Subgroups — C₁₃₉×#35629 #48030225

Order 35584.

1722 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2514×C₁₃₉	C₂	1	4	yes	maximal, complemented
2	#2513×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	#2510×C₁₃₉	C₂	1	8	yes	maximal, complemented
4	#2495×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2494×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2311×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#2311×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	#401×C₁₃₉	C₂²	1	8	yes	—
21	#400×C₁₃₉	C₂²	1	8	yes	—
22	#397×C₁₃₉	C₂²	1	8	yes	—
23	#397×C₁₃₉	C₂²	1	8	yes	—
24	#391×C₁₃₉	C₂²	1	2	yes	—
25	#391×C₁₃₉	C₂²	1	2	yes	—
26	#391×C₁₃₉	C₂²	1	2	yes	—
27	#390×C₁₃₉	C₂²	1	2	yes	—
28	#390×C₁₃₉	C₂²	1	2	yes	—
29	#390×C₁₃₉	C₂²	1	2	yes	—
30	#389×C₁₃₉	C₂²	1	4	yes	—
31	#389×C₁₃₉	C₂²	1	2	yes	—
32	#389×C₁₃₉	C₂²	1	2	yes	—
33	#389×C₁₃₉	C₂²	1	4	yes	—
34	#388×C₁₃₉	C₂²	1	8	yes	—
35	#388×C₁₃₉	C₂²	1	8	yes	—
36	#387×C₁₃₉	C₂²	1	8	yes	—
37	#386×C₁₃₉	C₂²	1	4	yes	—
38	#386×C₁₃₉	C₂²	1	4	yes	—
39	#386×C₁₃₉	C₂²	1	4	yes	—
40	#385×C₁₃₉	C₂²	1	4	yes	—
41	#383×C₁₃₉	C₂²	1	8	yes	—
42	#382×C₁₃₉	C₂²	1	4	yes	—
43	#382×C₁₃₉	C₂²	1	2	yes	—
44	#382×C₁₃₉	C₂²	1	2	yes	—
45	#380×C₁₃₉	C₂²	1	4	yes	—
46	#380×C₁₃₉	C₂²	1	4	yes	—
47	#380×C₁₃₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
50	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
51	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
54	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
55	C₂×#41×C₁₃₉	—	2	4	no	—
56	C₂×#41×C₁₃₉	—	2	4	no	—
57	C₂×#41×C₁₃₉	—	2	4	no	—
58	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	#117×C₁₃₉	—	2	4	no	—
67	#117×C₁₃₉	—	2	4	no	—
68	#117×C₁₃₉	—	2	4	no	—
69	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₄²×C₁₃₉	—	2	4	no	—
89	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
96	#95×C₁₃₉	C₂³	1	8	yes	—
97	#95×C₁₃₉	C₂³	1	4	yes	—
98	#95×C₁₃₉	C₂³	1	8	yes	—
99	#95×C₁₃₉	C₂³	1	8	yes	—
100	#95×C₁₃₉	C₂³	1	8	yes	—
101	#95×C₁₃₉	C₂³	1	4	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	4	yes	—
105	#95×C₁₃₉	C₂³	1	4	yes	—
106	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
107	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
108	#41×C₁₃₉	—	4	16	no	—
109	C₂×Q₈×C₁₃₉	—	2	2	no	—
110	C₂×Q₈×C₁₃₉	—	2	2	no	—
111	C₂×Q₈×C₁₃₉	—	2	2	no	—
112	C₂×D₄×C₁₃₉	—	2	4	no	—
113	C₂×D₄×C₁₃₉	—	2	4	no	—
114	C₂×D₄×C₁₃₉	—	2	4	no	—
115	C₂×D₄×C₁₃₉	—	2	2	no	—
116	C₂×D₄×C₁₃₉	—	2	2	no	—
117	C₂×D₄×C₁₃₉	—	2	2	no	—
118	C₂²×C₄×C₁₃₉	—	2	4	no	—
119	C₂²×C₄×C₁₃₉	—	2	4	no	—
120	C₂²×C₄×C₁₃₉	—	2	4	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	4	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	4	2	no	—
125	C₂²×C₄×C₁₃₉	—	4	2	no	—
126	C₂²×C₄×C₁₃₉	—	4	4	no	—
127	C₂²×C₄×C₁₃₉	—	4	4	no	—
128	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
129	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
130	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₁₃₉	—	2	4	no	—
142	C₄⋊C₄×C₁₃₉	—	2	4	no	—
143	C₄⋊C₄×C₁₃₉	—	2	4	no	—
144	C₄⋊C₄×C₁₃₉	—	2	4	no	—
145	C₄⋊C₄×C₁₃₉	—	2	4	no	—
146	C₄⋊C₄×C₁₃₉	—	2	4	no	—
147	C₄⋊C₄×C₁₃₉	—	2	4	no	—
148	C₄⋊C₄×C₁₃₉	—	4	4	no	—
149	C₄⋊C₄×C₁₃₉	—	4	4	no	—
150	C₄⋊C₄×C₁₃₉	—	4	8	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
156	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
157	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
158	C₄²×C₁₃₉	—	2	4	no	—
159	C₄²×C₁₃₉	—	2	2	no	—
160	C₄²×C₁₃₉	—	2	2	no	—
161	C₄²×C₁₃₉	—	2	4	no	—
162	C₄²×C₁₃₉	—	2	4	no	—
163	C₄²×C₁₃₉	—	2	4	no	—
164	C₄²×C₁₃₉	—	4	8	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	2	no	—
168	C₂³×C₁₃₉	—	2	2	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	4	no	—
171	C₂³×C₁₃₉	—	2	4	no	—
172	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
173	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
174	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
175	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
176	Q₈×C₁₃₉	—	4	4	no	—
177	D₄×C₁₃₉	—	4	8	no	—
178	D₄×C₁₃₉	—	4	4	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	4	no	—
182	C₂×C₄×C₁₃₉	—	2	4	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	4	no	—
185	C₂×C₄×C₁₃₉	—	2	4	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₄×C₁₃₉	—	2	8	no	—
192	C₂×C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₄×C₁₃₉	—	2	4	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	2	no	—
196	C₂×C₄×C₁₃₉	—	2	4	no	—
197	C₂×C₄×C₁₃₉	—	2	8	no	—
198	C₂×C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	2	2	no	—
201	C₂×C₄×C₁₃₉	—	4	8	no	—
202	C₂×C₄×C₁₃₉	—	4	8	no	—
203	C₂×C₄×C₁₃₉	—	8	4	no	—
204	C₂×C₄×C₁₃₉	—	8	4	no	—
205	C₂×C₄×C₁₃₉	#126	1	16	yes	—
206	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
209	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
210	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
211	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
212	C₂²×C₁₃₉	—	2	4	no	—
213	C₂²×C₁₃₉	—	2	2	no	—
214	C₂²×C₁₃₉	—	2	2	no	—
215	C₂²×C₁₃₉	—	2	4	no	—
216	C₂²×C₁₃₉	—	4	2	no	—
217	C₂²×C₁₃₉	—	4	4	no	—
218	C₂²×C₁₃₉	—	4	2	no	—
219	C₂²×C₁₃₉	—	4	2	no	—
220	C₂²×C₁₃₉	—	4	4	no	—
221	C₂²×C₁₃₉	C₂×#126	1	4	yes	—
222	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
223	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
224	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
225	C₂²×C₁₃₉	#585	1	2	yes	—
226	C₂²×C₁₃₉	#585	1	2	yes	—
227	C₄×C₁₃₉	—	4	2	no	—
228	C₄×C₁₃₉	—	4	4	no	—
229	C₄×C₁₃₉	—	4	2	no	—
230	C₄×C₁₃₉	—	4	2	no	—
231	C₄×C₁₃₉	—	4	4	no	—
232	C₄×C₁₃₉	—	4	4	no	—
233	C₄×C₁₃₉	—	4	4	no	—
234	C₄×C₁₃₉	—	4	4	no	—
235	C₄×C₁₃₉	C₂×#126	1	4	yes	—
236	C₄×C₁₃₉	C₂×#126	1	4	yes	—
237	C₂×C₁₃₉	—	2	4	no	—
238	C₂×C₁₃₉	—	8	2	no	—
239	C₂×C₁₃₉	C₂²×#126	1	1	yes	characteristic
240	C₂×C₁₃₉	#3493	1	2	yes	—
241	C₂×C₁₃₉	#3510	1	1	yes	characteristic
242	C₂×C₁₃₉	#3510	1	1	yes	characteristic
243	C₂×C₁₃₉	#3512	1	2	yes	—
244	#35629	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₁₃₉	#35629	1	1	yes	characteristic, direct product factor, Sylow
246	#2514	C₂×C₁₃₉	1	4	yes	complemented
247	#2513	C₂×C₁₃₉	1	4	yes	complemented
248	#2510	C₂×C₁₃₉	1	8	yes	complemented
249	#2495	C₂×C₁₃₉	1	4	yes	complemented
250	#2494	C₂×C₁₃₉	1	4	yes	complemented
251	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
252	#2311	C₂×C₁₃₉	1	1	yes	characteristic
253	#2311	C₂×C₁₃₉	1	1	yes	characteristic
254	#2297	C₂×C₁₃₉	1	1	yes	characteristic
255	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
256	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
257	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
258	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
259	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
260	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
261	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
264	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
265	#401	C₂²×C₁₃₉	1	8	yes	—
266	#400	C₂²×C₁₃₉	1	8	yes	—
267	#397	C₂²×C₁₃₉	1	8	yes	—
268	#397	C₂²×C₁₃₉	1	8	yes	—
269	#391	C₂²×C₁₃₉	1	2	yes	—
270	#391	C₂²×C₁₃₉	1	2	yes	—
271	#391	C₂²×C₁₃₉	1	2	yes	—
272	#390	C₂²×C₁₃₉	1	2	yes	—
273	#390	C₂²×C₁₃₉	1	2	yes	—
274	#390	C₂²×C₁₃₉	1	2	yes	—
275	#389	C₂²×C₁₃₉	1	4	yes	—
276	#389	C₂²×C₁₃₉	1	4	yes	—
277	#389	C₂²×C₁₃₉	1	2	yes	—
278	#389	C₂²×C₁₃₉	1	2	yes	—
279	#388	C₂²×C₁₃₉	1	8	yes	—
280	#388	C₂²×C₁₃₉	1	8	yes	—
281	#387	C₂²×C₁₃₉	1	8	yes	—
282	#386	C₂²×C₁₃₉	1	4	yes	—
283	#386	C₂²×C₁₃₉	1	4	yes	—
284	#386	C₂²×C₁₃₉	1	4	yes	—
285	#385	C₂²×C₁₃₉	1	4	yes	—
286	#383	C₂²×C₁₃₉	1	8	yes	—
287	#382	C₂²×C₁₃₉	1	2	yes	—
288	#382	C₂²×C₁₃₉	1	2	yes	—
289	#382	C₂²×C₁₃₉	1	4	yes	—
290	#380	C₂²×C₁₃₉	1	4	yes	—
291	#380	C₂²×C₁₃₉	1	4	yes	—
292	#380	C₂²×C₁₃₉	1	4	yes	—
293	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
294	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
295	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
296	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
297	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
298	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
299	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
300	C₂×#41	—	2	4	no	—
301	C₂×#41	—	2	4	no	—
302	C₂×#41	—	2	4	no	—
303	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
305	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
307	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
309	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
310	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
311	#117	—	2	4	no	—
312	#117	—	2	4	no	—
313	#117	—	2	4	no	—
314	C₂×C₄⋊C₄	—	2	4	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
335	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
337	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
340	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
341	#95	C₂³×C₁₃₉	1	8	yes	—
342	#95	C₂³×C₁₃₉	1	8	yes	—
343	#95	C₂³×C₁₃₉	1	8	yes	—
344	#95	C₂³×C₁₃₉	1	4	yes	—
345	#95	C₂³×C₁₃₉	1	4	yes	—
346	#95	C₂³×C₁₃₉	1	4	yes	—
347	#95	C₂³×C₁₃₉	1	4	yes	—
348	#95	C₂³×C₁₃₉	1	8	yes	—
349	#95	C₂³×C₁₃₉	1	8	yes	—
350	#95	C₂³×C₁₃₉	1	8	yes	—
351	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
352	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
353	#41	—	4	16	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
374	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
375	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	8	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	8	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	4	8	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
418	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
419	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
420	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
421	Q₈	—	4	4	no	—
422	D₄	—	4	8	no	—
423	D₄	—	4	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	#126×C₁₃₉	1	16	yes	—
451	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
452	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
453	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
454	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
456	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	C₂×#126×C₁₃₉	1	4	yes	—
467	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
468	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
469	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
470	C₂²	#585×C₁₃₉	1	2	yes	—
471	C₂²	#585×C₁₃₉	1	2	yes	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	4	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	4	no	—
480	C₄	C₂×#126×C₁₃₉	1	4	yes	—
481	C₄	C₂×#126×C₁₃₉	1	4	yes	—
482	C₂	—	2	4	no	—
483	C₂	—	8	2	no	—
484	C₂	C₂²×#126×C₁₃₉	1	1	yes	characteristic
485	C₂	#3493×C₁₃₉	1	2	yes	—
486	C₂	#3510×C₁₃₉	1	1	yes	characteristic
487	C₂	#3510×C₁₃₉	1	1	yes	characteristic
488	C₂	#3512×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
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. #2514×C₁₃₉	C₂	semidirect
2. #2513×C₁₃₉	C₂	semidirect
3. #2510×C₁₃₉	C₂	semidirect
4. #2495×C₁₃₉	C₂	semidirect
5. #2494×C₁₃₉	C₂	semidirect
6. #2316×C₁₃₉	C₂	semidirect
10. #2296×C₁₃₉	C₂	semidirect
11. C₂×#382×C₁₃₉	C₂	semidirect
12. #2274×C₁₃₉	C₂	semidirect
244. #35629	C₁₃₉	direct (N × H)
245. C₁₃₉	#35629	direct (N × H)
246. #2514	C₂×C₁₃₉	semidirect
247. #2513	C₂×C₁₃₉	semidirect
248. #2510	C₂×C₁₃₉	semidirect
249. #2495	C₂×C₁₃₉	semidirect
250. #2494	C₂×C₁₃₉	semidirect
251. #2316	C₂×C₁₃₉	semidirect
255. #2296	C₂×C₁₃₉	semidirect
256. C₂×#382	C₂×C₁₃₉	semidirect
257. #2274	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2514×C₁₃₉	2
#2513×C₁₃₉	2
#2510×C₁₃₉	2
#2495×C₁₃₉	2
#2494×C₁₃₉	2
#2316×C₁₃₉	2
#2311×C₁₃₉	2
#2297×C₁₃₉	2
#2296×C₁₃₉	2
C₂×#382×C₁₃₉	2
#2274×C₁₃₉	2
#35629	139

Subgroups — C139×#35629 #48030225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35629 #48030225