Subgroups — C₁₃₉×#36175 #48030771

Order 35584.

1718 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2527×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2523×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2514×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2495×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2494×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2447×C₁₃₉	C₂	1	2	yes	maximal
11	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2367×C₁₃₉	C₂	1	2	yes	maximal
13	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2356×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2283×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
27	#401×C₁₃₉	C₂²	1	4	yes	—
28	#400×C₁₃₉	C₂²	1	4	yes	—
29	#397×C₁₃₉	C₂²	1	4	yes	—
30	#397×C₁₃₉	C₂²	1	4	yes	—
31	#397×C₁₃₉	C₂²	1	4	yes	—
32	#393×C₁₃₉	C₂²	1	4	yes	—
33	#391×C₁₃₉	C₂²	1	2	yes	—
34	#391×C₁₃₉	C₂²	1	2	yes	—
35	#391×C₁₃₉	C₂²	1	2	yes	—
36	#391×C₁₃₉	C₂²	1	2	yes	—
37	#391×C₁₃₉	C₂²	1	4	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#391×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	1	yes	characteristic
43	#389×C₁₃₉	C₂²	1	1	yes	characteristic
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	4	yes	—
48	#387×C₁₃₉	C₂²	1	4	yes	—
49	#387×C₁₃₉	C₂²	1	2	yes	—
50	#387×C₁₃₉	C₂²	1	4	yes	—
51	#387×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	2	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#385×C₁₃₉	C₂²	1	4	yes	—
55	#385×C₁₃₉	C₂²	1	4	yes	—
56	#383×C₁₃₉	C₂²	1	4	yes	—
57	#383×C₁₃₉	C₂²	1	4	yes	—
58	#382×C₁₃₉	C₂²	1	2	yes	—
59	#382×C₁₃₉	C₂²	1	1	yes	characteristic
60	#382×C₁₃₉	C₂²	1	2	yes	—
61	#382×C₁₃₉	C₂²	1	2	yes	—
62	#381×C₁₃₉	C₂²	1	4	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	#380×C₁₃₉	C₂²	1	2	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	#376×C₁₃₉	C₂²	1	4	yes	—
82	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
90	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
91	#125×C₁₃₉	—	2	4	no	—
92	#124×C₁₃₉	—	2	8	no	—
93	C₄×Q₈×C₁₃₉	—	2	8	no	—
94	C₄×D₄×C₁₃₉	—	2	4	no	—
95	C₄×D₄×C₁₃₉	—	2	4	no	—
96	C₄×D₄×C₁₃₉	—	2	4	no	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃₉	—	2	8	no	—
122	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
136	#95×C₁₃₉	C₂³	1	2	yes	—
137	#95×C₁₃₉	C₂³	1	2	yes	—
138	#95×C₁₃₉	C₂³	1	4	yes	—
139	#95×C₁₃₉	C₂³	1	4	yes	—
140	#95×C₁₃₉	C₂³	1	4	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	2	yes	—
145	#95×C₁₃₉	C₂³	1	4	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	2	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	2	yes	—
152	#95×C₁₃₉	C₂³	1	2	yes	—
153	#95×C₁₃₉	C₂³	1	2	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	4	yes	—
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂×Q₈×C₁₃₉	—	2	4	no	—
159	C₂×Q₈×C₁₃₉	—	2	4	no	—
160	C₂×Q₈×C₁₃₉	—	2	4	no	—
161	C₂×Q₈×C₁₃₉	—	2	4	no	—
162	C₂×Q₈×C₁₃₉	—	4	2	no	—
163	C₂×Q₈×C₁₃₉	—	4	2	no	—
164	C₂×D₄×C₁₃₉	—	2	2	no	—
165	C₂×D₄×C₁₃₉	—	2	2	no	—
166	C₂×D₄×C₁₃₉	#41	1	4	yes	—
167	C₂²×C₄×C₁₃₉	—	2	4	no	—
168	C₂²×C₄×C₁₃₉	—	2	4	no	—
169	C₂²×C₄×C₁₃₉	—	2	4	no	—
170	C₂²×C₄×C₁₃₉	—	2	4	no	—
171	C₂²×C₄×C₁₃₉	—	2	4	no	—
172	C₂²×C₄×C₁₃₉	—	2	4	no	—
173	C₂²×C₄×C₁₃₉	—	2	4	no	—
174	C₂²×C₄×C₁₃₉	—	4	2	no	—
175	C₂²×C₄×C₁₃₉	—	4	2	no	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₄⋊C₄×C₁₃₉	—	2	2	no	—
193	C₄⋊C₄×C₁₃₉	—	2	2	no	—
194	C₄⋊C₄×C₁₃₉	—	2	8	no	—
195	C₄⋊C₄×C₁₃₉	—	2	4	no	—
196	C₄⋊C₄×C₁₃₉	—	2	4	no	—
197	C₄⋊C₄×C₁₃₉	—	2	2	no	—
198	C₄⋊C₄×C₁₃₉	—	2	2	no	—
199	C₄⋊C₄×C₁₃₉	—	2	4	no	—
200	C₄⋊C₄×C₁₃₉	—	2	4	no	—
201	C₄⋊C₄×C₁₃₉	—	2	4	no	—
202	C₄⋊C₄×C₁₃₉	—	2	4	no	—
203	C₄⋊C₄×C₁₃₉	—	2	2	no	—
204	C₄⋊C₄×C₁₃₉	—	2	2	no	—
205	C₄⋊C₄×C₁₃₉	—	4	2	no	—
206	C₄⋊C₄×C₁₃₉	—	4	2	no	—
207	C₄⋊C₄×C₁₃₉	—	4	4	no	—
208	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
209	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
210	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
214	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
215	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
216	C₄²×C₁₃₉	—	2	4	no	—
217	C₄²×C₁₃₉	—	2	4	no	—
218	C₄²×C₁₃₉	—	2	4	no	—
219	C₄²×C₁₃₉	—	2	2	no	—
220	C₄²×C₁₃₉	—	2	2	no	—
221	C₄²×C₁₃₉	—	2	4	no	—
222	C₄²×C₁₃₉	—	2	8	no	—
223	C₄²×C₁₃₉	—	2	4	no	—
224	C₄²×C₁₃₉	—	2	2	no	—
225	C₄²×C₁₃₉	—	4	4	no	—
226	C₄²×C₁₃₉	—	4	1	no	—
227	C₄²×C₁₃₉	—	4	1	no	—
228	C₄²×C₁₃₉	#41	1	4	yes	—
229	C₄²×C₁₃₉	#41	1	4	yes	—
230	C₂³×C₁₃₉	—	2	2	no	—
231	C₂³×C₁₃₉	—	2	2	no	—
232	C₂³×C₁₃₉	—	2	2	no	—
233	C₂³×C₁₃₉	—	2	2	no	—
234	C₂³×C₁₃₉	—	2	2	no	—
235	C₂³×C₁₃₉	—	2	2	no	—
236	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
237	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
238	Q₈×C₁₃₉	—	4	8	no	—
239	Q₈×C₁₃₉	—	8	4	no	—
240	D₄×C₁₃₉	—	2	8	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	1	no	—
243	C₂×C₄×C₁₃₉	—	2	1	no	—
244	C₂×C₄×C₁₃₉	—	2	2	no	—
245	C₂×C₄×C₁₃₉	—	2	1	no	—
246	C₂×C₄×C₁₃₉	—	2	1	no	—
247	C₂×C₄×C₁₃₉	—	2	1	no	—
248	C₂×C₄×C₁₃₉	—	2	1	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	1	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	1	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	4	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	4	no	—
264	C₂×C₄×C₁₃₉	—	2	4	no	—
265	C₂×C₄×C₁₃₉	—	2	1	no	—
266	C₂×C₄×C₁₃₉	—	2	1	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	2	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	4	no	—
272	C₂×C₄×C₁₃₉	—	2	1	no	—
273	C₂×C₄×C₁₃₉	—	2	1	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	2	no	—
276	C₂×C₄×C₁₃₉	—	2	4	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	4	8	no	—
280	C₂×C₄×C₁₃₉	—	4	8	no	—
281	C₂×C₄×C₁₃₉	—	4	8	no	—
282	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
283	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
284	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
285	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
286	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
287	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
288	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
289	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
290	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
291	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₁₃₉	—	2	4	no	—
293	C₂²×C₁₃₉	—	2	4	no	—
294	C₂²×C₁₃₉	—	2	4	no	—
295	C₂²×C₁₃₉	—	4	2	no	—
296	C₂²×C₁₃₉	—	4	2	no	—
297	C₂²×C₁₃₉	—	4	2	no	—
298	C₂²×C₁₃₉	—	4	2	no	—
299	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
301	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
302	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
303	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂²×C₁₃₉	#585	1	1	yes	characteristic
305	C₂²×C₁₃₉	#585	1	1	yes	characteristic
306	C₄×C₁₃₉	—	2	2	no	—
307	C₄×C₁₃₉	—	2	2	no	—
308	C₄×C₁₃₉	—	2	4	no	—
309	C₄×C₁₃₉	—	2	2	no	—
310	C₄×C₁₃₉	—	4	4	no	—
311	C₄×C₁₃₉	—	4	2	no	—
312	C₄×C₁₃₉	—	4	2	no	—
313	C₄×C₁₃₉	—	4	2	no	—
314	C₄×C₁₃₉	—	4	2	no	—
315	C₄×C₁₃₉	—	4	4	no	—
316	C₄×C₁₃₉	—	4	1	no	—
317	C₄×C₁₃₉	—	4	2	no	—
318	C₄×C₁₃₉	—	4	2	no	—
319	C₄×C₁₃₉	—	4	1	no	—
320	C₄×C₁₃₉	#529	1	4	yes	—
321	C₄×C₁₃₉	#556	1	4	yes	—
322	C₂×C₁₃₉	—	4	4	no	—
323	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
324	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
325	C₂×C₁₃₉	#3475	1	1	yes	characteristic
326	C₂×C₁₃₉	#3475	1	1	yes	characteristic
327	C₂×C₁₃₉	#3510	1	1	yes	characteristic
328	C₂×C₁₃₉	#3515	1	1	yes	characteristic
329	C₂×C₁₃₉	#3518	1	1	yes	characteristic
330	#36175	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₁₃₉	#36175	1	1	yes	characteristic, direct product factor, Sylow
332	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
333	#2851	C₂×C₁₃₉	1	2	yes	complemented
334	#2563	C₂×C₁₃₉	1	1	yes	characteristic
335	#2547	C₂×C₁₃₉	1	1	yes	characteristic
336	#2527	C₂×C₁₃₉	1	4	yes	complemented
337	#2523	C₂×C₁₃₉	1	4	yes	complemented
338	#2514	C₂×C₁₃₉	1	2	yes	complemented
339	#2495	C₂×C₁₃₉	1	2	yes	complemented
340	#2494	C₂×C₁₃₉	1	2	yes	complemented
341	#2447	C₂×C₁₃₉	1	2	yes	—
342	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
343	#2367	C₂×C₁₃₉	1	2	yes	—
344	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
345	#2356	C₂×C₁₃₉	1	2	yes	complemented
346	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
347	#2283	C₂×C₁₃₉	1	2	yes	complemented
348	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
350	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
351	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
352	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
353	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
354	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
357	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
358	#401	C₂²×C₁₃₉	1	4	yes	—
359	#400	C₂²×C₁₃₉	1	4	yes	—
360	#397	C₂²×C₁₃₉	1	4	yes	—
361	#397	C₂²×C₁₃₉	1	4	yes	—
362	#397	C₂²×C₁₃₉	1	4	yes	—
363	#393	C₂²×C₁₃₉	1	4	yes	—
364	#391	C₂²×C₁₃₉	1	2	yes	—
365	#391	C₂²×C₁₃₉	1	2	yes	—
366	#391	C₂²×C₁₃₉	1	2	yes	—
367	#391	C₂²×C₁₃₉	1	2	yes	—
368	#391	C₂²×C₁₃₉	1	2	yes	—
369	#391	C₂²×C₁₃₉	1	2	yes	—
370	#391	C₂²×C₁₃₉	1	4	yes	—
371	#390	C₂²×C₁₃₉	1	2	yes	—
372	#389	C₂²×C₁₃₉	1	1	yes	characteristic
373	#389	C₂²×C₁₃₉	1	1	yes	characteristic
374	#389	C₂²×C₁₃₉	1	2	yes	—
375	#389	C₂²×C₁₃₉	1	2	yes	—
376	#389	C₂²×C₁₃₉	1	2	yes	—
377	#388	C₂²×C₁₃₉	1	4	yes	—
378	#388	C₂²×C₁₃₉	1	4	yes	—
379	#387	C₂²×C₁₃₉	1	2	yes	—
380	#387	C₂²×C₁₃₉	1	2	yes	—
381	#387	C₂²×C₁₃₉	1	4	yes	—
382	#387	C₂²×C₁₃₉	1	4	yes	—
383	#387	C₂²×C₁₃₉	1	4	yes	—
384	#387	C₂²×C₁₃₉	1	4	yes	—
385	#385	C₂²×C₁₃₉	1	4	yes	—
386	#385	C₂²×C₁₃₉	1	4	yes	—
387	#383	C₂²×C₁₃₉	1	4	yes	—
388	#383	C₂²×C₁₃₉	1	4	yes	—
389	#382	C₂²×C₁₃₉	1	1	yes	characteristic
390	#382	C₂²×C₁₃₉	1	2	yes	—
391	#382	C₂²×C₁₃₉	1	2	yes	—
392	#382	C₂²×C₁₃₉	1	2	yes	—
393	#381	C₂²×C₁₃₉	1	4	yes	—
394	#380	C₂²×C₁₃₉	1	2	yes	—
395	#380	C₂²×C₁₃₉	1	2	yes	—
396	#380	C₂²×C₁₃₉	1	2	yes	—
397	#380	C₂²×C₁₃₉	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
400	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
401	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
404	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
412	#376	C₂²×C₁₃₉	1	4	yes	—
413	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
415	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
416	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
418	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
419	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
420	C₄⋊Q₈	—	2	4	no	—
421	C₄⋊Q₈	—	2	4	no	—
422	#125	—	2	4	no	—
423	#124	—	2	8	no	—
424	C₄×Q₈	—	2	8	no	—
425	C₄×D₄	—	2	4	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	4	no	—
428	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
452	C₂×C₄²	—	2	8	no	—
453	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
456	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
457	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
458	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
460	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
465	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
467	#95	C₂³×C₁₃₉	1	2	yes	—
468	#95	C₂³×C₁₃₉	1	4	yes	—
469	#95	C₂³×C₁₃₉	1	4	yes	—
470	#95	C₂³×C₁₃₉	1	4	yes	—
471	#95	C₂³×C₁₃₉	1	2	yes	—
472	#95	C₂³×C₁₃₉	1	2	yes	—
473	#95	C₂³×C₁₃₉	1	2	yes	—
474	#95	C₂³×C₁₃₉	1	2	yes	—
475	#95	C₂³×C₁₃₉	1	4	yes	—
476	#95	C₂³×C₁₃₉	1	4	yes	—
477	#95	C₂³×C₁₃₉	1	4	yes	—
478	#95	C₂³×C₁₃₉	1	2	yes	—
479	#95	C₂³×C₁₃₉	1	4	yes	—
480	#95	C₂³×C₁₃₉	1	2	yes	—
481	#95	C₂³×C₁₃₉	1	2	yes	—
482	#95	C₂³×C₁₃₉	1	2	yes	—
483	#95	C₂³×C₁₃₉	1	4	yes	—
484	#95	C₂³×C₁₃₉	1	4	yes	—
485	#95	C₂³×C₁₃₉	1	4	yes	—
486	#95	C₂³×C₁₃₉	1	4	yes	—
487	#95	C₂³×C₁₃₉	1	4	yes	—
488	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	4	2	no	—
494	C₂×Q₈	—	4	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	#41×C₁₃₉	1	4	yes	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	8	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	4	no	—
539	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	8	no	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	4	4	no	—
546	C₂²⋊C₄	—	4	4	no	—
547	C₄²	—	2	4	no	—
548	C₄²	—	2	4	no	—
549	C₄²	—	2	4	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	8	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	4	4	no	—
557	C₄²	—	4	1	no	—
558	C₄²	—	4	1	no	—
559	C₄²	#41×C₁₃₉	1	4	yes	—
560	C₄²	#41×C₁₃₉	1	4	yes	—
561	C₂³	—	2	2	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
568	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
569	Q₈	—	4	8	no	—
570	Q₈	—	8	4	no	—
571	D₄	—	2	8	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
614	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
615	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
616	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
617	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
618	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
619	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
620	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
621	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
622	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
631	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
632	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
633	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
634	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
635	C₂²	#585×C₁₃₉	1	1	yes	characteristic
636	C₂²	#585×C₁₃₉	1	1	yes	characteristic
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	4	no	—
640	C₄	—	2	2	no	—
641	C₄	—	4	4	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	4	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	1	no	—
651	C₄	#529×C₁₃₉	1	4	yes	—
652	C₄	#556×C₁₃₉	1	4	yes	—
653	C₂	—	4	4	no	—
654	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
655	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
656	C₂	#3475×C₁₃₉	1	1	yes	characteristic
657	C₂	#3475×C₁₃₉	1	1	yes	characteristic
658	C₂	#3510×C₁₃₉	1	1	yes	characteristic
659	C₂	#3515×C₁₃₉	1	1	yes	characteristic
660	C₂	#3518×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2862×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
5. #2527×C₁₃₉	C₂	semidirect
6. #2523×C₁₃₉	C₂	semidirect
7. #2514×C₁₃₉	C₂	semidirect
8. #2495×C₁₃₉	C₂	semidirect
9. #2494×C₁₃₉	C₂	semidirect
11. #2369×C₁₃₉	C₂	semidirect
13. #2365×C₁₃₉	C₂	semidirect
14. #2356×C₁₃₉	C₂	semidirect
15. C₄×#125×C₁₃₉	C₂	semidirect
16. #2283×C₁₃₉	C₂	semidirect
330. #36175	C₁₃₉	direct (N × H)
331. C₁₃₉	#36175	direct (N × H)
332. #2862	C₂×C₁₃₉	semidirect
333. #2851	C₂×C₁₃₉	semidirect
336. #2527	C₂×C₁₃₉	semidirect
337. #2523	C₂×C₁₃₉	semidirect
338. #2514	C₂×C₁₃₉	semidirect
339. #2495	C₂×C₁₃₉	semidirect
340. #2494	C₂×C₁₃₉	semidirect
342. #2369	C₂×C₁₃₉	semidirect
344. #2365	C₂×C₁₃₉	semidirect
345. #2356	C₂×C₁₃₉	semidirect
346. C₄×#125	C₂×C₁₃₉	semidirect
347. #2283	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2862×C₁₃₉	2
#2851×C₁₃₉	2
#2563×C₁₃₉	2
#2547×C₁₃₉	2
#2527×C₁₃₉	2
#2523×C₁₃₉	2
#2514×C₁₃₉	2
#2495×C₁₃₉	2
#2494×C₁₃₉	2
#2447×C₁₃₉	2
#2369×C₁₃₉	2
#2367×C₁₃₉	2
#2365×C₁₃₉	2
#2356×C₁₃₉	2
C₄×#125×C₁₃₉	2
#2283×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36175	139

Subgroups — C139×#36175 #48030771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36175 #48030771