Subgroups — C₂×#1470×C₁₃₉ #48011971

Order 35584.

1002 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#431×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1470×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#324×C₁₃₉	C₂	1	4	yes	maximal
6	C₂×#125×C₁₃₉	—	2	1	no	—
7	C₂×#125×C₁₃₉	—	2	1	no	—
8	C₂×#125×C₁₃₉	—	2	1	no	—
9	C₂×#125×C₁₃₉	—	2	1	no	—
10	C₂×#125×C₁₃₉	—	2	2	no	—
11	C₂×#125×C₁₃₉	—	2	2	no	—
12	C₂×#125×C₁₃₉	C₄	1	4	yes	—
13	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₃₉	C₄	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	#432×C₁₃₉	—	2	2	no	—
20	#432×C₁₃₉	C₂²	1	4	yes	—
21	#431×C₁₃₉	—	2	2	no	—
22	#431×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#97×C₁₃₉	—	2	1	no	—
28	C₂×C₄×C₈×C₁₃₉	—	2	1	no	—
29	#324×C₁₃₉	C₂²	1	16	yes	—
30	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₃₉	—	2	2	no	—
36	C₂²×C₈×C₁₃₉	—	2	2	no	—
37	#125×C₁₃₉	—	2	4	no	—
38	#125×C₁₃₉	—	2	4	no	—
39	#125×C₁₃₉	—	2	4	no	—
40	#125×C₁₃₉	—	2	4	no	—
41	#125×C₁₃₉	—	2	4	no	—
42	#125×C₁₃₉	—	2	4	no	—
43	#125×C₁₃₉	—	2	4	no	—
44	#125×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
69	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
71	C₄⋊C₈×C₁₃₉	—	2	4	no	—
72	C₄⋊C₈×C₁₃₉	—	2	4	no	—
73	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
74	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
75	C₂²⋊C₈×C₁₃₉	C₂³	1	4	yes	—
76	C₂²⋊C₈×C₁₃₉	C₂³	1	4	yes	—
77	#97×C₁₃₉	—	2	4	no	—
78	C₄×C₈×C₁₃₉	—	2	4	no	—
79	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	4	no	—
82	C₂²×C₄×C₁₃₉	—	2	2	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	2	no	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	8	no	—
87	C₂²×C₄×C₁₃₉	—	4	2	no	—
88	C₂²×C₄×C₁₃₉	—	4	4	no	—
89	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₃₉	—	2	4	no	—
106	C₂×C₈×C₁₃₉	—	2	4	no	—
107	C₂×C₈×C₁₃₉	—	4	4	no	—
108	C₂×C₈×C₁₃₉	—	4	4	no	—
109	C₄⋊C₄×C₁₃₉	—	2	4	no	—
110	C₄⋊C₄×C₁₃₉	—	2	4	no	—
111	C₄⋊C₄×C₁₃₉	—	2	4	no	—
112	C₄⋊C₄×C₁₃₉	—	2	8	no	—
113	C₄⋊C₄×C₁₃₉	—	2	8	no	—
114	C₄⋊C₄×C₁₃₉	—	2	4	no	—
115	C₄⋊C₄×C₁₃₉	—	2	4	no	—
116	C₄⋊C₄×C₁₃₉	—	2	4	no	—
117	C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₄⋊C₄×C₁₃₉	—	2	4	no	—
119	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
124	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
127	C₂³×C₁₃₉	—	2	2	no	—
128	C₂³×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₁₃₉	#131	1	4	yes	—
132	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₄×C₁₃₉	—	2	2	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	2	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₄×C₁₃₉	—	2	4	no	—
144	C₂×C₄×C₁₃₉	—	2	8	no	—
145	C₂×C₄×C₁₃₉	—	4	1	no	—
146	C₂×C₄×C₁₃₉	—	4	1	no	—
147	C₂×C₄×C₁₃₉	—	4	1	no	—
148	C₂×C₄×C₁₃₉	—	4	1	no	—
149	C₂×C₄×C₁₃₉	—	4	4	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	4	4	no	—
152	C₂×C₄×C₁₃₉	—	4	4	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	#101	1	4	yes	—
155	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₁₃₉	—	4	4	no	—
164	C₈×C₁₃₉	—	4	4	no	—
165	C₂²×C₁₃₉	—	2	1	no	—
166	C₂²×C₁₃₉	—	2	1	no	—
167	C₂²×C₁₃₉	—	2	1	no	—
168	C₂²×C₁₃₉	—	2	1	no	—
169	C₂²×C₁₃₉	—	2	8	no	—
170	C₂²×C₁₃₉	#408	1	2	yes	—
171	C₂²×C₁₃₉	#408	1	2	yes	—
172	C₂²×C₁₃₉	#410	1	2	yes	—
173	C₂²×C₁₃₉	C₂×#101	1	2	yes	—
174	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₁₃₉	C₂×#131	1	2	yes	—
176	C₄×C₁₃₉	—	2	2	no	—
177	C₄×C₁₃₉	—	2	2	no	—
178	C₄×C₁₃₉	—	2	1	no	—
179	C₄×C₁₃₉	—	2	1	no	—
180	C₄×C₁₃₉	—	2	1	no	—
181	C₄×C₁₃₉	—	2	1	no	—
182	C₄×C₁₃₉	—	2	2	no	—
183	C₄×C₁₃₉	—	4	4	no	—
184	C₄×C₁₃₉	—	4	4	no	—
185	C₄×C₁₃₉	C₂×#101	1	4	yes	—
186	C₂×C₁₃₉	—	2	2	no	—
187	C₂×C₁₃₉	—	2	2	no	—
188	C₂×C₁₃₉	#1470	1	4	yes	direct product factor
189	C₂×C₁₃₉	C₂×#408	1	1	yes	characteristic
190	C₂×C₁₃₉	C₂×#410	1	1	yes	characteristic
191	C₂×C₁₃₉	C₂²×#101	1	1	yes	characteristic
192	C₂×#1470	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₉	C₂×#1470	1	1	yes	characteristic, direct product factor, Sylow
194	C₂²×#125	C₂×C₁₃₉	1	1	yes	characteristic
195	C₂×#432	C₂×C₁₃₉	1	1	yes	characteristic
196	C₂×#431	C₂×C₁₃₉	1	1	yes	characteristic
197	#1470	C₂×C₁₃₉	1	8	yes	direct product factor
198	C₂×#324	C₂×C₁₃₉	1	4	yes	—
199	C₂×#125	—	2	1	no	—
200	C₂×#125	—	2	1	no	—
201	C₂×#125	—	2	1	no	—
202	C₂×#125	—	2	1	no	—
203	C₂×#125	—	2	2	no	—
204	C₂×#125	—	2	2	no	—
205	C₂×#125	C₄×C₁₃₉	1	4	yes	—
206	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
207	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	2	yes	—
209	C₂²×C₄⋊C₄	C₄×C₁₃₉	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
211	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
212	#432	—	2	2	no	—
213	#432	C₂²×C₁₃₉	1	4	yes	—
214	#431	—	2	2	no	—
215	#431	C₂²×C₁₃₉	1	4	yes	—
216	C₂×C₄⋊C₈	—	2	1	no	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
220	C₂×#97	—	2	1	no	—
221	C₂×C₄×C₈	—	2	1	no	—
222	#324	C₂²×C₁₃₉	1	16	yes	—
223	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
224	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
225	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
226	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
227	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	#125	—	2	4	no	—
231	#125	—	2	4	no	—
232	#125	—	2	4	no	—
233	#125	—	2	4	no	—
234	#125	—	2	4	no	—
235	#125	—	2	4	no	—
236	#125	—	2	4	no	—
237	#125	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
256	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
257	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
262	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
263	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	4	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	C₂³×C₁₃₉	1	4	yes	—
269	C₂²⋊C₈	C₂³×C₁₃₉	1	4	yes	—
270	#97	—	2	4	no	—
271	C₄×C₈	—	2	4	no	—
272	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
283	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
313	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
314	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
315	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
316	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
317	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
318	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
319	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
323	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
324	C₂³	#131×C₁₃₉	1	4	yes	—
325	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	#101×C₁₃₉	1	4	yes	—
348	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
356	C₈	—	4	4	no	—
357	C₈	—	4	4	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	8	no	—
363	C₂²	#408×C₁₃₉	1	2	yes	—
364	C₂²	#408×C₁₃₉	1	2	yes	—
365	C₂²	#410×C₁₃₉	1	2	yes	—
366	C₂²	C₂×#101×C₁₃₉	1	2	yes	—
367	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
368	C₂²	C₂×#131×C₁₃₉	1	2	yes	—
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	4	no	—
378	C₄	C₂×#101×C₁₃₉	1	4	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	2	2	no	—
381	C₂	#1470×C₁₃₉	1	4	yes	direct product factor
382	C₂	C₂×#408×C₁₃₉	1	1	yes	characteristic
383	C₂	C₂×#410×C₁₃₉	1	1	yes	characteristic
384	C₂	C₂²×#101×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ 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. #1470×C₁₃₉	C₂	direct (N × H)
188. C₂×C₁₃₉	#1470	direct (N × H)
192. C₂×#1470	C₁₃₉	direct (N × H)
193. C₁₃₉	C₂×#1470	direct (N × H)
197. #1470	C₂×C₁₃₉	direct (N × H)
381. C₂	#1470×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×#125×C₁₃₉	2
C₂×#432×C₁₃₉	2
C₂×#431×C₁₃₉	2
#1470×C₁₃₉	2
C₂×#324×C₁₃₉	2
C₂×#1470	139

Subgroups — C2×#1470×C139 #48011971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1470×C₁₃₉ #48011971