Subgroups — C₁₃₉×#37319 #48031915

Order 35584.

2212 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2867×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2864×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2709×C₁₃₉	C₂	1	8	yes	maximal, complemented
4	#2673×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2619×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2445×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2428×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2328×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
11	C₂×#127×C₁₃₉	C₂²	1	8	yes	—
12	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
13	C₂×#123×C₁₃₉	C₂²	1	8	yes	—
14	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
15	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
16	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
18	#394×C₁₃₉	C₂²	1	4	yes	—
19	#394×C₁₃₉	C₂²	1	4	yes	—
20	#394×C₁₃₉	C₂²	1	8	yes	—
21	#394×C₁₃₉	C₂²	1	8	yes	—
22	#394×C₁₃₉	C₂²	1	8	yes	—
23	#392×C₁₃₉	C₂²	1	4	yes	—
24	#392×C₁₃₉	C₂²	1	4	yes	—
25	#392×C₁₃₉	C₂²	1	8	yes	—
26	#390×C₁₃₉	C₂²	1	4	yes	—
27	#390×C₁₃₉	C₂²	1	4	yes	—
28	#389×C₁₃₉	C₂²	1	4	yes	—
29	#388×C₁₃₉	C₂²	1	4	yes	—
30	#387×C₁₃₉	C₂²	1	4	yes	—
31	#387×C₁₃₉	C₂²	1	8	yes	—
32	#386×C₁₃₉	C₂²	1	8	yes	—
33	#386×C₁₃₉	C₂²	1	8	yes	—
34	#386×C₁₃₉	C₂²	1	8	yes	—
35	#386×C₁₃₉	C₂²	1	8	yes	—
36	#382×C₁₃₉	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	#376×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
42	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
43	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
44	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
45	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
46	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
47	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
49	#127×C₁₃₉	—	2	8	no	—
50	#127×C₁₃₉	—	4	8	no	—
51	#127×C₁₃₉	—	4	16	no	—
52	#123×C₁₃₉	—	4	16	no	—
53	#121×C₁₃₉	—	4	16	no	—
54	#121×C₁₃₉	—	4	8	no	—
55	C₄×D₄×C₁₃₉	—	4	8	no	—
56	#117×C₁₃₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
69	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
73	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
74	#95×C₁₃₉	C₂³	1	4	yes	—
75	#95×C₁₃₉	C₂³	1	4	yes	—
76	#95×C₁₃₉	C₂³	1	4	yes	—
77	#95×C₁₃₉	C₂³	1	4	yes	—
78	#95×C₁₃₉	C₂³	1	4	yes	—
79	#95×C₁₃₉	C₂³	1	8	yes	—
80	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
81	C₂⁴×C₁₃₉	C₂⁴	1	8	yes	—
82	C₂×D₄×C₁₃₉	—	2	8	no	—
83	C₂×D₄×C₁₃₉	—	2	8	no	—
84	C₂×D₄×C₁₃₉	—	2	8	no	—
85	C₂×D₄×C₁₃₉	—	2	8	no	—
86	C₂×D₄×C₁₃₉	—	2	8	no	—
87	C₂×D₄×C₁₃₉	—	2	16	no	—
88	C₂×D₄×C₁₃₉	—	2	16	no	—
89	C₂×D₄×C₁₃₉	—	4	8	no	—
90	C₂×D₄×C₁₃₉	—	4	8	no	—
91	C₂×D₄×C₁₃₉	—	4	8	no	—
92	C₂×D₄×C₁₃₉	—	4	8	no	—
93	C₂×D₄×C₁₃₉	—	4	8	no	—
94	C₂×D₄×C₁₃₉	—	4	8	no	—
95	C₂×D₄×C₁₃₉	—	4	8	no	—
96	C₂×D₄×C₁₃₉	—	4	8	no	—
97	C₂×D₄×C₁₃₉	—	4	8	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	4	no	—
100	C₂²×C₄×C₁₃₉	—	4	8	no	—
101	C₂²×C₄×C₁₃₉	—	4	8	no	—
102	C₂²×C₄×C₁₃₉	—	4	8	no	—
103	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₉	—	2	4	no	—
111	C₄⋊C₄×C₁₃₉	—	2	8	no	—
112	C₄⋊C₄×C₁₃₉	—	2	16	no	—
113	C₄⋊C₄×C₁₃₉	—	2	8	no	—
114	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
116	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
117	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
118	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
119	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
120	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
121	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
122	C₄²×C₁₃₉	—	2	2	no	—
123	C₄²×C₁₃₉	—	2	4	no	—
124	C₄²×C₁₃₉	—	2	8	no	—
125	C₄²×C₁₃₉	—	2	4	no	—
126	C₄²×C₁₃₉	#41	1	4	yes	—
127	C₂³×C₁₃₉	—	2	1	no	—
128	C₂³×C₁₃₉	—	2	8	no	—
129	C₂³×C₁₃₉	—	2	4	no	—
130	C₂³×C₁₃₉	—	2	8	no	—
131	C₂³×C₁₃₉	—	2	8	no	—
132	C₂³×C₁₃₉	—	2	8	no	—
133	C₂³×C₁₃₉	—	2	8	no	—
134	C₂³×C₁₃₉	—	2	8	no	—
135	C₂³×C₁₃₉	—	2	2	no	—
136	C₂³×C₁₃₉	—	2	8	no	—
137	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
138	D₄×C₁₃₉	—	4	16	no	—
139	D₄×C₁₃₉	—	8	8	no	—
140	D₄×C₁₃₉	—	8	8	no	—
141	D₄×C₁₃₉	—	8	16	no	—
142	D₄×C₁₃₉	—	8	16	no	—
143	D₄×C₁₃₉	—	8	16	no	—
144	C₂×C₄×C₁₃₉	—	2	4	no	—
145	C₂×C₄×C₁₃₉	—	2	4	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	2	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	4	no	—
150	C₂×C₄×C₁₃₉	—	2	4	no	—
151	C₂×C₄×C₁₃₉	—	2	4	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	2	8	no	—
155	C₂×C₄×C₁₃₉	—	2	8	no	—
156	C₂×C₄×C₁₃₉	—	2	8	no	—
157	C₂×C₄×C₁₃₉	—	4	4	no	—
158	C₂×C₄×C₁₃₉	—	8	16	no	—
159	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
161	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	8	yes	—
162	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
163	C₂²×C₁₃₉	—	4	1	no	—
164	C₂²×C₁₃₉	—	4	8	no	—
165	C₂²×C₁₃₉	—	4	8	no	—
166	C₂²×C₁₃₉	—	4	8	no	—
167	C₂²×C₁₃₉	—	4	2	no	—
168	C₂²×C₁₃₉	—	4	8	no	—
169	C₂²×C₁₃₉	—	4	8	no	—
170	C₂²×C₁₃₉	—	4	4	no	—
171	C₂²×C₁₃₉	—	4	8	no	—
172	C₂²×C₁₃₉	—	4	8	no	—
173	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
174	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
175	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	4	yes	—
176	C₄×C₁₃₉	—	2	4	no	—
177	C₄×C₁₃₉	—	2	8	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	—	4	2	no	—
180	C₄×C₁₃₉	—	4	4	no	—
181	C₄×C₁₃₉	—	4	8	no	—
182	C₄×C₁₃₉	#540	1	4	yes	—
183	C₂×C₁₃₉	—	8	1	no	—
184	C₂×C₁₃₉	—	8	8	no	—
185	C₂×C₁₃₉	C₂×#540	1	1	yes	characteristic
186	C₂×C₁₃₉	#3508	1	2	yes	—
187	C₂×C₁₃₉	#3543	1	4	yes	—
188	#37319	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃₉	#37319	1	1	yes	characteristic, direct product factor, Sylow
190	#2867	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	#2864	C₂×C₁₃₉	1	1	yes	characteristic, complemented
192	#2709	C₂×C₁₃₉	1	8	yes	complemented
193	#2673	C₂×C₁₃₉	1	8	yes	complemented
194	#2619	C₂×C₁₃₉	1	2	yes	complemented
195	#2445	C₂×C₁₃₉	1	4	yes	complemented
196	#2428	C₂×C₁₃₉	1	4	yes	complemented
197	#2328	C₂×C₁₃₉	1	2	yes	complemented
198	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
199	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
200	C₂×#127	C₂²×C₁₃₉	1	8	yes	—
201	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
202	C₂×#123	C₂²×C₁₃₉	1	8	yes	—
203	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
204	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
205	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
206	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
207	#394	C₂²×C₁₃₉	1	4	yes	—
208	#394	C₂²×C₁₃₉	1	4	yes	—
209	#394	C₂²×C₁₃₉	1	8	yes	—
210	#394	C₂²×C₁₃₉	1	8	yes	—
211	#394	C₂²×C₁₃₉	1	8	yes	—
212	#392	C₂²×C₁₃₉	1	4	yes	—
213	#392	C₂²×C₁₃₉	1	4	yes	—
214	#392	C₂²×C₁₃₉	1	8	yes	—
215	#390	C₂²×C₁₃₉	1	4	yes	—
216	#390	C₂²×C₁₃₉	1	4	yes	—
217	#389	C₂²×C₁₃₉	1	4	yes	—
218	#388	C₂²×C₁₃₉	1	4	yes	—
219	#387	C₂²×C₁₃₉	1	8	yes	—
220	#387	C₂²×C₁₃₉	1	4	yes	—
221	#386	C₂²×C₁₃₉	1	8	yes	—
222	#386	C₂²×C₁₃₉	1	8	yes	—
223	#386	C₂²×C₁₃₉	1	8	yes	—
224	#386	C₂²×C₁₃₉	1	8	yes	—
225	#382	C₂²×C₁₃₉	1	2	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
227	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
228	#376	C₂²×C₁₃₉	1	1	yes	characteristic
229	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
230	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
231	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
232	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
233	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
234	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
235	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
236	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
238	#127	—	2	8	no	—
239	#127	—	4	8	no	—
240	#127	—	4	16	no	—
241	#123	—	4	16	no	—
242	#121	—	4	16	no	—
243	#121	—	4	8	no	—
244	C₄×D₄	—	4	8	no	—
245	#117	—	2	4	no	—
246	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
258	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
262	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
263	#95	C₂³×C₁₃₉	1	4	yes	—
264	#95	C₂³×C₁₃₉	1	4	yes	—
265	#95	C₂³×C₁₃₉	1	4	yes	—
266	#95	C₂³×C₁₃₉	1	4	yes	—
267	#95	C₂³×C₁₃₉	1	4	yes	—
268	#95	C₂³×C₁₃₉	1	8	yes	—
269	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
270	C₂⁴	C₂⁴×C₁₃₉	1	8	yes	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	2	8	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	16	no	—
278	C₂×D₄	—	4	8	no	—
279	C₂×D₄	—	4	8	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂×D₄	—	4	8	no	—
282	C₂×D₄	—	4	8	no	—
283	C₂×D₄	—	4	8	no	—
284	C₂×D₄	—	4	8	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	8	no	—
290	C₂²×C₄	—	4	8	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
293	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
295	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	8	no	—
305	C₂²⋊C₄	—	4	8	no	—
306	C₂²⋊C₄	—	4	8	no	—
307	C₂²⋊C₄	—	4	8	no	—
308	C₂²⋊C₄	—	4	8	no	—
309	C₂²⋊C₄	—	4	8	no	—
310	C₂²⋊C₄	—	4	8	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	4	no	—
313	C₄²	—	2	8	no	—
314	C₄²	—	2	4	no	—
315	C₄²	#41×C₁₃₉	1	4	yes	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	8	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	8	no	—
326	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
327	D₄	—	4	16	no	—
328	D₄	—	8	16	no	—
329	D₄	—	8	16	no	—
330	D₄	—	8	8	no	—
331	D₄	—	8	8	no	—
332	D₄	—	8	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	16	no	—
348	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
349	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
350	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	8	yes	—
351	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
352	C₂²	—	4	8	no	—
353	C₂²	—	4	8	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	8	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	4	2	no	—
362	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
363	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
364	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	4	yes	—
365	C₄	—	2	8	no	—
366	C₄	—	2	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	8	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	2	no	—
371	C₄	#540×C₁₃₉	1	4	yes	—
372	C₂	—	8	8	no	—
373	C₂	—	8	1	no	—
374	C₂	C₂×#540×C₁₃₉	1	1	yes	characteristic
375	C₂	#3508×C₁₃₉	1	2	yes	—
376	C₂	#3543×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2867×C₁₃₉	C₂	semidirect
2. #2864×C₁₃₉	C₂	semidirect
3. #2709×C₁₃₉	C₂	semidirect
4. #2673×C₁₃₉	C₂	semidirect
5. #2619×C₁₃₉	C₂	semidirect
6. #2445×C₁₃₉	C₂	semidirect
7. #2428×C₁₃₉	C₂	semidirect
8. #2328×C₁₃₉	C₂	semidirect
9. #2298×C₁₃₉	C₂	semidirect
188. #37319	C₁₃₉	direct (N × H)
189. C₁₃₉	#37319	direct (N × H)
190. #2867	C₂×C₁₃₉	semidirect
191. #2864	C₂×C₁₃₉	semidirect
192. #2709	C₂×C₁₃₉	semidirect
193. #2673	C₂×C₁₃₉	semidirect
194. #2619	C₂×C₁₃₉	semidirect
195. #2445	C₂×C₁₃₉	semidirect
196. #2428	C₂×C₁₃₉	semidirect
197. #2328	C₂×C₁₃₉	semidirect
198. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2867×C₁₃₉	2
#2864×C₁₃₉	2
#2709×C₁₃₉	2
#2673×C₁₃₉	2
#2619×C₁₃₉	2
#2445×C₁₃₉	2
#2428×C₁₃₉	2
#2328×C₁₃₉	2
#2298×C₁₃₉	2
#37319	139

Subgroups — C139×#37319 #48031915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37319 #48031915