Subgroups — C₁₃₉×#20839 #48015435

Order 35584.

1458 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#1851×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1850×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#1729×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#131×C₁₃₉	—	2	4	no	—
12	C₂×#131×C₁₃₉	—	2	4	no	—
13	C₂×#131×C₁₃₉	—	2	4	no	—
14	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
22	#424×C₁₃₉	—	2	4	no	—
23	#423×C₁₃₉	—	2	4	no	—
24	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
27	#408×C₁₃₉	—	2	4	no	—
28	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
29	#391×C₁₃₉	C₄	1	1	yes	characteristic
30	#391×C₁₃₉	C₄	1	1	yes	characteristic
31	#390×C₁₃₉	C₄	1	1	yes	characteristic
32	#390×C₁₃₉	C₄	1	1	yes	characteristic
33	#386×C₁₃₉	C₄	1	4	yes	—
34	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
35	#336×C₁₃₉	C₂²	1	2	yes	—
36	#336×C₁₃₉	C₂²	1	4	yes	—
37	#336×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#41×C₁₃₉	—	2	2	no	—
39	C₂×#41×C₁₃₉	—	2	2	no	—
40	C₂×#41×C₁₃₉	—	2	2	no	—
41	C₂×#41×C₁₃₉	—	2	2	no	—
42	C₂×#41×C₁₃₉	D₄	1	4	yes	—
43	C₂×#41×C₁₃₉	Q₈	1	4	yes	—
44	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
46	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
50	#131×C₁₃₉	—	2	32	no	—
51	C₂×M₁₆×C₁₃₉	—	2	4	no	—
52	C₂×M₁₆×C₁₃₉	—	2	2	no	—
53	C₂×M₁₆×C₁₃₉	—	2	2	no	—
54	C₂×M₁₆×C₁₃₉	—	2	2	no	—
55	C₂×M₁₆×C₁₃₉	—	2	2	no	—
56	C₂×M₁₆×C₁₃₉	—	2	2	no	—
57	C₂×M₁₆×C₁₃₉	—	2	4	no	—
58	C₂×M₁₆×C₁₃₉	—	2	4	no	—
59	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
60	C₂²×C₈×C₁₃₉	—	2	4	no	—
61	C₂²×C₈×C₁₃₉	—	2	2	no	—
62	C₂²×C₈×C₁₃₉	—	2	2	no	—
63	C₂²×C₈×C₁₃₉	—	2	4	no	—
64	C₂²×C₈×C₁₃₉	—	2	4	no	—
65	C₂²×C₈×C₁₃₉	—	2	2	no	—
66	C₂²×C₈×C₁₃₉	—	2	2	no	—
67	C₂²×C₈×C₁₃₉	—	2	2	no	—
68	C₂²×C₈×C₁₃₉	D₄	1	4	yes	—
69	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
74	#117×C₁₃₉	—	2	2	no	—
75	#117×C₁₃₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
81	C₂×C₄²×C₁₃₉	—	2	2	no	—
82	C₂×C₄²×C₁₃₉	—	2	2	no	—
83	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
87	C₄⋊C₈×C₁₃₉	—	2	8	no	—
88	C₄⋊C₈×C₁₃₉	—	2	4	no	—
89	C₄⋊C₈×C₁₃₉	—	2	4	no	—
90	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
91	#95×C₁₃₉	C₂×C₄	1	4	yes	—
92	#95×C₁₃₉	C₂×C₄	1	4	yes	—
93	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
94	C₂⁴×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
95	#41×C₁₃₉	—	2	8	no	—
96	#41×C₁₃₉	—	2	8	no	—
97	#41×C₁₃₉	—	2	8	no	—
98	#41×C₁₃₉	—	2	8	no	—
99	C₂×Q₈×C₁₃₉	—	2	2	no	—
100	C₂×Q₈×C₁₃₉	—	2	2	no	—
101	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	4	yes	—
102	C₂×D₄×C₁₃₉	—	2	4	no	—
103	C₂×D₄×C₁₃₉	—	2	4	no	—
104	C₂×D₄×C₁₃₉	—	2	2	no	—
105	C₂×D₄×C₁₃₉	—	2	2	no	—
106	C₂×D₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
107	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	2	no	—
110	C₂²×C₄×C₁₃₉	—	2	2	no	—
111	C₂²×C₄×C₁₃₉	—	2	2	no	—
112	C₂²×C₄×C₁₃₉	—	2	4	no	—
113	C₂²×C₄×C₁₃₉	—	2	4	no	—
114	C₂²×C₄×C₁₃₉	—	4	2	no	—
115	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
128	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₃₉	—	2	16	no	—
131	M₁₆×C₁₃₉	—	2	8	no	—
132	M₁₆×C₁₃₉	—	4	4	no	—
133	C₂×C₈×C₁₃₉	—	2	16	no	—
134	C₂×C₈×C₁₃₉	—	2	8	no	—
135	C₂×C₈×C₁₃₉	—	2	1	no	—
136	C₂×C₈×C₁₃₉	—	2	1	no	—
137	C₂×C₈×C₁₃₉	—	2	1	no	—
138	C₂×C₈×C₁₃₉	—	2	2	no	—
139	C₂×C₈×C₁₃₉	—	2	2	no	—
140	C₂×C₈×C₁₃₉	—	2	1	no	—
141	C₂×C₈×C₁₃₉	—	2	2	no	—
142	C₂×C₈×C₁₃₉	—	2	2	no	—
143	C₂×C₈×C₁₃₉	—	2	2	no	—
144	C₂×C₈×C₁₃₉	—	2	2	no	—
145	C₂×C₈×C₁₃₉	—	2	2	no	—
146	C₂×C₈×C₁₃₉	—	2	2	no	—
147	C₂×C₈×C₁₃₉	—	4	4	no	—
148	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₃₉	C₂×D₄	1	4	yes	—
150	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₁₃₉	—	2	2	no	—
152	C₄⋊C₄×C₁₃₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
156	C₄²×C₁₃₉	—	2	2	no	—
157	C₄²×C₁₃₉	—	2	2	no	—
158	C₄²×C₁₃₉	—	2	2	no	—
159	C₄²×C₁₃₉	—	2	2	no	—
160	C₄²×C₁₃₉	—	2	2	no	—
161	C₄²×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	2	no	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	2	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	4	no	—
167	C₂³×C₁₃₉	—	2	4	no	—
168	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
169	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
170	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
171	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
172	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
173	Q₈×C₁₃₉	—	2	8	no	—
174	D₄×C₁₃₉	—	2	16	no	—
175	D₄×C₁₃₉	—	2	8	no	—
176	C₂×C₄×C₁₃₉	—	2	2	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	4	no	—
181	C₂×C₄×C₁₃₉	—	2	4	no	—
182	C₂×C₄×C₁₃₉	—	2	4	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	2	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	2	no	—
190	C₂×C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₄×C₁₃₉	—	4	8	no	—
192	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
193	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₃₉	#120	1	4	yes	—
197	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
198	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
199	C₂×C₄×C₁₃₉	#123	1	4	yes	—
200	C₂×C₄×C₁₃₉	#131	1	4	yes	complemented
201	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
207	C₈×C₁₃₉	—	2	2	no	—
208	C₈×C₁₃₉	—	2	4	no	—
209	C₈×C₁₃₉	—	2	2	no	—
210	C₈×C₁₃₉	—	4	2	no	—
211	C₈×C₁₃₉	—	4	2	no	—
212	C₂²×C₁₃₉	—	2	4	no	—
213	C₂²×C₁₃₉	—	2	2	no	—
214	C₂²×C₁₃₉	—	2	2	no	—
215	C₂²×C₁₃₉	—	2	4	no	—
216	C₂²×C₁₃₉	—	2	8	no	—
217	C₂²×C₁₃₉	—	2	4	no	—
218	C₂²×C₁₃₉	—	4	2	no	—
219	C₂²×C₁₃₉	—	4	2	no	—
220	C₂²×C₁₃₉	—	4	4	no	—
221	C₂²×C₁₃₉	#385	1	4	yes	—
222	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₁₃₉	C₂×#131	1	2	yes	—
226	C₂²×C₁₃₉	#568	1	2	yes	—
227	C₄×C₁₃₉	—	2	4	no	—
228	C₄×C₁₃₉	—	2	4	no	—
229	C₄×C₁₃₉	—	4	2	no	—
230	C₄×C₁₃₉	—	4	2	no	—
231	C₄×C₁₃₉	—	4	2	no	—
232	C₄×C₁₃₉	#385	1	4	yes	—
233	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
234	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
236	C₄×C₁₃₉	C₂×#123	1	1	yes	characteristic
237	C₂×C₁₃₉	—	2	4	no	—
238	C₂×C₁₃₉	—	4	4	no	—
239	C₂×C₁₃₉	C₂×#385	1	1	yes	characteristic
240	C₂×C₁₃₉	#2906	1	2	yes	—
241	C₂×C₁₃₉	#2931	1	1	yes	characteristic
242	C₂×C₁₃₉	#2932	1	1	yes	characteristic
243	C₂×C₁₃₉	#2933	1	2	yes	—
244	#20839	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₁₃₉	#20839	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×#131	C₂×C₁₃₉	1	1	yes	characteristic
247	C₂×#424	C₂×C₁₃₉	1	1	yes	characteristic, complemented
248	C₂×#423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
249	C₂×#408	C₂×C₁₃₉	1	1	yes	characteristic
250	#2297	C₂×C₁₃₉	1	1	yes	characteristic
251	#1851	C₂×C₁₃₉	1	4	yes	complemented
252	#1850	C₂×C₁₃₉	1	4	yes	complemented
253	#1729	C₂×C₁₃₉	1	1	yes	characteristic, complemented
254	C₂×#336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
255	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₂×#131	—	2	4	no	—
257	C₂×#131	—	2	4	no	—
258	C₂×#131	—	2	4	no	—
259	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
260	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₁₃₉	1	2	yes	—
263	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
264	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
266	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
267	#424	—	2	4	no	—
268	#423	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
270	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	—
271	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
272	#408	—	2	4	no	—
273	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
274	#391	C₄×C₁₃₉	1	1	yes	characteristic
275	#391	C₄×C₁₃₉	1	1	yes	characteristic
276	#390	C₄×C₁₃₉	1	1	yes	characteristic
277	#390	C₄×C₁₃₉	1	1	yes	characteristic
278	#386	C₄×C₁₃₉	1	4	yes	—
279	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
280	#336	C₂²×C₁₃₉	1	2	yes	—
281	#336	C₂²×C₁₃₉	1	4	yes	—
282	#336	C₂²×C₁₃₉	1	2	yes	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	D₄×C₁₃₉	1	4	yes	—
288	C₂×#41	Q₈×C₁₃₉	1	4	yes	—
289	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
290	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
291	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×C₁₃₉	1	2	yes	—
293	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
295	#131	—	2	32	no	—
296	C₂×M₁₆	—	2	4	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	4	no	—
303	C₂×M₁₆	—	2	4	no	—
304	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
305	C₂²×C₈	—	2	4	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	4	no	—
309	C₂²×C₈	—	2	4	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	D₄×C₁₃₉	1	4	yes	—
314	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
315	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
316	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
319	#117	—	2	2	no	—
320	#117	—	2	2	no	—
321	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
329	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
332	C₄⋊C₈	—	2	8	no	—
333	C₄⋊C₈	—	2	4	no	—
334	C₄⋊C₈	—	2	4	no	—
335	C₂²⋊C₈	—	2	8	no	—
336	#95	C₂×C₄×C₁₃₉	1	4	yes	—
337	#95	C₂×C₄×C₁₃₉	1	4	yes	—
338	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
339	C₂⁴	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
340	#41	—	2	8	no	—
341	#41	—	2	8	no	—
342	#41	—	2	8	no	—
343	#41	—	2	8	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	4	yes	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
352	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
365	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
370	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
371	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
372	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
373	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
375	M₁₆	—	2	16	no	—
376	M₁₆	—	2	8	no	—
377	M₁₆	—	4	4	no	—
378	C₂×C₈	—	2	16	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₁₃₉	1	4	yes	—
395	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
414	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
415	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
416	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
417	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
418	Q₈	—	2	8	no	—
419	D₄	—	2	16	no	—
420	D₄	—	2	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
438	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
439	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
440	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
441	C₂×C₄	#120×C₁₃₉	1	4	yes	—
442	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
443	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
444	C₂×C₄	#123×C₁₃₉	1	4	yes	—
445	C₂×C₄	#131×C₁₃₉	1	4	yes	complemented
446	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
449	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	4	no	—
454	C₈	—	2	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	#385×C₁₃₉	1	4	yes	—
467	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
468	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
469	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
470	C₂²	C₂×#131×C₁₃₉	1	2	yes	—
471	C₂²	#568×C₁₃₉	1	2	yes	—
472	C₄	—	2	4	no	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	#385×C₁₃₉	1	4	yes	—
478	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
479	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
480	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
481	C₄	C₂×#123×C₁₃₉	1	1	yes	characteristic
482	C₂	—	2	4	no	—
483	C₂	—	4	4	no	—
484	C₂	C₂×#385×C₁₃₉	1	1	yes	characteristic
485	C₂	#2906×C₁₃₉	1	2	yes	—
486	C₂	#2931×C₁₃₉	1	1	yes	characteristic
487	C₂	#2932×C₁₃₉	1	1	yes	characteristic
488	C₂	#2933×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂³×C₁₃₉	C₂³×C₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#424×C₁₃₉	C₂	semidirect
3. C₂×#423×C₁₃₉	C₂	semidirect
6. #1851×C₁₃₉	C₂	semidirect
7. #1850×C₁₃₉	C₂	semidirect
8. #1729×C₁₃₉	C₂	semidirect
9. C₂×#336×C₁₃₉	C₂	semidirect
200. C₂×C₄×C₁₃₉	#131	semidirect
244. #20839	C₁₃₉	direct (N × H)
245. C₁₃₉	#20839	direct (N × H)
247. C₂×#424	C₂×C₁₃₉	semidirect
248. C₂×#423	C₂×C₁₃₉	semidirect
251. #1851	C₂×C₁₃₉	semidirect
252. #1850	C₂×C₁₃₉	semidirect
253. #1729	C₂×C₁₃₉	semidirect
254. C₂×#336	C₂×C₁₃₉	semidirect
445. C₂×C₄	#131×C₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#131×C₁₃₉	2
C₂×#424×C₁₃₉	2
C₂×#423×C₁₃₉	2
C₂×#408×C₁₃₉	2
#2297×C₁₃₉	2
#1851×C₁₃₉	2
#1850×C₁₃₉	2
#1729×C₁₃₉	2
C₂×#336×C₁₃₉	2
#20839	139

Subgroups — C139×#20839 #48015435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20839 #48015435