Subgroups — C₁₃₉×#10750 #48005346

Order 35584.

1258 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#101×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1736×C₁₃₉	C₂	1	2	yes	maximal
5	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
8	#519×C₁₃₉	—	2	2	no	—
9	#519×C₁₃₉	—	2	4	no	—
10	#519×C₁₃₉	C₄	1	4	yes	complemented
11	C₂×C₄×Q₈×C₁₃₉	—	2	4	no	—
12	C₂×#117×C₁₃₉	—	2	2	no	—
13	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#101×C₁₃₉	—	2	2	no	—
17	C₂×#101×C₁₃₉	—	2	2	no	—
18	C₂×#101×C₁₃₉	C₄	1	4	yes	complemented
19	#391×C₁₃₉	—	2	2	no	—
20	#391×C₁₃₉	C₄	1	4	yes	complemented
21	C₂×#95×C₁₃₉	—	2	2	no	—
22	#340×C₁₃₉	—	2	4	no	—
23	#339×C₁₃₉	—	2	4	no	—
24	C₂²×Q₈×C₁₃₉	—	2	2	no	—
25	C₂²×Q₈×C₁₃₉	—	2	2	no	—
26	C₂²×Q₈×C₁₃₉	—	2	2	no	—
27	C₂²×Q₈×C₁₃₉	—	2	2	no	—
28	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
30	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₂²×Q₈×C₁₃₉	D₄	1	2	yes	—
32	C₂²×Q₈×C₁₃₉	D₄	1	2	yes	—
33	C₂²×Q₈×C₁₃₉	Q₈	1	2	yes	—
34	C₂³×C₄×C₁₃₉	—	2	1	no	—
35	C₂³×C₄×C₁₃₉	—	2	1	no	—
36	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₁₃₉	—	2	2	no	—
39	C₂×M₁₆×C₁₃₉	—	2	2	no	—
40	C₂×M₁₆×C₁₃₉	—	2	2	no	—
41	C₂×M₁₆×C₁₃₉	—	2	2	no	—
42	C₂×M₁₆×C₁₃₉	—	2	2	no	—
43	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₃₉	—	2	2	no	—
45	C₄×Q₈×C₁₃₉	—	2	16	no	—
46	C₄×Q₈×C₁₃₉	—	2	16	no	—
47	#117×C₁₃₉	—	2	8	no	—
48	#117×C₁₃₉	—	2	8	no	—
49	#117×C₁₃₉	—	2	2	no	—
50	#117×C₁₃₉	—	2	2	no	—
51	#117×C₁₃₉	C₂×C₄	1	4	yes	—
52	#117×C₁₃₉	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₄²×C₁₃₉	—	2	4	no	—
61	C₂×C₄²×C₁₃₉	—	2	2	no	—
62	C₂×C₄²×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	—	2	2	no	—
64	C₂×C₄²×C₁₃₉	—	2	1	no	—
65	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
66	#101×C₁₃₉	—	2	8	no	—
67	#95×C₁₃₉	—	2	8	no	—
68	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
69	C₂×Q₈×C₁₃₉	—	2	4	no	—
70	C₂×Q₈×C₁₃₉	—	2	4	no	—
71	C₂×Q₈×C₁₃₉	—	2	4	no	—
72	C₂×Q₈×C₁₃₉	—	2	4	no	—
73	C₂×Q₈×C₁₃₉	—	2	4	no	—
74	C₂×Q₈×C₁₃₉	—	2	4	no	—
75	C₂×Q₈×C₁₃₉	—	2	4	no	—
76	C₂×Q₈×C₁₃₉	—	2	4	no	—
77	C₂×Q₈×C₁₃₉	—	2	4	no	—
78	C₂×Q₈×C₁₃₉	—	2	4	no	—
79	C₂×Q₈×C₁₃₉	—	2	4	no	—
80	C₂×Q₈×C₁₃₉	—	2	4	no	—
81	C₂×Q₈×C₁₃₉	C₄²	1	4	yes	—
82	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	4	yes	—
83	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	4	yes	—
84	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	2	no	—
89	C₂²×C₄×C₁₃₉	—	2	4	no	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	4	no	—
92	C₂²×C₄×C₁₃₉	—	2	2	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	—	4	1	no	—
95	C₂²×C₄×C₁₃₉	—	4	1	no	—
96	C₂²×C₄×C₁₃₉	—	4	4	no	—
97	C₂²×C₄×C₁₃₉	—	4	1	no	—
98	C₂²×C₄×C₁₃₉	—	4	1	no	—
99	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
111	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
112	M₁₆×C₁₃₉	—	2	4	no	—
113	M₁₆×C₁₃₉	—	2	4	no	—
114	M₁₆×C₁₃₉	—	4	2	no	—
115	M₁₆×C₁₃₉	—	4	2	no	—
116	C₂×C₈×C₁₃₉	—	2	4	no	—
117	C₂×C₈×C₁₃₉	—	4	2	no	—
118	C₂×C₈×C₁₃₉	—	4	2	no	—
119	C₄⋊C₄×C₁₃₉	—	2	16	no	—
120	C₄⋊C₄×C₁₃₉	—	2	4	no	—
121	C₄⋊C₄×C₁₃₉	—	2	4	no	—
122	C₄⋊C₄×C₁₃₉	—	4	2	no	—
123	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
124	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
126	C₄²×C₁₃₉	—	2	16	no	—
127	C₄²×C₁₃₉	—	2	4	no	—
128	C₄²×C₁₃₉	—	2	4	no	—
129	C₄²×C₁₃₉	—	2	4	no	—
130	C₄²×C₁₃₉	—	4	2	no	—
131	C₂³×C₁₃₉	—	2	2	no	—
132	C₂³×C₁₃₉	—	2	2	no	—
133	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₃₉	#120	1	1	yes	characteristic
137	C₂³×C₁₃₉	#120	1	1	yes	characteristic
138	C₂³×C₁₃₉	#123	1	1	yes	characteristic
139	C₂³×C₁₃₉	#123	1	1	yes	characteristic
140	Q₈×C₁₃₉	—	2	8	no	—
141	Q₈×C₁₃₉	—	2	8	no	—
142	Q₈×C₁₃₉	—	2	8	no	—
143	Q₈×C₁₃₉	—	2	8	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	4	no	—
148	C₂×C₄×C₁₃₉	—	2	4	no	—
149	C₂×C₄×C₁₃₉	—	2	4	no	—
150	C₂×C₄×C₁₃₉	—	2	4	no	—
151	C₂×C₄×C₁₃₉	—	2	8	no	—
152	C₂×C₄×C₁₃₉	—	4	4	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	4	no	—
157	C₂×C₄×C₁₃₉	—	4	4	no	—
158	C₂×C₄×C₁₃₉	—	4	4	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	—	8	2	no	—
161	C₂×C₄×C₁₃₉	—	8	2	no	—
162	C₂×C₄×C₁₃₉	#95	1	8	yes	—
163	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃₉	#117	1	2	yes	—
169	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₃₉	#120	1	2	yes	—
174	C₂×C₄×C₁₃₉	#121	1	2	yes	—
175	C₂×C₄×C₁₃₉	#121	1	2	yes	—
176	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₃₉	#123	1	2	yes	—
179	C₈×C₁₃₉	—	4	4	no	—
180	C₂²×C₁₃₉	—	2	2	no	—
181	C₂²×C₁₃₉	—	2	2	no	—
182	C₂²×C₁₃₉	—	2	2	no	—
183	C₂²×C₁₃₉	—	2	2	no	—
184	C₂²×C₁₃₉	—	2	1	no	—
185	C₂²×C₁₃₉	—	2	1	no	—
186	C₂²×C₁₃₉	—	2	1	no	—
187	C₂²×C₁₃₉	—	2	1	no	—
188	C₂²×C₁₃₉	C₂×#95	1	1	yes	characteristic
189	C₂²×C₁₃₉	#379	1	1	yes	characteristic
190	C₂²×C₁₃₉	#381	1	1	yes	characteristic
191	C₂²×C₁₃₉	#385	1	1	yes	characteristic
192	C₂²×C₁₃₉	#385	1	1	yes	characteristic
193	C₂²×C₁₃₉	#386	1	1	yes	characteristic
194	C₂²×C₁₃₉	#386	1	1	yes	characteristic
195	C₂²×C₁₃₉	#454	1	2	yes	—
196	C₂²×C₁₃₉	#456	1	2	yes	—
197	C₄×C₁₃₉	—	2	8	no	—
198	C₄×C₁₃₉	—	4	4	no	—
199	C₄×C₁₃₉	—	4	8	no	—
200	C₄×C₁₃₉	—	8	2	no	—
201	C₄×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
202	C₄×C₁₃₉	#380	1	2	yes	—
203	C₄×C₁₃₉	#385	1	2	yes	—
204	C₄×C₁₃₉	#386	1	2	yes	—
205	C₂×C₁₃₉	—	2	1	no	—
206	C₂×C₁₃₉	—	2	1	no	—
207	C₂×C₁₃₉	—	2	1	no	—
208	C₂×C₁₃₉	—	2	1	no	—
209	C₂×C₁₃₉	C₂²⋊#95	1	1	yes	characteristic
210	C₂×C₁₃₉	#1793	1	2	yes	—
211	C₂×C₁₃₉	#1857	1	2	yes	—
212	C₂×C₁₃₉	#1886	1	1	yes	characteristic
213	C₂×C₁₃₉	#1888	1	1	yes	characteristic
214	#10750	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₉	#10750	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic
217	C₂²×#101	C₂×C₁₃₉	1	1	yes	characteristic
218	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic
219	#1736	C₂×C₁₃₉	1	2	yes	—
220	C₂×#339	C₂×C₁₃₉	1	2	yes	—
221	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
223	#519	—	2	2	no	—
224	#519	—	2	4	no	—
225	#519	C₄×C₁₃₉	1	4	yes	complemented
226	C₂×C₄×Q₈	—	2	4	no	—
227	C₂×#117	—	2	2	no	—
228	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
230	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
231	C₂×#101	—	2	2	no	—
232	C₂×#101	—	2	2	no	—
233	C₂×#101	C₄×C₁₃₉	1	4	yes	complemented
234	#391	—	2	2	no	—
235	#391	C₄×C₁₃₉	1	4	yes	complemented
236	C₂×#95	—	2	2	no	—
237	#340	—	2	4	no	—
238	#339	—	2	4	no	—
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
244	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
245	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
246	C₂²×Q₈	D₄×C₁₃₉	1	2	yes	—
247	C₂²×Q₈	D₄×C₁₃₉	1	2	yes	—
248	C₂²×Q₈	Q₈×C₁₃₉	1	2	yes	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
259	C₂²×C₈	—	2	2	no	—
260	C₄×Q₈	—	2	16	no	—
261	C₄×Q₈	—	2	16	no	—
262	#117	—	2	8	no	—
263	#117	—	2	8	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	C₂×C₄×C₁₃₉	1	4	yes	—
267	#117	D₄×C₁₃₉	1	4	yes	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
273	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	4	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
281	#101	—	2	8	no	—
282	#95	—	2	8	no	—
283	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	C₄²×C₁₃₉	1	4	yes	—
297	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	4	yes	—
298	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	4	yes	—
299	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
316	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
324	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
325	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
326	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
327	M₁₆	—	2	4	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	4	2	no	—
330	M₁₆	—	4	2	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₄⋊C₄	—	2	16	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₄²	—	2	16	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	4	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
349	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
350	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
351	C₂³	#120×C₁₃₉	1	1	yes	characteristic
352	C₂³	#120×C₁₃₉	1	1	yes	characteristic
353	C₂³	#123×C₁₃₉	1	1	yes	characteristic
354	C₂³	#123×C₁₃₉	1	1	yes	characteristic
355	Q₈	—	2	8	no	—
356	Q₈	—	2	8	no	—
357	Q₈	—	2	8	no	—
358	Q₈	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	8	2	no	—
377	C₂×C₄	#95×C₁₃₉	1	8	yes	—
378	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄	#117×C₁₃₉	1	2	yes	—
384	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
387	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
388	C₂×C₄	#120×C₁₃₉	1	2	yes	—
389	C₂×C₄	#121×C₁₃₉	1	2	yes	—
390	C₂×C₄	#121×C₁₃₉	1	2	yes	—
391	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
392	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
393	C₂×C₄	#123×C₁₃₉	1	2	yes	—
394	C₈	—	4	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	C₂×#95×C₁₃₉	1	1	yes	characteristic
404	C₂²	#379×C₁₃₉	1	1	yes	characteristic
405	C₂²	#381×C₁₃₉	1	1	yes	characteristic
406	C₂²	#385×C₁₃₉	1	1	yes	characteristic
407	C₂²	#385×C₁₃₉	1	1	yes	characteristic
408	C₂²	#386×C₁₃₉	1	1	yes	characteristic
409	C₂²	#386×C₁₃₉	1	1	yes	characteristic
410	C₂²	#454×C₁₃₉	1	2	yes	—
411	C₂²	#456×C₁₃₉	1	2	yes	—
412	C₄	—	2	8	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	8	no	—
415	C₄	—	8	2	no	—
416	C₄	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
417	C₄	#380×C₁₃₉	1	2	yes	—
418	C₄	#385×C₁₃₉	1	2	yes	—
419	C₄	#386×C₁₃₉	1	2	yes	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	C₂²⋊#95×C₁₃₉	1	1	yes	characteristic
425	C₂	#1793×C₁₃₉	1	2	yes	—
426	C₂	#1857×C₁₃₉	1	2	yes	—
427	C₂	#1886×C₁₃₉	1	1	yes	characteristic
428	C₂	#1888×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	#120
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
10. #519×C₁₃₉	C₄	semidirect
18. C₂×#101×C₁₃₉	C₄	semidirect
20. #391×C₁₃₉	C₄	semidirect
214. #10750	C₁₃₉	direct (N × H)
215. C₁₃₉	#10750	direct (N × H)
225. #519	C₄×C₁₃₉	semidirect
233. C₂×#101	C₄×C₁₃₉	semidirect
235. #391	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×#519×C₁₃₉	2
C₂²×#101×C₁₃₉	2
C₂×#391×C₁₃₉	2
#1736×C₁₃₉	2
C₂×#339×C₁₃₉	2
#10750	139

Subgroups — C139×#10750 #48005346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10750 #48005346