Subgroups — C₁₃₉×#37150 #48031746

Order 35584.

1880 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2808×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2785×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2723×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2685×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2684×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2679×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2632×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2518×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2321×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#126×C₁₃₉	C₂²	1	4	yes	complemented
15	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
18	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
23	#399×C₁₃₉	C₂²	1	4	yes	complemented
24	#397×C₁₃₉	C₂²	1	4	yes	complemented
25	#397×C₁₃₉	C₂²	1	4	yes	complemented
26	#396×C₁₃₉	C₂²	1	4	yes	complemented
27	#395×C₁₃₉	C₂²	1	2	yes	complemented
28	#395×C₁₃₉	C₂²	1	2	yes	complemented
29	#394×C₁₃₉	C₂²	1	4	yes	—
30	#394×C₁₃₉	C₂²	1	4	yes	—
31	#394×C₁₃₉	C₂²	1	2	yes	—
32	#394×C₁₃₉	C₂²	1	4	yes	—
33	#394×C₁₃₉	C₂²	1	4	yes	—
34	#394×C₁₃₉	C₂²	1	2	yes	—
35	#393×C₁₃₉	C₂²	1	4	yes	complemented
36	#393×C₁₃₉	C₂²	1	4	yes	complemented
37	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	1	yes	characteristic
40	#390×C₁₃₉	C₂²	1	4	yes	—
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	complemented
44	#389×C₁₃₉	C₂²	1	2	yes	complemented
45	#389×C₁₃₉	C₂²	1	2	yes	complemented
46	#388×C₁₃₉	C₂²	1	4	yes	complemented
47	#388×C₁₃₉	C₂²	1	4	yes	complemented
48	#388×C₁₃₉	C₂²	1	4	yes	complemented
49	#388×C₁₃₉	C₂²	1	4	yes	complemented
50	#388×C₁₃₉	C₂²	1	4	yes	complemented
51	#388×C₁₃₉	C₂²	1	4	yes	complemented
52	#388×C₁₃₉	C₂²	1	4	yes	complemented
53	#388×C₁₃₉	C₂²	1	4	yes	complemented
54	#387×C₁₃₉	C₂²	1	4	yes	complemented
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	2	yes	—
57	#386×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	2	yes	complemented
59	#383×C₁₃₉	C₂²	1	2	yes	complemented
60	#382×C₁₃₉	C₂²	1	4	yes	complemented
61	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#379×C₁₃₉	C₂²	1	2	yes	complemented
63	#379×C₁₃₉	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
66	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
76	#126×C₁₃₉	—	4	8	no	—
77	#124×C₁₃₉	—	2	4	no	—
78	#124×C₁₃₉	—	4	4	no	—
79	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
80	#120×C₁₃₉	—	2	8	no	—
81	#120×C₁₃₉	—	4	8	no	—
82	C₄×Q₈×C₁₃₉	—	4	2	no	—
83	C₄×D₄×C₁₃₉	—	4	2	no	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
119	#95×C₁₃₉	C₂³	1	2	yes	—
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	2	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	4	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₃₉	—	2	4	no	—
130	C₂⁴×C₁₃₉	—	4	2	no	—
131	C₂⁴×C₁₃₉	—	4	2	no	—
132	C₂⁴×C₁₃₉	—	4	4	no	—
133	C₂⁴×C₁₃₉	—	4	4	no	—
134	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
136	C₂×Q₈×C₁₃₉	—	2	2	no	—
137	C₂×Q₈×C₁₃₉	—	4	1	no	—
138	C₂×Q₈×C₁₃₉	—	4	1	no	—
139	C₂×Q₈×C₁₃₉	—	4	4	no	—
140	C₂×Q₈×C₁₃₉	—	4	2	no	—
141	C₂×D₄×C₁₃₉	—	2	8	no	—
142	C₂×D₄×C₁₃₉	—	2	4	no	—
143	C₂×D₄×C₁₃₉	—	4	1	no	—
144	C₂×D₄×C₁₃₉	—	4	1	no	—
145	C₂×D₄×C₁₃₉	—	4	4	no	—
146	C₂×D₄×C₁₃₉	—	4	4	no	—
147	C₂×D₄×C₁₃₉	—	4	2	no	—
148	C₂×D₄×C₁₃₉	—	4	2	no	—
149	C₂×D₄×C₁₃₉	—	4	2	no	—
150	C₂×D₄×C₁₃₉	—	4	4	no	—
151	C₂×D₄×C₁₃₉	#41	1	4	yes	—
152	C₂²×C₄×C₁₃₉	—	2	4	no	—
153	C₂²×C₄×C₁₃₉	—	4	2	no	—
154	C₂²×C₄×C₁₃₉	—	4	4	no	—
155	C₂²×C₄×C₁₃₉	—	4	4	no	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₄⋊C₄×C₁₃₉	—	2	8	no	—
169	C₄⋊C₄×C₁₃₉	—	4	2	no	—
170	C₄⋊C₄×C₁₃₉	—	4	2	no	—
171	C₄⋊C₄×C₁₃₉	—	4	1	no	—
172	C₄⋊C₄×C₁₃₉	—	4	1	no	—
173	C₄⋊C₄×C₁₃₉	—	4	2	no	—
174	C₄⋊C₄×C₁₃₉	—	4	4	no	—
175	C₄⋊C₄×C₁₃₉	—	4	4	no	—
176	C₄⋊C₄×C₁₃₉	—	4	4	no	—
177	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
178	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
182	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
184	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
185	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
191	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
192	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
193	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
194	C₄²×C₁₃₉	—	2	2	no	—
195	C₄²×C₁₃₉	—	2	2	no	—
196	C₄²×C₁₃₉	—	2	4	no	—
197	C₄²×C₁₃₉	—	2	4	no	—
198	C₄²×C₁₃₉	—	4	1	no	—
199	C₄²×C₁₃₉	—	4	2	no	—
200	C₄²×C₁₃₉	—	4	4	no	—
201	C₂³×C₁₃₉	—	2	4	no	—
202	C₂³×C₁₃₉	—	2	2	no	—
203	C₂³×C₁₃₉	—	2	2	no	—
204	C₂³×C₁₃₉	—	2	4	no	—
205	C₂³×C₁₃₉	—	2	4	no	—
206	C₂³×C₁₃₉	—	2	4	no	—
207	C₂³×C₁₃₉	—	2	4	no	—
208	C₂³×C₁₃₉	—	2	4	no	—
209	C₂³×C₁₃₉	—	2	4	no	—
210	C₂³×C₁₃₉	—	2	4	no	—
211	C₂³×C₁₃₉	—	2	4	no	—
212	C₂³×C₁₃₉	—	4	8	no	—
213	C₂³×C₁₃₉	—	8	8	no	—
214	C₂³×C₁₃₉	—	8	4	no	—
215	C₂³×C₁₃₉	—	8	4	no	—
216	C₂³×C₁₃₉	—	8	8	no	—
217	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
218	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
219	Q₈×C₁₃₉	—	4	4	no	—
220	Q₈×C₁₃₉	—	8	4	no	—
221	D₄×C₁₃₉	—	4	4	no	—
222	D₄×C₁₃₉	—	8	4	no	—
223	D₄×C₁₃₉	—	8	8	no	—
224	D₄×C₁₃₉	—	8	4	no	—
225	C₂×C₄×C₁₃₉	—	2	1	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	2	1	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	4	no	—
232	C₂×C₄×C₁₃₉	—	2	2	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	1	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	4	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	4	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	4	no	—
247	C₂×C₄×C₁₃₉	—	2	4	no	—
248	C₂×C₄×C₁₃₉	—	2	4	no	—
249	C₂×C₄×C₁₃₉	—	2	4	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	8	4	no	—
252	C₂×C₄×C₁₃₉	—	8	4	no	—
253	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
254	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
255	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
256	C₂²×C₁₃₉	—	2	4	no	—
257	C₂²×C₁₃₉	—	2	8	no	—
258	C₂²×C₁₃₉	—	4	2	no	—
259	C₂²×C₁₃₉	—	4	2	no	—
260	C₂²×C₁₃₉	—	4	4	no	—
261	C₂²×C₁₃₉	—	4	4	no	—
262	C₂²×C₁₃₉	—	4	4	no	—
263	C₂²×C₁₃₉	—	4	4	no	—
264	C₂²×C₁₃₉	—	4	4	no	—
265	C₂²×C₁₃₉	—	4	4	no	—
266	C₂²×C₁₃₉	—	4	4	no	—
267	C₂²×C₁₃₉	—	4	4	no	—
268	C₂²×C₁₃₉	—	8	16	no	—
269	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
271	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
272	C₂²×C₁₃₉	#585	1	1	yes	characteristic
273	C₂²×C₁₃₉	#585	1	2	yes	—
274	C₄×C₁₃₉	—	2	2	no	—
275	C₄×C₁₃₉	—	2	2	no	—
276	C₄×C₁₃₉	—	2	4	no	—
277	C₄×C₁₃₉	—	4	2	no	—
278	C₄×C₁₃₉	—	4	2	no	—
279	C₄×C₁₃₉	—	4	4	no	—
280	C₄×C₁₃₉	—	4	2	no	—
281	C₄×C₁₃₉	—	4	1	no	—
282	C₄×C₁₃₉	—	4	4	no	—
283	C₄×C₁₃₉	—	4	2	no	—
284	C₄×C₁₃₉	—	4	4	no	—
285	C₂×C₁₃₉	—	4	4	no	—
286	C₂×C₁₃₉	—	8	4	no	—
287	C₂×C₁₃₉	#3459	1	1	yes	characteristic
288	C₂×C₁₃₉	#3514	1	2	yes	—
289	C₂×C₁₃₉	#3545	1	1	yes	characteristic
290	C₂×C₁₃₉	#3549	1	1	yes	characteristic
291	C₂×C₁₃₉	#3560	1	2	yes	—
292	#37150	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₁₃₉	#37150	1	1	yes	characteristic, direct product factor, Sylow
294	#2860	C₂×C₁₃₉	1	2	yes	complemented
295	#2808	C₂×C₁₃₉	1	2	yes	complemented
296	#2785	C₂×C₁₃₉	1	2	yes	complemented
297	#2723	C₂×C₁₃₉	1	4	yes	complemented
298	#2685	C₂×C₁₃₉	1	4	yes	complemented
299	#2684	C₂×C₁₃₉	1	2	yes	complemented
300	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
301	#2679	C₂×C₁₃₉	1	1	yes	characteristic
302	#2632	C₂×C₁₃₉	1	2	yes	complemented
303	#2518	C₂×C₁₃₉	1	4	yes	complemented
304	#2472	C₂×C₁₃₉	1	4	yes	complemented
305	#2321	C₂×C₁₃₉	1	2	yes	complemented
306	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
307	C₂×#126	C₂²×C₁₃₉	1	4	yes	complemented
308	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
309	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
311	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
312	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
313	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
314	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
316	#399	C₂²×C₁₃₉	1	4	yes	complemented
317	#397	C₂²×C₁₃₉	1	4	yes	complemented
318	#397	C₂²×C₁₃₉	1	4	yes	complemented
319	#396	C₂²×C₁₃₉	1	4	yes	complemented
320	#395	C₂²×C₁₃₉	1	2	yes	complemented
321	#395	C₂²×C₁₃₉	1	2	yes	complemented
322	#394	C₂²×C₁₃₉	1	2	yes	—
323	#394	C₂²×C₁₃₉	1	2	yes	—
324	#394	C₂²×C₁₃₉	1	4	yes	—
325	#394	C₂²×C₁₃₉	1	4	yes	—
326	#394	C₂²×C₁₃₉	1	4	yes	—
327	#394	C₂²×C₁₃₉	1	4	yes	—
328	#393	C₂²×C₁₃₉	1	4	yes	complemented
329	#393	C₂²×C₁₃₉	1	4	yes	complemented
330	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
331	#390	C₂²×C₁₃₉	1	4	yes	—
332	#390	C₂²×C₁₃₉	1	2	yes	—
333	#390	C₂²×C₁₃₉	1	2	yes	—
334	#390	C₂²×C₁₃₉	1	2	yes	—
335	#390	C₂²×C₁₃₉	1	1	yes	characteristic
336	#389	C₂²×C₁₃₉	1	2	yes	complemented
337	#389	C₂²×C₁₃₉	1	2	yes	complemented
338	#389	C₂²×C₁₃₉	1	2	yes	complemented
339	#388	C₂²×C₁₃₉	1	4	yes	complemented
340	#388	C₂²×C₁₃₉	1	4	yes	complemented
341	#388	C₂²×C₁₃₉	1	4	yes	complemented
342	#388	C₂²×C₁₃₉	1	4	yes	complemented
343	#388	C₂²×C₁₃₉	1	4	yes	complemented
344	#388	C₂²×C₁₃₉	1	4	yes	complemented
345	#388	C₂²×C₁₃₉	1	4	yes	complemented
346	#388	C₂²×C₁₃₉	1	4	yes	complemented
347	#387	C₂²×C₁₃₉	1	4	yes	complemented
348	#386	C₂²×C₁₃₉	1	2	yes	—
349	#386	C₂²×C₁₃₉	1	4	yes	—
350	#386	C₂²×C₁₃₉	1	4	yes	—
351	#385	C₂²×C₁₃₉	1	2	yes	complemented
352	#383	C₂²×C₁₃₉	1	2	yes	complemented
353	#382	C₂²×C₁₃₉	1	4	yes	complemented
354	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
355	#379	C₂²×C₁₃₉	1	2	yes	complemented
356	#379	C₂²×C₁₃₉	1	4	yes	complemented
357	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
358	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
359	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
360	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
361	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
363	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
364	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
365	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
366	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
368	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
369	#126	—	4	8	no	—
370	#124	—	2	4	no	—
371	#124	—	4	4	no	—
372	C₂²⋊Q₈	—	4	8	no	—
373	#120	—	2	8	no	—
374	#120	—	4	8	no	—
375	C₄×Q₈	—	4	2	no	—
376	C₄×D₄	—	4	2	no	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂×C₂²⋊C₄	—	4	4	no	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
405	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
407	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
412	#95	C₂³×C₁₃₉	1	4	yes	—
413	#95	C₂³×C₁₃₉	1	4	yes	—
414	#95	C₂³×C₁₃₉	1	4	yes	—
415	#95	C₂³×C₁₃₉	1	2	yes	—
416	#95	C₂³×C₁₃₉	1	4	yes	—
417	#95	C₂³×C₁₃₉	1	4	yes	—
418	#95	C₂³×C₁₃₉	1	4	yes	—
419	#95	C₂³×C₁₃₉	1	2	yes	—
420	#95	C₂³×C₁₃₉	1	4	yes	—
421	#95	C₂³×C₁₃₉	1	4	yes	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	—	4	4	no	—
426	C₂⁴	—	4	4	no	—
427	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
428	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	4	1	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	—	4	2	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	#41×C₁₃₉	1	4	yes	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	4	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₄⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂²⋊C₄	—	4	4	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	4	4	no	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₂²⋊C₄	—	4	4	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	—	4	4	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	4	1	no	—
492	C₄²	—	4	2	no	—
493	C₄²	—	4	4	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	4	8	no	—
506	C₂³	—	8	8	no	—
507	C₂³	—	8	4	no	—
508	C₂³	—	8	4	no	—
509	C₂³	—	8	8	no	—
510	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
511	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
512	Q₈	—	4	4	no	—
513	Q₈	—	8	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	8	4	no	—
516	D₄	—	8	8	no	—
517	D₄	—	8	4	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	8	4	no	—
545	C₂×C₄	—	8	4	no	—
546	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
547	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
548	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	8	16	no	—
562	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
563	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
564	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
565	C₂²	#585×C₁₃₉	1	2	yes	—
566	C₂²	#585×C₁₃₉	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	2	no	—
578	C₂	—	4	4	no	—
579	C₂	—	8	4	no	—
580	C₂	#3459×C₁₃₉	1	1	yes	characteristic
581	C₂	#3514×C₁₃₉	1	2	yes	—
582	C₂	#3545×C₁₃₉	1	1	yes	characteristic
583	C₂	#3549×C₁₃₉	1	1	yes	characteristic
584	C₂	#3560×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2679×C₁₃₉	C₂
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. #2860×C₁₃₉	C₂	semidirect
2. #2808×C₁₃₉	C₂	semidirect
3. #2785×C₁₃₉	C₂	semidirect
4. #2723×C₁₃₉	C₂	semidirect
5. #2685×C₁₃₉	C₂	semidirect
6. #2684×C₁₃₉	C₂	semidirect
7. #2683×C₁₃₉	C₂	semidirect
9. #2632×C₁₃₉	C₂	semidirect
10. #2518×C₁₃₉	C₂	semidirect
11. #2472×C₁₃₉	C₂	semidirect
12. #2321×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
14. C₂×#126×C₁₃₉	C₂²	semidirect
17. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
20. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
23. #399×C₁₃₉	C₂²	semidirect
24. #397×C₁₃₉	C₂²	semidirect
25. #397×C₁₃₉	C₂²	semidirect
26. #396×C₁₃₉	C₂²	semidirect
27. #395×C₁₃₉	C₂²	semidirect
28. #395×C₁₃₉	C₂²	semidirect
35. #393×C₁₃₉	C₂²	semidirect
36. #393×C₁₃₉	C₂²	semidirect
37. #391×C₁₃₉	C₂²	semidirect
43. #389×C₁₃₉	C₂²	semidirect
44. #389×C₁₃₉	C₂²	semidirect
45. #389×C₁₃₉	C₂²	semidirect
46. #388×C₁₃₉	C₂²	semidirect
47. #388×C₁₃₉	C₂²	semidirect
48. #388×C₁₃₉	C₂²	semidirect
49. #388×C₁₃₉	C₂²	semidirect
50. #388×C₁₃₉	C₂²	semidirect
51. #388×C₁₃₉	C₂²	semidirect
52. #388×C₁₃₉	C₂²	semidirect
53. #388×C₁₃₉	C₂²	semidirect
54. #387×C₁₃₉	C₂²	semidirect
58. #385×C₁₃₉	C₂²	semidirect
59. #383×C₁₃₉	C₂²	semidirect
60. #382×C₁₃₉	C₂²	semidirect
61. #382×C₁₃₉	C₂²	semidirect
62. #379×C₁₃₉	C₂²	semidirect
63. #379×C₁₃₉	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
66. C₄³×C₁₃₉	C₂²	semidirect
292. #37150	C₁₃₉	direct (N × H)
293. C₁₃₉	#37150	direct (N × H)
294. #2860	C₂×C₁₃₉	semidirect
295. #2808	C₂×C₁₃₉	semidirect
296. #2785	C₂×C₁₃₉	semidirect
297. #2723	C₂×C₁₃₉	semidirect
298. #2685	C₂×C₁₃₉	semidirect
299. #2684	C₂×C₁₃₉	semidirect
300. #2683	C₂×C₁₃₉	semidirect
302. #2632	C₂×C₁₃₉	semidirect
303. #2518	C₂×C₁₃₉	semidirect
304. #2472	C₂×C₁₃₉	semidirect
305. #2321	C₂×C₁₃₉	semidirect
306. C₄×#124	C₂×C₁₃₉	semidirect
307. C₂×#126	C₂²×C₁₃₉	semidirect
310. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
313. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
315. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
316. #399	C₂²×C₁₃₉	semidirect
317. #397	C₂²×C₁₃₉	semidirect
318. #397	C₂²×C₁₃₉	semidirect
319. #396	C₂²×C₁₃₉	semidirect
320. #395	C₂²×C₁₃₉	semidirect
321. #395	C₂²×C₁₃₉	semidirect
328. #393	C₂²×C₁₃₉	semidirect
329. #393	C₂²×C₁₃₉	semidirect
330. #391	C₂²×C₁₃₉	semidirect
336. #389	C₂²×C₁₃₉	semidirect
337. #389	C₂²×C₁₃₉	semidirect
338. #389	C₂²×C₁₃₉	semidirect
339. #388	C₂²×C₁₃₉	semidirect
340. #388	C₂²×C₁₃₉	semidirect
341. #388	C₂²×C₁₃₉	semidirect
342. #388	C₂²×C₁₃₉	semidirect
343. #388	C₂²×C₁₃₉	semidirect
344. #388	C₂²×C₁₃₉	semidirect
345. #388	C₂²×C₁₃₉	semidirect
346. #388	C₂²×C₁₃₉	semidirect
347. #387	C₂²×C₁₃₉	semidirect
351. #385	C₂²×C₁₃₉	semidirect
352. #383	C₂²×C₁₃₉	semidirect
353. #382	C₂²×C₁₃₉	semidirect
354. #382	C₂²×C₁₃₉	semidirect
355. #379	C₂²×C₁₃₉	semidirect
356. #379	C₂²×C₁₃₉	semidirect
357. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
358. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
359. C₄³	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2808×C₁₃₉	2
#2785×C₁₃₉	2
#2723×C₁₃₉	2
#2685×C₁₃₉	2
#2684×C₁₃₉	2
#2683×C₁₃₉	2
#2679×C₁₃₉	2
#2632×C₁₃₉	2
#2518×C₁₃₉	2
#2472×C₁₃₉	2
#2321×C₁₃₉	2
C₄×#124×C₁₃₉	2
#37150	139

Subgroups — C139×#37150 #48031746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37150 #48031746