Subgroups — C₁₃₉×#22381 #48016977

Order 35584.

614 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1940×C₁₃₉	C₂	1	2	yes	maximal
3	#1917×C₁₃₉	C₂	1	2	yes	maximal
4	#1917×C₁₃₉	C₂	1	2	yes	maximal
5	#1917×C₁₃₉	C₂	1	2	yes	maximal
6	#1916×C₁₃₉	C₂	1	2	yes	maximal
7	#1839×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#1771×C₁₃₉	C₂	1	2	yes	maximal
9	C₄×C₄⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#125×C₁₃₉	C₄	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	#389×C₁₃₉	C₄	1	1	yes	characteristic
19	#389×C₁₃₉	C₄	1	1	yes	characteristic
20	#387×C₁₃₉	C₄	1	2	yes	—
21	#387×C₁₃₉	C₄	1	2	yes	—
22	#382×C₁₃₉	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
28	#336×C₁₃₉	C₂²	1	2	yes	—
29	#336×C₁₃₉	C₂²	1	2	yes	—
30	#336×C₁₃₉	C₂²	1	2	yes	—
31	#336×C₁₃₉	C₂²	1	1	yes	characteristic
32	#336×C₁₃₉	C₂²	1	2	yes	—
33	#336×C₁₃₉	C₂²	1	1	yes	characteristic
34	#336×C₁₃₉	C₂²	1	2	yes	—
35	#336×C₁₃₉	C₂²	1	2	yes	—
36	#336×C₁₃₉	C₂²	1	2	yes	—
37	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
41	#125×C₁₃₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₁₃₉	—	2	4	no	—
60	C₄⋊C₈×C₁₃₉	—	2	4	no	—
61	C₄⋊C₈×C₁₃₉	—	4	2	no	—
62	#97×C₁₃₉	—	2	4	no	—
63	#97×C₁₃₉	—	4	2	no	—
64	C₄×C₈×C₁₃₉	—	4	1	no	—
65	C₄×C₈×C₁₃₉	—	4	1	no	—
66	#95×C₁₃₉	C₂×C₄	1	2	yes	—
67	#95×C₁₃₉	C₂×C₄	1	2	yes	—
68	#95×C₁₃₉	C₂×C₄	1	2	yes	—
69	#95×C₁₃₉	C₂×C₄	1	2	yes	—
70	#95×C₁₃₉	C₂×C₄	1	2	yes	—
71	#95×C₁₃₉	C₂×C₄	1	2	yes	—
72	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₃₉	—	2	2	no	—
84	C₂×C₈×C₁₃₉	—	2	2	no	—
85	C₂×C₈×C₁₃₉	—	2	2	no	—
86	C₂×C₈×C₁₃₉	—	2	2	no	—
87	C₂×C₈×C₁₃₉	—	2	2	no	—
88	C₂×C₈×C₁₃₉	—	2	2	no	—
89	C₂×C₈×C₁₃₉	—	2	2	no	—
90	C₂×C₈×C₁₃₉	—	2	2	no	—
91	C₂×C₈×C₁₃₉	—	2	2	no	—
92	C₂×C₈×C₁₃₉	—	2	2	no	—
93	C₂×C₈×C₁₃₉	—	2	2	no	—
94	C₂×C₈×C₁₃₉	#41	1	4	yes	—
95	C₄⋊C₄×C₁₃₉	—	2	4	no	—
96	C₄⋊C₄×C₁₃₉	—	2	4	no	—
97	C₄⋊C₄×C₁₃₉	—	2	2	no	—
98	C₄⋊C₄×C₁₃₉	—	2	2	no	—
99	C₄⋊C₄×C₁₃₉	—	2	4	no	—
100	C₄⋊C₄×C₁₃₉	—	4	1	no	—
101	C₄⋊C₄×C₁₃₉	—	4	1	no	—
102	C₄⋊C₄×C₁₃₉	—	4	2	no	—
103	C₄²×C₁₃₉	—	2	2	no	—
104	C₄²×C₁₃₉	—	2	2	no	—
105	C₄²×C₁₃₉	—	2	2	no	—
106	C₄²×C₁₃₉	—	2	2	no	—
107	C₄²×C₁₃₉	—	2	1	no	—
108	C₄²×C₁₃₉	—	2	2	no	—
109	C₄²×C₁₃₉	—	2	2	no	—
110	C₄²×C₁₃₉	—	2	1	no	—
111	C₄²×C₁₃₉	—	2	2	no	—
112	C₄²×C₁₃₉	—	4	1	no	—
113	C₄²×C₁₃₉	—	4	1	no	—
114	C₄²×C₁₃₉	M₁₆	1	4	yes	—
115	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
116	C₂×C₄×C₁₃₉	—	2	1	no	—
117	C₂×C₄×C₁₃₉	—	2	1	no	—
118	C₂×C₄×C₁₃₉	—	2	1	no	—
119	C₂×C₄×C₁₃₉	—	2	1	no	—
120	C₂×C₄×C₁₃₉	—	2	1	no	—
121	C₂×C₄×C₁₃₉	—	2	1	no	—
122	C₂×C₄×C₁₃₉	—	2	1	no	—
123	C₂×C₄×C₁₃₉	—	2	1	no	—
124	C₂×C₄×C₁₃₉	—	2	2	no	—
125	C₂×C₄×C₁₃₉	—	2	2	no	—
126	C₂×C₄×C₁₃₉	—	2	1	no	—
127	C₂×C₄×C₁₃₉	—	2	1	no	—
128	C₂×C₄×C₁₃₉	—	2	2	no	—
129	C₂×C₄×C₁₃₉	—	2	2	no	—
130	C₂×C₄×C₁₃₉	—	2	2	no	—
131	C₂×C₄×C₁₃₉	—	2	2	no	—
132	C₂×C₄×C₁₃₉	—	2	1	no	—
133	C₂×C₄×C₁₃₉	—	2	2	no	—
134	C₂×C₄×C₁₃₉	—	2	2	no	—
135	C₂×C₄×C₁₃₉	—	2	1	no	—
136	C₂×C₄×C₁₃₉	—	2	1	no	—
137	C₂×C₄×C₁₃₉	—	2	1	no	—
138	C₂×C₄×C₁₃₉	—	2	2	no	—
139	C₂×C₄×C₁₃₉	—	2	2	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	2	no	—
142	C₂×C₄×C₁₃₉	C₂×M₁₆	1	2	yes	—
143	C₂×C₄×C₁₃₉	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₁₃₉	C₂×M₁₆	1	2	yes	—
145	C₂×C₄×C₁₃₉	#131	1	2	yes	—
146	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
147	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
149	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
150	C₈×C₁₃₉	—	2	4	no	—
151	C₈×C₁₃₉	—	4	2	no	—
152	C₈×C₁₃₉	—	4	2	no	—
153	C₈×C₁₃₉	—	4	2	no	—
154	C₂²×C₁₃₉	C₄×#41	1	1	yes	characteristic
155	C₂²×C₁₃₉	#519	1	1	yes	characteristic
156	C₂²×C₁₃₉	#520	1	1	yes	characteristic
157	C₂²×C₁₃₉	C₂²×M₁₆	1	1	yes	characteristic
158	C₂²×C₁₃₉	C₂×#131	1	1	yes	characteristic
159	C₂²×C₁₃₉	#568	1	1	yes	characteristic
160	C₂²×C₁₃₉	#568	1	1	yes	characteristic
161	C₄×C₁₃₉	—	2	2	no	—
162	C₄×C₁₃₉	—	2	2	no	—
163	C₄×C₁₃₉	—	2	2	no	—
164	C₄×C₁₃₉	—	2	2	no	—
165	C₄×C₁₃₉	—	4	2	no	—
166	C₄×C₁₃₉	—	4	1	no	—
167	C₄×C₁₃₉	—	4	2	no	—
168	C₄×C₁₃₉	—	4	1	no	—
169	C₄×C₁₃₉	—	4	2	no	—
170	C₄×C₁₃₉	—	4	2	no	—
171	C₄×C₁₃₉	#539	1	2	yes	—
172	C₄×C₁₃₉	#541	1	2	yes	—
173	C₂×C₁₃₉	#2336	1	1	yes	characteristic
174	C₂×C₁₃₉	#2965	1	1	yes	characteristic
175	C₂×C₁₃₉	#2967	1	1	yes	characteristic
176	C₂×C₁₃₉	#2983	1	1	yes	characteristic
177	C₂×C₁₃₉	#2985	1	1	yes	characteristic
178	C₂×C₁₃₉	#2989	1	1	yes	characteristic
179	C₂×C₁₃₉	#2992	1	1	yes	characteristic
180	#22381	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₉	#22381	1	1	yes	characteristic, direct product factor, Sylow
182	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic
183	#1940	C₂×C₁₃₉	1	2	yes	—
184	#1917	C₂×C₁₃₉	1	2	yes	—
185	#1917	C₂×C₁₃₉	1	2	yes	—
186	#1917	C₂×C₁₃₉	1	2	yes	—
187	#1916	C₂×C₁₃₉	1	2	yes	—
188	#1839	C₂×C₁₃₉	1	1	yes	characteristic
189	#1771	C₂×C₁₃₉	1	2	yes	—
190	C₄×C₄⋊C₈	C₂×C₁₃₉	1	1	yes	characteristic
191	C₂×#125	C₄×C₁₃₉	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
195	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
196	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
199	#389	C₄×C₁₃₉	1	1	yes	characteristic
200	#389	C₄×C₁₃₉	1	1	yes	characteristic
201	#387	C₄×C₁₃₉	1	2	yes	—
202	#387	C₄×C₁₃₉	1	2	yes	—
203	#382	C₄×C₁₃₉	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
208	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
209	#336	C₂²×C₁₃₉	1	2	yes	—
210	#336	C₂²×C₁₃₉	1	2	yes	—
211	#336	C₂²×C₁₃₉	1	1	yes	characteristic
212	#336	C₂²×C₁₃₉	1	1	yes	characteristic
213	#336	C₂²×C₁₃₉	1	2	yes	—
214	#336	C₂²×C₁₃₉	1	2	yes	—
215	#336	C₂²×C₁₃₉	1	2	yes	—
216	#336	C₂²×C₁₃₉	1	2	yes	—
217	#336	C₂²×C₁₃₉	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
221	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
222	#125	—	2	4	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
231	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
240	C₄⋊C₈	—	2	4	no	—
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	—	4	2	no	—
243	#97	—	2	4	no	—
244	#97	—	4	2	no	—
245	C₄×C₈	—	4	1	no	—
246	C₄×C₈	—	4	1	no	—
247	#95	C₂×C₄×C₁₃₉	1	2	yes	—
248	#95	C₂×C₄×C₁₃₉	1	2	yes	—
249	#95	C₂×C₄×C₁₃₉	1	2	yes	—
250	#95	C₂×C₄×C₁₃₉	1	2	yes	—
251	#95	C₂×C₄×C₁₃₉	1	2	yes	—
252	#95	C₂×C₄×C₁₃₉	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
263	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	#41×C₁₃₉	1	4	yes	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	4	1	no	—
282	C₄⋊C₄	—	4	1	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	4	1	no	—
294	C₄²	—	4	1	no	—
295	C₄²	M₁₆×C₁₃₉	1	4	yes	—
296	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	C₂×M₁₆×C₁₃₉	1	2	yes	—
324	C₂×C₄	C₂×M₁₆×C₁₃₉	1	2	yes	—
325	C₂×C₄	C₂×M₁₆×C₁₃₉	1	2	yes	—
326	C₂×C₄	#131×C₁₃₉	1	2	yes	—
327	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
328	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
329	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
330	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
331	C₈	—	2	4	no	—
332	C₈	—	4	2	no	—
333	C₈	—	4	2	no	—
334	C₈	—	4	2	no	—
335	C₂²	C₄×#41×C₁₃₉	1	1	yes	characteristic
336	C₂²	#519×C₁₃₉	1	1	yes	characteristic
337	C₂²	#520×C₁₃₉	1	1	yes	characteristic
338	C₂²	C₂²×M₁₆×C₁₃₉	1	1	yes	characteristic
339	C₂²	C₂×#131×C₁₃₉	1	1	yes	characteristic
340	C₂²	#568×C₁₃₉	1	1	yes	characteristic
341	C₂²	#568×C₁₃₉	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	2	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	#539×C₁₃₉	1	2	yes	—
353	C₄	#541×C₁₃₉	1	2	yes	—
354	C₂	#2336×C₁₃₉	1	1	yes	characteristic
355	C₂	#2965×C₁₃₉	1	1	yes	characteristic
356	C₂	#2967×C₁₃₉	1	1	yes	characteristic
357	C₂	#2983×C₁₃₉	1	1	yes	characteristic
358	C₂	#2985×C₁₃₉	1	1	yes	characteristic
359	C₂	#2989×C₁₃₉	1	1	yes	characteristic
360	C₂	#2992×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle, prime radical	C₂³×C₁₃₉	C₂³×C₄
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
180. #22381	C₁₃₉	direct (N × H)
181. C₁₃₉	#22381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#125×C₁₃₉	2
#1940×C₁₃₉	2
#1917×C₁₃₉	2
#1916×C₁₃₉	2
#1839×C₁₃₉	2
#1771×C₁₃₉	2
C₄×C₄⋊C₈×C₁₃₉	2
#22381	139

Subgroups — C139×#22381 #48016977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#22381 #48016977