Subgroups — C₁₃₉×#37286 #48031882

Order 35584.

1774 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2781×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	#2718×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2705×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2693×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2619×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2509×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2324×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
24	#400×C₁₃₉	C₂²	1	4	yes	—
25	#400×C₁₃₉	C₂²	1	4	yes	—
26	#399×C₁₃₉	C₂²	1	4	yes	—
27	#398×C₁₃₉	C₂²	1	4	yes	—
28	#397×C₁₃₉	C₂²	1	4	yes	—
29	#396×C₁₃₉	C₂²	1	4	yes	—
30	#396×C₁₃₉	C₂²	1	4	yes	—
31	#396×C₁₃₉	C₂²	1	4	yes	—
32	#394×C₁₃₉	C₂²	1	4	yes	—
33	#394×C₁₃₉	C₂²	1	4	yes	—
34	#394×C₁₃₉	C₂²	1	4	yes	—
35	#392×C₁₃₉	C₂²	1	4	yes	—
36	#390×C₁₃₉	C₂²	1	2	yes	—
37	#390×C₁₃₉	C₂²	1	2	yes	—
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	4	yes	—
40	#390×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	4	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	4	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#387×C₁₃₉	C₂²	1	4	yes	—
51	#386×C₁₃₉	C₂²	1	4	yes	—
52	#386×C₁₃₉	C₂²	1	4	yes	—
53	#386×C₁₃₉	C₂²	1	4	yes	—
54	#385×C₁₃₉	C₂²	1	4	yes	—
55	#385×C₁₃₉	C₂²	1	4	yes	—
56	#384×C₁₃₉	C₂²	1	1	yes	characteristic
57	#384×C₁₃₉	C₂²	1	2	yes	—
58	#382×C₁₃₉	C₂²	1	2	yes	—
59	#382×C₁₃₉	C₂²	1	1	yes	characteristic
60	#380×C₁₃₉	C₂²	1	4	yes	—
61	#380×C₁₃₉	C₂²	1	2	yes	—
62	#380×C₁₃₉	C₂²	1	2	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
73	#127×C₁₃₉	—	4	2	no	—
74	#126×C₁₃₉	—	4	8	no	—
75	#125×C₁₃₉	—	4	2	no	—
76	#123×C₁₃₉	—	4	8	no	—
77	#123×C₁₃₉	—	4	8	no	—
78	#121×C₁₃₉	—	2	8	no	—
79	C₄×D₄×C₁₃₉	—	4	4	no	—
80	#117×C₁₃₉	—	4	2	no	—
81	#117×C₁₃₉	—	4	2	no	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄⋊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	2	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₃₉	—	2	4	no	—
112	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
122	#95×C₁₃₉	C₂³	1	2	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	2	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	#95×C₁₃₉	C₂³	1	2	yes	—
130	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
131	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
132	C₂×D₄×C₁₃₉	—	2	8	no	—
133	C₂×D₄×C₁₃₉	—	2	4	no	—
134	C₂×D₄×C₁₃₉	—	2	4	no	—
135	C₂×D₄×C₁₃₉	—	2	4	no	—
136	C₂×D₄×C₁₃₉	—	4	4	no	—
137	C₂×D₄×C₁₃₉	—	4	4	no	—
138	C₂×D₄×C₁₃₉	—	4	4	no	—
139	C₂×D₄×C₁₃₉	—	4	4	no	—
140	C₂×D₄×C₁₃₉	—	4	4	no	—
141	C₂²×C₄×C₁₃₉	—	2	2	no	—
142	C₂²×C₄×C₁₃₉	—	2	2	no	—
143	C₂²×C₄×C₁₃₉	—	2	4	no	—
144	C₂²×C₄×C₁₃₉	—	2	4	no	—
145	C₂²×C₄×C₁₃₉	—	4	2	no	—
146	C₂²×C₄×C₁₃₉	—	4	4	no	—
147	C₂²×C₄×C₁₃₉	—	4	4	no	—
148	C₂²×C₄×C₁₃₉	—	4	4	no	—
149	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
150	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₁₃₉	—	2	4	no	—
162	C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₄⋊C₄×C₁₃₉	—	2	4	no	—
164	C₄⋊C₄×C₁₃₉	—	2	8	no	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₄⋊C₄×C₁₃₉	—	4	2	no	—
168	C₄⋊C₄×C₁₃₉	—	4	2	no	—
169	C₄⋊C₄×C₁₃₉	—	4	4	no	—
170	C₄⋊C₄×C₁₃₉	—	4	2	no	—
171	C₄⋊C₄×C₁₃₉	—	4	2	no	—
172	C₄⋊C₄×C₁₃₉	—	4	4	no	—
173	C₄⋊C₄×C₁₃₉	—	4	4	no	—
174	C₄⋊C₄×C₁₃₉	—	4	4	no	—
175	C₄⋊C₄×C₁₃₉	—	4	4	no	—
176	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
178	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
180	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
181	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
182	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
184	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
185	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
189	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
190	C₄²×C₁₃₉	—	2	2	no	—
191	C₄²×C₁₃₉	—	2	4	no	—
192	C₄²×C₁₃₉	—	2	2	no	—
193	C₄²×C₁₃₉	—	2	4	no	—
194	C₄²×C₁₃₉	—	2	2	no	—
195	C₄²×C₁₃₉	—	2	2	no	—
196	C₄²×C₁₃₉	—	4	4	no	—
197	C₂³×C₁₃₉	—	2	1	no	—
198	C₂³×C₁₃₉	—	2	2	no	—
199	C₂³×C₁₃₉	—	2	1	no	—
200	C₂³×C₁₃₉	—	2	2	no	—
201	C₂³×C₁₃₉	—	2	4	no	—
202	C₂³×C₁₃₉	—	2	4	no	—
203	C₂³×C₁₃₉	—	2	4	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	C₂×#41	1	2	yes	—
209	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
210	D₄×C₁₃₉	—	4	8	no	—
211	D₄×C₁₃₉	—	8	8	no	—
212	D₄×C₁₃₉	—	8	8	no	—
213	C₂×C₄×C₁₃₉	—	2	2	no	—
214	C₂×C₄×C₁₃₉	—	2	1	no	—
215	C₂×C₄×C₁₃₉	—	2	1	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	8	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	4	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	4	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	4	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	4	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	4	8	no	—
243	C₂×C₄×C₁₃₉	—	8	8	no	—
244	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
246	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
247	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
248	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
249	C₂²×C₁₃₉	—	2	2	no	—
250	C₂²×C₁₃₉	—	2	4	no	—
251	C₂²×C₁₃₉	—	4	2	no	—
252	C₂²×C₁₃₉	—	4	1	no	—
253	C₂²×C₁₃₉	—	4	1	no	—
254	C₂²×C₁₃₉	—	4	4	no	—
255	C₂²×C₁₃₉	—	4	4	no	—
256	C₂²×C₁₃₉	—	4	4	no	—
257	C₂²×C₁₃₉	—	4	4	no	—
258	C₂²×C₁₃₉	—	4	4	no	—
259	C₂²×C₁₃₉	—	4	4	no	—
260	C₂²×C₁₃₉	—	4	4	no	—
261	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
262	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
264	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
265	C₂²×C₁₃₉	#585	1	2	yes	—
266	C₄×C₁₃₉	—	2	2	no	—
267	C₄×C₁₃₉	—	2	4	no	—
268	C₄×C₁₃₉	—	4	2	no	—
269	C₄×C₁₃₉	—	4	4	no	—
270	C₄×C₁₃₉	—	4	2	no	—
271	C₄×C₁₃₉	—	4	2	no	—
272	C₄×C₁₃₉	—	4	4	no	—
273	C₄×C₁₃₉	—	4	2	no	—
274	C₄×C₁₃₉	—	4	2	no	—
275	C₄×C₁₃₉	—	4	4	no	—
276	C₄×C₁₃₉	#539	1	4	yes	—
277	C₂×C₁₃₉	—	4	2	no	—
278	C₂×C₁₃₉	—	8	4	no	—
279	C₂×C₁₃₉	C₂×#539	1	1	yes	characteristic
280	C₂×C₁₃₉	#3494	1	2	yes	—
281	C₂×C₁₃₉	#3546	1	2	yes	—
282	C₂×C₁₃₉	#3548	1	1	yes	characteristic
283	C₂×C₁₃₉	#3557	1	1	yes	characteristic
284	#37286	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₁₃₉	#37286	1	1	yes	characteristic, direct product factor, Sylow
286	#2854	C₂×C₁₃₉	1	2	yes	complemented
287	#2781	C₂×C₁₃₉	1	4	yes	complemented
288	#2718	C₂×C₁₃₉	1	4	yes	complemented
289	#2705	C₂×C₁₃₉	1	4	yes	complemented
290	#2693	C₂×C₁₃₉	1	4	yes	complemented
291	#2629	C₂×C₁₃₉	1	1	yes	characteristic, complemented
292	#2619	C₂×C₁₃₉	1	1	yes	characteristic
293	#2512	C₂×C₁₃₉	1	2	yes	complemented
294	#2509	C₂×C₁₃₉	1	2	yes	complemented
295	#2454	C₂×C₁₃₉	1	2	yes	complemented
296	#2445	C₂×C₁₃₉	1	2	yes	complemented
297	#2324	C₂×C₁₃₉	1	2	yes	complemented
298	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
299	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
300	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
301	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
302	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
303	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
304	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
306	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
308	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
309	#400	C₂²×C₁₃₉	1	4	yes	—
310	#400	C₂²×C₁₃₉	1	4	yes	—
311	#399	C₂²×C₁₃₉	1	4	yes	—
312	#398	C₂²×C₁₃₉	1	4	yes	—
313	#397	C₂²×C₁₃₉	1	4	yes	—
314	#396	C₂²×C₁₃₉	1	4	yes	—
315	#396	C₂²×C₁₃₉	1	4	yes	—
316	#396	C₂²×C₁₃₉	1	4	yes	—
317	#394	C₂²×C₁₃₉	1	4	yes	—
318	#394	C₂²×C₁₃₉	1	4	yes	—
319	#394	C₂²×C₁₃₉	1	4	yes	—
320	#392	C₂²×C₁₃₉	1	4	yes	—
321	#390	C₂²×C₁₃₉	1	2	yes	—
322	#390	C₂²×C₁₃₉	1	4	yes	—
323	#390	C₂²×C₁₃₉	1	2	yes	—
324	#390	C₂²×C₁₃₉	1	2	yes	—
325	#390	C₂²×C₁₃₉	1	2	yes	—
326	#389	C₂²×C₁₃₉	1	2	yes	—
327	#389	C₂²×C₁₃₉	1	2	yes	—
328	#389	C₂²×C₁₃₉	1	2	yes	—
329	#389	C₂²×C₁₃₉	1	2	yes	—
330	#389	C₂²×C₁₃₉	1	4	yes	—
331	#388	C₂²×C₁₃₉	1	4	yes	—
332	#388	C₂²×C₁₃₉	1	4	yes	—
333	#388	C₂²×C₁₃₉	1	4	yes	—
334	#388	C₂²×C₁₃₉	1	4	yes	—
335	#387	C₂²×C₁₃₉	1	4	yes	—
336	#386	C₂²×C₁₃₉	1	4	yes	—
337	#386	C₂²×C₁₃₉	1	4	yes	—
338	#386	C₂²×C₁₃₉	1	4	yes	—
339	#385	C₂²×C₁₃₉	1	4	yes	—
340	#385	C₂²×C₁₃₉	1	4	yes	—
341	#384	C₂²×C₁₃₉	1	1	yes	characteristic
342	#384	C₂²×C₁₃₉	1	2	yes	—
343	#382	C₂²×C₁₃₉	1	1	yes	characteristic
344	#382	C₂²×C₁₃₉	1	2	yes	—
345	#380	C₂²×C₁₃₉	1	2	yes	—
346	#380	C₂²×C₁₃₉	1	2	yes	—
347	#380	C₂²×C₁₃₉	1	4	yes	—
348	#380	C₂²×C₁₃₉	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
352	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
353	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
354	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
355	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
358	#127	—	4	2	no	—
359	#126	—	4	8	no	—
360	#125	—	4	2	no	—
361	#123	—	4	8	no	—
362	#123	—	4	8	no	—
363	#121	—	2	8	no	—
364	C₄×D₄	—	4	4	no	—
365	#117	—	4	2	no	—
366	#117	—	4	2	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	4	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	4	yes	—
396	C₂×C₄²	—	2	4	no	—
397	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
404	#95	C₂³×C₁₃₉	1	2	yes	—
405	#95	C₂³×C₁₃₉	1	2	yes	—
406	#95	C₂³×C₁₃₉	1	2	yes	—
407	#95	C₂³×C₁₃₉	1	2	yes	—
408	#95	C₂³×C₁₃₉	1	4	yes	—
409	#95	C₂³×C₁₃₉	1	4	yes	—
410	#95	C₂³×C₁₃₉	1	4	yes	—
411	#95	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	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
416	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	4	4	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₄⋊C₄	—	4	4	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	2	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	4	4	no	—
472	C₂²⋊C₄	—	4	4	no	—
473	C₂²⋊C₄	—	4	4	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	4	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	4	4	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
494	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
495	D₄	—	4	8	no	—
496	D₄	—	8	8	no	—
497	D₄	—	8	8	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	—	8	8	no	—
529	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
530	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
531	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
532	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
533	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
547	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
548	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
549	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
550	C₂²	#585×C₁₃₉	1	2	yes	—
551	C₄	—	2	2	no	—
552	C₄	—	2	4	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	4	no	—
561	C₄	#539×C₁₃₉	1	4	yes	—
562	C₂	—	4	2	no	—
563	C₂	—	8	4	no	—
564	C₂	C₂×#539×C₁₃₉	1	1	yes	characteristic
565	C₂	#3494×C₁₃₉	1	2	yes	—
566	C₂	#3546×C₁₃₉	1	2	yes	—
567	C₂	#3548×C₁₃₉	1	1	yes	characteristic
568	C₂	#3557×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2619×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. #2854×C₁₃₉	C₂	semidirect
2. #2781×C₁₃₉	C₂	semidirect
3. #2718×C₁₃₉	C₂	semidirect
4. #2705×C₁₃₉	C₂	semidirect
5. #2693×C₁₃₉	C₂	semidirect
6. #2629×C₁₃₉	C₂	semidirect
8. #2512×C₁₃₉	C₂	semidirect
9. #2509×C₁₃₉	C₂	semidirect
10. #2454×C₁₃₉	C₂	semidirect
11. #2445×C₁₃₉	C₂	semidirect
12. #2324×C₁₃₉	C₂	semidirect
13. #2285×C₁₃₉	C₂	semidirect
284. #37286	C₁₃₉	direct (N × H)
285. C₁₃₉	#37286	direct (N × H)
286. #2854	C₂×C₁₃₉	semidirect
287. #2781	C₂×C₁₃₉	semidirect
288. #2718	C₂×C₁₃₉	semidirect
289. #2705	C₂×C₁₃₉	semidirect
290. #2693	C₂×C₁₃₉	semidirect
291. #2629	C₂×C₁₃₉	semidirect
293. #2512	C₂×C₁₃₉	semidirect
294. #2509	C₂×C₁₃₉	semidirect
295. #2454	C₂×C₁₃₉	semidirect
296. #2445	C₂×C₁₃₉	semidirect
297. #2324	C₂×C₁₃₉	semidirect
298. #2285	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2854×C₁₃₉	2
#2781×C₁₃₉	2
#2718×C₁₃₉	2
#2705×C₁₃₉	2
#2693×C₁₃₉	2
#2629×C₁₃₉	2
#2619×C₁₃₉	2
#2512×C₁₃₉	2
#2509×C₁₃₉	2
#2454×C₁₃₉	2
#2445×C₁₃₉	2
#2324×C₁₃₉	2
#2285×C₁₃₉	2
#37286	139

Subgroups — C139×#37286 #48031882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37286 #48031882