Subgroups — C₁₃₉×#25449 #48020045

Order 35584.

862 conjugacy classes of subgroups.

The subgroup lattice has 478 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×#474×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2083×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2067×C₁₃₉	C₂	1	2	yes	maximal
7	#1988×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1947×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×C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	#500×C₁₃₉	—	2	4	no	—
19	#474×C₁₃₉	—	2	4	no	—
20	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	#399×C₁₃₉	—	2	2	no	—
30	#391×C₁₃₉	—	2	1	no	—
31	#390×C₁₃₉	C₂²	1	2	yes	—
32	#389×C₁₃₉	C₂²	1	2	yes	—
33	#387×C₁₃₉	—	2	2	no	—
34	#384×C₁₃₉	C₂²	1	2	yes	—
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	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
55	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
56	C₄×Q₈×C₁₃₉	—	4	4	no	—
57	C₄×D₄×C₁₃₉	—	2	2	no	—
58	C₄×D₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
74	C₂×C₄²×C₁₃₉	—	2	2	no	—
75	C₂×C₄²×C₁₃₉	—	2	1	no	—
76	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
78	#107×C₁₃₉	—	2	4	no	—
79	#107×C₁₃₉	—	2	4	no	—
80	#107×C₁₃₉	—	2	4	no	—
81	C₄⋊C₈×C₁₃₉	—	2	4	no	—
82	C₄⋊C₈×C₁₃₉	—	2	2	no	—
83	#102×C₁₃₉	—	2	2	no	—
84	#102×C₁₃₉	—	2	4	no	—
85	#102×C₁₃₉	Q₈	1	4	yes	complemented
86	C₄×C₈×C₁₃₉	—	2	2	no	—
87	#95×C₁₃₉	—	2	1	no	—
88	#95×C₁₃₉	—	2	2	no	—
89	#95×C₁₃₉	—	2	2	no	—
90	#95×C₁₃₉	D₄	1	2	yes	—
91	C₂⁴×C₁₃₉	—	2	1	no	—
92	C₂×Q₈×C₁₃₉	—	2	4	no	—
93	C₂×Q₈×C₁₃₉	—	4	2	no	—
94	C₂×Q₈×C₁₃₉	—	4	2	no	—
95	C₂×Q₈×C₁₃₉	—	4	2	no	—
96	C₂×Q₈×C₁₃₉	—	4	2	no	—
97	C₂×Q₈×C₁₃₉	—	4	2	no	—
98	C₂×D₄×C₁₃₉	—	2	1	no	—
99	C₂×D₄×C₁₃₉	—	2	1	no	—
100	C₂×D₄×C₁₃₉	—	2	1	no	—
101	C₂×D₄×C₁₃₉	—	2	1	no	—
102	C₂×D₄×C₁₃₉	—	2	1	no	—
103	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₃₉	—	2	1	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	1	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	2	1	no	—
109	C₂²×C₄×C₁₃₉	—	4	2	no	—
110	C₂²×C₄×C₁₃₉	—	4	2	no	—
111	C₂²×C₄×C₁₃₉	—	4	2	no	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₃₉	—	2	1	no	—
118	C₂×C₈×C₁₃₉	—	2	1	no	—
119	C₂×C₈×C₁₃₉	—	2	1	no	—
120	C₂×C₈×C₁₃₉	—	2	1	no	—
121	C₂×C₈×C₁₃₉	—	2	2	no	—
122	C₂×C₈×C₁₃₉	—	2	2	no	—
123	C₂×C₈×C₁₃₉	—	2	2	no	—
124	C₂×C₈×C₁₃₉	C₂×Q₈	1	2	yes	—
125	C₂×C₈×C₁₃₉	#41	1	2	yes	—
126	C₄⋊C₄×C₁₃₉	—	2	4	no	—
127	C₄⋊C₄×C₁₃₉	—	2	2	no	—
128	C₄⋊C₄×C₁₃₉	—	2	2	no	—
129	C₄⋊C₄×C₁₃₉	—	2	1	no	—
130	C₄⋊C₄×C₁₃₉	—	2	1	no	—
131	C₄⋊C₄×C₁₃₉	—	2	2	no	—
132	C₄⋊C₄×C₁₃₉	—	2	1	no	—
133	C₄⋊C₄×C₁₃₉	—	2	1	no	—
134	C₄⋊C₄×C₁₃₉	—	2	2	no	—
135	C₄⋊C₄×C₁₃₉	—	2	1	no	—
136	C₄⋊C₄×C₁₃₉	—	4	4	no	—
137	C₄⋊C₄×C₁₃₉	—	4	2	no	—
138	C₄⋊C₄×C₁₃₉	—	4	4	no	—
139	C₄⋊C₄×C₁₃₉	—	4	4	no	—
140	C₄⋊C₄×C₁₃₉	D₈	1	4	yes	—
141	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
143	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
144	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
145	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
146	C₄²×C₁₃₉	—	2	2	no	—
147	C₄²×C₁₃₉	—	2	2	no	—
148	C₄²×C₁₃₉	—	4	4	no	—
149	C₄²×C₁₃₉	—	4	2	no	—
150	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃₉	#41	1	2	yes	—
152	C₂³×C₁₃₉	—	2	2	no	—
153	C₂³×C₁₃₉	—	4	1	no	—
154	C₂³×C₁₃₉	—	4	1	no	—
155	C₂³×C₁₃₉	—	4	1	no	—
156	C₂³×C₁₃₉	—	4	1	no	—
157	C₂³×C₁₃₉	—	4	1	no	—
158	C₂³×C₁₃₉	—	4	1	no	—
159	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₃₉	—	4	8	no	—
161	Q₈×C₁₃₉	—	8	4	no	—
162	D₄×C₁₃₉	—	2	2	no	—
163	D₄×C₁₃₉	—	2	2	no	—
164	D₄×C₁₃₉	—	4	1	no	—
165	D₄×C₁₃₉	—	4	1	no	—
166	C₂×C₄×C₁₃₉	—	2	2	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	1	no	—
169	C₂×C₄×C₁₃₉	—	2	1	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	—	2	2	no	—
172	C₂×C₄×C₁₃₉	—	2	2	no	—
173	C₂×C₄×C₁₃₉	—	2	2	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	4	1	no	—
176	C₂×C₄×C₁₃₉	—	4	2	no	—
177	C₂×C₄×C₁₃₉	—	4	2	no	—
178	C₂×C₄×C₁₃₉	—	4	1	no	—
179	C₂×C₄×C₁₃₉	—	4	1	no	—
180	C₂×C₄×C₁₃₉	—	4	2	no	—
181	C₂×C₄×C₁₃₉	—	4	1	no	—
182	C₂×C₄×C₁₃₉	—	4	1	no	—
183	C₂×C₄×C₁₃₉	—	4	2	no	—
184	C₂×C₄×C₁₃₉	—	4	1	no	—
185	C₂×C₄×C₁₃₉	—	4	2	no	—
186	C₂×C₄×C₁₃₉	—	4	1	no	—
187	C₂×C₄×C₁₃₉	—	4	1	no	—
188	C₂×C₄×C₁₃₉	—	8	4	no	—
189	C₂×C₄×C₁₃₉	#121	1	2	yes	—
190	C₂×C₄×C₁₃₉	#121	1	2	yes	—
191	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
192	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₃₉	—	2	2	no	—
201	C₈×C₁₃₉	—	2	2	no	—
202	C₈×C₁₃₉	—	4	2	no	—
203	C₂²×C₁₃₉	—	4	2	no	—
204	C₂²×C₁₃₉	—	4	2	no	—
205	C₂²×C₁₃₉	—	4	2	no	—
206	C₂²×C₁₃₉	—	8	1	no	—
207	C₂²×C₁₃₉	—	8	1	no	—
208	C₂²×C₁₃₉	—	8	1	no	—
209	C₂²×C₁₃₉	—	8	1	no	—
210	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
211	C₂²×C₁₃₉	#547	1	1	yes	characteristic
212	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
213	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
214	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₁₃₉	#578	1	1	yes	characteristic
216	C₂²×C₁₃₉	#578	1	1	yes	characteristic
217	C₄×C₁₃₉	—	2	4	no	—
218	C₄×C₁₃₉	—	2	2	no	—
219	C₄×C₁₃₉	—	4	2	no	—
220	C₄×C₁₃₉	—	4	2	no	—
221	C₄×C₁₃₉	—	4	4	no	—
222	C₄×C₁₃₉	—	8	1	no	—
223	C₄×C₁₃₉	—	8	1	no	—
224	C₄×C₁₃₉	—	8	2	no	—
225	C₄×C₁₃₉	#459	1	4	yes	—
226	C₄×C₁₃₉	#533	1	1	yes	characteristic
227	C₄×C₁₃₉	#541	1	1	yes	characteristic
228	C₄×C₁₃₉	#548	1	1	yes	characteristic
229	C₄×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
230	C₂×C₁₃₉	—	8	2	no	—
231	C₂×C₁₃₉	#2429	1	1	yes	characteristic
232	C₂×C₁₃₉	C₂×#459	1	1	yes	characteristic
233	C₂×C₁₃₉	#3044	1	1	yes	characteristic
234	C₂×C₁₃₉	#3334	1	1	yes	characteristic
235	C₂×C₁₃₉	#3353	1	1	yes	characteristic
236	C₂×C₁₃₉	Q₈×D₈	1	1	yes	characteristic
237	C₂×C₁₃₉	#3386	1	1	yes	characteristic
238	#25449	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₃₉	#25449	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×#500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	C₂×#474	C₂×C₁₃₉	1	1	yes	characteristic
242	#2542	C₂×C₁₃₉	1	1	yes	characteristic
243	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
244	#2083	C₂×C₁₃₉	1	2	yes	complemented
245	#2067	C₂×C₁₃₉	1	2	yes	—
246	#1988	C₂×C₁₃₉	1	1	yes	characteristic, complemented
247	#1947	C₂×C₁₃₉	1	2	yes	complemented
248	#1939	C₂×C₁₃₉	1	1	yes	characteristic, complemented
249	#1925	C₂×C₁₃₉	1	2	yes	—
250	C₄×#102	C₂×C₁₃₉	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	C₂×C₂²⋊Q₈	—	2	1	no	—
255	C₂×C₄×Q₈	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
257	#500	—	2	4	no	—
258	#474	—	2	4	no	—
259	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
260	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
261	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
262	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
264	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
266	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
268	#399	—	2	2	no	—
269	#391	—	2	1	no	—
270	#390	C₂²×C₁₃₉	1	2	yes	—
271	#389	C₂²×C₁₃₉	1	2	yes	—
272	#387	—	2	2	no	—
273	#384	C₂²×C₁₃₉	1	2	yes	—
274	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
275	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
277	#340	C₂²×C₁₃₉	1	2	yes	—
278	#340	C₂²×C₁₃₉	1	1	yes	characteristic
279	#340	C₂²×C₁₃₉	1	2	yes	—
280	#340	C₂²×C₁₃₉	1	1	yes	characteristic
281	#336	C₂²×C₁₃₉	1	2	yes	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	D₄×C₁₃₉	1	4	yes	—
293	C₂²⋊Q₈	—	4	4	no	—
294	C₂²⋊Q₈	—	4	4	no	—
295	C₄×Q₈	—	4	4	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
317	#107	—	2	4	no	—
318	#107	—	2	4	no	—
319	#107	—	2	4	no	—
320	C₄⋊C₈	—	2	4	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	4	no	—
324	#102	Q₈×C₁₃₉	1	4	yes	complemented
325	C₄×C₈	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	D₄×C₁₃₉	1	2	yes	—
330	C₂⁴	—	2	1	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂×Q₈×C₁₃₉	1	2	yes	—
364	C₂×C₈	#41×C₁₃₉	1	2	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	D₈×C₁₃₉	1	4	yes	—
380	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
381	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	4	4	no	—
388	C₄²	—	4	2	no	—
389	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
390	C₄²	#41×C₁₃₉	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
399	Q₈	—	4	8	no	—
400	Q₈	—	8	4	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	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	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	#121×C₁₃₉	1	2	yes	—
429	C₂×C₄	#121×C₁₃₉	1	2	yes	—
430	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
431	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
432	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
433	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
437	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
450	C₂²	#547×C₁₃₉	1	1	yes	characteristic
451	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
452	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
453	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
454	C₂²	#578×C₁₃₉	1	1	yes	characteristic
455	C₂²	#578×C₁₃₉	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	4	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	1	no	—
464	C₄	#459×C₁₃₉	1	4	yes	—
465	C₄	#533×C₁₃₉	1	1	yes	characteristic
466	C₄	#541×C₁₃₉	1	1	yes	characteristic
467	C₄	#548×C₁₃₉	1	1	yes	characteristic
468	C₄	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
469	C₂	—	8	2	no	—
470	C₂	#2429×C₁₃₉	1	1	yes	characteristic
471	C₂	C₂×#459×C₁₃₉	1	1	yes	characteristic
472	C₂	#3044×C₁₃₉	1	1	yes	characteristic
473	C₂	#3334×C₁₃₉	1	1	yes	characteristic
474	C₂	#3353×C₁₃₉	1	1	yes	characteristic
475	C₂	Q₈×D₈×C₁₃₉	1	1	yes	characteristic
476	C₂	#3386×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. #2365×C₁₃₉	C₂	semidirect
5. #2083×C₁₃₉	C₂	semidirect
7. #1988×C₁₃₉	C₂	semidirect
8. #1947×C₁₃₉	C₂	semidirect
9. #1939×C₁₃₉	C₂	semidirect
85. #102×C₁₃₉	Q₈	semidirect
238. #25449	C₁₃₉	direct (N × H)
239. C₁₃₉	#25449	direct (N × H)
240. C₂×#500	C₂×C₁₃₉	semidirect
243. #2365	C₂×C₁₃₉	semidirect
244. #2083	C₂×C₁₃₉	semidirect
246. #1988	C₂×C₁₃₉	semidirect
247. #1947	C₂×C₁₃₉	semidirect
248. #1939	C₂×C₁₃₉	semidirect
324. #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×#474×C₁₃₉	2
#2542×C₁₃₉	2
#2365×C₁₃₉	2
#2083×C₁₃₉	2
#2067×C₁₃₉	2
#1988×C₁₃₉	2
#1947×C₁₃₉	2
#1939×C₁₃₉	2
#1925×C₁₃₉	2
C₄×#102×C₁₃₉	2
#25449	139

Subgroups — C139×#25449 #48020045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#25449 #48020045