Subgroups — C₁₃₉×#21395 #48015991

Order 35584.

1518 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1987×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1982×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1874×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1762×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	—	2	1	no	—
9	#532×C₁₃₉	—	2	4	no	—
10	#532×C₁₃₉	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₉	—	2	1	no	—
14	C₂×#121×C₁₃₉	—	2	1	no	—
15	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₉	—	2	1	no	—
20	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
21	#432×C₁₃₉	—	2	4	no	—
22	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
24	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
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	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#95×C₁₃₉	—	2	1	no	—
31	#340×C₁₃₉	C₂²	1	8	yes	—
32	C₂×#41×C₁₃₉	—	2	8	no	—
33	C₂×#41×C₁₃₉	—	4	8	no	—
34	C₂²×Q₈×C₁₃₉	—	2	1	no	—
35	C₂²×D₄×C₁₃₉	—	2	2	no	—
36	C₂²×D₄×C₁₃₉	—	2	1	no	—
37	C₂²×D₄×C₁₃₉	—	2	1	no	—
38	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₉	—	2	2	no	—
40	C₂³×C₄×C₁₃₉	—	2	2	no	—
41	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
47	#127×C₁₃₉	—	2	2	no	—
48	#127×C₁₃₉	C₂×C₄	1	4	yes	complemented
49	#124×C₁₃₉	—	2	8	no	—
50	#121×C₁₃₉	—	2	8	no	—
51	#121×C₁₃₉	—	2	4	no	—
52	#121×C₁₃₉	C₂×C₄	1	8	yes	—
53	C₄×D₄×C₁₃₉	—	2	8	no	—
54	C₄×D₄×C₁₃₉	—	2	4	no	—
55	C₄×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
56	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	—	2	2	no	—
64	C₂×C₄²×C₁₃₉	—	2	2	no	—
65	C₂×C₄²×C₁₃₉	—	4	4	no	—
66	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
70	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₃₉	—	2	4	no	—
73	#102×C₁₃₉	—	2	16	no	—
74	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
75	#97×C₁₃₉	—	2	4	no	—
76	#95×C₁₃₉	—	2	2	no	—
77	#95×C₁₃₉	—	2	2	no	—
78	C₂⁴×C₁₃₉	—	2	2	no	—
79	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
80	#41×C₁₃₉	—	4	32	no	—
81	C₂×Q₈×C₁₃₉	—	2	4	no	—
82	C₂×Q₈×C₁₃₉	—	4	4	no	—
83	C₂×D₄×C₁₃₉	—	2	8	no	—
84	C₂×D₄×C₁₃₉	—	2	4	no	—
85	C₂×D₄×C₁₃₉	—	2	4	no	—
86	C₂×D₄×C₁₃₉	—	2	2	no	—
87	C₂×D₄×C₁₃₉	—	2	8	no	—
88	C₂×D₄×C₁₃₉	—	4	4	no	—
89	C₂×D₄×C₁₃₉	—	4	8	no	—
90	C₂×D₄×C₁₃₉	—	4	2	no	—
91	C₂×D₄×C₁₃₉	—	4	2	no	—
92	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₃₉	—	2	4	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	4	no	—
97	C₂²×C₄×C₁₃₉	—	2	8	no	—
98	C₂²×C₄×C₁₃₉	—	2	4	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	8	no	—
101	C₂²×C₄×C₁₃₉	—	4	8	no	—
102	C₂²×C₄×C₁₃₉	—	4	4	no	—
103	C₂²×C₄×C₁₃₉	—	4	4	no	—
104	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
106	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₁₃₉	—	2	4	no	—
115	C₂×C₈×C₁₃₉	—	2	8	no	—
116	C₄⋊C₄×C₁₃₉	—	2	8	no	—
117	C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₄⋊C₄×C₁₃₉	—	2	2	no	—
119	C₄⋊C₄×C₁₃₉	—	2	4	no	—
120	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
121	C₄⋊C₄×C₁₃₉	#41	1	8	yes	complemented
122	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
123	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
124	C₄²×C₁₃₉	—	4	4	no	—
125	C₄²×C₁₃₉	—	4	4	no	—
126	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
127	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
132	C₂³×C₁₃₉	—	2	2	no	—
133	C₂³×C₁₃₉	—	2	1	no	—
134	C₂³×C₁₃₉	—	2	1	no	—
135	C₂³×C₁₃₉	—	2	4	no	—
136	C₂³×C₁₃₉	—	4	4	no	—
137	C₂³×C₁₃₉	—	4	4	no	—
138	C₂³×C₁₃₉	—	4	2	no	—
139	C₂³×C₁₃₉	—	4	2	no	—
140	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
142	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃₉	—	4	8	no	—
144	D₄×C₁₃₉	—	2	8	no	—
145	D₄×C₁₃₉	—	4	8	no	—
146	D₄×C₁₃₉	—	4	16	no	—
147	D₄×C₁₃₉	—	4	4	no	—
148	D₄×C₁₃₉	—	4	8	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	1	no	—
154	C₂×C₄×C₁₃₉	—	2	8	no	—
155	C₂×C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	8	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	8	no	—
160	C₂×C₄×C₁₃₉	—	4	16	no	—
161	C₂×C₄×C₁₃₉	—	4	16	no	—
162	C₂×C₄×C₁₃₉	—	4	4	no	—
163	C₂×C₄×C₁₃₉	—	4	4	no	—
164	C₂×C₄×C₁₃₉	—	4	4	no	—
165	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₁₃₉	#137	1	2	yes	—
172	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
175	C₈×C₁₃₉	—	4	4	no	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	2	4	no	—
178	C₂²×C₁₃₉	—	2	2	no	—
179	C₂²×C₁₃₉	—	2	2	no	—
180	C₂²×C₁₃₉	—	4	4	no	—
181	C₂²×C₁₃₉	—	4	4	no	—
182	C₂²×C₁₃₉	—	4	4	no	—
183	C₂²×C₁₃₉	—	8	4	no	—
184	C₂²×C₁₃₉	—	8	4	no	—
185	C₂²×C₁₃₉	#418	1	4	yes	—
186	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₁₃₉	#525	1	2	yes	—
188	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
190	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
191	C₄×C₁₃₉	—	2	2	no	—
192	C₄×C₁₃₉	—	2	2	no	—
193	C₄×C₁₃₉	—	2	2	no	—
194	C₄×C₁₃₉	—	2	2	no	—
195	C₄×C₁₃₉	—	4	8	no	—
196	C₄×C₁₃₉	—	4	4	no	—
197	C₄×C₁₃₉	#417	1	4	yes	—
198	C₄×C₁₃₉	C₄×#41	1	2	yes	—
199	C₄×C₁₃₉	#532	1	2	yes	—
200	C₂×C₁₃₉	—	2	4	no	—
201	C₂×C₁₃₉	—	8	4	no	—
202	C₂×C₁₃₉	#2297	1	1	yes	characteristic
203	C₂×C₁₃₉	C₂×#418	1	1	yes	characteristic
204	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
205	C₂×C₁₃₉	#3109	1	2	yes	—
206	C₂×C₁₃₉	#3112	1	2	yes	—
207	#21395	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₉	#21395	1	1	yes	characteristic, direct product factor, Sylow
209	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
210	C₂×#432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
211	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
212	#1987	C₂×C₁₃₉	1	2	yes	complemented
213	#1982	C₂×C₁₃₉	1	2	yes	complemented
214	#1874	C₂×C₁₃₉	1	4	yes	complemented
215	#1762	C₂×C₁₃₉	1	4	yes	complemented
216	C₂²×#41	—	2	1	no	—
217	#532	—	2	4	no	—
218	#532	C₄×C₁₃₉	1	8	yes	complemented
219	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
220	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
221	C₂×#124	—	2	1	no	—
222	C₂×#121	—	2	1	no	—
223	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
227	C₂²×C₄²	—	2	1	no	—
228	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
229	#432	—	2	4	no	—
230	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
231	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
233	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
238	C₂×#95	—	2	1	no	—
239	#340	C₂²×C₁₃₉	1	8	yes	—
240	C₂×#41	—	2	8	no	—
241	C₂×#41	—	4	8	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
250	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
255	#127	—	2	2	no	—
256	#127	C₂×C₄×C₁₃₉	1	4	yes	complemented
257	#124	—	2	8	no	—
258	#121	—	2	8	no	—
259	#121	—	2	4	no	—
260	#121	C₂×C₄×C₁₃₉	1	8	yes	—
261	C₄×D₄	—	2	8	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	8	no	—
267	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	4	4	no	—
274	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
275	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
278	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
280	C₄⋊C₈	—	2	4	no	—
281	#102	—	2	16	no	—
282	C₂²⋊C₈	—	2	4	no	—
283	#97	—	2	4	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
288	#41	—	4	32	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	8	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	4	8	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
313	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	8	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
329	C₄⋊C₄	#41×C₁₃₉	1	8	yes	complemented
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₄²	—	4	4	no	—
333	C₄²	—	4	4	no	—
334	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
335	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
336	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
337	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
338	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
339	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
349	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
350	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
351	Q₈	—	4	8	no	—
352	D₄	—	2	8	no	—
353	D₄	—	4	8	no	—
354	D₄	—	4	16	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	—	4	16	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
378	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
379	C₂×C₄	#137×C₁₃₉	1	2	yes	—
380	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
383	C₈	—	4	4	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	#418×C₁₃₉	1	4	yes	—
394	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
395	C₂²	#525×C₁₃₉	1	2	yes	—
396	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
397	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
398	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	8	no	—
404	C₄	—	4	4	no	—
405	C₄	#417×C₁₃₉	1	4	yes	—
406	C₄	C₄×#41×C₁₃₉	1	2	yes	—
407	C₄	#532×C₁₃₉	1	2	yes	—
408	C₂	—	2	4	no	—
409	C₂	—	8	4	no	—
410	C₂	#2297×C₁₃₉	1	1	yes	characteristic
411	C₂	C₂×#418×C₁₃₉	1	1	yes	characteristic
412	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
413	C₂	#3109×C₁₃₉	1	2	yes	—
414	C₂	#3112×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	C₂×#532×C₁₃₉	C₂
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
2. C₂×#432×C₁₃₉	C₂	semidirect
3. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
4. #1987×C₁₃₉	C₂	semidirect
5. #1982×C₁₃₉	C₂	semidirect
6. #1874×C₁₃₉	C₂	semidirect
7. #1762×C₁₃₉	C₂	semidirect
10. #532×C₁₃₉	C₄	semidirect
46. C₄⋊Q₈×C₁₃₉	C₂×C₄	semidirect
48. #127×C₁₃₉	C₂×C₄	semidirect
55. C₄×D₄×C₁₃₉	C₂×C₄	semidirect
121. C₄⋊C₄×C₁₃₉	#41	semidirect
207. #21395	C₁₃₉	direct (N × H)
208. C₁₃₉	#21395	direct (N × H)
210. C₂×#432	C₂×C₁₃₉	semidirect
211. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
212. #1987	C₂×C₁₃₉	semidirect
213. #1982	C₂×C₁₃₉	semidirect
214. #1874	C₂×C₁₃₉	semidirect
215. #1762	C₂×C₁₃₉	semidirect
218. #532	C₄×C₁₃₉	semidirect
254. C₄⋊Q₈	C₂×C₄×C₁₃₉	semidirect
256. #127	C₂×C₄×C₁₃₉	semidirect
263. C₄×D₄	C₂×C₄×C₁₃₉	semidirect
329. C₄⋊C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₃₉	2
C₂×#432×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#1987×C₁₃₉	2
#1982×C₁₃₉	2
#1874×C₁₃₉	2
#1762×C₁₃₉	2
#21395	139

Subgroups — C139×#21395 #48015991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21395 #48015991