Subgroups — C₁₃₉×#10751 #48005347

Order 35584.

1254 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#410×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1733×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
7	#568×C₁₃₉	—	2	2	no	—
8	#568×C₁₃₉	—	2	4	no	—
9	#568×C₁₃₉	C₄	1	4	yes	complemented
10	C₂×#131×C₁₃₉	—	2	4	no	—
11	C₂²×M₁₆×C₁₃₉	—	2	2	no	—
12	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
14	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	#410×C₁₃₉	—	2	2	no	—
17	#410×C₁₃₉	C₄	1	4	yes	complemented
18	C₂×#99×C₁₃₉	—	2	2	no	—
19	#391×C₁₃₉	C₄	1	2	yes	complemented
20	#390×C₁₃₉	C₄	1	2	yes	complemented
21	#386×C₁₃₉	—	2	2	no	—
22	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
23	#339×C₁₃₉	—	2	4	no	—
24	#339×C₁₃₉	—	2	4	no	—
25	C₂×#41×C₁₃₉	—	2	2	no	—
26	C₂×#41×C₁₃₉	—	2	2	no	—
27	C₂×#41×C₁₃₉	—	2	2	no	—
28	C₂×#41×C₁₃₉	—	2	2	no	—
29	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
30	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₃₉	D₄	1	2	yes	—
32	C₂×#41×C₁₃₉	Q₈	1	2	yes	—
33	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
36	C₂³×C₄×C₁₃₉	—	2	1	no	—
37	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	#131×C₁₃₉	—	2	16	no	—
40	#131×C₁₃₉	—	2	16	no	—
41	C₂×M₁₆×C₁₃₉	—	2	4	no	—
42	C₂×M₁₆×C₁₃₉	—	2	8	no	—
43	C₂×M₁₆×C₁₃₉	—	2	8	no	—
44	C₂×M₁₆×C₁₃₉	—	2	2	no	—
45	C₂×M₁₆×C₁₃₉	—	2	2	no	—
46	C₂×M₁₆×C₁₃₉	—	2	2	no	—
47	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
48	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
49	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
50	C₂²×C₈×C₁₃₉	—	2	4	no	—
51	C₂²×C₈×C₁₃₉	—	2	2	no	—
52	#117×C₁₃₉	—	2	2	no	—
53	#117×C₁₃₉	—	2	2	no	—
54	#117×C₁₃₉	—	2	2	no	—
55	#117×C₁₃₉	—	2	2	no	—
56	#117×C₁₃₉	—	2	2	no	—
57	#117×C₁₃₉	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
63	C₂×C₄²×C₁₃₉	—	2	2	no	—
64	C₂×C₄²×C₁₃₉	—	2	2	no	—
65	C₂×C₄²×C₁₃₉	—	2	2	no	—
66	C₂×C₄²×C₁₃₉	—	2	1	no	—
67	C₂×C₄²×C₁₃₉	—	2	1	no	—
68	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
69	#99×C₁₃₉	—	2	8	no	—
70	#95×C₁₃₉	—	2	4	no	—
71	C₂⁴×C₁₃₉	C₂²⋊C₄	1	2	yes	—
72	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
73	#41×C₁₃₉	—	2	4	no	—
74	#41×C₁₃₉	—	2	4	no	—
75	#41×C₁₃₉	—	2	4	no	—
76	#41×C₁₃₉	—	2	4	no	—
77	#41×C₁₃₉	—	2	4	no	—
78	#41×C₁₃₉	—	2	4	no	—
79	#41×C₁₃₉	—	2	4	no	—
80	#41×C₁₃₉	—	2	4	no	—
81	C₂×Q₈×C₁₃₉	—	2	2	no	—
82	C₂×Q₈×C₁₃₉	—	2	2	no	—
83	C₂×Q₈×C₁₃₉	C₄²	1	2	yes	—
84	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₁₃₉	—	2	4	no	—
86	C₂×D₄×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	2	2	no	—
89	C₂×D₄×C₁₃₉	C₄²	1	2	yes	—
90	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
91	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
92	C₂×D₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	4	4	no	—
100	C₂²×C₄×C₁₃₉	—	4	2	no	—
101	C₂²×C₄×C₁₃₉	—	4	2	no	—
102	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
114	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
115	M₁₆×C₁₃₉	—	2	16	no	—
116	M₁₆×C₁₃₉	—	2	4	no	—
117	M₁₆×C₁₃₉	—	2	4	no	—
118	M₁₆×C₁₃₉	—	2	4	no	—
119	M₁₆×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
120	C₂×C₈×C₁₃₉	—	2	16	no	—
121	C₂×C₈×C₁₃₉	—	2	4	no	—
122	C₂×C₈×C₁₃₉	—	2	4	no	—
123	C₂×C₈×C₁₃₉	—	2	4	no	—
124	C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₄⋊C₄×C₁₃₉	—	2	4	no	—
126	C₄⋊C₄×C₁₃₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
128	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
129	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
131	C₄²×C₁₃₉	—	2	4	no	—
132	C₄²×C₁₃₉	—	2	4	no	—
133	C₄²×C₁₃₉	—	4	1	no	—
134	C₄²×C₁₃₉	—	4	2	no	—
135	C₄²×C₁₃₉	—	4	1	no	—
136	C₄²×C₁₃₉	—	4	1	no	—
137	C₄²×C₁₃₉	—	4	1	no	—
138	C₂³×C₁₃₉	—	2	2	no	—
139	C₂³×C₁₃₉	—	2	2	no	—
140	C₂³×C₁₃₉	—	4	2	no	—
141	C₂³×C₁₃₉	—	4	4	no	—
142	C₂³×C₁₃₉	#95	1	4	yes	—
143	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₃₉	#121	1	2	yes	—
147	C₂³×C₁₃₉	#121	1	2	yes	—
148	Q₈×C₁₃₉	—	2	4	no	—
149	Q₈×C₁₃₉	—	2	4	no	—
150	D₄×C₁₃₉	—	2	8	no	—
151	D₄×C₁₃₉	—	2	8	no	—
152	D₄×C₁₃₉	—	2	4	no	—
153	D₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	2	2	no	—
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	4	2	no	—
162	C₂×C₄×C₁₃₉	—	4	8	no	—
163	C₂×C₄×C₁₃₉	—	4	2	no	—
164	C₂×C₄×C₁₃₉	—	4	4	no	—
165	C₂×C₄×C₁₃₉	—	4	4	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	8	4	no	—
168	C₂×C₄×C₁₃₉	#95	1	4	yes	—
169	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₉	#117	1	2	yes	—
175	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₃₉	#120	1	2	yes	—
180	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
181	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
182	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
185	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
186	C₂×C₄×C₁₃₉	#123	1	2	yes	—
187	C₈×C₁₃₉	—	2	8	no	—
188	C₂²×C₁₃₉	—	2	2	no	—
189	C₂²×C₁₃₉	—	2	4	no	—
190	C₂²×C₁₃₉	—	2	4	no	—
191	C₂²×C₁₃₉	—	4	2	no	—
192	C₂²×C₁₃₉	—	4	1	no	—
193	C₂²×C₁₃₉	—	4	1	no	—
194	C₂²×C₁₃₉	—	4	4	no	—
195	C₂²×C₁₃₉	—	4	4	no	—
196	C₂²×C₁₃₉	—	8	2	no	—
197	C₂²×C₁₃₉	C₂×#95	1	1	yes	characteristic
198	C₂²×C₁₃₉	#380	1	2	yes	—
199	C₂²×C₁₃₉	#386	1	1	yes	characteristic
200	C₂²×C₁₃₉	#386	1	2	yes	—
201	C₂²×C₁₃₉	#386	1	1	yes	characteristic
202	C₄×C₁₃₉	—	2	4	no	—
203	C₄×C₁₃₉	—	4	4	no	—
204	C₄×C₁₃₉	—	8	4	no	—
205	C₄×C₁₃₉	—	8	2	no	—
206	C₄×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
207	C₄×C₁₃₉	#379	1	1	yes	characteristic
208	C₄×C₁₃₉	#381	1	1	yes	characteristic
209	C₄×C₁₃₉	#385	1	1	yes	characteristic
210	C₄×C₁₃₉	#385	1	1	yes	characteristic
211	C₄×C₁₃₉	#385	1	2	yes	—
212	C₂×C₁₃₉	—	2	1	no	—
213	C₂×C₁₃₉	—	2	2	no	—
214	C₂×C₁₃₉	—	2	1	no	—
215	C₂×C₁₃₉	—	2	2	no	—
216	C₂×C₁₃₉	—	4	4	no	—
217	C₂×C₁₃₉	C₂²⋊#95	1	1	yes	characteristic
218	C₂×C₁₃₉	#1884	1	2	yes	—
219	#10751	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₁₃₉	#10751	1	1	yes	characteristic, direct product factor, Sylow
221	C₂×#568	C₂×C₁₃₉	1	1	yes	characteristic
222	C₂×#410	C₂×C₁₃₉	1	1	yes	characteristic
223	#2297	C₂×C₁₃₉	1	1	yes	characteristic
224	#1733	C₂×C₁₃₉	1	2	yes	complemented
225	C₂×#339	C₂×C₁₃₉	1	2	yes	complemented
226	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
227	#568	—	2	2	no	—
228	#568	—	2	4	no	—
229	#568	C₄×C₁₃₉	1	4	yes	complemented
230	C₂×#131	—	2	4	no	—
231	C₂²×M₁₆	—	2	2	no	—
232	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
233	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
234	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
236	#410	—	2	2	no	—
237	#410	C₄×C₁₃₉	1	4	yes	complemented
238	C₂×#99	—	2	2	no	—
239	#391	C₄×C₁₃₉	1	2	yes	complemented
240	#390	C₄×C₁₃₉	1	2	yes	complemented
241	#386	—	2	2	no	—
242	C₄×C₂²⋊C₄	—	2	2	no	—
243	#339	—	2	4	no	—
244	#339	—	2	4	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
250	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
251	C₂×#41	D₄×C₁₃₉	1	2	yes	—
252	C₂×#41	Q₈×C₁₃₉	1	2	yes	—
253	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
254	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
255	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
259	#131	—	2	16	no	—
260	#131	—	2	16	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	8	no	—
263	C₂×M₁₆	—	2	8	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
268	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
269	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
270	C₂²×C₈	—	2	4	no	—
271	C₂²×C₈	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	#117	C₂×C₄×C₁₃₉	1	4	yes	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
289	#99	—	2	8	no	—
290	#95	—	2	4	no	—
291	C₂⁴	C₂²⋊C₄×C₁₃₉	1	2	yes	—
292	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₄²×C₁₃₉	1	2	yes	—
304	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	2	yes	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₄²×C₁₃₉	1	2	yes	—
310	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
311	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
312	C₂×D₄	C₄⋊C₄×C₁₃₉	1	2	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
323	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
324	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
332	C₂²×C₄	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
333	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
334	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
335	M₁₆	—	2	16	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
340	C₂×C₈	—	2	16	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	8	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₄²	—	2	4	no	—
352	C₄²	—	2	4	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	4	no	—
362	C₂³	#95×C₁₃₉	1	4	yes	—
363	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
364	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
365	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
366	C₂³	#121×C₁₃₉	1	2	yes	—
367	C₂³	#121×C₁₃₉	1	2	yes	—
368	Q₈	—	2	4	no	—
369	Q₈	—	2	4	no	—
370	D₄	—	2	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	#95×C₁₃₉	1	4	yes	—
389	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
394	C₂×C₄	#117×C₁₃₉	1	2	yes	—
395	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
396	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
397	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
398	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
399	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄	#120×C₁₃₉	1	2	yes	—
401	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
403	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
404	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
405	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄	#123×C₁₃₉	1	2	yes	—
407	C₈	—	2	8	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×#95×C₁₃₉	1	1	yes	characteristic
418	C₂²	#380×C₁₃₉	1	2	yes	—
419	C₂²	#386×C₁₃₉	1	1	yes	characteristic
420	C₂²	#386×C₁₃₉	1	2	yes	—
421	C₂²	#386×C₁₃₉	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	8	4	no	—
425	C₄	—	8	2	no	—
426	C₄	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
427	C₄	#379×C₁₃₉	1	1	yes	characteristic
428	C₄	#381×C₁₃₉	1	1	yes	characteristic
429	C₄	#385×C₁₃₉	1	1	yes	characteristic
430	C₄	#385×C₁₃₉	1	1	yes	characteristic
431	C₄	#385×C₁₃₉	1	2	yes	—
432	C₂	—	2	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	2	no	—
436	C₂	—	4	4	no	—
437	C₂	C₂²⋊#95×C₁₃₉	1	1	yes	characteristic
438	C₂	#1884×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	#120
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	#386
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1733×C₁₃₉	C₂	semidirect
5. C₂×#339×C₁₃₉	C₂	semidirect
9. #568×C₁₃₉	C₄	semidirect
17. #410×C₁₃₉	C₄	semidirect
19. #391×C₁₃₉	C₄	semidirect
20. #390×C₁₃₉	C₄	semidirect
119. M₁₆×C₁₃₉	C₂²⋊C₄	semidirect
219. #10751	C₁₃₉	direct (N × H)
220. C₁₃₉	#10751	direct (N × H)
224. #1733	C₂×C₁₃₉	semidirect
225. C₂×#339	C₂×C₁₃₉	semidirect
229. #568	C₄×C₁₃₉	semidirect
237. #410	C₄×C₁₃₉	semidirect
239. #391	C₄×C₁₃₉	semidirect
240. #390	C₄×C₁₃₉	semidirect
339. M₁₆	C₂²⋊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×#568×C₁₃₉	2
C₂×#410×C₁₃₉	2
#2297×C₁₃₉	2
#1733×C₁₃₉	2
C₂×#339×C₁₃₉	2
#10751	139

Subgroups — C139×#10751 #48005347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10751 #48005347