no	—
79	C₂²×C₄×C₁₃₉	—	2	8	no	—
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	4	no	—
82	C₂²×C₄×C₁₃₉	—	4	4	no	—
83	C₂²×C₄×C₁₃₉	—	4	4	no	—
84	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
86	C₂²×C₄×C₁₃₉	D₈	1	4	yes	—
87	C₂²×C₄×C₁₃₉	SD₁₆	1	4	yes	—
88	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₃₉	—	2	4	no	—
97	C₂×C₈×C₁₃₉	—	2	8	no	—
98	C₄⋊C₄×C₁₃₉	—	2	8	no	—
99	C₄⋊C₄×C₁₃₉	—	2	8	no	—
100	C₄⋊C₄×C₁₃₉	—	2	8	no	—
101	C₄⋊C₄×C₁₃₉	—	2	4	no	—
102	C₄⋊C₄×C₁₃₉	—	2	8	no	—
103	C₄⋊C₄×C₁₃₉	—	4	4	no	—
104	C₄⋊C₄×C₁₃₉	—	4	4	no	—
105	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
106	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
107	C₄²×C₁₃₉	—	4	4	no	—
108	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
109	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
110	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
111	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
112	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
113	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
114	C₂³×C₁₃₉	—	2	2	no	—
115	C₂³×C₁₃₉	—	2	2	no	—
116	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
118	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
119	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₁₃₉	—	4	16	no	—
121	Q₈×C₁₃₉	—	4	16	no	—
122	C₂×C₄×C₁₃₉	—	2	2	no	—
123	C₂×C₄×C₁₃₉	—	2	2	no	—
124	C₂×C₄×C₁₃₉	—	2	4	no	—
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	—	4	4	no	—
129	C₂×C₄×C₁₃₉	—	4	4	no	—
130	C₂×C₄×C₁₃₉	—	4	16	no	—
131	C₂×C₄×C₁₃₉	—	4	4	no	—
132	C₂×C₄×C₁₃₉	—	4	4	no	—
133	C₂×C₄×C₁₃₉	—	4	4	no	—
134	C₂×C₄×C₁₃₉	#102	1	16	yes	—
135	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
141	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
142	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
143	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₁₃₉	#137	1	4	yes	—
145	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
148	C₈×C₁₃₉	—	4	4	no	—
149	C₂²×C₁₃₉	—	2	2	no	—
150	C₂²×C₁₃₉	—	2	2	no	—
151	C₂²×C₁₃₉	—	2	4	no	—
152	C₂²×C₁₃₉	—	2	4	no	—
153	C₂²×C₁₃₉	C₂×#102	1	4	yes	—
154	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₁₃₉	#536	1	2	yes	—
156	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
157	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
158	C₂²×C₁₃₉	C₂×#137	1	2	yes	—
159	C₄×C₁₃₉	—	2	2	no	—
160	C₄×C₁₃₉	—	2	2	no	—
161	C₄×C₁₃₉	—	4	8	no	—
162	C₄×C₁₃₉	—	8	4	no	—
163	C₄×C₁₃₉	C₂×#102	1	4	yes	—
164	C₄×C₁₃₉	C₂×#102	1	4	yes	—
165	C₄×C₁₃₉	#419	1	4	yes	—
166	C₄×C₁₃₉	#519	1	2	yes	—
167	C₄×C₁₃₉	#536	1	2	yes	—
168	C₂×C₁₃₉	—	2	4	no	—
169	C₂×C₁₃₉	#2310	1	1	yes	characteristic
170	C₂×C₁₃₉	C₂²×#102	1	1	yes	characteristic
171	C₂×C₁₃₉	C₂×#419	1	1	yes	characteristic
172	C₂×C₁₃₉	#3226	1	2	yes	—
173	C₂×C₁₃₉	#3229	1	2	yes	—
174	#21833	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₁₃₉	#21833	1	1	yes	characteristic, direct product factor, Sylow
176	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
177	C₂×#431	C₂×C₁₃₉	1	1	yes	characteristic
178	#2285	C₂×C₁₃₉	1	1	yes	characteristic
179	#1990	C₂×C₁₃₉	1	4	yes	complemented
180	#1988	C₂×C₁₃₉	1	4	yes	complemented
181	#1823	C₂×C₁₃₉	1	4	yes	—
182	C₂³×Q₈	—	2	1	no	—
183	C₂×C₄⋊Q₈	—	2	1	no	—
184	C₂×C₄⋊Q₈	—	2	1	no	—
185	C₂×C₄⋊Q₈	—	2	4	no	—
186	C₂×C₄⋊Q₈	C₄×C₁₃₉	1	8	yes	complemented
187	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
188	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
189	C₂×#117	—	2	1	no	—
190	C₂²×C₄⋊C₄	—	2	1	no	—
191	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
192	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
193	#431	—	2	4	no	—
194	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
197	#384	C₂²×C₁₃₉	1	2	yes	—
198	#382	—	2	1	no	—
199	#380	—	2	1	no	—
200	#380	C₂²×C₁₃₉	1	2	yes	—
201	C₄×C₄⋊C₄	—	2	1	no	—
202	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
203	#340	C₂²×C₁₃₉	1	16	yes	—
204	C₂²×Q₈	—	2	8	no	—
205	C₂²×Q₈	—	2	2	no	—
206	C₂²×Q₈	—	2	2	no	—
207	C₂²×Q₈	—	4	4	no	—
208	C₂²×Q₈	—	4	4	no	—
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
211	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
214	C₄⋊Q₈	—	2	8	no	—
215	C₄⋊Q₈	—	2	8	no	—
216	C₄⋊Q₈	—	2	4	no	—
217	C₄⋊Q₈	—	2	4	no	—
218	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	8	yes	—
219	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	8	yes	—
220	#117	—	4	4	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
234	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
237	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
239	C₄⋊C₈	—	2	4	no	—
240	C₂²⋊C₈	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
245	C₂×Q₈	—	2	8	no	—
246	C₂×Q₈	—	2	8	no	—
247	C₂×Q₈	—	4	32	no	—
248	C₂×Q₈	—	4	4	no	—
249	C₂×Q₈	—	4	4	no	—
250	C₂×Q₈	—	4	4	no	—
251	C₂×Q₈	—	4	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
260	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
261	C₂²×C₄	D₈×C₁₃₉	1	4	yes	—
262	C₂²×C₄	SD₁₆×C₁₃₉	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
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	2	yes	—
267	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	8	no	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₄²	—	4	4	no	—
283	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
284	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
285	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
286	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
287	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
288	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
292	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
293	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
294	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
295	Q₈	—	4	16	no	—
296	Q₈	—	4	16	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	#102×C₁₃₉	1	16	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
312	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
313	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
314	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
315	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
316	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
317	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
318	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
319	C₂×C₄	#137×C₁₃₉	1	4	yes	—
320	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
322	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
323	C₈	—	4	4	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	C₂×#102×C₁₃₉	1	4	yes	—
329	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
330	C₂²	#536×C₁₃₉	1	2	yes	—
331	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
332	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
333	C₂²	C₂×#137×C₁₃₉	1	2	yes	—
334	C₄	—	2	2	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	8	no	—
337	C₄	—	8	4	no	—
338	C₄	C₂×#102×C₁₃₉	1	4	yes	—
339	C₄	C₂×#102×C₁₃₉	1	4	yes	—
340	C₄	#419×C₁₃₉	1	4	yes	—
341	C₄	#519×C₁₃₉	1	2	yes	—
342	C₄	#536×C₁₃₉	1	2	yes	—
343	C₂	—	2	4	no	—
344	C₂	#2310×C₁₃₉	1	1	yes	characteristic
345	C₂	C₂²×#102×C₁₃₉	1	1	yes	characteristic
346	C₂	C₂×#419×C₁₃₉	1	1	yes	characteristic
347	C₂	#3226×C₁₃₉	1	2	yes	—
348	C₂	#3229×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1990×C₁₃₉	C₂	semidirect
5. #1988×C₁₃₉	C₂	semidirect
11. C₂×C₄⋊Q₈×C₁₃₉	C₄	semidirect
174. #21833	C₁₃₉	direct (N × H)
175. C₁₃₉	#21833	direct (N × H)
179. #1990	C₂×C₁₃₉	semidirect
180. #1988	C₂×C₁₃₉	semidirect
186. C₂×C₄⋊Q₈	C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₁₃₉	2
C₂×#431×C₁₃₉	2
#2285×C₁₃₉	2
#1990×C₁₃₉	2
#1988×C₁₃₉	2
#1823×C₁₃₉	2
#21833	139

Subgroups — C139×#21833 #48016429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21833 #48016429