Subgroups — C₁₃₉×#25450 #48020046

Order 35584.

778 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2085×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2067×C₁₃₉	C₂	1	2	yes	maximal
7	#1987×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1949×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1939×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#1925×C₁₃₉	C₂	1	2	yes	maximal
11	C₄×#102×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	#500×C₁₃₉	—	2	4	no	—
16	#476×C₁₃₉	—	2	4	no	—
17	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	#393×C₁₃₉	—	2	2	no	—
27	#391×C₁₃₉	—	2	2	no	—
28	#390×C₁₃₉	C₂²	1	2	yes	—
29	#389×C₁₃₉	—	2	1	no	—
30	#389×C₁₃₉	C₂²	1	2	yes	—
31	#382×C₁₃₉	C₂²	1	2	yes	—
32	#380×C₁₃₉	—	2	1	no	—
33	#380×C₁₃₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	#340×C₁₃₉	C₂²	1	1	yes	characteristic
39	#340×C₁₃₉	C₂²	1	1	yes	characteristic
40	#340×C₁₃₉	C₂²	1	2	yes	—
41	#340×C₁₃₉	C₂²	1	2	yes	—
42	#336×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₉	—	2	1	no	—
44	C₂²×Q₈×C₁₃₉	—	2	1	no	—
45	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₉	—	2	1	no	—
47	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
51	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
52	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₉	D₄	1	4	yes	—
54	C₄×D₄×C₁₃₉	—	2	2	no	—
55	C₄×D₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₄²×C₁₃₉	—	2	1	no	—
70	C₂×C₄²×C₁₃₉	—	2	2	no	—
71	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
73	#107×C₁₃₉	—	2	4	no	—
74	#107×C₁₃₉	—	2	4	no	—
75	#106×C₁₃₉	—	2	4	no	—
76	C₄⋊C₈×C₁₃₉	—	2	4	no	—
77	C₄⋊C₈×C₁₃₉	—	2	2	no	—
78	#102×C₁₃₉	—	2	2	no	—
79	#102×C₁₃₉	—	2	4	no	—
80	#102×C₁₃₉	Q₈	1	4	yes	complemented
81	C₄×C₈×C₁₃₉	—	2	2	no	—
82	#95×C₁₃₉	—	2	2	no	—
83	#95×C₁₃₉	—	2	2	no	—
84	#95×C₁₃₉	—	2	1	no	—
85	#95×C₁₃₉	—	2	2	no	—
86	#95×C₁₃₉	—	2	2	no	—
87	#95×C₁₃₉	D₄	1	2	yes	—
88	C₂⁴×C₁₃₉	—	2	1	no	—
89	C₂×Q₈×C₁₃₉	—	2	4	no	—
90	C₂×Q₈×C₁₃₉	—	4	2	no	—
91	C₂×Q₈×C₁₃₉	—	8	1	no	—
92	C₂×Q₈×C₁₃₉	—	8	1	no	—
93	C₂×Q₈×C₁₃₉	—	8	1	no	—
94	C₂×Q₈×C₁₃₉	—	8	1	no	—
95	C₂×D₄×C₁₃₉	—	2	1	no	—
96	C₂×D₄×C₁₃₉	—	2	1	no	—
97	C₂×D₄×C₁₃₉	—	2	1	no	—
98	C₂×D₄×C₁₃₉	—	2	1	no	—
99	C₂×D₄×C₁₃₉	—	2	1	no	—
100	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	2	2	no	—
103	C₂²×C₄×C₁₃₉	—	2	1	no	—
104	C₂²×C₄×C₁₃₉	—	2	1	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	4	2	no	—
107	C₂²×C₄×C₁₃₉	—	4	2	no	—
108	C₂²×C₄×C₁₃₉	—	4	2	no	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₁₃₉	—	2	1	no	—
115	C₂×C₈×C₁₃₉	—	2	1	no	—
116	C₂×C₈×C₁₃₉	—	2	1	no	—
117	C₂×C₈×C₁₃₉	—	2	1	no	—
118	C₂×C₈×C₁₃₉	—	2	2	no	—
119	C₂×C₈×C₁₃₉	—	2	2	no	—
120	C₂×C₈×C₁₃₉	—	2	2	no	—
121	C₂×C₈×C₁₃₉	C₂×Q₈	1	2	yes	—
122	C₂×C₈×C₁₃₉	#41	1	2	yes	—
123	C₄⋊C₄×C₁₃₉	—	2	4	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	2	2	no	—
126	C₄⋊C₄×C₁₃₉	—	2	2	no	—
127	C₄⋊C₄×C₁₃₉	—	2	1	no	—
128	C₄⋊C₄×C₁₃₉	—	2	1	no	—
129	C₄⋊C₄×C₁₃₉	—	2	2	no	—
130	C₄⋊C₄×C₁₃₉	—	2	1	no	—
131	C₄⋊C₄×C₁₃₉	—	2	1	no	—
132	C₄⋊C₄×C₁₃₉	—	2	2	no	—
133	C₄⋊C₄×C₁₃₉	—	2	1	no	—
134	C₄⋊C₄×C₁₃₉	—	4	2	no	—
135	C₄⋊C₄×C₁₃₉	—	8	2	no	—
136	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
138	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
140	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
141	C₄²×C₁₃₉	—	2	2	no	—
142	C₄²×C₁₃₉	—	2	2	no	—
143	C₄²×C₁₃₉	—	4	2	no	—
144	C₄²×C₁₃₉	—	8	2	no	—
145	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃₉	#41	1	2	yes	—
147	C₂³×C₁₃₉	—	2	2	no	—
148	C₂³×C₁₃₉	—	4	1	no	—
149	C₂³×C₁₃₉	—	4	1	no	—
150	C₂³×C₁₃₉	—	4	1	no	—
151	C₂³×C₁₃₉	—	4	1	no	—
152	C₂³×C₁₃₉	—	4	1	no	—
153	C₂³×C₁₃₉	—	4	1	no	—
154	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃₉	—	8	4	no	—
156	Q₈×C₁₃₉	—	8	4	no	—
157	D₄×C₁₃₉	—	2	2	no	—
158	D₄×C₁₃₉	—	2	2	no	—
159	D₄×C₁₃₉	—	4	1	no	—
160	D₄×C₁₃₉	—	4	1	no	—
161	C₂×C₄×C₁₃₉	—	2	1	no	—
162	C₂×C₄×C₁₃₉	—	2	1	no	—
163	C₂×C₄×C₁₃₉	—	2	4	no	—
164	C₂×C₄×C₁₃₉	—	2	2	no	—
165	C₂×C₄×C₁₃₉	—	2	2	no	—
166	C₂×C₄×C₁₃₉	—	2	2	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	2	no	—
171	C₂×C₄×C₁₃₉	—	4	1	no	—
172	C₂×C₄×C₁₃₉	—	4	1	no	—
173	C₂×C₄×C₁₃₉	—	4	2	no	—
174	C₂×C₄×C₁₃₉	—	4	2	no	—
175	C₂×C₄×C₁₃₉	—	4	1	no	—
176	C₂×C₄×C₁₃₉	—	4	2	no	—
177	C₂×C₄×C₁₃₉	—	4	1	no	—
178	C₂×C₄×C₁₃₉	—	4	1	no	—
179	C₂×C₄×C₁₃₉	—	4	1	no	—
180	C₂×C₄×C₁₃₉	—	4	1	no	—
181	C₂×C₄×C₁₃₉	—	4	2	no	—
182	C₂×C₄×C₁₃₉	—	4	2	no	—
183	C₂×C₄×C₁₃₉	—	4	1	no	—
184	C₂×C₄×C₁₃₉	—	8	4	no	—
185	C₂×C₄×C₁₃₉	#121	1	2	yes	—
186	C₂×C₄×C₁₃₉	#121	1	2	yes	—
187	C₂×C₄×C₁₃₉	#135	1	2	yes	—
188	C₂×C₄×C₁₃₉	#137	1	2	yes	—
189	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₁₃₉	—	2	2	no	—
196	C₈×C₁₃₉	—	2	2	no	—
197	C₈×C₁₃₉	—	4	2	no	—
198	C₂²×C₁₃₉	—	4	2	no	—
199	C₂²×C₁₃₉	—	4	2	no	—
200	C₂²×C₁₃₉	—	4	2	no	—
201	C₂²×C₁₃₉	—	8	1	no	—
202	C₂²×C₁₃₉	—	8	1	no	—
203	C₂²×C₁₃₉	—	8	1	no	—
204	C₂²×C₁₃₉	—	8	1	no	—
205	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
206	C₂²×C₁₃₉	#547	1	1	yes	characteristic
207	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
208	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
209	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
210	C₂²×C₁₃₉	#576	1	1	yes	characteristic
211	C₂²×C₁₃₉	#576	1	1	yes	characteristic
212	C₄×C₁₃₉	—	2	2	no	—
213	C₄×C₁₃₉	—	4	2	no	—
214	C₄×C₁₃₉	—	4	2	no	—
215	C₄×C₁₃₉	—	4	2	no	—
216	C₄×C₁₃₉	—	4	4	no	—
217	C₄×C₁₃₉	—	8	1	no	—
218	C₄×C₁₃₉	—	8	1	no	—
219	C₄×C₁₃₉	—	8	2	no	—
220	C₄×C₁₃₉	#464	1	4	yes	—
221	C₄×C₁₃₉	#533	1	1	yes	characteristic
222	C₄×C₁₃₉	#541	1	1	yes	characteristic
223	C₄×C₁₃₉	#548	1	1	yes	characteristic
224	C₄×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
225	C₂×C₁₃₉	—	8	2	no	—
226	C₂×C₁₃₉	#2429	1	1	yes	characteristic
227	C₂×C₁₃₉	C₂×#464	1	1	yes	characteristic
228	C₂×C₁₃₉	#3041	1	1	yes	characteristic
229	C₂×C₁₃₉	#3341	1	1	yes	characteristic
230	C₂×C₁₃₉	#3357	1	1	yes	characteristic
231	C₂×C₁₃₉	#3380	1	1	yes	characteristic
232	C₂×C₁₃₉	#3385	1	1	yes	characteristic
233	#25450	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₁₃₉	#25450	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×#500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
236	C₂×#476	C₂×C₁₃₉	1	1	yes	characteristic
237	#2563	C₂×C₁₃₉	1	1	yes	characteristic
238	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
239	#2085	C₂×C₁₃₉	1	2	yes	complemented
240	#2067	C₂×C₁₃₉	1	2	yes	—
241	#1987	C₂×C₁₃₉	1	1	yes	characteristic, complemented
242	#1949	C₂×C₁₃₉	1	2	yes	complemented
243	#1939	C₂×C₁₃₉	1	1	yes	characteristic, complemented
244	#1925	C₂×C₁₃₉	1	2	yes	—
245	C₄×#102	C₂×C₁₃₉	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
249	#500	—	2	4	no	—
250	#476	—	2	4	no	—
251	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
252	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
253	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
258	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
260	#393	—	2	2	no	—
261	#391	—	2	2	no	—
262	#390	C₂²×C₁₃₉	1	2	yes	—
263	#389	—	2	1	no	—
264	#389	C₂²×C₁₃₉	1	2	yes	—
265	#382	C₂²×C₁₃₉	1	2	yes	—
266	#380	—	2	1	no	—
267	#380	—	2	1	no	—
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
270	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
272	#340	C₂²×C₁₃₉	1	2	yes	—
273	#340	C₂²×C₁₃₉	1	1	yes	characteristic
274	#340	C₂²×C₁₃₉	1	2	yes	—
275	#340	C₂²×C₁₃₉	1	1	yes	characteristic
276	#336	C₂²×C₁₃₉	1	2	yes	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	D₄×C₁₃₉	1	4	yes	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
307	#107	—	2	4	no	—
308	#107	—	2	4	no	—
309	#106	—	2	4	no	—
310	C₄⋊C₈	—	2	4	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	4	no	—
314	#102	Q₈×C₁₃₉	1	4	yes	complemented
315	C₄×C₈	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	D₄×C₁₃₉	1	2	yes	—
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	8	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	—	8	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂×Q₈×C₁₃₉	1	2	yes	—
356	C₂×C₈	#41×C₁₃₉	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
371	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	8	2	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	8	2	no	—
379	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
380	C₄²	#41×C₁₃₉	1	2	yes	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
389	Q₈	—	8	4	no	—
390	Q₈	—	8	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	#121×C₁₃₉	1	2	yes	—
420	C₂×C₄	#121×C₁₃₉	1	2	yes	—
421	C₂×C₄	#135×C₁₃₉	1	2	yes	—
422	C₂×C₄	#137×C₁₃₉	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	2	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
440	C₂²	#547×C₁₃₉	1	1	yes	characteristic
441	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
442	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
443	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
444	C₂²	#576×C₁₃₉	1	1	yes	characteristic
445	C₂²	#576×C₁₃₉	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	#464×C₁₃₉	1	4	yes	—
455	C₄	#533×C₁₃₉	1	1	yes	characteristic
456	C₄	#541×C₁₃₉	1	1	yes	characteristic
457	C₄	#548×C₁₃₉	1	1	yes	characteristic
458	C₄	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	#2429×C₁₃₉	1	1	yes	characteristic
461	C₂	C₂×#464×C₁₃₉	1	1	yes	characteristic
462	C₂	#3041×C₁₃₉	1	1	yes	characteristic
463	C₂	#3341×C₁₃₉	1	1	yes	characteristic
464	C₂	#3357×C₁₃₉	1	1	yes	characteristic
465	C₂	#3380×C₁₃₉	1	1	yes	characteristic
466	C₂	#3385×C₁₃₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#500×C₁₃₉	C₂	semidirect
4. #2369×C₁₃₉	C₂	semidirect
5. #2085×C₁₃₉	C₂	semidirect
7. #1987×C₁₃₉	C₂	semidirect
8. #1949×C₁₃₉	C₂	semidirect
9. #1939×C₁₃₉	C₂	semidirect
80. #102×C₁₃₉	Q₈	semidirect
233. #25450	C₁₃₉	direct (N × H)
234. C₁₃₉	#25450	direct (N × H)
235. C₂×#500	C₂×C₁₃₉	semidirect
238. #2369	C₂×C₁₃₉	semidirect
239. #2085	C₂×C₁₃₉	semidirect
241. #1987	C₂×C₁₃₉	semidirect
242. #1949	C₂×C₁₃₉	semidirect
243. #1939	C₂×C₁₃₉	semidirect
314. #102	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#500×C₁₃₉	2
C₂×#476×C₁₃₉	2
#2563×C₁₃₉	2
#2369×C₁₃₉	2
#2085×C₁₃₉	2
#2067×C₁₃₉	2
#1987×C₁₃₉	2
#1949×C₁₃₉	2
#1939×C₁₃₉	2
#1925×C₁₃₉	2
C₄×#102×C₁₃₉	2
#25450	139

Subgroups — C139×#25450 #48020046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#25450 #48020046