Subgroups — C₂×#1788×C₁₃₉ #48015192

Order 35584.

4070 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×#102×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂²×C₂²⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1788×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#41×C₁₃₉	—	2	8	no	—
8	C₂²×#41×C₁₃₉	—	2	8	no	—
9	C₂²×#41×C₁₃₉	—	2	4	no	—
10	C₂²×#41×C₁₃₉	—	2	2	no	—
11	C₂²×#41×C₁₃₉	C₄	1	8	yes	complemented
12	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
13	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃₉	—	2	1	no	—
15	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃₉	—	2	1	no	—
17	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
21	C₂×#103×C₁₃₉	—	2	8	no	—
22	C₂×#103×C₁₃₉	C₂²	1	8	yes	complemented
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	#380×C₁₃₉	—	2	2	no	—
28	#380×C₁₃₉	C₂²	1	4	yes	complemented
29	C₂×#95×C₁₃₉	—	2	1	no	—
30	C₂⁵×C₁₃₉	—	2	1	no	—
31	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
32	C₂×#41×C₁₃₉	—	2	32	no	—
33	C₂×#41×C₁₃₉	—	2	64	no	—
34	C₂×#41×C₁₃₉	—	2	32	no	—
35	C₂×#41×C₁₃₉	—	2	16	no	—
36	C₂×#41×C₁₃₉	—	2	32	no	—
37	C₂×#41×C₁₃₉	—	2	16	no	—
38	C₂×#41×C₁₃₉	—	2	16	no	—
39	C₂×#41×C₁₃₉	—	2	8	no	—
40	C₂×#41×C₁₃₉	C₂×C₄	1	16	yes	complemented
41	C₂²×Q₈×C₁₃₉	—	2	2	no	—
42	C₂²×Q₈×C₁₃₉	—	2	4	no	—
43	C₂²×Q₈×C₁₃₉	—	2	1	no	—
44	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
45	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	—
46	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₃₉	—	2	16	no	—
48	C₂²×D₄×C₁₃₉	—	2	8	no	—
49	C₂²×D₄×C₁₃₉	—	2	4	no	—
50	C₂²×D₄×C₁₃₉	—	2	1	no	—
51	C₂²×D₄×C₁₃₉	—	2	4	no	—
52	C₂²×D₄×C₁₃₉	—	2	2	no	—
53	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
54	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
55	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃₉	—	2	16	no	—
57	C₂³×C₄×C₁₃₉	—	2	1	no	—
58	C₂³×C₄×C₁₃₉	—	2	8	no	—
59	C₂³×C₄×C₁₃₉	—	2	4	no	—
60	C₂³×C₄×C₁₃₉	—	2	4	no	—
61	C₂³×C₄×C₁₃₉	—	2	4	no	—
62	C₂³×C₄×C₁₃₉	—	2	2	no	—
63	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
64	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
65	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
67	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃₉	—	2	4	no	—
70	C₂²×C₈×C₁₃₉	—	2	4	no	—
71	C₂²×C₈×C₁₃₉	—	2	4	no	—
72	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
79	#103×C₁₃₉	—	2	16	no	—
80	#102×C₁₃₉	—	2	16	no	—
81	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
82	#95×C₁₃₉	—	2	4	no	—
83	C₂⁴×C₁₃₉	—	2	4	no	—
84	C₂⁴×C₁₃₉	—	2	4	no	—
85	C₂⁴×C₁₃₉	—	2	8	no	—
86	C₂⁴×C₁₃₉	—	2	4	no	—
87	C₂⁴×C₁₃₉	—	2	2	no	—
88	C₂⁴×C₁₃₉	—	2	2	no	—
89	C₂⁴×C₁₃₉	—	2	2	no	—
90	C₂⁴×C₁₃₉	—	4	4	no	—
91	C₂⁴×C₁₃₉	—	4	2	no	—
92	C₂⁴×C₁₃₉	—	4	2	no	—
93	C₂⁴×C₁₃₉	C₂²⋊C₄	1	4	yes	—
94	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
95	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
96	#41×C₁₃₉	—	2	64	no	—
97	#41×C₁₃₉	—	2	128	no	—
98	#41×C₁₃₉	—	2	32	no	—
99	#41×C₁₃₉	—	2	32	no	—
100	C₂×Q₈×C₁₃₉	—	2	4	no	—
101	C₂×Q₈×C₁₃₉	—	2	8	no	—
102	C₂×Q₈×C₁₃₉	—	2	8	no	—
103	C₂×Q₈×C₁₃₉	—	2	16	no	—
104	C₂×Q₈×C₁₃₉	—	2	2	no	—
105	C₂×Q₈×C₁₃₉	—	2	4	no	—
106	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	16	yes	complemented
107	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
108	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
109	C₂×D₄×C₁₃₉	—	2	32	no	—
110	C₂×D₄×C₁₃₉	—	2	64	no	—
111	C₂×D₄×C₁₃₉	—	2	16	no	—
112	C₂×D₄×C₁₃₉	—	2	8	no	—
113	C₂×D₄×C₁₃₉	—	2	4	no	—
114	C₂×D₄×C₁₃₉	—	2	16	no	—
115	C₂×D₄×C₁₃₉	—	2	8	no	—
116	C₂×D₄×C₁₃₉	—	2	4	no	—
117	C₂×D₄×C₁₃₉	—	2	2	no	—
118	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	16	yes	complemented
119	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
120	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₁₃₉	—	2	32	no	—
122	C₂²×C₄×C₁₃₉	—	2	64	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	2	4	no	—
125	C₂²×C₄×C₁₃₉	—	2	8	no	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	16	no	—
128	C₂²×C₄×C₁₃₉	—	2	8	no	—
129	C₂²×C₄×C₁₃₉	—	2	8	no	—
130	C₂²×C₄×C₁₃₉	—	2	8	no	—
131	C₂²×C₄×C₁₃₉	—	2	16	no	—
132	C₂²×C₄×C₁₃₉	—	2	4	no	—
133	C₂²×C₄×C₁₃₉	—	2	4	no	—
134	C₂²×C₄×C₁₃₉	—	2	4	no	—
135	C₂²×C₄×C₁₃₉	—	4	4	no	—
136	C₂²×C₄×C₁₃₉	—	4	4	no	—
137	C₂²×C₄×C₁₃₉	—	4	4	no	—
138	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
139	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
140	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₂×C₈×C₁₃₉	—	2	4	no	—
150	C₂×C₈×C₁₃₉	—	2	4	no	—
151	C₂×C₈×C₁₃₉	—	2	4	no	—
152	C₂×C₈×C₁₃₉	—	4	8	no	—
153	C₄⋊C₄×C₁₃₉	—	2	4	no	—
154	C₄⋊C₄×C₁₃₉	—	2	4	no	—
155	C₄⋊C₄×C₁₃₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
157	C₂³×C₁₃₉	—	2	4	no	—
158	C₂³×C₁₃₉	—	2	4	no	—
159	C₂³×C₁₃₉	—	2	8	no	—
160	C₂³×C₁₃₉	—	2	4	no	—
161	C₂³×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	2	no	—
163	C₂³×C₁₃₉	—	2	8	no	—
164	C₂³×C₁₃₉	—	2	16	no	—
165	C₂³×C₁₃₉	—	2	8	no	—
166	C₂³×C₁₃₉	—	2	8	no	—
167	C₂³×C₁₃₉	—	4	4	no	—
168	C₂³×C₁₃₉	—	4	2	no	—
169	C₂³×C₁₃₉	—	4	2	no	—
170	C₂³×C₁₃₉	—	4	8	no	—
171	C₂³×C₁₃₉	—	4	8	no	—
172	C₂³×C₁₃₉	—	4	8	no	—
173	C₂³×C₁₃₉	—	4	16	no	—
174	C₂³×C₁₃₉	—	4	8	no	—
175	C₂³×C₁₃₉	—	4	16	no	—
176	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂³×C₁₃₉	#120	1	4	yes	—
179	C₂³×C₁₃₉	#135	1	4	yes	—
180	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
181	C₂³×C₁₃₉	#137	1	2	yes	—
182	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₃₉	—	2	4	no	—
184	Q₈×C₁₃₉	—	2	8	no	—
185	Q₈×C₁₃₉	—	2	16	no	—
186	Q₈×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	complemented
187	D₄×C₁₃₉	—	2	64	no	—
188	D₄×C₁₃₉	—	2	4	no	—
189	D₄×C₁₃₉	—	2	8	no	—
190	D₄×C₁₃₉	—	2	16	no	—
191	D₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	complemented
192	C₂×C₄×C₁₃₉	—	2	64	no	—
193	C₂×C₄×C₁₃₉	—	2	4	no	—
194	C₂×C₄×C₁₃₉	—	2	4	no	—
195	C₂×C₄×C₁₃₉	—	2	8	no	—
196	C₂×C₄×C₁₃₉	—	2	8	no	—
197	C₂×C₄×C₁₃₉	—	2	16	no	—
198	C₂×C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₄×C₁₃₉	—	2	4	no	—
200	C₂×C₄×C₁₃₉	—	2	8	no	—
201	C₂×C₄×C₁₃₉	—	2	16	no	—
202	C₂×C₄×C₁₃₉	—	4	4	no	—
203	C₂×C₄×C₁₃₉	—	4	4	no	—
204	C₂×C₄×C₁₃₉	—	4	4	no	—
205	C₂×C₄×C₁₃₉	—	8	8	no	—
206	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
207	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
208	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
209	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₃₉	#120	1	8	yes	—
211	C₂×C₄×C₁₃₉	#120	1	4	yes	—
212	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₁₃₉	—	4	4	no	—
217	C₂²×C₁₃₉	—	2	4	no	—
218	C₂²×C₁₃₉	—	2	4	no	—
219	C₂²×C₁₃₉	—	2	4	no	—
220	C₂²×C₁₃₉	—	2	8	no	—
221	C₂²×C₁₃₉	—	4	4	no	—
222	C₂²×C₁₃₉	—	4	4	no	—
223	C₂²×C₁₃₉	—	4	4	no	—
224	C₂²×C₁₃₉	—	4	8	no	—
225	C₂²×C₁₃₉	—	4	4	no	—
226	C₂²×C₁₃₉	—	4	8	no	—
227	C₂²×C₁₃₉	—	4	16	no	—
228	C₂²×C₁₃₉	—	4	32	no	—
229	C₂²×C₁₃₉	#379	1	4	yes	—
230	C₂²×C₁₃₉	#416	1	4	yes	—
231	C₂²×C₁₃₉	#417	1	4	yes	—
232	C₂²×C₁₃₉	#449	1	8	yes	—
233	C₂²×C₁₃₉	#452	1	8	yes	—
234	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₁₃₉	C₂×#120	1	2	yes	—
236	C₂²×C₁₃₉	C₂×#135	1	2	yes	—
237	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
239	C₄×C₁₃₉	—	2	4	no	—
240	C₄×C₁₃₉	—	2	8	no	—
241	C₄×C₁₃₉	—	8	4	no	—
242	C₄×C₁₃₉	#379	1	4	yes	—
243	C₄×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₄×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₄×C₁₃₉	C₂×#120	1	2	yes	—
246	C₂×C₁₃₉	—	4	4	no	—
247	C₂×C₁₃₉	—	4	8	no	—
248	C₂×C₁₃₉	#1788	1	8	yes	direct product factor
249	C₂×C₁₃₉	C₂×#379	1	1	yes	characteristic
250	C₂×C₁₃₉	C₂×#416	1	1	yes	characteristic
251	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
252	C₂×C₁₃₉	C₂×#449	1	2	yes	—
253	C₂×C₁₃₉	C₂×#452	1	2	yes	—
254	C₂×#1788	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₁₃₉	C₂×#1788	1	1	yes	characteristic, direct product factor, Sylow
256	C₂³×#41	C₂×C₁₃₉	1	1	yes	characteristic
257	C₂²×#103	C₂×C₁₃₉	1	2	yes	complemented
258	C₂²×#102	C₂×C₁₃₉	1	2	yes	complemented
259	C₂²×C₂²⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
260	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic, complemented
261	#1788	C₂×C₁₃₉	1	8	yes	direct product factor
262	C₂²×#41	—	2	8	no	—
263	C₂²×#41	—	2	8	no	—
264	C₂²×#41	—	2	4	no	—
265	C₂²×#41	—	2	2	no	—
266	C₂²×#41	C₄×C₁₃₉	1	8	yes	complemented
267	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
268	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂³×D₄	—	2	1	no	—
270	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
271	C₂⁴×C₄	—	2	1	no	—
272	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
275	C₂²×C₂²⋊C₄	—	2	1	no	—
276	C₂×#103	—	2	8	no	—
277	C₂×#103	C₂²×C₁₃₉	1	8	yes	complemented
278	C₂×#102	—	2	8	no	—
279	C₂×#102	C₂²×C₁₃₉	1	8	yes	complemented
280	C₂×C₂²⋊C₈	—	2	4	no	—
281	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
282	#380	—	2	2	no	—
283	#380	C₂²×C₁₃₉	1	4	yes	complemented
284	C₂×#95	—	2	1	no	—
285	C₂⁵	—	2	1	no	—
286	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
287	C₂×#41	—	2	32	no	—
288	C₂×#41	—	2	64	no	—
289	C₂×#41	—	2	32	no	—
290	C₂×#41	—	2	16	no	—
291	C₂×#41	—	2	32	no	—
292	C₂×#41	—	2	16	no	—
293	C₂×#41	—	2	16	no	—
294	C₂×#41	—	2	8	no	—
295	C₂×#41	C₂×C₄×C₁₃₉	1	16	yes	complemented
296	C₂²×Q₈	—	2	2	no	—
297	C₂²×Q₈	—	2	4	no	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
300	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	—
301	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
302	C₂²×D₄	—	2	16	no	—
303	C₂²×D₄	—	2	8	no	—
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
309	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
310	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
311	C₂³×C₄	—	2	16	no	—
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	8	no	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	2	2	no	—
318	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
319	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
321	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
322	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
324	C₂²×C₈	—	2	4	no	—
325	C₂²×C₈	—	2	4	no	—
326	C₂²×C₈	—	2	4	no	—
327	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
332	C₂×C₂²⋊C₄	—	2	4	no	—
333	C₂×C₂²⋊C₄	—	4	4	no	—
334	#103	—	2	16	no	—
335	#102	—	2	16	no	—
336	C₂²⋊C₈	—	2	8	no	—
337	#95	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	8	no	—
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	4	4	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	C₂²⋊C₄×C₁₃₉	1	4	yes	—
349	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
350	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
351	#41	—	2	64	no	—
352	#41	—	2	128	no	—
353	#41	—	2	32	no	—
354	#41	—	2	32	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	2	8	no	—
357	C₂×Q₈	—	2	8	no	—
358	C₂×Q₈	—	2	16	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	16	yes	complemented
362	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
363	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
364	C₂×D₄	—	2	32	no	—
365	C₂×D₄	—	2	64	no	—
366	C₂×D₄	—	2	16	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	16	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	16	yes	complemented
374	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
375	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
376	C₂²×C₄	—	2	32	no	—
377	C₂²×C₄	—	2	64	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	16	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	16	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
394	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
395	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
396	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
399	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	4	8	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	8	no	—
412	C₂³	—	2	8	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	16	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	16	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	16	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
432	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
433	C₂³	#120×C₁₃₉	1	4	yes	—
434	C₂³	#135×C₁₃₉	1	4	yes	—
435	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
436	C₂³	#137×C₁₃₉	1	2	yes	—
437	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
438	Q₈	—	2	4	no	—
439	Q₈	—	2	8	no	—
440	Q₈	—	2	16	no	—
441	Q₈	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
442	D₄	—	2	64	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	8	no	—
445	D₄	—	2	16	no	—
446	D₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
447	C₂×C₄	—	2	64	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	16	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	16	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	8	8	no	—
461	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
462	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
463	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
464	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
465	C₂×C₄	#120×C₁₃₉	1	8	yes	—
466	C₂×C₄	#120×C₁₃₉	1	4	yes	—
467	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
471	C₈	—	4	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	4	16	no	—
477	C₂²	—	4	32	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	8	no	—
484	C₂²	#379×C₁₃₉	1	4	yes	—
485	C₂²	#416×C₁₃₉	1	4	yes	—
486	C₂²	#417×C₁₃₉	1	4	yes	—
487	C₂²	#449×C₁₃₉	1	8	yes	—
488	C₂²	#452×C₁₃₉	1	8	yes	—
489	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
490	C₂²	C₂×#120×C₁₃₉	1	2	yes	—
491	C₂²	C₂×#135×C₁₃₉	1	2	yes	—
492	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
493	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
494	C₄	—	2	4	no	—
495	C₄	—	2	8	no	—
496	C₄	—	8	4	no	—
497	C₄	#379×C₁₃₉	1	4	yes	—
498	C₄	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
499	C₄	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
500	C₄	C₂×#120×C₁₃₉	1	2	yes	—
501	C₂	—	4	4	no	—
502	C₂	—	4	8	no	—
503	C₂	#1788×C₁₃₉	1	8	yes	direct product factor
504	C₂	C₂×#379×C₁₃₉	1	1	yes	characteristic
505	C₂	C₂×#416×C₁₃₉	1	1	yes	characteristic
506	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
507	C₂	C₂×#449×C₁₃₉	1	2	yes	—
508	C₂	C₂×#452×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×#41×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. C₂²×#103×C₁₃₉	C₂	semidirect
3. C₂²×#102×C₁₃₉	C₂	semidirect
4. C₂²×C₂²⋊C₈×C₁₃₉	C₂	semidirect
5. C₂×#380×C₁₃₉	C₂	semidirect
6. #1788×C₁₃₉	C₂	direct (N × H)
11. C₂²×#41×C₁₃₉	C₄	semidirect
22. C₂×#103×C₁₃₉	C₂²	semidirect
24. C₂×#102×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊C₈×C₁₃₉	C₂²	semidirect
28. #380×C₁₃₉	C₂²	semidirect
40. C₂×#41×C₁₃₉	C₂×C₄	semidirect
106. C₂×Q₈×C₁₃₉	C₂²⋊C₄	semidirect
118. C₂×D₄×C₁₃₉	C₂²⋊C₄	semidirect
186. Q₈×C₁₃₉	C₂×C₂²⋊C₄	semidirect
191. D₄×C₁₃₉	C₂×C₂²⋊C₄	semidirect
248. C₂×C₁₃₉	#1788	direct (N × H)
254. C₂×#1788	C₁₃₉	direct (N × H)
255. C₁₃₉	C₂×#1788	direct (N × H)
257. C₂²×#103	C₂×C₁₃₉	semidirect
258. C₂²×#102	C₂×C₁₃₉	semidirect
259. C₂²×C₂²⋊C₈	C₂×C₁₃₉	semidirect
260. C₂×#380	C₂×C₁₃₉	semidirect
261. #1788	C₂×C₁₃₉	direct (N × H)
266. C₂²×#41	C₄×C₁₃₉	semidirect
277. C₂×#103	C₂²×C₁₃₉	semidirect
279. C₂×#102	C₂²×C₁₃₉	semidirect
281. C₂×C₂²⋊C₈	C₂²×C₁₃₉	semidirect
283. #380	C₂²×C₁₃₉	semidirect
295. C₂×#41	C₂×C₄×C₁₃₉	semidirect
361. C₂×Q₈	C₂²⋊C₄×C₁₃₉	semidirect
373. C₂×D₄	C₂²⋊C₄×C₁₃₉	semidirect
441. Q₈	C₂×C₂²⋊C₄×C₁₃₉	semidirect
446. D₄	C₂×C₂²⋊C₄×C₁₃₉	semidirect
503. C₂	#1788×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
C₂³×#41×C₁₃₉	2
C₂²×#103×C₁₃₉	2
C₂²×#102×C₁₃₉	2
C₂²×C₂²⋊C₈×C₁₃₉	2
C₂×#380×C₁₃₉	2
#1788×C₁₃₉	2
C₂×#1788	139

Subgroups — C2×#1788×C139 #48015192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1788×C₁₃₉ #48015192