Subgroups — C₂×#1510×C₁₃₉ #48012147

Order 35584.

1790 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#381×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1510×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#327×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	C₂³×D₄×C₁₃₉	—	2	1	no	—
7	C₂³×D₄×C₁₃₉	C₄	1	1	yes	characteristic, complemented
8	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₉	—	2	1	no	—
10	C₂×#121×C₁₃₉	—	2	1	no	—
11	C₂×#121×C₁₃₉	—	2	2	no	—
12	C₂×#121×C₁₃₉	—	2	1	no	—
13	C₂×#121×C₁₃₉	—	2	2	no	—
14	C₂×#121×C₁₃₉	C₄	1	2	yes	complemented
15	C₂×#121×C₁₃₉	C₄	1	4	yes	complemented
16	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
20	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
21	#407×C₁₃₉	—	2	2	no	—
22	#407×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊C₈×C₁₃₉	—	2	1	no	—
24	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	complemented
25	#381×C₁₃₉	—	2	2	no	—
26	#381×C₁₃₉	C₂²	1	4	yes	complemented
27	C₂×#95×C₁₃₉	—	2	1	no	—
28	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
29	#327×C₁₃₉	C₂²	1	16	yes	complemented
30	C₂⁵×C₁₃₉	—	2	1	no	—
31	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₃₉	—	2	4	no	—
33	C₂²×D₄×C₁₃₉	—	2	2	no	—
34	C₂²×D₄×C₁₃₉	—	2	4	no	—
35	C₂²×D₄×C₁₃₉	—	2	2	no	—
36	C₂²×D₄×C₁₃₉	—	2	2	no	—
37	C₂²×D₄×C₁₃₉	—	2	1	no	—
38	C₂²×D₄×C₁₃₉	—	4	4	no	—
39	C₂²×D₄×C₁₃₉	—	4	8	no	—
40	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
42	C₂³×C₄×C₁₃₉	—	2	1	no	—
43	C₂³×C₄×C₁₃₉	—	2	2	no	—
44	C₂³×C₄×C₁₃₉	—	4	4	no	—
45	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
51	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
53	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₃₉	—	2	4	no	—
56	C₂×M₁₆×C₁₃₉	—	4	4	no	—
57	C₂²×C₈×C₁₃₉	—	2	2	no	—
58	#121×C₁₃₉	—	2	4	no	—
59	#121×C₁₃₉	—	2	4	no	—
60	#121×C₁₃₉	—	2	4	no	—
61	#121×C₁₃₉	—	2	2	no	—
62	#121×C₁₃₉	—	2	4	no	—
63	#121×C₁₃₉	—	2	2	no	—
64	#121×C₁₃₉	—	2	4	no	—
65	#121×C₁₃₉	C₂×C₄	1	4	yes	—
66	#121×C₁₃₉	C₂×C₄	1	8	yes	complemented
67	#121×C₁₃₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
72	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
78	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
79	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₉	C₂³	1	4	yes	complemented
81	#95×C₁₃₉	—	2	4	no	—
82	#95×C₁₃₉	—	2	2	no	—
83	#95×C₁₃₉	C₂³	1	4	yes	complemented
84	C₂⁴×C₁₃₉	—	2	4	no	—
85	C₂⁴×C₁₃₉	—	2	4	no	—
86	C₂⁴×C₁₃₉	—	2	4	no	—
87	C₂⁴×C₁₃₉	—	2	2	no	—
88	C₂⁴×C₁₃₉	—	4	2	no	—
89	C₂⁴×C₁₃₉	—	4	4	no	—
90	C₂⁴×C₁₃₉	—	4	4	no	—
91	C₂⁴×C₁₃₉	—	4	4	no	—
92	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
94	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
96	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₃₉	—	2	4	no	—
98	C₂×D₄×C₁₃₉	—	2	8	no	—
99	C₂×D₄×C₁₃₉	—	2	4	no	—
100	C₂×D₄×C₁₃₉	—	2	2	no	—
101	C₂×D₄×C₁₃₉	—	2	4	no	—
102	C₂×D₄×C₁₃₉	—	4	4	no	—
103	C₂×D₄×C₁₃₉	—	4	8	no	—
104	C₂×D₄×C₁₃₉	—	4	8	no	—
105	C₂×D₄×C₁₃₉	—	4	4	no	—
106	C₂×D₄×C₁₃₉	—	4	16	no	—
107	C₂×D₄×C₁₃₉	—	4	16	no	—
108	C₂×D₄×C₁₃₉	—	4	8	no	—
109	C₂×D₄×C₁₃₉	—	4	8	no	—
110	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₁₃₉	—	2	4	no	—
112	C₂²×C₄×C₁₃₉	—	2	4	no	—
113	C₂²×C₄×C₁₃₉	—	2	4	no	—
114	C₂²×C₄×C₁₃₉	—	2	2	no	—
115	C₂²×C₄×C₁₃₉	—	2	4	no	—
116	C₂²×C₄×C₁₃₉	—	4	4	no	—
117	C₂²×C₄×C₁₃₉	—	4	2	no	—
118	C₂²×C₄×C₁₃₉	—	4	2	no	—
119	C₂²×C₄×C₁₃₉	—	4	4	no	—
120	C₂²×C₄×C₁₃₉	—	4	2	no	—
121	C₂²×C₄×C₁₃₉	—	4	4	no	—
122	C₂²×C₄×C₁₃₉	—	4	2	no	—
123	C₂²×C₄×C₁₃₉	—	4	4	no	—
124	C₂²×C₄×C₁₃₉	—	4	4	no	—
125	C₂²×C₄×C₁₃₉	—	4	4	no	—
126	C₂²×C₄×C₁₃₉	—	4	4	no	—
127	C₂²×C₄×C₁₃₉	—	4	4	no	—
128	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
129	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
133	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
134	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
135	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
146	M₁₆×C₁₃₉	—	4	8	no	—
147	C₂×C₈×C₁₃₉	—	2	4	no	—
148	C₂×C₈×C₁₃₉	—	4	4	no	—
149	C₄⋊C₄×C₁₃₉	—	2	2	no	—
150	C₄⋊C₄×C₁₃₉	—	2	4	no	—
151	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
152	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
156	C₂³×C₁₃₉	—	2	2	no	—
157	C₂³×C₁₃₉	—	2	2	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	2	2	no	—
160	C₂³×C₁₃₉	—	2	4	no	—
161	C₂³×C₁₃₉	—	2	4	no	—
162	C₂³×C₁₃₉	—	2	4	no	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	4	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	4	no	—
168	C₂³×C₁₃₉	—	4	2	no	—
169	C₂³×C₁₃₉	—	4	2	no	—
170	C₂³×C₁₃₉	—	4	16	no	—
171	C₂³×C₁₃₉	—	4	8	no	—
172	C₂³×C₁₃₉	—	4	8	no	—
173	C₂³×C₁₃₉	—	4	8	no	—
174	C₂³×C₁₃₉	—	4	4	no	—
175	C₂³×C₁₃₉	—	4	4	no	—
176	C₂³×C₁₃₉	—	4	4	no	—
177	C₂³×C₁₃₉	—	8	16	no	—
178	C₂³×C₁₃₉	#99	1	4	yes	—
179	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
184	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
185	D₄×C₁₃₉	—	4	4	no	—
186	D₄×C₁₃₉	—	4	4	no	—
187	D₄×C₁₃₉	—	4	8	no	—
188	D₄×C₁₃₉	—	4	16	no	—
189	D₄×C₁₃₉	—	4	8	no	—
190	D₄×C₁₃₉	—	4	8	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₄×C₁₃₉	—	2	4	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	4	no	—
196	C₂×C₄×C₁₃₉	—	2	2	no	—
197	C₂×C₄×C₁₃₉	—	2	4	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	4	no	—
200	C₂×C₄×C₁₃₉	—	4	2	no	—
201	C₂×C₄×C₁₃₉	—	4	2	no	—
202	C₂×C₄×C₁₃₉	—	4	2	no	—
203	C₂×C₄×C₁₃₉	—	4	1	no	—
204	C₂×C₄×C₁₃₉	—	4	2	no	—
205	C₂×C₄×C₁₃₉	—	4	1	no	—
206	C₂×C₄×C₁₃₉	—	4	2	no	—
207	C₂×C₄×C₁₃₉	—	4	1	no	—
208	C₂×C₄×C₁₃₉	—	4	2	no	—
209	C₂×C₄×C₁₃₉	—	4	1	no	—
210	C₂×C₄×C₁₃₉	—	4	8	no	—
211	C₂×C₄×C₁₃₉	—	4	4	no	—
212	C₂×C₄×C₁₃₉	—	4	4	no	—
213	C₂×C₄×C₁₃₉	—	4	4	no	—
214	C₂×C₄×C₁₃₉	—	4	4	no	—
215	C₂×C₄×C₁₃₉	—	8	8	no	—
216	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
222	C₈×C₁₃₉	—	4	4	no	—
223	C₂²×C₁₃₉	—	2	1	no	—
224	C₂²×C₁₃₉	—	2	1	no	—
225	C₂²×C₁₃₉	—	2	2	no	—
226	C₂²×C₁₃₉	—	2	1	no	—
227	C₂²×C₁₃₉	—	2	2	no	—
228	C₂²×C₁₃₉	—	2	1	no	—
229	C₂²×C₁₃₉	—	2	8	no	—
230	C₂²×C₁₃₉	—	2	8	no	—
231	C₂²×C₁₃₉	—	2	2	no	—
232	C₂²×C₁₃₉	—	2	2	no	—
233	C₂²×C₁₃₉	—	2	2	no	—
234	C₂²×C₁₃₉	—	4	8	no	—
235	C₂²×C₁₃₉	—	4	8	no	—
236	C₂²×C₁₃₉	—	4	4	no	—
237	C₂²×C₁₃₉	—	4	4	no	—
238	C₂²×C₁₃₉	—	4	4	no	—
239	C₂²×C₁₃₉	—	4	4	no	—
240	C₂²×C₁₃₉	—	8	16	no	—
241	C₂²×C₁₃₉	—	8	8	no	—
242	C₂²×C₁₃₉	C₂×#99	1	4	yes	—
243	C₂²×C₁₃₉	C₂×#99	1	2	yes	—
244	C₂²×C₁₃₉	#418	1	2	yes	—
245	C₂²×C₁₃₉	#418	1	2	yes	—
246	C₂²×C₁₃₉	#421	1	2	yes	—
247	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
249	C₄×C₁₃₉	—	2	1	no	—
250	C₄×C₁₃₉	—	2	1	no	—
251	C₄×C₁₃₉	—	2	2	no	—
252	C₄×C₁₃₉	—	2	1	no	—
253	C₄×C₁₃₉	—	2	2	no	—
254	C₄×C₁₃₉	—	2	1	no	—
255	C₄×C₁₃₉	—	4	4	no	—
256	C₄×C₁₃₉	—	8	4	no	—
257	C₂×C₁₃₉	—	2	2	no	—
258	C₂×C₁₃₉	—	2	4	no	—
259	C₂×C₁₃₉	—	2	2	no	—
260	C₂×C₁₃₉	—	4	2	no	—
261	C₂×C₁₃₉	—	8	4	no	—
262	C₂×C₁₃₉	#1510	1	4	yes	direct product factor
263	C₂×C₁₃₉	C₂²×#99	1	1	yes	characteristic
264	C₂×C₁₃₉	C₂×#418	1	1	yes	characteristic
265	C₂×C₁₃₉	C₂×#421	1	1	yes	characteristic
266	C₂×#1510	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₁₃₉	C₂×#1510	1	1	yes	characteristic, direct product factor, Sylow
268	C₂²×#121	C₂×C₁₃₉	1	1	yes	characteristic
269	C₂×#407	C₂×C₁₃₉	1	1	yes	characteristic, complemented
270	C₂×#381	C₂×C₁₃₉	1	1	yes	characteristic, complemented
271	#1510	C₂×C₁₃₉	1	8	yes	direct product factor
272	C₂×#327	C₂×C₁₃₉	1	4	yes	complemented
273	C₂³×D₄	—	2	1	no	—
274	C₂³×D₄	C₄×C₁₃₉	1	1	yes	characteristic, complemented
275	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
276	C₂²×M₁₆	—	2	1	no	—
277	C₂×#121	—	2	1	no	—
278	C₂×#121	—	2	2	no	—
279	C₂×#121	—	2	1	no	—
280	C₂×#121	—	2	2	no	—
281	C₂×#121	C₄×C₁₃₉	1	2	yes	complemented
282	C₂×#121	C₄×C₁₃₉	1	4	yes	complemented
283	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
284	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
285	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	1	yes	characteristic, complemented
286	C₂²×C₂²⋊C₄	—	2	1	no	—
287	C₂²×C₂²⋊C₄	—	2	1	no	—
288	#407	—	2	2	no	—
289	#407	C₂²×C₁₃₉	1	4	yes	complemented
290	C₂×C₂²⋊C₈	—	2	1	no	—
291	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	complemented
292	#381	—	2	2	no	—
293	#381	C₂²×C₁₃₉	1	4	yes	complemented
294	C₂×#95	—	2	1	no	—
295	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
296	#327	C₂²×C₁₃₉	1	16	yes	complemented
297	C₂⁵	—	2	1	no	—
298	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	4	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	4	4	no	—
306	C₂²×D₄	—	4	8	no	—
307	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
308	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
313	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
314	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
315	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
317	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
318	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
320	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	4	4	no	—
324	C₂²×C₈	—	2	2	no	—
325	#121	—	2	4	no	—
326	#121	—	2	4	no	—
327	#121	—	2	4	no	—
328	#121	—	2	2	no	—
329	#121	—	2	4	no	—
330	#121	—	2	2	no	—
331	#121	—	2	4	no	—
332	#121	C₂×C₄×C₁₃₉	1	4	yes	—
333	#121	C₂×C₄×C₁₃₉	1	8	yes	complemented
334	#121	C₂³×C₁₃₉	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
339	C₂×C₂²⋊C₄	—	2	4	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₈	—	2	4	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₂²⋊C₈	C₂³×C₁₃₉	1	4	yes	complemented
348	#95	—	2	4	no	—
349	#95	—	2	2	no	—
350	#95	C₂³×C₁₃₉	1	4	yes	complemented
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	4	no	—
355	C₂⁴	—	4	2	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	—	4	4	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
360	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
361	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
362	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
363	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	8	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	16	no	—
374	C₂×D₄	—	4	16	no	—
375	C₂×D₄	—	4	8	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
396	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
398	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
400	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
401	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
402	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
404	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
413	M₁₆	—	4	8	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	4	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	4	8	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	16	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	8	16	no	—
445	C₂³	#99×C₁₃₉	1	4	yes	—
446	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
447	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
448	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
449	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
450	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
451	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
452	D₄	—	4	4	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	16	no	—
456	D₄	—	4	8	no	—
457	D₄	—	4	8	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	8	8	no	—
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
485	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
487	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
489	C₈	—	4	4	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	8	no	—
502	C₂²	—	4	8	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	8	16	no	—
508	C₂²	—	8	8	no	—
509	C₂²	C₂×#99×C₁₃₉	1	4	yes	—
510	C₂²	C₂×#99×C₁₃₉	1	2	yes	—
511	C₂²	#418×C₁₃₉	1	2	yes	—
512	C₂²	#418×C₁₃₉	1	2	yes	—
513	C₂²	#421×C₁₃₉	1	2	yes	—
514	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
515	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	4	no	—
523	C₄	—	8	4	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	4	no	—
526	C₂	—	2	2	no	—
527	C₂	—	4	2	no	—
528	C₂	—	8	4	no	—
529	C₂	#1510×C₁₃₉	1	4	yes	direct product factor
530	C₂	C₂²×#99×C₁₃₉	1	1	yes	characteristic
531	C₂	C₂×#418×C₁₃₉	1	1	yes	characteristic
532	C₂	C₂×#421×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×#121×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#407×C₁₃₉	C₂	semidirect
3. C₂×#381×C₁₃₉	C₂	semidirect
4. #1510×C₁₃₉	C₂	direct (N × H)
5. C₂×#327×C₁₃₉	C₂	semidirect
7. C₂³×D₄×C₁₃₉	C₄	semidirect
14. C₂×#121×C₁₃₉	C₄	semidirect
15. C₂×#121×C₁₃₉	C₄	semidirect
18. C₂²×C₄⋊C₄×C₁₃₉	C₄	semidirect
22. #407×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₁₃₉	C₂²	semidirect
26. #381×C₁₃₉	C₂²	semidirect
28. C₂×#95×C₁₃₉	C₂²	semidirect
29. #327×C₁₃₉	C₂²	semidirect
41. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
66. #121×C₁₃₉	C₂×C₄	semidirect
71. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
80. C₂²⋊C₈×C₁₃₉	C₂³	semidirect
83. #95×C₁₃₉	C₂³	semidirect
262. C₂×C₁₃₉	#1510	direct (N × H)
266. C₂×#1510	C₁₃₉	direct (N × H)
267. C₁₃₉	C₂×#1510	direct (N × H)
269. C₂×#407	C₂×C₁₃₉	semidirect
270. C₂×#381	C₂×C₁₃₉	semidirect
271. #1510	C₂×C₁₃₉	direct (N × H)
272. C₂×#327	C₂×C₁₃₉	semidirect
274. C₂³×D₄	C₄×C₁₃₉	semidirect
281. C₂×#121	C₄×C₁₃₉	semidirect
282. C₂×#121	C₄×C₁₃₉	semidirect
285. C₂²×C₄⋊C₄	C₄×C₁₃₉	semidirect
289. #407	C₂²×C₁₃₉	semidirect
291. C₂×C₂²⋊C₈	C₂²×C₁₃₉	semidirect
293. #381	C₂²×C₁₃₉	semidirect
295. C₂×#95	C₂²×C₁₃₉	semidirect
296. #327	C₂²×C₁₃₉	semidirect
308. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
333. #121	C₂×C₄×C₁₃₉	semidirect
338. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
347. C₂²⋊C₈	C₂³×C₁₃₉	semidirect
350. #95	C₂³×C₁₃₉	semidirect
529. C₂	#1510×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
C₂²×#121×C₁₃₉	2
C₂×#407×C₁₃₉	2
C₂×#381×C₁₃₉	2
#1510×C₁₃₉	2
C₂×#327×C₁₃₉	2
C₂×#1510	139

Subgroups — C2×#1510×C139 #48012147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1510×C₁₃₉ #48012147