Subgroups — C₁₃₉×#21872 #48016468

Order 35584.

1150 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2317×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1992×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1991×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1961×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1957×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1875×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1874×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1804×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#1802×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#540×C₁₃₉	—	2	4	no	—
13	#540×C₁₃₉	C₄	1	8	yes	complemented
14	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₁₃₉	—	2	2	no	—
17	C₂×#121×C₁₃₉	—	2	2	no	—
18	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	#433×C₁₃₉	—	2	4	no	—
24	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	#389×C₁₃₉	—	2	2	no	—
33	#385×C₁₃₉	—	2	2	no	—
34	#384×C₁₃₉	C₂²	1	1	yes	characteristic
35	#384×C₁₃₉	C₂²	1	1	yes	characteristic
36	#382×C₁₃₉	C₂²	1	1	yes	characteristic
37	#382×C₁₃₉	C₂²	1	1	yes	characteristic
38	#340×C₁₃₉	C₂²	1	2	yes	—
39	#340×C₁₃₉	C₂²	1	2	yes	—
40	#340×C₁₃₉	C₂²	1	2	yes	—
41	#340×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃₉	—	2	2	no	—
43	C₂²×D₄×C₁₃₉	—	2	2	no	—
44	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃₉	—	2	2	no	—
46	C₂³×C₄×C₁₃₉	—	2	1	no	—
47	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
50	#127×C₁₃₉	—	2	2	no	—
51	#127×C₁₃₉	C₂×C₄	1	4	yes	complemented
52	#125×C₁₃₉	—	2	2	no	—
53	#125×C₁₃₉	C₂×C₄	1	4	yes	complemented
54	#123×C₁₃₉	—	2	16	no	—
55	#121×C₁₃₉	—	2	4	no	—
56	#121×C₁₃₉	—	2	16	no	—
57	#121×C₁₃₉	C₂×C₄	1	8	yes	—
58	C₄×D₄×C₁₃₉	—	2	4	no	—
59	C₄×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
60	#117×C₁₃₉	—	4	2	no	—
61	#117×C₁₃₉	C₂×C₄	1	4	yes	—
62	#117×C₁₃₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
78	C₂×C₄²×C₁₃₉	—	2	1	no	—
79	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₁₃₉	—	2	4	no	—
82	#102×C₁₃₉	—	4	2	no	—
83	#102×C₁₃₉	—	4	2	no	—
84	#102×C₁₃₉	—	4	2	no	—
85	#102×C₁₃₉	—	4	2	no	—
86	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
87	#97×C₁₃₉	—	2	2	no	—
88	C₄×C₈×C₁₃₉	—	2	2	no	—
89	#95×C₁₃₉	—	2	2	no	—
90	#95×C₁₃₉	—	2	2	no	—
91	C₂⁴×C₁₃₉	—	2	2	no	—
92	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₁₃₉	—	2	8	no	—
94	C₂×D₄×C₁₃₉	—	2	8	no	—
95	C₂×D₄×C₁₃₉	—	2	2	no	—
96	C₂×D₄×C₁₃₉	—	2	2	no	—
97	C₂×D₄×C₁₃₉	—	2	2	no	—
98	C₂×D₄×C₁₃₉	—	2	2	no	—
99	C₂×D₄×C₁₃₉	—	2	2	no	—
100	C₂×D₄×C₁₃₉	—	8	2	no	—
101	C₂×D₄×C₁₃₉	—	8	2	no	—
102	C₂×D₄×C₁₃₉	—	8	2	no	—
103	C₂×D₄×C₁₃₉	—	8	2	no	—
104	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	2	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	2	8	no	—
109	C₂²×C₄×C₁₃₉	—	2	1	no	—
110	C₂²×C₄×C₁₃₉	—	2	1	no	—
111	C₂²×C₄×C₁₃₉	—	2	1	no	—
112	C₂²×C₄×C₁₃₉	—	2	1	no	—
113	C₂²×C₄×C₁₃₉	—	4	2	no	—
114	C₂²×C₄×C₁₃₉	—	8	2	no	—
115	C₂²×C₄×C₁₃₉	—	8	2	no	—
116	C₂²×C₄×C₁₃₉	—	8	2	no	—
117	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₃₉	—	2	2	no	—
124	C₂×C₈×C₁₃₉	—	2	2	no	—
125	C₂×C₈×C₁₃₉	—	2	2	no	—
126	C₂×C₈×C₁₃₉	—	2	2	no	—
127	C₂×C₈×C₁₃₉	—	2	2	no	—
128	C₂×C₈×C₁₃₉	—	2	2	no	—
129	C₄⋊C₄×C₁₃₉	—	2	8	no	—
130	C₄⋊C₄×C₁₃₉	—	2	2	no	—
131	C₄⋊C₄×C₁₃₉	—	2	2	no	—
132	C₄⋊C₄×C₁₃₉	—	2	2	no	—
133	C₄⋊C₄×C₁₃₉	—	2	2	no	—
134	C₄⋊C₄×C₁₃₉	—	2	2	no	—
135	C₄⋊C₄×C₁₃₉	—	4	2	no	—
136	C₄⋊C₄×C₁₃₉	—	8	2	no	—
137	C₄⋊C₄×C₁₃₉	—	8	2	no	—
138	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
139	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
141	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
142	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
143	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
144	C₄²×C₁₃₉	—	4	2	no	—
145	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
149	C₂³×C₁₃₉	—	2	1	no	—
150	C₂³×C₁₃₉	—	2	1	no	—
151	C₂³×C₁₃₉	—	2	2	no	—
152	C₂³×C₁₃₉	—	2	2	no	—
153	C₂³×C₁₃₉	—	2	4	no	—
154	C₂³×C₁₃₉	—	4	2	no	—
155	C₂³×C₁₃₉	—	4	2	no	—
156	C₂³×C₁₃₉	—	4	2	no	—
157	C₂³×C₁₃₉	—	4	2	no	—
158	C₂³×C₁₃₉	—	4	2	no	—
159	C₂³×C₁₃₉	—	4	2	no	—
160	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₁₃₉	—	2	4	no	—
163	D₄×C₁₃₉	—	2	4	no	—
164	D₄×C₁₃₉	—	4	2	no	—
165	D₄×C₁₃₉	—	4	2	no	—
166	D₄×C₁₃₉	—	8	8	no	—
167	D₄×C₁₃₉	—	8	8	no	—
168	C₂×C₄×C₁₃₉	—	2	1	no	—
169	C₂×C₄×C₁₃₉	—	2	1	no	—
170	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
175	C₂×C₄×C₁₃₉	—	2	4	no	—
176	C₂×C₄×C₁₃₉	—	2	4	no	—
177	C₂×C₄×C₁₃₉	—	4	2	no	—
178	C₂×C₄×C₁₃₉	—	4	2	no	—
179	C₂×C₄×C₁₃₉	—	4	1	no	—
180	C₂×C₄×C₁₃₉	—	4	1	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	2	no	—
185	C₂×C₄×C₁₃₉	—	4	2	no	—
186	C₂×C₄×C₁₃₉	—	4	2	no	—
187	C₂×C₄×C₁₃₉	—	8	8	no	—
188	C₂×C₄×C₁₃₉	—	8	4	no	—
189	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
190	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₁₃₉	—	4	2	no	—
197	C₈×C₁₃₉	—	4	2	no	—
198	C₂²×C₁₃₉	—	2	2	no	—
199	C₂²×C₁₃₉	—	2	4	no	—
200	C₂²×C₁₃₉	—	4	1	no	—
201	C₂²×C₁₃₉	—	4	1	no	—
202	C₂²×C₁₃₉	—	4	2	no	—
203	C₂²×C₁₃₉	—	4	4	no	—
204	C₂²×C₁₃₉	—	4	4	no	—
205	C₂²×C₁₃₉	—	4	4	no	—
206	C₂²×C₁₃₉	—	8	2	no	—
207	C₂²×C₁₃₉	—	8	2	no	—
208	C₂²×C₁₃₉	—	8	2	no	—
209	C₂²×C₁₃₉	—	8	2	no	—
210	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₃₉	#535	1	1	yes	characteristic
212	C₂²×C₁₃₉	#536	1	1	yes	characteristic
213	C₂²×C₁₃₉	#576	1	2	yes	—
214	C₂²×C₁₃₉	#577	1	2	yes	—
215	C₄×C₁₃₉	—	2	2	no	—
216	C₄×C₁₃₉	—	2	4	no	—
217	C₄×C₁₃₉	—	2	4	no	—
218	C₄×C₁₃₉	—	4	4	no	—
219	C₄×C₁₃₉	—	8	1	no	—
220	C₄×C₁₃₉	—	8	1	no	—
221	C₄×C₁₃₉	—	8	1	no	—
222	C₄×C₁₃₉	—	8	1	no	—
223	C₄×C₁₃₉	#520	1	2	yes	—
224	C₄×C₁₃₉	#537	1	2	yes	—
225	C₂×C₁₃₉	—	4	2	no	—
226	C₂×C₁₃₉	—	8	4	no	—
227	C₂×C₁₃₉	#2311	1	1	yes	characteristic
228	C₂×C₁₃₉	#2897	1	2	yes	—
229	C₂×C₁₃₉	#3220	1	1	yes	characteristic
230	C₂×C₁₃₉	#3221	1	1	yes	characteristic
231	C₂×C₁₃₉	#3241	1	2	yes	—
232	#21872	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₁₃₉	#21872	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×#540	C₂×C₁₃₉	1	1	yes	characteristic
235	C₂×#433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
236	#2317	C₂×C₁₃₉	1	1	yes	characteristic, complemented
237	#1992	C₂×C₁₃₉	1	1	yes	characteristic, complemented
238	#1991	C₂×C₁₃₉	1	1	yes	characteristic, complemented
239	#1961	C₂×C₁₃₉	1	1	yes	characteristic, complemented
240	#1957	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	#1875	C₂×C₁₃₉	1	2	yes	complemented
242	#1874	C₂×C₁₃₉	1	2	yes	complemented
243	#1804	C₂×C₁₃₉	1	2	yes	complemented
244	#1802	C₂×C₁₃₉	1	2	yes	complemented
245	#540	—	2	4	no	—
246	#540	C₄×C₁₃₉	1	8	yes	complemented
247	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
248	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
249	C₂×#123	—	2	2	no	—
250	C₂×#121	—	2	2	no	—
251	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
252	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
253	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
254	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
256	#433	—	2	4	no	—
257	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
258	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
259	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
260	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
261	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
263	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
265	#389	—	2	2	no	—
266	#385	—	2	2	no	—
267	#384	C₂²×C₁₃₉	1	1	yes	characteristic
268	#384	C₂²×C₁₃₉	1	1	yes	characteristic
269	#382	C₂²×C₁₃₉	1	1	yes	characteristic
270	#382	C₂²×C₁₃₉	1	1	yes	characteristic
271	#340	C₂²×C₁₃₉	1	2	yes	—
272	#340	C₂²×C₁₃₉	1	2	yes	—
273	#340	C₂²×C₁₃₉	1	2	yes	—
274	#340	C₂²×C₁₃₉	1	2	yes	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
283	#127	—	2	2	no	—
284	#127	C₂×C₄×C₁₃₉	1	4	yes	complemented
285	#125	—	2	2	no	—
286	#125	C₂×C₄×C₁₃₉	1	4	yes	complemented
287	#123	—	2	16	no	—
288	#121	—	2	4	no	—
289	#121	—	2	16	no	—
290	#121	C₂×C₄×C₁₃₉	1	8	yes	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
293	#117	—	4	2	no	—
294	#117	C₂×C₄×C₁₃₉	1	4	yes	—
295	#117	D₄×C₁₃₉	1	4	yes	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	4	2	no	—
301	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×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×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
314	C₄⋊C₈	—	2	4	no	—
315	#102	—	4	2	no	—
316	#102	—	4	2	no	—
317	#102	—	4	2	no	—
318	#102	—	4	2	no	—
319	C₂²⋊C₈	—	2	4	no	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂×D₄	—	8	2	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂×D₄	—	8	2	no	—
337	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	—	8	2	no	—
350	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	—	8	2	no	—
371	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
372	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
379	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
380	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
381	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	8	8	no	—
400	D₄	—	8	8	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	8	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
424	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
425	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
428	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
444	C₂²	#535×C₁₃₉	1	1	yes	characteristic
445	C₂²	#536×C₁₃₉	1	1	yes	characteristic
446	C₂²	#576×C₁₃₉	1	2	yes	—
447	C₂²	#577×C₁₃₉	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	#520×C₁₃₉	1	2	yes	—
457	C₄	#537×C₁₃₉	1	2	yes	—
458	C₂	—	4	2	no	—
459	C₂	—	8	4	no	—
460	C₂	#2311×C₁₃₉	1	1	yes	characteristic
461	C₂	#2897×C₁₃₉	1	2	yes	—
462	C₂	#3220×C₁₃₉	1	1	yes	characteristic
463	C₂	#3221×C₁₃₉	1	1	yes	characteristic
464	C₂	#3241×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#540×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#433×C₁₃₉	C₂	semidirect
3. #2317×C₁₃₉	C₂	semidirect
4. #1992×C₁₃₉	C₂	semidirect
5. #1991×C₁₃₉	C₂	semidirect
6. #1961×C₁₃₉	C₂	semidirect
7. #1957×C₁₃₉	C₂	semidirect
8. #1875×C₁₃₉	C₂	semidirect
9. #1874×C₁₃₉	C₂	semidirect
10. #1804×C₁₃₉	C₂	semidirect
11. #1802×C₁₃₉	C₂	semidirect
13. #540×C₁₃₉	C₄	semidirect
51. #127×C₁₃₉	C₂×C₄	semidirect
53. #125×C₁₃₉	C₂×C₄	semidirect
59. C₄×D₄×C₁₃₉	C₂×C₄	semidirect
232. #21872	C₁₃₉	direct (N × H)
233. C₁₃₉	#21872	direct (N × H)
235. C₂×#433	C₂×C₁₃₉	semidirect
236. #2317	C₂×C₁₃₉	semidirect
237. #1992	C₂×C₁₃₉	semidirect
238. #1991	C₂×C₁₃₉	semidirect
239. #1961	C₂×C₁₃₉	semidirect
240. #1957	C₂×C₁₃₉	semidirect
241. #1875	C₂×C₁₃₉	semidirect
242. #1874	C₂×C₁₃₉	semidirect
243. #1804	C₂×C₁₃₉	semidirect
244. #1802	C₂×C₁₃₉	semidirect
246. #540	C₄×C₁₃₉	semidirect
284. #127	C₂×C₄×C₁₃₉	semidirect
286. #125	C₂×C₄×C₁₃₉	semidirect
292. C₄×D₄	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₁₃₉	2
C₂×#433×C₁₃₉	2
#2317×C₁₃₉	2
#1992×C₁₃₉	2
#1991×C₁₃₉	2
#1961×C₁₃₉	2
#1957×C₁₃₉	2
#1875×C₁₃₉	2
#1874×C₁₃₉	2
#1804×C₁₃₉	2
#1802×C₁₃₉	2
#21872	139

Subgroups — C139×#21872 #48016468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21872 #48016468