Subgroups — C₁₃₉×#15145 #48009741

Order 35584.

1566 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#398×C₁₃₉	C₂	1	4	yes	maximal
2	C₂×#389×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#384×C₁₃₉	C₂	1	2	yes	maximal
5	#1444×C₁₃₉	C₂	1	4	yes	maximal
6	C₄⋊#95×C₁₃₉	C₂	1	2	yes	maximal
7	C₄×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	8	yes	—
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
17	#398×C₁₃₉	—	2	16	no	—
18	#389×C₁₃₉	—	2	4	no	—
19	#384×C₁₃₉	—	2	8	no	—
20	#384×C₁₃₉	—	2	4	no	—
21	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
23	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
25	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
26	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
27	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
30	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
35	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
36	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
37	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
38	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
49	C₂×C₄²×C₁₃₉	—	2	4	no	—
50	C₂×C₄²×C₁₃₉	—	2	4	no	—
51	C₂×C₄²×C₁₃₉	—	2	4	no	—
52	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
53	C₂×C₄²×C₁₃₉	Q₈	1	8	yes	—
54	#95×C₁₃₉	—	2	16	no	—
55	#95×C₁₃₉	—	2	4	no	—
56	#95×C₁₃₉	D₄	1	8	yes	—
57	#95×C₁₃₉	Q₈	1	8	yes	—
58	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
59	C₂²×C₄×C₁₃₉	—	2	4	no	—
60	C₂²×C₄×C₁₃₉	—	2	4	no	—
61	C₂²×C₄×C₁₃₉	—	2	2	no	—
62	C₂²×C₄×C₁₃₉	—	2	2	no	—
63	C₂²×C₄×C₁₃₉	—	2	2	no	—
64	C₂²×C₄×C₁₃₉	—	2	4	no	—
65	C₂²×C₄×C₁₃₉	—	2	2	no	—
66	C₂²×C₄×C₁₃₉	—	2	4	no	—
67	C₂²×C₄×C₁₃₉	—	2	2	no	—
68	C₂²×C₄×C₁₃₉	—	2	4	no	—
69	C₂²×C₄×C₁₃₉	—	2	2	no	—
70	C₂²×C₄×C₁₃₉	—	2	4	no	—
71	C₂²×C₄×C₁₃₉	—	2	4	no	—
72	C₂²×C₄×C₁₃₉	—	2	2	no	—
73	C₂²×C₄×C₁₃₉	—	2	8	no	—
74	C₂²×C₄×C₁₃₉	—	2	4	no	—
75	C₂²×C₄×C₁₃₉	—	2	4	no	—
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	8	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
82	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
88	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
90	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
92	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
93	C₄⋊C₄×C₁₃₉	—	2	8	no	—
94	C₄⋊C₄×C₁₃₉	—	4	32	no	—
95	C₄⋊C₄×C₁₃₉	—	4	8	no	—
96	C₄⋊C₄×C₁₃₉	—	4	8	no	—
97	C₄⋊C₄×C₁₃₉	—	4	4	no	—
98	C₄⋊C₄×C₁₃₉	—	4	8	no	—
99	C₄⋊C₄×C₁₃₉	—	4	8	no	—
100	C₄²×C₁₃₉	—	2	16	no	—
101	C₄²×C₁₃₉	—	2	8	no	—
102	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
103	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
104	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
105	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
106	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
107	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
108	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
109	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
110	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
111	C₂×C₄×C₁₃₉	—	2	8	no	—
112	C₂×C₄×C₁₃₉	—	2	2	no	—
113	C₂×C₄×C₁₃₉	—	2	2	no	—
114	C₂×C₄×C₁₃₉	—	2	2	no	—
115	C₂×C₄×C₁₃₉	—	2	2	no	—
116	C₂×C₄×C₁₃₉	—	2	8	no	—
117	C₂×C₄×C₁₃₉	—	2	8	no	—
118	C₂×C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄×C₁₃₉	—	2	8	no	—
120	C₂×C₄×C₁₃₉	—	2	8	no	—
121	C₂×C₄×C₁₃₉	—	2	8	no	—
122	C₂×C₄×C₁₃₉	—	2	8	no	—
123	C₂×C₄×C₁₃₉	—	2	4	no	—
124	C₂×C₄×C₁₃₉	—	2	8	no	—
125	C₂×C₄×C₁₃₉	—	4	2	no	—
126	C₂×C₄×C₁₃₉	—	4	2	no	—
127	C₂×C₄×C₁₃₉	—	4	4	no	—
128	C₂×C₄×C₁₃₉	—	4	4	no	—
129	C₂×C₄×C₁₃₉	—	4	2	no	—
130	C₂×C₄×C₁₃₉	—	4	2	no	—
131	C₂×C₄×C₁₃₉	—	4	4	no	—
132	C₂×C₄×C₁₃₉	—	4	4	no	—
133	C₂×C₄×C₁₃₉	—	4	2	no	—
134	C₂×C₄×C₁₃₉	—	4	8	no	—
135	C₂×C₄×C₁₃₉	—	4	8	no	—
136	C₂×C₄×C₁₃₉	—	4	8	no	—
137	C₂×C₄×C₁₃₉	#121	1	4	yes	—
138	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	8	yes	—
139	C₂×C₄×C₁₃₉	#123	1	4	yes	—
140	C₂×C₄×C₁₃₉	#125	1	8	yes	—
141	C₂×C₄×C₁₃₉	#127	1	4	yes	—
142	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	16	yes	—
143	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	4	yes	—
144	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	4	yes	—
145	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
146	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	2	yes	—
147	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
148	C₂²×C₁₃₉	C₂×#125	1	2	yes	—
149	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
150	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
151	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	4	yes	—
152	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
153	C₂²×C₁₃₉	#535	1	1	yes	characteristic
154	C₂²×C₁₃₉	#536	1	1	yes	characteristic
155	C₂²×C₁₃₉	#544	1	4	yes	—
156	C₂²×C₁₃₉	D₄²	1	2	yes	—
157	C₂²×C₁₃₉	#547	1	4	yes	—
158	C₂²×C₁₃₉	D₄×Q₈	1	2	yes	—
159	C₂²×C₁₃₉	#550	1	2	yes	—
160	C₂²×C₁₃₉	#554	1	4	yes	—
161	C₂²×C₁₃₉	#557	1	2	yes	—
162	C₄×C₁₃₉	—	2	16	no	—
163	C₄×C₁₃₉	—	2	4	no	—
164	C₄×C₁₃₉	—	2	4	no	—
165	C₄×C₁₃₉	—	4	4	no	—
166	C₄×C₁₃₉	—	8	2	no	—
167	C₄×C₁₃₉	—	8	4	no	—
168	C₄×C₁₃₉	#398	1	8	yes	complemented
169	C₂×C₁₃₉	C₂×#398	1	1	yes	characteristic
170	C₂×C₁₃₉	#2440	1	4	yes	—
171	C₂×C₁₃₉	#2501	1	1	yes	characteristic
172	C₂×C₁₃₉	#2502	1	1	yes	characteristic
173	C₂×C₁₃₉	#2541	1	1	yes	characteristic
174	C₂×C₁₃₉	#2546	1	1	yes	characteristic
175	C₂×C₁₃₉	#2552	1	4	yes	—
176	C₂×C₁₃₉	#2660	1	1	yes	characteristic
177	C₂×C₁₃₉	#2868	1	1	yes	characteristic
178	#15145	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₁₃₉	#15145	1	1	yes	characteristic, direct product factor, Sylow
180	C₂×#398	C₂×C₁₃₉	1	4	yes	—
181	C₂×#389	C₂×C₁₃₉	1	1	yes	characteristic
182	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic
183	C₂×#384	C₂×C₁₃₉	1	2	yes	—
184	#1444	C₂×C₁₃₉	1	4	yes	—
185	C₄⋊#95	C₂×C₁₃₉	1	2	yes	—
186	C₄×#95	C₂×C₁₃₉	1	1	yes	characteristic
187	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
188	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
191	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	8	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
194	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
195	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
196	#398	—	2	16	no	—
197	#389	—	2	4	no	—
198	#384	—	2	8	no	—
199	#384	—	2	4	no	—
200	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
201	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
202	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
203	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
204	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
205	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
207	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
209	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	16	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	—	2	4	no	—
217	C₂×C₄⋊C₄	—	2	4	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	16	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	—	2	8	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	4	8	no	—
226	C₂×C₄⋊C₄	—	4	4	no	—
227	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
228	C₂×C₄²	—	2	4	no	—
229	C₂×C₄²	—	2	4	no	—
230	C₂×C₄²	—	2	4	no	—
231	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
232	C₂×C₄²	Q₈×C₁₃₉	1	8	yes	—
233	#95	—	2	4	no	—
234	#95	—	2	16	no	—
235	#95	D₄×C₁₃₉	1	8	yes	—
236	#95	Q₈×C₁₃₉	1	8	yes	—
237	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
266	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
267	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
268	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
269	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
270	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
271	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	4	32	no	—
274	C₄⋊C₄	—	4	8	no	—
275	C₄⋊C₄	—	4	8	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	4	8	no	—
278	C₄⋊C₄	—	4	8	no	—
279	C₄²	—	2	16	no	—
280	C₄²	—	2	8	no	—
281	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
282	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
283	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
284	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
285	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
286	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
287	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
288	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
289	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	#121×C₁₃₉	1	4	yes	—
317	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	8	yes	—
318	C₂×C₄	#123×C₁₃₉	1	4	yes	—
319	C₂×C₄	#125×C₁₃₉	1	8	yes	—
320	C₂×C₄	#127×C₁₃₉	1	4	yes	—
321	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	16	yes	—
322	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	4	yes	—
323	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	4	yes	—
324	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
325	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	2	yes	—
326	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
327	C₂²	C₂×#125×C₁₃₉	1	2	yes	—
328	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
329	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
330	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	4	yes	—
331	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
332	C₂²	#535×C₁₃₉	1	1	yes	characteristic
333	C₂²	#536×C₁₃₉	1	1	yes	characteristic
334	C₂²	#544×C₁₃₉	1	4	yes	—
335	C₂²	D₄²×C₁₃₉	1	2	yes	—
336	C₂²	#547×C₁₃₉	1	4	yes	—
337	C₂²	D₄×Q₈×C₁₃₉	1	2	yes	—
338	C₂²	#550×C₁₃₉	1	2	yes	—
339	C₂²	#554×C₁₃₉	1	4	yes	—
340	C₂²	#557×C₁₃₉	1	2	yes	—
341	C₄	—	2	16	no	—
342	C₄	—	2	4	no	—
343	C₄	—	2	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	8	4	no	—
346	C₄	—	8	2	no	—
347	C₄	#398×C₁₃₉	1	8	yes	complemented
348	C₂	C₂×#398×C₁₃₉	1	1	yes	characteristic
349	C₂	#2440×C₁₃₉	1	4	yes	—
350	C₂	#2501×C₁₃₉	1	1	yes	characteristic
351	C₂	#2502×C₁₃₉	1	1	yes	characteristic
352	C₂	#2541×C₁₃₉	1	1	yes	characteristic
353	C₂	#2546×C₁₃₉	1	1	yes	characteristic
354	C₂	#2552×C₁₃₉	1	4	yes	—
355	C₂	#2660×C₁₃₉	1	1	yes	characteristic
356	C₂	#2868×C₁₃₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
168. C₄×C₁₃₉	#398	semidirect
178. #15145	C₁₃₉	direct (N × H)
179. C₁₃₉	#15145	direct (N × H)
347. C₄	#398×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#398×C₁₃₉	2
C₂×#389×C₁₃₉	2
C₂×#384×C₁₃₉	2
#1444×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
C₄×#95×C₁₃₉	2
#15145	139

Subgroups — C139×#15145 #48009741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#15145 #48009741