Subgroups — C₂×#1540×C₁₃₉ #48012291

Order 35584.

1330 conjugacy classes of subgroups.

The subgroup lattice has 450 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×#431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1540×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#332×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂×#331×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₃₉	—	2	1	no	—
8	C₂³×C₈×C₁₃₉	—	2	1	no	—
9	#532×C₁₃₉	—	2	2	no	—
10	#532×C₁₃₉	—	2	2	no	—
11	#532×C₁₃₉	C₄	1	4	yes	—
12	#532×C₁₃₉	C₂²	1	4	yes	—
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₉	—	2	1	no	—
16	C₂×#121×C₁₃₉	—	2	1	no	—
17	C₂×#121×C₁₃₉	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃₉	C₄	1	2	yes	—
20	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
21	#431×C₁₃₉	—	2	2	no	—
22	#431×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₁₃₉	—	2	2	no	—
24	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
25	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
29	C₂×C₄×C₈×C₁₃₉	—	2	1	no	—
30	#332×C₁₃₉	C₂²	1	8	yes	complemented
31	#331×C₁₃₉	C₂²	1	8	yes	complemented
32	C₂×#41×C₁₃₉	—	2	4	no	—
33	C₂×#41×C₁₃₉	—	2	4	no	—
34	C₂×#41×C₁₃₉	—	4	4	no	—
35	C₂×#41×C₁₃₉	—	4	4	no	—
36	C₂²×Q₈×C₁₃₉	—	2	1	no	—
37	C₂²×D₄×C₁₃₉	—	2	2	no	—
38	C₂²×D₄×C₁₃₉	—	2	1	no	—
39	C₂²×D₄×C₁₃₉	—	2	1	no	—
40	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃₉	—	2	2	no	—
42	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₉	—	2	2	no	—
46	C₂²×C₈×C₁₃₉	—	2	2	no	—
47	C₂²×C₈×C₁₃₉	—	2	4	no	—
48	C₂²×C₈×C₁₃₉	—	4	4	no	—
49	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
50	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
52	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
53	#127×C₁₃₉	—	2	1	no	—
54	#127×C₁₃₉	—	2	1	no	—
55	#127×C₁₃₉	C₂×C₄	1	2	yes	—
56	#127×C₁₃₉	C₂³	1	2	yes	—
57	#124×C₁₃₉	—	2	4	no	—
58	#124×C₁₃₉	—	2	4	no	—
59	#121×C₁₃₉	—	2	4	no	—
60	#121×C₁₃₉	—	2	4	no	—
61	#121×C₁₃₉	—	2	4	no	—
62	#121×C₁₃₉	C₂×C₄	1	8	yes	—
63	C₄×D₄×C₁₃₉	—	2	4	no	—
64	C₄×D₄×C₁₃₉	—	2	4	no	—
65	C₄×D₄×C₁₃₉	—	2	4	no	—
66	C₄×D₄×C₁₃₉	C₂×C₄	1	8	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
71	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
79	C₄⋊C₈×C₁₃₉	—	2	2	no	—
80	C₄⋊C₈×C₁₃₉	—	2	4	no	—
81	C₄⋊C₈×C₁₃₉	—	2	2	no	—
82	C₄⋊C₈×C₁₃₉	C₂³	1	4	yes	—
83	C₄⋊C₈×C₁₃₉	C₂³	1	4	yes	—
84	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
85	C₄×C₈×C₁₃₉	—	2	4	no	—
86	C₂⁴×C₁₃₉	—	2	2	no	—
87	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
88	#41×C₁₃₉	—	4	16	no	—
89	#41×C₁₃₉	—	4	8	no	—
90	#41×C₁₃₉	—	4	8	no	—
91	C₂×Q₈×C₁₃₉	—	2	2	no	—
92	C₂×Q₈×C₁₃₉	—	2	2	no	—
93	C₂×Q₈×C₁₃₉	—	4	2	no	—
94	C₂×Q₈×C₁₃₉	—	4	2	no	—
95	C₂×D₄×C₁₃₉	—	2	8	no	—
96	C₂×D₄×C₁₃₉	—	2	2	no	—
97	C₂×D₄×C₁₃₉	—	2	2	no	—
98	C₂×D₄×C₁₃₉	—	2	2	no	—
99	C₂×D₄×C₁₃₉	—	2	2	no	—
100	C₂×D₄×C₁₃₉	—	2	2	no	—
101	C₂×D₄×C₁₃₉	—	4	4	no	—
102	C₂×D₄×C₁₃₉	—	4	8	no	—
103	C₂×D₄×C₁₃₉	—	4	2	no	—
104	C₂×D₄×C₁₃₉	—	4	2	no	—
105	C₂×D₄×C₁₃₉	—	4	4	no	—
106	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₃₉	—	2	4	no	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	8	no	—
110	C₂²×C₄×C₁₃₉	—	4	2	no	—
111	C₂²×C₄×C₁₃₉	—	4	8	no	—
112	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₉	D₈	1	4	yes	—
119	C₂²×C₄×C₁₃₉	SD₁₆	1	4	yes	—
120	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃₉	—	2	4	no	—
127	C₂×C₈×C₁₃₉	—	2	4	no	—
128	C₂×C₈×C₁₃₉	—	4	4	no	—
129	C₂×C₈×C₁₃₉	—	4	8	no	—
130	C₂×C₈×C₁₃₉	—	4	4	no	—
131	C₄⋊C₄×C₁₃₉	—	2	2	no	—
132	C₄⋊C₄×C₁₃₉	—	2	2	no	—
133	C₄⋊C₄×C₁₃₉	—	2	2	no	—
134	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
135	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
136	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
137	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
138	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
139	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
140	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
141	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
147	C₂³×C₁₃₉	—	2	2	no	—
148	C₂³×C₁₃₉	—	2	2	no	—
149	C₂³×C₁₃₉	—	2	4	no	—
150	C₂³×C₁₃₉	—	4	4	no	—
151	C₂³×C₁₃₉	—	4	4	no	—
152	C₂³×C₁₃₉	—	4	4	no	—
153	C₂³×C₁₃₉	#102	1	4	yes	—
154	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	Q₈×C₁₃₉	—	4	2	no	—
157	Q₈×C₁₃₉	—	4	2	no	—
158	Q₈×C₁₃₉	—	4	4	no	—
159	D₄×C₁₃₉	—	4	4	no	—
160	D₄×C₁₃₉	—	4	4	no	—
161	D₄×C₁₃₉	—	4	16	no	—
162	D₄×C₁₃₉	—	4	2	no	—
163	D₄×C₁₃₉	—	4	2	no	—
164	D₄×C₁₃₉	—	4	4	no	—
165	D₄×C₁₃₉	—	4	4	no	—
166	D₄×C₁₃₉	—	4	4	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	—	2	4	no	—
172	C₂×C₄×C₁₃₉	—	2	4	no	—
173	C₂×C₄×C₁₃₉	—	4	2	no	—
174	C₂×C₄×C₁₃₉	—	4	2	no	—
175	C₂×C₄×C₁₃₉	—	4	4	no	—
176	C₂×C₄×C₁₃₉	—	4	16	no	—
177	C₂×C₄×C₁₃₉	#102	1	4	yes	—
178	C₂×C₄×C₁₃₉	#102	1	8	yes	—
179	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
186	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
187	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
188	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₁₃₉	#135	1	4	yes	—
190	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₁₃₉	—	4	4	no	—
194	C₈×C₁₃₉	—	4	4	no	—
195	C₂²×C₁₃₉	—	2	8	no	—
196	C₂²×C₁₃₉	—	2	2	no	—
197	C₂²×C₁₃₉	—	2	2	no	—
198	C₂²×C₁₃₉	—	4	4	no	—
199	C₂²×C₁₃₉	—	4	4	no	—
200	C₂²×C₁₃₉	—	4	4	no	—
201	C₂²×C₁₃₉	—	8	8	no	—
202	C₂²×C₁₃₉	#413	1	2	yes	—
203	C₂²×C₁₃₉	C₂×#102	1	4	yes	—
204	C₂²×C₁₃₉	C₂×#102	1	2	yes	—
205	C₂²×C₁₃₉	#416	1	2	yes	—
206	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₄×C₁₃₉	—	2	2	no	—
208	C₄×C₁₃₉	—	2	1	no	—
209	C₄×C₁₃₉	—	2	1	no	—
210	C₄×C₁₃₉	—	2	2	no	—
211	C₄×C₁₃₉	—	4	4	no	—
212	C₄×C₁₃₉	C₂×#102	1	4	yes	—
213	C₄×C₁₃₉	C₂×#102	1	2	yes	—
214	C₄×C₁₃₉	#416	1	2	yes	—
215	C₄×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
216	C₄×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
217	C₄×C₁₃₉	C₂×#135	1	2	yes	—
218	C₂×C₁₃₉	—	2	4	no	—
219	C₂×C₁₃₉	—	8	4	no	—
220	C₂×C₁₃₉	#1540	1	4	yes	direct product factor
221	C₂×C₁₃₉	C₂×#413	1	1	yes	characteristic
222	C₂×C₁₃₉	C₂²×#102	1	1	yes	characteristic
223	C₂×C₁₃₉	C₂×#416	1	1	yes	characteristic
224	C₂×#1540	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₁₃₉	C₂×#1540	1	1	yes	characteristic, direct product factor, Sylow
226	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
227	C₂×#431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
228	C₂²×C₄⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
229	#1540	C₂×C₁₃₉	1	8	yes	direct product factor
230	C₂×#332	C₂×C₁₃₉	1	2	yes	complemented
231	C₂×#331	C₂×C₁₃₉	1	2	yes	complemented
232	C₂²×#41	—	2	1	no	—
233	C₂³×C₈	—	2	1	no	—
234	#532	—	2	2	no	—
235	#532	—	2	2	no	—
236	#532	C₄×C₁₃₉	1	4	yes	—
237	#532	C₂²×C₁₃₉	1	4	yes	—
238	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
239	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
240	C₂×#124	—	2	1	no	—
241	C₂×#121	—	2	1	no	—
242	C₂×#121	C₄×C₁₃₉	1	2	yes	—
243	C₂×C₄×D₄	—	2	1	no	—
244	C₂×C₄×D₄	C₄×C₁₃₉	1	2	yes	—
245	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
246	#431	—	2	2	no	—
247	#431	C₂²×C₁₃₉	1	4	yes	complemented
248	C₂×C₄⋊C₈	—	2	2	no	—
249	C₂×C₄⋊C₈	—	2	1	no	—
250	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
252	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
253	C₂×C₂²⋊C₈	—	2	1	no	—
254	C₂×C₄×C₈	—	2	1	no	—
255	#332	C₂²×C₁₃₉	1	8	yes	complemented
256	#331	C₂²×C₁₃₉	1	8	yes	complemented
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	4	4	no	—
260	C₂×#41	—	4	4	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
268	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
269	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	4	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	4	4	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
277	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	C₂×C₄×C₁₃₉	1	2	yes	—
281	#127	C₂³×C₁₃₉	1	2	yes	—
282	#124	—	2	4	no	—
283	#124	—	2	4	no	—
284	#121	—	2	4	no	—
285	#121	—	2	4	no	—
286	#121	—	2	4	no	—
287	#121	C₂×C₄×C₁₃₉	1	8	yes	—
288	C₄×D₄	—	2	4	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	C₂×C₄×C₁₃₉	1	8	yes	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
297	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
298	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
301	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	C₂³×C₁₃₉	1	4	yes	—
308	C₄⋊C₈	C₂³×C₁₃₉	1	4	yes	—
309	C₂²⋊C₈	—	2	4	no	—
310	C₄×C₈	—	2	4	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
313	#41	—	4	16	no	—
314	#41	—	4	8	no	—
315	#41	—	4	8	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	8	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	8	no	—
337	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
339	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
340	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
341	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
342	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
343	C₂²×C₄	D₈×C₁₃₉	1	4	yes	—
344	C₂²×C₄	SD₁₆×C₁₃₉	1	4	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	—	4	8	no	—
355	C₂×C₈	—	4	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	2	8	no	—
362	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
363	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
364	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
365	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
366	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
367	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
368	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
369	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
371	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	#102×C₁₃₉	1	4	yes	—
379	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
380	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
381	Q₈	—	4	4	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	16	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	#102×C₁₃₉	1	4	yes	—
403	C₂×C₄	#102×C₁₃₉	1	8	yes	—
404	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
410	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
411	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
412	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
413	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	4	yes	—
414	C₂×C₄	#135×C₁₃₉	1	4	yes	—
415	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
418	C₈	—	4	4	no	—
419	C₈	—	4	4	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	8	no	—
427	C₂²	#413×C₁₃₉	1	2	yes	—
428	C₂²	C₂×#102×C₁₃₉	1	4	yes	—
429	C₂²	C₂×#102×C₁₃₉	1	2	yes	—
430	C₂²	#416×C₁₃₉	1	2	yes	—
431	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	4	no	—
437	C₄	C₂×#102×C₁₃₉	1	4	yes	—
438	C₄	C₂×#102×C₁₃₉	1	2	yes	—
439	C₄	#416×C₁₃₉	1	2	yes	—
440	C₄	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
441	C₄	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
442	C₄	C₂×#135×C₁₃₉	1	2	yes	—
443	C₂	—	2	4	no	—
444	C₂	—	8	4	no	—
445	C₂	#1540×C₁₃₉	1	4	yes	direct product factor
446	C₂	C₂×#413×C₁₃₉	1	1	yes	characteristic
447	C₂	C₂²×#102×C₁₃₉	1	1	yes	characteristic
448	C₂	C₂×#416×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₃₉	C₂	semidirect
3. C₂²×C₄⋊C₈×C₁₃₉	C₂	semidirect
4. #1540×C₁₃₉	C₂	direct (N × H)
5. C₂×#332×C₁₃₉	C₂	semidirect
6. C₂×#331×C₁₃₉	C₂	semidirect
22. #431×C₁₃₉	C₂²	semidirect
27. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
30. #332×C₁₃₉	C₂²	semidirect
31. #331×C₁₃₉	C₂²	semidirect
220. C₂×C₁₃₉	#1540	direct (N × H)
224. C₂×#1540	C₁₃₉	direct (N × H)
225. C₁₃₉	C₂×#1540	direct (N × H)
227. C₂×#431	C₂×C₁₃₉	semidirect
228. C₂²×C₄⋊C₈	C₂×C₁₃₉	semidirect
229. #1540	C₂×C₁₃₉	direct (N × H)
230. C₂×#332	C₂×C₁₃₉	semidirect
231. C₂×#331	C₂×C₁₃₉	semidirect
247. #431	C₂²×C₁₃₉	semidirect
252. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
255. #332	C₂²×C₁₃₉	semidirect
256. #331	C₂²×C₁₃₉	semidirect
445. C₂	#1540×C₁₃₉	direct (N × H)

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×#431×C₁₃₉	2
C₂²×C₄⋊C₈×C₁₃₉	2
#1540×C₁₃₉	2
C₂×#332×C₁₃₉	2
C₂×#331×C₁₃₉	2
C₂×#1540	139

Subgroups — C2×#1540×C139 #48012291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1540×C₁₃₉ #48012291