Subgroups — C₂×#1802×C₁₃₉ #48015237

Order 35584.

2030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₁₃₉	C₂	1	2	yes	maximal
4	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1802×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₃₉	—	2	1	no	—
9	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
11	C₂×C₄×D₄×C₁₃₉	—	2	4	no	—
12	C₂×C₄×D₄×C₁₃₉	C₄	1	8	yes	complemented
13	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
19	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×#102×C₁₃₉	—	2	8	no	—
23	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
24	#384×C₁₃₉	—	2	2	no	—
25	#384×C₁₃₉	C₂²	1	4	yes	complemented
26	#340×C₁₃₉	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₃₉	—	2	1	no	—
28	C₂²×D₄×C₁₃₉	—	2	1	no	—
29	C₂²×D₄×C₁₃₉	—	2	2	no	—
30	C₂²×D₄×C₁₃₉	—	2	2	no	—
31	C₂²×D₄×C₁₃₉	—	2	2	no	—
32	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
33	C₂²×D₄×C₁₃₉	D₄	1	4	yes	—
34	C₂²×D₄×C₁₃₉	Q₈	1	4	yes	—
35	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	—	2	1	no	—
37	C₂³×C₄×C₁₃₉	—	2	8	no	—
38	C₂³×C₄×C₁₃₉	—	2	4	no	—
39	C₂³×C₄×C₁₃₉	—	2	2	no	—
40	C₂³×C₄×C₁₃₉	—	4	4	no	—
41	C₂³×C₄×C₁₃₉	—	4	4	no	—
42	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₉	—	2	4	no	—
46	C₂²×C₈×C₁₃₉	—	2	4	no	—
47	C₂²×C₈×C₁₃₉	—	2	4	no	—
48	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
49	C₄×D₄×C₁₃₉	—	2	16	no	—
50	C₄×D₄×C₁₃₉	—	2	8	no	—
51	C₄×D₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
52	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
66	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
69	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
70	C₄⋊C₈×C₁₃₉	—	2	8	no	—
71	#102×C₁₃₉	—	2	16	no	—
72	C₂⁴×C₁₃₉	—	2	4	no	—
73	C₂⁴×C₁₃₉	—	2	4	no	—
74	C₂⁴×C₁₃₉	—	2	4	no	—
75	C₂⁴×C₁₃₉	—	2	2	no	—
76	C₂⁴×C₁₃₉	—	4	2	no	—
77	C₂⁴×C₁₃₉	—	4	2	no	—
78	C₂⁴×C₁₃₉	—	4	2	no	—
79	C₂⁴×C₁₃₉	—	4	2	no	—
80	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
81	C₂×D₄×C₁₃₉	—	2	4	no	—
82	C₂×D₄×C₁₃₉	—	2	8	no	—
83	C₂×D₄×C₁₃₉	—	2	8	no	—
84	C₂×D₄×C₁₃₉	—	2	4	no	—
85	C₂×D₄×C₁₃₉	—	2	8	no	—
86	C₂×D₄×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	2	2	no	—
89	C₂×D₄×C₁₃₉	—	2	2	no	—
90	C₂×D₄×C₁₃₉	C₄⋊C₄	1	16	yes	complemented
91	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
92	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
93	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
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	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	16	no	—
99	C₂²×C₄×C₁₃₉	—	2	4	no	—
100	C₂²×C₄×C₁₃₉	—	4	2	no	—
101	C₂²×C₄×C₁₃₉	—	4	2	no	—
102	C₂²×C₄×C₁₃₉	—	4	32	no	—
103	C₂²×C₄×C₁₃₉	—	4	8	no	—
104	C₂²×C₄×C₁₃₉	—	4	8	no	—
105	C₂²×C₄×C₁₃₉	—	4	4	no	—
106	C₂²×C₄×C₁₃₉	—	4	4	no	—
107	C₂²×C₄×C₁₃₉	—	4	4	no	—
108	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
109	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
110	C₂²×C₄×C₁₃₉	D₈	1	4	yes	—
111	C₂²×C₄×C₁₃₉	SD₁₆	1	4	yes	—
112	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
120	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
121	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₃₉	—	2	4	no	—
123	C₂×C₈×C₁₃₉	—	2	4	no	—
124	C₂×C₈×C₁₃₉	—	2	4	no	—
125	C₂×C₈×C₁₃₉	—	4	8	no	—
126	C₄⋊C₄×C₁₃₉	—	2	4	no	—
127	C₄⋊C₄×C₁₃₉	—	2	2	no	—
128	C₄⋊C₄×C₁₃₉	—	2	4	no	—
129	C₄⋊C₄×C₁₃₉	—	2	4	no	—
130	C₄⋊C₄×C₁₃₉	—	4	8	no	—
131	C₄⋊C₄×C₁₃₉	—	4	4	no	—
132	C₄⋊C₄×C₁₃₉	—	4	8	no	—
133	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
134	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
135	C₄²×C₁₃₉	C₂²⋊C₄	1	8	yes	—
136	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
137	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
138	C₂³×C₁₃₉	—	2	4	no	—
139	C₂³×C₁₃₉	—	2	4	no	—
140	C₂³×C₁₃₉	—	2	4	no	—
141	C₂³×C₁₃₉	—	2	16	no	—
142	C₂³×C₁₃₉	—	4	2	no	—
143	C₂³×C₁₃₉	—	4	2	no	—
144	C₂³×C₁₃₉	—	4	2	no	—
145	C₂³×C₁₃₉	—	4	2	no	—
146	C₂³×C₁₃₉	—	4	8	no	—
147	C₂³×C₁₃₉	—	4	8	no	—
148	C₂³×C₁₃₉	—	4	8	no	—
149	C₂³×C₁₃₉	—	4	8	no	—
150	C₂³×C₁₃₉	—	4	8	no	—
151	C₂³×C₁₃₉	—	4	8	no	—
152	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₁₃₉	#121	1	2	yes	—
154	C₂³×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
155	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
156	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
157	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
158	C₂³×C₁₃₉	#137	1	2	yes	—
159	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₁₃₉	—	2	4	no	—
161	D₄×C₁₃₉	—	2	4	no	—
162	D₄×C₁₃₉	—	2	4	no	—
163	D₄×C₁₃₉	—	2	16	no	—
164	D₄×C₁₃₉	C₂×C₄⋊C₄	1	8	yes	complemented
165	C₂×C₄×C₁₃₉	—	2	2	no	—
166	C₂×C₄×C₁₃₉	—	2	2	no	—
167	C₂×C₄×C₁₃₉	—	2	8	no	—
168	C₂×C₄×C₁₃₉	—	2	4	no	—
169	C₂×C₄×C₁₃₉	—	4	2	no	—
170	C₂×C₄×C₁₃₉	—	4	2	no	—
171	C₂×C₄×C₁₃₉	—	4	8	no	—
172	C₂×C₄×C₁₃₉	—	4	32	no	—
173	C₂×C₄×C₁₃₉	—	4	4	no	—
174	C₂×C₄×C₁₃₉	—	4	4	no	—
175	C₂×C₄×C₁₃₉	—	4	4	no	—
176	C₂×C₄×C₁₃₉	—	8	8	no	—
177	C₂×C₄×C₁₃₉	#102	1	16	yes	complemented
178	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
182	C₂×C₄×C₁₃₉	#117	1	4	yes	—
183	C₂×C₄×C₁₃₉	#121	1	4	yes	—
184	C₂×C₄×C₁₃₉	#121	1	2	yes	—
185	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
186	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
188	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
195	C₈×C₁₃₉	—	4	4	no	—
196	C₂²×C₁₃₉	—	2	8	no	—
197	C₂²×C₁₃₉	—	4	32	no	—
198	C₂²×C₁₃₉	—	4	4	no	—
199	C₂²×C₁₃₉	—	4	4	no	—
200	C₂²×C₁₃₉	—	4	4	no	—
201	C₂²×C₁₃₉	—	4	4	no	—
202	C₂²×C₁₃₉	—	4	4	no	—
203	C₂²×C₁₃₉	—	4	4	no	—
204	C₂²×C₁₃₉	#380	1	4	yes	—
205	C₂²×C₁₃₉	C₂×#102	1	4	yes	—
206	C₂²×C₁₃₉	#417	1	4	yes	—
207	C₂²×C₁₃₉	#459	1	4	yes	—
208	C₂²×C₁₃₉	#461	1	4	yes	—
209	C₂²×C₁₃₉	#474	1	4	yes	—
210	C₂²×C₁₃₉	#476	1	4	yes	—
211	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
213	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
215	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
218	C₄×C₁₃₉	—	2	4	no	—
219	C₄×C₁₃₉	—	4	4	no	—
220	C₄×C₁₃₉	—	8	4	no	—
221	C₄×C₁₃₉	#380	1	4	yes	—
222	C₄×C₁₃₉	C₂×#102	1	8	yes	complemented
223	C₄×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₄×C₁₃₉	C₂×#117	1	1	yes	characteristic
225	C₄×C₁₃₉	C₂×#121	1	1	yes	characteristic
226	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₁₃₉	—	4	8	no	—
228	C₂×C₁₃₉	#1802	1	8	yes	direct product factor
229	C₂×C₁₃₉	C₂×#380	1	1	yes	characteristic
230	C₂×C₁₃₉	C₂²×#102	1	1	yes	characteristic
231	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
232	C₂×C₁₃₉	C₂×#459	1	1	yes	characteristic
233	C₂×C₁₃₉	C₂×#461	1	1	yes	characteristic
234	C₂×C₁₃₉	C₂×#474	1	1	yes	characteristic
235	C₂×C₁₃₉	C₂×#476	1	1	yes	characteristic
236	C₂×#1802	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₁₃₉	C₂×#1802	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic
239	C₂²×C₄⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
240	C₂²×#102	C₂×C₁₃₉	1	2	yes	—
241	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic, complemented
242	#1802	C₂×C₁₃₉	1	8	yes	direct product factor
243	C₂×#340	C₂×C₁₃₉	1	2	yes	complemented
244	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
245	C₂⁴×C₄	—	2	1	no	—
246	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
247	C₂×C₄×D₄	—	2	2	no	—
248	C₂×C₄×D₄	—	2	4	no	—
249	C₂×C₄×D₄	C₄×C₁₃₉	1	8	yes	complemented
250	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	C₂²×C₄⋊C₄	—	2	1	no	—
253	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	—	2	1	no	—
256	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
259	C₂×#102	—	2	8	no	—
260	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
261	#384	—	2	2	no	—
262	#384	C₂²×C₁₃₉	1	4	yes	complemented
263	#340	C₂²×C₁₃₉	1	8	yes	complemented
264	C₂⁵	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
270	C₂²×D₄	D₄×C₁₃₉	1	4	yes	—
271	C₂²×D₄	Q₈×C₁₃₉	1	4	yes	—
272	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	—	2	8	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	4	4	no	—
278	C₂³×C₄	—	4	4	no	—
279	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
280	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₂²×C₈	—	2	4	no	—
283	C₂²×C₈	—	2	4	no	—
284	C₂²×C₈	—	2	4	no	—
285	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
286	C₄×D₄	—	2	16	no	—
287	C₄×D₄	—	2	8	no	—
288	C₄×D₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	4	4	no	—
297	C₂×C₄⋊C₄	—	4	4	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
304	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
305	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
306	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
307	C₄⋊C₈	—	2	8	no	—
308	#102	—	2	16	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	—	4	2	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₄⋊C₄×C₁₃₉	1	16	yes	complemented
328	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
329	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
330	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	16	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	32	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	—	4	8	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
346	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
347	C₂²×C₄	D₈×C₁₃₉	1	4	yes	—
348	C₂²×C₄	SD₁₆×C₁₃₉	1	4	yes	—
349	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
355	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
356	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
357	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	4	8	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	4	8	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	8	no	—
370	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
371	C₂²⋊C₄	—	2	16	no	—
372	C₄²	C₂²⋊C₄×C₁₃₉	1	8	yes	—
373	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
374	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	16	no	—
379	C₂³	—	4	8	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	4	8	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
390	C₂³	#121×C₁₃₉	1	2	yes	—
391	C₂³	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
392	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
393	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
394	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
395	C₂³	#137×C₁₃₉	1	2	yes	—
396	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	16	no	—
401	D₄	C₂×C₄⋊C₄×C₁₃₉	1	8	yes	complemented
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	32	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	#102×C₁₃₉	1	16	yes	complemented
415	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
418	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
419	C₂×C₄	#117×C₁₃₉	1	4	yes	—
420	C₂×C₄	#121×C₁₃₉	1	4	yes	—
421	C₂×C₄	#121×C₁₃₉	1	2	yes	—
422	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
423	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
424	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
425	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
432	C₈	—	4	4	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	32	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	#380×C₁₃₉	1	4	yes	—
442	C₂²	C₂×#102×C₁₃₉	1	4	yes	—
443	C₂²	#417×C₁₃₉	1	4	yes	—
444	C₂²	#459×C₁₃₉	1	4	yes	—
445	C₂²	#461×C₁₃₉	1	4	yes	—
446	C₂²	#474×C₁₃₉	1	4	yes	—
447	C₂²	#476×C₁₃₉	1	4	yes	—
448	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
449	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
450	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
451	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
452	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
453	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
454	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
455	C₄	—	2	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	4	no	—
458	C₄	#380×C₁₃₉	1	4	yes	—
459	C₄	C₂×#102×C₁₃₉	1	8	yes	complemented
460	C₄	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
461	C₄	C₂×#117×C₁₃₉	1	1	yes	characteristic
462	C₄	C₂×#121×C₁₃₉	1	1	yes	characteristic
463	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
464	C₂	—	4	8	no	—
465	C₂	#1802×C₁₃₉	1	8	yes	direct product factor
466	C₂	C₂×#380×C₁₃₉	1	1	yes	characteristic
467	C₂	C₂²×#102×C₁₃₉	1	1	yes	characteristic
468	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
469	C₂	C₂×#459×C₁₃₉	1	1	yes	characteristic
470	C₂	C₂×#461×C₁₃₉	1	1	yes	characteristic
471	C₂	C₂×#474×C₁₃₉	1	1	yes	characteristic
472	C₂	C₂×#476×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₁₃₉	C₂	semidirect
4. C₂×#384×C₁₃₉	C₂	semidirect
5. #1802×C₁₃₉	C₂	direct (N × H)
6. C₂×#340×C₁₃₉	C₂	semidirect
12. C₂×C₄×D₄×C₁₃₉	C₄	semidirect
21. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
25. #384×C₁₃₉	C₂²	semidirect
26. #340×C₁₃₉	C₂²	semidirect
51. C₄×D₄×C₁₃₉	C₂×C₄	semidirect
90. C₂×D₄×C₁₃₉	C₄⋊C₄	semidirect
164. D₄×C₁₃₉	C₂×C₄⋊C₄	semidirect
177. C₂×C₄×C₁₃₉	#102	semidirect
222. C₄×C₁₃₉	C₂×#102	semidirect
228. C₂×C₁₃₉	#1802	direct (N × H)
236. C₂×#1802	C₁₃₉	direct (N × H)
237. C₁₃₉	C₂×#1802	direct (N × H)
239. C₂²×C₄⋊C₈	C₂×C₁₃₉	semidirect
241. C₂×#384	C₂×C₁₃₉	semidirect
242. #1802	C₂×C₁₃₉	direct (N × H)
243. C₂×#340	C₂×C₁₃₉	semidirect
249. C₂×C₄×D₄	C₄×C₁₃₉	semidirect
258. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
262. #384	C₂²×C₁₃₉	semidirect
263. #340	C₂²×C₁₃₉	semidirect
288. C₄×D₄	C₂×C₄×C₁₃₉	semidirect
327. C₂×D₄	C₄⋊C₄×C₁₃₉	semidirect
401. D₄	C₂×C₄⋊C₄×C₁₃₉	semidirect
414. C₂×C₄	#102×C₁₃₉	semidirect
459. C₄	C₂×#102×C₁₃₉	semidirect
465. C₂	#1802×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×C₄×D₄×C₁₃₉	2
C₂²×C₄⋊C₈×C₁₃₉	2
C₂²×#102×C₁₃₉	2
C₂×#384×C₁₃₉	2
#1802×C₁₃₉	2
C₂×#340×C₁₃₉	2
C₂×#1802	139

Subgroups — C2×#1802×C139 #48015237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1802×C₁₃₉ #48015237