Subgroups — C₁₃₉×#36457 #48031053

Order 35584.

2614 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2858×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2563×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2548×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2491×C₁₃₉	C₂	1	12	yes	maximal, complemented
7	#2341×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₄×#124×C₁₃₉	C₂	1	3	yes	maximal, complemented
9	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
11	Q₈²×C₁₃₉	—	2	8	no	—
12	#550×C₁₃₉	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
15	C₂×#127×C₁₃₉	C₂²	1	3	yes	—
16	C₂×#124×C₁₃₉	C₂²	1	3	yes	—
17	C₂×#124×C₁₃₉	C₂²	1	12	yes	—
18	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
24	#394×C₁₃₉	C₂²	1	12	yes	—
25	#393×C₁₃₉	C₂²	1	12	yes	—
26	#391×C₁₃₉	C₂²	1	1	yes	characteristic
27	#390×C₁₃₉	C₂²	1	6	yes	—
28	#390×C₁₃₉	C₂²	1	12	yes	—
29	#390×C₁₃₉	C₂²	1	3	yes	—
30	#390×C₁₃₉	C₂²	1	12	yes	—
31	#388×C₁₃₉	C₂²	1	12	yes	—
32	#382×C₁₃₉	C₂²	1	3	yes	—
33	#380×C₁₃₉	C₂²	1	12	yes	—
34	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
36	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	12	yes	—
37	C₄³×C₁₃₉	C₂²	1	3	yes	—
38	C₂×#41×C₁₃₉	—	2	8	no	—
39	C₂×#41×C₁₃₉	—	2	16	no	—
40	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
42	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
44	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
45	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
46	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
47	C₄⋊Q₈×C₁₃₉	—	2	24	no	—
48	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
49	#127×C₁₃₉	—	2	12	no	—
50	#124×C₁₃₉	—	2	12	no	—
51	#124×C₁₃₉	—	4	24	no	—
52	#121×C₁₃₉	—	2	24	no	—
53	C₄×Q₈×C₁₃₉	—	2	8	no	—
54	C₄×Q₈×C₁₃₉	—	2	8	no	—
55	C₄×Q₈×C₁₃₉	—	2	12	no	—
56	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
57	C₄×D₄×C₁₃₉	—	2	12	no	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
66	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
67	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	24	yes	—
68	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
69	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
70	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
71	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
72	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
74	#95×C₁₃₉	C₂³	1	4	yes	—
75	#95×C₁₃₉	C₂³	1	12	yes	—
76	#95×C₁₃₉	C₂³	1	6	yes	—
77	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
78	#41×C₁₃₉	—	4	32	no	—
79	C₂×Q₈×C₁₃₉	—	2	2	no	—
80	C₂×Q₈×C₁₃₉	—	2	12	no	—
81	C₂×Q₈×C₁₃₉	—	2	2	no	—
82	C₂×Q₈×C₁₃₉	—	4	12	no	—
83	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
84	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
85	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
86	C₂×D₄×C₁₃₉	—	2	6	no	—
87	C₂×D₄×C₁₃₉	—	2	12	no	—
88	C₂×D₄×C₁₃₉	—	2	12	no	—
89	C₂×D₄×C₁₃₉	—	2	6	no	—
90	C₂×D₄×C₁₃₉	—	2	24	no	—
91	C₂×D₄×C₁₃₉	—	2	6	no	—
92	C₂×D₄×C₁₃₉	—	4	12	no	—
93	C₂²×C₄×C₁₃₉	—	2	12	no	—
94	C₂²×C₄×C₁₃₉	—	2	24	no	—
95	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
97	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
98	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
99	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
102	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
103	C₄⋊C₄×C₁₃₉	—	2	2	no	—
104	C₄⋊C₄×C₁₃₉	—	2	12	no	—
105	C₄⋊C₄×C₁₃₉	—	2	12	no	—
106	C₄⋊C₄×C₁₃₉	—	2	6	no	—
107	C₄⋊C₄×C₁₃₉	—	2	12	no	—
108	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
109	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
111	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
112	C₂²⋊C₄×C₁₃₉	—	4	24	no	—
113	C₄²×C₁₃₉	—	2	12	no	—
114	C₄²×C₁₃₉	—	2	12	no	—
115	C₄²×C₁₃₉	—	2	6	no	—
116	C₄²×C₁₃₉	—	2	12	no	—
117	C₄²×C₁₃₉	—	2	2	no	—
118	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
119	C₂³×C₁₃₉	—	2	6	no	—
120	C₂³×C₁₃₉	—	2	6	no	—
121	C₂³×C₁₃₉	—	2	12	no	—
122	C₂³×C₁₃₉	—	2	12	no	—
123	C₂³×C₁₃₉	—	2	6	no	—
124	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
125	Q₈×C₁₃₉	—	2	8	no	—
126	Q₈×C₁₃₉	—	8	12	no	—
127	Q₈×C₁₃₉	#124	1	16	yes	complemented
128	D₄×C₁₃₉	—	4	24	no	—
129	D₄×C₁₃₉	—	4	12	no	—
130	D₄×C₁₃₉	—	8	12	no	—
131	C₂×C₄×C₁₃₉	—	2	2	no	—
132	C₂×C₄×C₁₃₉	—	2	2	no	—
133	C₂×C₄×C₁₃₉	—	2	6	no	—
134	C₂×C₄×C₁₃₉	—	2	2	no	—
135	C₂×C₄×C₁₃₉	—	2	2	no	—
136	C₂×C₄×C₁₃₉	—	2	6	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	6	no	—
139	C₂×C₄×C₁₃₉	—	2	6	no	—
140	C₂×C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₄×C₁₃₉	—	2	6	no	—
142	C₂×C₄×C₁₃₉	—	2	12	no	—
143	C₂×C₄×C₁₃₉	—	4	24	no	—
144	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
145	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
146	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
148	C₂×C₄×C₁₃₉	C₂×#41	1	12	yes	—
149	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
150	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
151	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
152	C₂²×C₁₃₉	—	4	6	no	—
153	C₂²×C₁₃₉	—	4	6	no	—
154	C₂²×C₁₃₉	—	4	12	no	—
155	C₂²×C₁₃₉	—	4	6	no	—
156	C₂²×C₁₃₉	—	4	12	no	—
157	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
158	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
159	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
160	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
161	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
162	C₄×C₁₃₉	—	2	4	no	—
163	C₄×C₁₃₉	—	2	6	no	—
164	C₄×C₁₃₉	—	2	4	no	—
165	C₄×C₁₃₉	—	4	2	no	—
166	C₄×C₁₃₉	—	4	6	no	—
167	C₄×C₁₃₉	—	4	6	no	—
168	C₄×C₁₃₉	C₂×#124	1	12	yes	—
169	C₄×C₁₃₉	#548	1	4	yes	—
170	C₂×C₁₃₉	—	8	6	no	—
171	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
172	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
173	C₂×C₁₃₉	#3483	1	2	yes	—
174	C₂×C₁₃₉	#3498	1	1	yes	characteristic
175	C₂×C₁₃₉	#3522	1	2	yes	—
176	#36457	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃₉	#36457	1	1	yes	characteristic, direct product factor, Sylow
178	C₂×Q₈²	C₂×C₁₃₉	1	1	yes	characteristic, complemented
179	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic
180	#2858	C₂×C₁₃₉	1	3	yes	complemented
181	#2563	C₂×C₁₃₉	1	3	yes	complemented
182	#2548	C₂×C₁₃₉	1	3	yes	complemented
183	#2491	C₂×C₁₃₉	1	12	yes	complemented
184	#2341	C₂×C₁₃₉	1	4	yes	complemented
185	C₄×#124	C₂×C₁₃₉	1	3	yes	complemented
186	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
188	Q₈²	—	2	8	no	—
189	#550	—	2	8	no	—
190	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
192	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
193	C₂×#124	C₂²×C₁₃₉	1	3	yes	—
194	C₂×#124	C₂²×C₁₃₉	1	12	yes	—
195	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
196	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
199	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
201	#394	C₂²×C₁₃₉	1	12	yes	—
202	#393	C₂²×C₁₃₉	1	12	yes	—
203	#391	C₂²×C₁₃₉	1	1	yes	characteristic
204	#390	C₂²×C₁₃₉	1	6	yes	—
205	#390	C₂²×C₁₃₉	1	12	yes	—
206	#390	C₂²×C₁₃₉	1	12	yes	—
207	#390	C₂²×C₁₃₉	1	3	yes	—
208	#388	C₂²×C₁₃₉	1	12	yes	—
209	#382	C₂²×C₁₃₉	1	3	yes	—
210	#380	C₂²×C₁₃₉	1	12	yes	—
211	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
212	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	12	yes	—
214	C₄³	C₂²×C₁₃₉	1	3	yes	—
215	C₂×#41	—	2	8	no	—
216	C₂×#41	—	2	16	no	—
217	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
218	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
219	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
220	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
221	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
222	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
223	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
224	C₄⋊Q₈	—	2	24	no	—
225	C₄⋊Q₈	—	2	12	no	—
226	#127	—	2	12	no	—
227	#124	—	2	12	no	—
228	#124	—	4	24	no	—
229	#121	—	2	24	no	—
230	C₄×Q₈	—	2	8	no	—
231	C₄×Q₈	—	2	8	no	—
232	C₄×Q₈	—	2	12	no	—
233	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
234	C₄×D₄	—	2	12	no	—
235	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
244	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	24	yes	—
245	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
246	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
247	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
248	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
249	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
251	#95	C₂³×C₁₃₉	1	4	yes	—
252	#95	C₂³×C₁₃₉	1	12	yes	—
253	#95	C₂³×C₁₃₉	1	6	yes	—
254	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
255	#41	—	4	32	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	12	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	4	12	no	—
260	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
261	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
262	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
263	C₂×D₄	—	2	6	no	—
264	C₂×D₄	—	2	12	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	24	no	—
268	C₂×D₄	—	2	6	no	—
269	C₂×D₄	—	4	12	no	—
270	C₂²×C₄	—	2	12	no	—
271	C₂²×C₄	—	2	24	no	—
272	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
274	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
275	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
276	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
278	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
279	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	12	no	—
282	C₄⋊C₄	—	2	12	no	—
283	C₄⋊C₄	—	2	6	no	—
284	C₄⋊C₄	—	2	12	no	—
285	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
286	C₂²⋊C₄	—	2	12	no	—
287	C₂²⋊C₄	—	2	24	no	—
288	C₂²⋊C₄	—	2	24	no	—
289	C₂²⋊C₄	—	4	24	no	—
290	C₄²	—	2	12	no	—
291	C₄²	—	2	12	no	—
292	C₄²	—	2	6	no	—
293	C₄²	—	2	12	no	—
294	C₄²	—	2	2	no	—
295	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
296	C₂³	—	2	6	no	—
297	C₂³	—	2	6	no	—
298	C₂³	—	2	12	no	—
299	C₂³	—	2	12	no	—
300	C₂³	—	2	6	no	—
301	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
302	Q₈	—	2	8	no	—
303	Q₈	—	8	12	no	—
304	Q₈	#124×C₁₃₉	1	16	yes	complemented
305	D₄	—	4	24	no	—
306	D₄	—	4	12	no	—
307	D₄	—	8	12	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	6	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	6	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	6	no	—
316	C₂×C₄	—	2	6	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	4	24	no	—
321	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
322	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
323	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
324	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
325	C₂×C₄	C₂×#41×C₁₃₉	1	12	yes	—
326	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
327	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
328	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
329	C₂²	—	4	6	no	—
330	C₂²	—	4	6	no	—
331	C₂²	—	4	12	no	—
332	C₂²	—	4	6	no	—
333	C₂²	—	4	12	no	—
334	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
335	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
336	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
337	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
338	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
339	C₄	—	2	4	no	—
340	C₄	—	2	6	no	—
341	C₄	—	2	4	no	—
342	C₄	—	4	2	no	—
343	C₄	—	4	6	no	—
344	C₄	—	4	6	no	—
345	C₄	C₂×#124×C₁₃₉	1	12	yes	—
346	C₄	#548×C₁₃₉	1	4	yes	—
347	C₂	—	8	6	no	—
348	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
349	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
350	C₂	#3483×C₁₃₉	1	2	yes	—
351	C₂	#3498×C₁₃₉	1	1	yes	characteristic
352	C₂	#3522×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#550×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈²×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2563×C₁₃₉	C₂	semidirect
5. #2548×C₁₃₉	C₂	semidirect
6. #2491×C₁₃₉	C₂	semidirect
7. #2341×C₁₃₉	C₂	semidirect
8. C₄×#124×C₁₃₉	C₂	semidirect
9. C₄²×Q₈×C₁₃₉	C₂	semidirect
85. C₂×Q₈×C₁₃₉	#41	semidirect
127. Q₈×C₁₃₉	#124	semidirect
176. #36457	C₁₃₉	direct (N × H)
177. C₁₃₉	#36457	direct (N × H)
178. C₂×Q₈²	C₂×C₁₃₉	semidirect
180. #2858	C₂×C₁₃₉	semidirect
181. #2563	C₂×C₁₃₉	semidirect
182. #2548	C₂×C₁₃₉	semidirect
183. #2491	C₂×C₁₃₉	semidirect
184. #2341	C₂×C₁₃₉	semidirect
185. C₄×#124	C₂×C₁₃₉	semidirect
186. C₄²×Q₈	C₂×C₁₃₉	semidirect
262. C₂×Q₈	#41×C₁₃₉	semidirect
304. Q₈	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₁₃₉	2
C₂×#550×C₁₃₉	2
#2858×C₁₃₉	2
#2563×C₁₃₉	2
#2548×C₁₃₉	2
#2491×C₁₃₉	2
#2341×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36457	139

Subgroups — C139×#36457 #48031053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36457 #48031053