Subgroups — C₂×#1874×C₁₃₉ #48015501

Order 35584.

2614 conjugacy classes of subgroups.

The subgroup lattice has 526 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	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂²×C₂²⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1874×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₁₃₉	—	2	1	no	—
8	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₃₉	—	2	1	no	—
10	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
12	C₂×#121×C₁₃₉	—	2	4	no	—
13	C₂×#121×C₁₃₉	—	2	2	no	—
14	C₂×#121×C₁₃₉	C₄	1	8	yes	complemented
15	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₁₃₉	—	2	2	no	—
17	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₃₉	—	2	8	no	—
19	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
23	C₂×#102×C₁₃₉	—	2	8	no	—
24	C₂×#102×C₁₃₉	C₂²	1	8	yes	complemented
25	C₂×C₂²⋊C₈×C₁₃₉	—	2	4	no	—
26	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	complemented
27	#340×C₁₃₉	C₂²	1	8	yes	complemented
28	C₂⁵×C₁₃₉	—	2	1	no	—
29	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₃₉	—	2	8	no	—
31	C₂²×D₄×C₁₃₉	—	2	4	no	—
32	C₂²×D₄×C₁₃₉	—	2	4	no	—
33	C₂²×D₄×C₁₃₉	—	2	1	no	—
34	C₂²×D₄×C₁₃₉	—	2	2	no	—
35	C₂²×D₄×C₁₃₉	—	2	4	no	—
36	C₂²×D₄×C₁₃₉	—	4	4	no	—
37	C₂²×D₄×C₁₃₉	—	4	4	no	—
38	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
39	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃₉	—	2	4	no	—
41	C₂³×C₄×C₁₃₉	—	2	4	no	—
42	C₂³×C₄×C₁₃₉	—	2	8	no	—
43	C₂³×C₄×C₁₃₉	—	2	4	no	—
44	C₂³×C₄×C₁₃₉	—	2	1	no	—
45	C₂³×C₄×C₁₃₉	—	2	2	no	—
46	C₂³×C₄×C₁₃₉	—	4	4	no	—
47	C₂³×C₄×C₁₃₉	—	4	4	no	—
48	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
50	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
52	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₉	—	2	4	no	—
55	C₂²×C₈×C₁₃₉	—	2	4	no	—
56	C₂²×C₈×C₁₃₉	—	2	4	no	—
57	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
58	#121×C₁₃₉	—	2	16	no	—
59	#121×C₁₃₉	—	2	8	no	—
60	#121×C₁₃₉	C₂×C₄	1	16	yes	complemented
61	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
63	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
70	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
75	#102×C₁₃₉	—	2	16	no	—
76	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
77	C₂⁴×C₁₃₉	—	2	2	no	—
78	C₂⁴×C₁₃₉	—	2	2	no	—
79	C₂⁴×C₁₃₉	—	2	2	no	—
80	C₂⁴×C₁₃₉	—	2	2	no	—
81	C₂⁴×C₁₃₉	—	2	4	no	—
82	C₂⁴×C₁₃₉	—	2	2	no	—
83	C₂⁴×C₁₃₉	—	4	2	no	—
84	C₂⁴×C₁₃₉	—	4	2	no	—
85	C₂⁴×C₁₃₉	—	4	2	no	—
86	C₂⁴×C₁₃₉	—	4	2	no	—
87	C₂⁴×C₁₃₉	—	4	2	no	—
88	C₂⁴×C₁₃₉	—	4	2	no	—
89	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
90	C₂⁴×C₁₃₉	D₈	1	4	yes	—
91	C₂⁴×C₁₃₉	SD₁₆	1	4	yes	—
92	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
93	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₁₃₉	—	2	16	no	—
95	C₂×D₄×C₁₃₉	—	2	4	no	—
96	C₂×D₄×C₁₃₉	—	2	16	no	—
97	C₂×D₄×C₁₃₉	—	2	4	no	—
98	C₂×D₄×C₁₃₉	—	2	2	no	—
99	C₂×D₄×C₁₃₉	—	2	4	no	—
100	C₂×D₄×C₁₃₉	—	4	32	no	—
101	C₂×D₄×C₁₃₉	—	4	8	no	—
102	C₂×D₄×C₁₃₉	—	4	8	no	—
103	C₂×D₄×C₁₃₉	—	4	2	no	—
104	C₂×D₄×C₁₃₉	—	4	8	no	—
105	C₂×D₄×C₁₃₉	—	4	2	no	—
106	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	complemented
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	16	no	—
110	C₂²×C₄×C₁₃₉	—	2	4	no	—
111	C₂²×C₄×C₁₃₉	—	2	16	no	—
112	C₂²×C₄×C₁₃₉	—	2	4	no	—
113	C₂²×C₄×C₁₃₉	—	2	4	no	—
114	C₂²×C₄×C₁₃₉	—	2	4	no	—
115	C₂²×C₄×C₁₃₉	—	2	16	no	—
116	C₂²×C₄×C₁₃₉	—	2	4	no	—
117	C₂²×C₄×C₁₃₉	—	2	8	no	—
118	C₂²×C₄×C₁₃₉	—	2	2	no	—
119	C₂²×C₄×C₁₃₉	—	2	4	no	—
120	C₂²×C₄×C₁₃₉	—	4	8	no	—
121	C₂²×C₄×C₁₃₉	—	4	32	no	—
122	C₂²×C₄×C₁₃₉	—	4	8	no	—
123	C₂²×C₄×C₁₃₉	—	4	4	no	—
124	C₂²×C₄×C₁₃₉	—	4	2	no	—
125	C₂²×C₄×C₁₃₉	—	4	2	no	—
126	C₂²×C₄×C₁₃₉	—	4	4	no	—
127	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
128	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
129	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₁₃₉	—	2	4	no	—
139	C₂×C₈×C₁₃₉	—	2	4	no	—
140	C₂×C₈×C₁₃₉	—	2	4	no	—
141	C₂×C₈×C₁₃₉	—	4	8	no	—
142	C₄⋊C₄×C₁₃₉	—	2	16	no	—
143	C₄⋊C₄×C₁₃₉	—	2	4	no	—
144	C₄⋊C₄×C₁₃₉	—	2	8	no	—
145	C₄⋊C₄×C₁₃₉	—	2	4	no	—
146	C₄⋊C₄×C₁₃₉	—	2	2	no	—
147	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	complemented
148	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
149	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
150	C₂³×C₁₃₉	—	2	2	no	—
151	C₂³×C₁₃₉	—	2	2	no	—
152	C₂³×C₁₃₉	—	2	2	no	—
153	C₂³×C₁₃₉	—	2	2	no	—
154	C₂³×C₁₃₉	—	2	8	no	—
155	C₂³×C₁₃₉	—	2	8	no	—
156	C₂³×C₁₃₉	—	2	8	no	—
157	C₂³×C₁₃₉	—	2	8	no	—
158	C₂³×C₁₃₉	—	2	8	no	—
159	C₂³×C₁₃₉	—	2	8	no	—
160	C₂³×C₁₃₉	—	2	4	no	—
161	C₂³×C₁₃₉	—	4	2	no	—
162	C₂³×C₁₃₉	—	4	2	no	—
163	C₂³×C₁₃₉	—	4	2	no	—
164	C₂³×C₁₃₉	—	4	2	no	—
165	C₂³×C₁₃₉	—	4	2	no	—
166	C₂³×C₁₃₉	—	4	2	no	—
167	C₂³×C₁₃₉	—	4	8	no	—
168	C₂³×C₁₃₉	—	4	8	no	—
169	C₂³×C₁₃₉	—	4	8	no	—
170	C₂³×C₁₃₉	—	8	4	no	—
171	C₂³×C₁₃₉	—	8	4	no	—
172	C₂³×C₁₃₉	—	8	4	no	—
173	C₂³×C₁₃₉	—	8	4	no	—
174	C₂³×C₁₃₉	#102	1	16	yes	complemented
175	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂³×C₁₃₉	#120	1	2	yes	—
178	C₂³×C₁₃₉	#123	1	2	yes	—
179	C₂³×C₁₃₉	C₂×D₈	1	4	yes	—
180	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
181	C₂³×C₁₃₉	C₂×SD₁₆	1	4	yes	—
182	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
183	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×C₁₃₉	#137	1	2	yes	—
185	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
186	D₄×C₁₃₉	—	2	8	no	—
187	D₄×C₁₃₉	—	4	32	no	—
188	D₄×C₁₃₉	—	4	4	no	—
189	D₄×C₁₃₉	—	4	8	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	8	no	—
193	C₂×C₄×C₁₃₉	—	2	8	no	—
194	C₂×C₄×C₁₃₉	—	2	8	no	—
195	C₂×C₄×C₁₃₉	—	2	16	no	—
196	C₂×C₄×C₁₃₉	—	2	4	no	—
197	C₂×C₄×C₁₃₉	—	2	8	no	—
198	C₂×C₄×C₁₃₉	—	4	32	no	—
199	C₂×C₄×C₁₃₉	—	4	4	no	—
200	C₂×C₄×C₁₃₉	—	4	2	no	—
201	C₂×C₄×C₁₃₉	—	4	2	no	—
202	C₂×C₄×C₁₃₉	—	4	4	no	—
203	C₂×C₄×C₁₃₉	—	4	8	no	—
204	C₂×C₄×C₁₃₉	—	4	16	no	—
205	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
208	C₂×C₄×C₁₃₉	#120	1	2	yes	—
209	C₂×C₄×C₁₃₉	#121	1	8	yes	—
210	C₂×C₄×C₁₃₉	#123	1	2	yes	—
211	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
215	C₈×C₁₃₉	—	4	4	no	—
216	C₂²×C₁₃₉	—	2	4	no	—
217	C₂²×C₁₃₉	—	2	4	no	—
218	C₂²×C₁₃₉	—	2	4	no	—
219	C₂²×C₁₃₉	—	2	32	no	—
220	C₂²×C₁₃₉	—	2	4	no	—
221	C₂²×C₁₃₉	—	2	4	no	—
222	C₂²×C₁₃₉	—	2	4	no	—
223	C₂²×C₁₃₉	—	4	4	no	—
224	C₂²×C₁₃₉	—	4	4	no	—
225	C₂²×C₁₃₉	—	4	4	no	—
226	C₂²×C₁₃₉	—	8	2	no	—
227	C₂²×C₁₃₉	—	8	2	no	—
228	C₂²×C₁₃₉	—	8	16	no	—
229	C₂²×C₁₃₉	—	8	2	no	—
230	C₂²×C₁₃₉	—	8	2	no	—
231	C₂²×C₁₃₉	#386	1	4	yes	—
232	C₂²×C₁₃₉	C₂×#102	1	4	yes	—
233	C₂²×C₁₃₉	C₂×#102	1	8	yes	complemented
234	C₂²×C₁₃₉	#417	1	4	yes	—
235	C₂²×C₁₃₉	#447	1	4	yes	—
236	C₂²×C₁₃₉	#448	1	4	yes	—
237	C₂²×C₁₃₉	#480	1	4	yes	—
238	C₂²×C₁₃₉	#481	1	4	yes	—
239	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
241	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
242	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
243	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
244	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
246	C₄×C₁₃₉	—	2	4	no	—
247	C₄×C₁₃₉	—	4	4	no	—
248	C₄×C₁₃₉	—	4	8	no	—
249	C₄×C₁₃₉	#386	1	4	yes	—
250	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
251	C₄×C₁₃₉	C₂×#121	1	2	yes	—
252	C₂×C₁₃₉	—	2	8	no	—
253	C₂×C₁₃₉	—	8	4	no	—
254	C₂×C₁₃₉	#1874	1	8	yes	direct product factor
255	C₂×C₁₃₉	C₂×#386	1	1	yes	characteristic
256	C₂×C₁₃₉	C₂²×#102	1	1	yes	characteristic
257	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
258	C₂×C₁₃₉	C₂×#447	1	1	yes	characteristic
259	C₂×C₁₃₉	C₂×#448	1	1	yes	characteristic
260	C₂×C₁₃₉	C₂×#480	1	1	yes	characteristic
261	C₂×C₁₃₉	C₂×#481	1	1	yes	characteristic
262	C₂×#1874	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₁₃₉	C₂×#1874	1	1	yes	characteristic, direct product factor, Sylow
264	C₂²×#121	C₂×C₁₃₉	1	1	yes	characteristic
265	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
266	C₂²×#102	C₂×C₁₃₉	1	2	yes	complemented
267	C₂²×C₂²⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	#1874	C₂×C₁₃₉	1	8	yes	direct product factor
269	C₂×#340	C₂×C₁₃₉	1	2	yes	complemented
270	C₂³×D₄	—	2	1	no	—
271	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
272	C₂⁴×C₄	—	2	1	no	—
273	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
275	C₂×#121	—	2	4	no	—
276	C₂×#121	—	2	2	no	—
277	C₂×#121	C₄×C₁₃₉	1	8	yes	complemented
278	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
279	C₂²×C₄⋊C₄	—	2	2	no	—
280	C₂²×C₄⋊C₄	—	2	1	no	—
281	C₂²×C₄⋊C₄	—	2	8	no	—
282	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
284	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
285	C₂²×C₂²⋊C₄	—	2	1	no	—
286	C₂×#102	—	2	8	no	—
287	C₂×#102	C₂²×C₁₃₉	1	8	yes	complemented
288	C₂×C₂²⋊C₈	—	2	4	no	—
289	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
290	#340	C₂²×C₁₃₉	1	8	yes	complemented
291	C₂⁵	—	2	1	no	—
292	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
293	C₂²×D₄	—	2	8	no	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	—	2	4	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	—	4	4	no	—
300	C₂²×D₄	—	4	4	no	—
301	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
302	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
303	C₂³×C₄	—	2	4	no	—
304	C₂³×C₄	—	2	4	no	—
305	C₂³×C₄	—	2	8	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	4	no	—
309	C₂³×C₄	—	4	4	no	—
310	C₂³×C₄	—	4	4	no	—
311	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
312	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
314	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
315	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
316	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
317	C₂²×C₈	—	2	4	no	—
318	C₂²×C₈	—	2	4	no	—
319	C₂²×C₈	—	2	4	no	—
320	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
321	#121	—	2	16	no	—
322	#121	—	2	8	no	—
323	#121	C₂×C₄×C₁₃₉	1	16	yes	complemented
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	16	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	16	no	—
332	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
333	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
334	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
336	C₂×C₂²⋊C₄	—	2	8	no	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	#102	—	2	16	no	—
339	C₂²⋊C₈	—	2	8	no	—
340	C₂⁴	—	2	2	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	—	4	2	no	—
350	C₂⁴	—	4	2	no	—
351	C₂⁴	—	4	2	no	—
352	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
353	C₂⁴	D₈×C₁₃₉	1	4	yes	—
354	C₂⁴	SD₁₆×C₁₃₉	1	4	yes	—
355	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
356	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
357	C₂×D₄	—	2	16	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	16	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	4	32	no	—
364	C₂×D₄	—	4	8	no	—
365	C₂×D₄	—	4	8	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	8	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	complemented
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	16	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	16	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	4	32	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
391	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
392	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
399	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	4	8	no	—
405	C₄⋊C₄	—	2	16	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	complemented
411	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
412	C₂²⋊C₄	—	2	16	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	8	4	no	—
434	C₂³	—	8	4	no	—
435	C₂³	—	8	4	no	—
436	C₂³	—	8	4	no	—
437	C₂³	#102×C₁₃₉	1	16	yes	complemented
438	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
439	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
440	C₂³	#120×C₁₃₉	1	2	yes	—
441	C₂³	#123×C₁₃₉	1	2	yes	—
442	C₂³	C₂×D₈×C₁₃₉	1	4	yes	—
443	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
444	C₂³	C₂×SD₁₆×C₁₃₉	1	4	yes	—
445	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
446	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
447	C₂³	#137×C₁₃₉	1	2	yes	—
448	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
449	D₄	—	2	8	no	—
450	D₄	—	4	32	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	8	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	16	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	4	32	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
469	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
470	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
471	C₂×C₄	#120×C₁₃₉	1	2	yes	—
472	C₂×C₄	#121×C₁₃₉	1	8	yes	—
473	C₂×C₄	#123×C₁₃₉	1	2	yes	—
474	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
478	C₈	—	4	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	32	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	16	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	#386×C₁₃₉	1	4	yes	—
495	C₂²	C₂×#102×C₁₃₉	1	4	yes	—
496	C₂²	C₂×#102×C₁₃₉	1	8	yes	complemented
497	C₂²	#417×C₁₃₉	1	4	yes	—
498	C₂²	#447×C₁₃₉	1	4	yes	—
499	C₂²	#448×C₁₃₉	1	4	yes	—
500	C₂²	#480×C₁₃₉	1	4	yes	—
501	C₂²	#481×C₁₃₉	1	4	yes	—
502	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
503	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
504	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
505	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
506	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
507	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
508	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
509	C₄	—	2	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	8	no	—
512	C₄	#386×C₁₃₉	1	4	yes	—
513	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
514	C₄	C₂×#121×C₁₃₉	1	2	yes	—
515	C₂	—	2	8	no	—
516	C₂	—	8	4	no	—
517	C₂	#1874×C₁₃₉	1	8	yes	direct product factor
518	C₂	C₂×#386×C₁₃₉	1	1	yes	characteristic
519	C₂	C₂²×#102×C₁₃₉	1	1	yes	characteristic
520	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
521	C₂	C₂×#447×C₁₃₉	1	1	yes	characteristic
522	C₂	C₂×#448×C₁₃₉	1	1	yes	characteristic
523	C₂	C₂×#480×C₁₃₉	1	1	yes	characteristic
524	C₂	C₂×#481×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	C₂²×#121×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₁₃₉	C₂	semidirect
3. C₂²×#102×C₁₃₉	C₂	semidirect
4. C₂²×C₂²⋊C₈×C₁₃₉	C₂	semidirect
5. #1874×C₁₃₉	C₂	direct (N × H)
6. C₂×#340×C₁₃₉	C₂	semidirect
14. C₂×#121×C₁₃₉	C₄	semidirect
21. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
24. C₂×#102×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊C₈×C₁₃₉	C₂²	semidirect
27. #340×C₁₃₉	C₂²	semidirect
38. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
60. #121×C₁₃₉	C₂×C₄	semidirect
69. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
70. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
106. C₂×D₄×C₁₃₉	C₂²×C₄	semidirect
147. C₄⋊C₄×C₁₃₉	C₂²×C₄	semidirect
148. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
174. C₂³×C₁₃₉	#102	semidirect
233. C₂²×C₁₃₉	C₂×#102	semidirect
254. C₂×C₁₃₉	#1874	direct (N × H)
262. C₂×#1874	C₁₃₉	direct (N × H)
263. C₁₃₉	C₂×#1874	direct (N × H)
265. C₂³×C₄⋊C₄	C₂×C₁₃₉	semidirect
266. C₂²×#102	C₂×C₁₃₉	semidirect
267. C₂²×C₂²⋊C₈	C₂×C₁₃₉	semidirect
268. #1874	C₂×C₁₃₉	direct (N × H)
269. C₂×#340	C₂×C₁₃₉	semidirect
277. C₂×#121	C₄×C₁₃₉	semidirect
284. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
287. C₂×#102	C₂²×C₁₃₉	semidirect
289. C₂×C₂²⋊C₈	C₂²×C₁₃₉	semidirect
290. #340	C₂²×C₁₃₉	semidirect
301. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
323. #121	C₂×C₄×C₁₃₉	semidirect
332. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
333. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
369. C₂×D₄	C₂²×C₄×C₁₃₉	semidirect
410. C₄⋊C₄	C₂²×C₄×C₁₃₉	semidirect
411. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
437. C₂³	#102×C₁₃₉	semidirect
496. C₂²	C₂×#102×C₁₃₉	semidirect
517. C₂	#1874×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
C₂³×C₄⋊C₄×C₁₃₉	2
C₂²×#102×C₁₃₉	2
C₂²×C₂²⋊C₈×C₁₃₉	2
#1874×C₁₃₉	2
C₂×#340×C₁₃₉	2
C₂×#1874	139

Subgroups — C2×#1874×C139 #48015501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1874×C₁₃₉ #48015501