Subgroups — C₁₃₉×#36196 #48030792

Order 35584.

1694 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2851×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2573×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2562×C₁₃₉	C₂	1	2	yes	maximal
5	#2533×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2497×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2496×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2466×C₁₃₉	C₂	1	4	yes	maximal
9	#2373×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2370×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2283×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
15	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
20	#400×C₁₃₉	C₂²	1	4	yes	—
21	#400×C₁₃₉	C₂²	1	4	yes	—
22	#400×C₁₃₉	C₂²	1	4	yes	—
23	#397×C₁₃₉	C₂²	1	4	yes	—
24	#396×C₁₃₉	C₂²	1	4	yes	—
25	#394×C₁₃₉	C₂²	1	4	yes	—
26	#389×C₁₃₉	C₂²	1	4	yes	—
27	#389×C₁₃₉	C₂²	1	4	yes	—
28	#389×C₁₃₉	C₂²	1	2	yes	—
29	#389×C₁₃₉	C₂²	1	4	yes	—
30	#389×C₁₃₉	C₂²	1	2	yes	—
31	#389×C₁₃₉	C₂²	1	2	yes	—
32	#388×C₁₃₉	C₂²	1	4	yes	—
33	#388×C₁₃₉	C₂²	1	4	yes	—
34	#388×C₁₃₉	C₂²	1	4	yes	—
35	#387×C₁₃₉	C₂²	1	4	yes	—
36	#387×C₁₃₉	C₂²	1	4	yes	—
37	#387×C₁₃₉	C₂²	1	4	yes	—
38	#387×C₁₃₉	C₂²	1	4	yes	—
39	#387×C₁₃₉	C₂²	1	4	yes	—
40	#387×C₁₃₉	C₂²	1	4	yes	—
41	#387×C₁₃₉	C₂²	1	4	yes	—
42	#385×C₁₃₉	C₂²	1	4	yes	—
43	#385×C₁₃₉	C₂²	1	4	yes	—
44	#384×C₁₃₉	C₂²	1	1	yes	characteristic
45	#384×C₁₃₉	C₂²	1	1	yes	characteristic
46	#383×C₁₃₉	C₂²	1	4	yes	—
47	#382×C₁₃₉	C₂²	1	1	yes	characteristic
48	#382×C₁₃₉	C₂²	1	2	yes	—
49	#381×C₁₃₉	C₂²	1	4	yes	—
50	#380×C₁₃₉	C₂²	1	2	yes	—
51	#380×C₁₃₉	C₂²	1	2	yes	—
52	#380×C₁₃₉	C₂²	1	2	yes	—
53	#380×C₁₃₉	C₂²	1	2	yes	—
54	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
65	#376×C₁₃₉	C₂²	1	4	yes	—
66	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
71	#126×C₁₃₉	—	2	16	no	—
72	#125×C₁₃₉	—	2	4	no	—
73	#125×C₁₃₉	—	2	8	no	—
74	C₄×D₄×C₁₃₉	—	2	8	no	—
75	C₄×D₄×C₁₃₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃₉	—	2	8	no	—
98	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
109	#95×C₁₃₉	C₂³	1	4	yes	—
110	#95×C₁₃₉	C₂³	1	4	yes	—
111	#95×C₁₃₉	C₂³	1	4	yes	—
112	#95×C₁₃₉	C₂³	1	4	yes	—
113	#95×C₁₃₉	C₂³	1	2	yes	—
114	#95×C₁₃₉	C₂³	1	4	yes	—
115	#95×C₁₃₉	C₂³	1	4	yes	—
116	#95×C₁₃₉	C₂³	1	4	yes	—
117	#95×C₁₃₉	C₂³	1	4	yes	—
118	#95×C₁₃₉	C₂³	1	4	yes	—
119	#95×C₁₃₉	C₂³	1	4	yes	—
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	1	yes	characteristic
122	#95×C₁₃₉	C₂³	1	2	yes	—
123	#95×C₁₃₉	C₂³	1	1	yes	characteristic
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	4	yes	—
126	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
127	C₂×D₄×C₁₃₉	—	2	4	no	—
128	C₂×D₄×C₁₃₉	—	2	2	no	—
129	C₂²×C₄×C₁₃₉	—	2	4	no	—
130	C₂²×C₄×C₁₃₉	—	2	4	no	—
131	C₂²×C₄×C₁₃₉	—	2	4	no	—
132	C₂²×C₄×C₁₃₉	—	2	4	no	—
133	C₂²×C₄×C₁₃₉	—	2	4	no	—
134	C₂²×C₄×C₁₃₉	—	2	4	no	—
135	C₂²×C₄×C₁₃₉	—	2	4	no	—
136	C₂²×C₄×C₁₃₉	—	4	2	no	—
137	C₂²×C₄×C₁₃₉	—	4	2	no	—
138	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₁₃₉	—	2	4	no	—
151	C₄⋊C₄×C₁₃₉	—	2	2	no	—
152	C₄⋊C₄×C₁₃₉	—	2	8	no	—
153	C₄⋊C₄×C₁₃₉	—	2	8	no	—
154	C₄⋊C₄×C₁₃₉	—	2	8	no	—
155	C₄⋊C₄×C₁₃₉	—	2	4	no	—
156	C₄⋊C₄×C₁₃₉	—	2	4	no	—
157	C₄⋊C₄×C₁₃₉	—	2	4	no	—
158	C₄⋊C₄×C₁₃₉	—	2	8	no	—
159	C₄⋊C₄×C₁₃₉	—	2	8	no	—
160	C₄⋊C₄×C₁₃₉	—	2	8	no	—
161	C₄⋊C₄×C₁₃₉	—	2	4	no	—
162	C₄⋊C₄×C₁₃₉	—	4	4	no	—
163	C₄⋊C₄×C₁₃₉	—	4	4	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
170	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	—
171	C₄²×C₁₃₉	—	2	4	no	—
172	C₄²×C₁₃₉	—	2	4	no	—
173	C₄²×C₁₃₉	—	2	4	no	—
174	C₄²×C₁₃₉	—	2	4	no	—
175	C₄²×C₁₃₉	—	2	8	no	—
176	C₄²×C₁₃₉	—	2	2	no	—
177	C₄²×C₁₃₉	—	4	2	no	—
178	C₄²×C₁₃₉	—	4	4	no	—
179	C₄²×C₁₃₉	—	4	4	no	—
180	C₄²×C₁₃₉	#41	1	4	yes	—
181	C₄²×C₁₃₉	#41	1	4	yes	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	2	no	—
184	C₂³×C₁₃₉	—	2	2	no	—
185	C₂³×C₁₃₉	—	2	2	no	—
186	C₂³×C₁₃₉	—	2	2	no	—
187	C₂³×C₁₃₉	—	2	2	no	—
188	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
189	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
190	D₄×C₁₃₉	—	2	8	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	2	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	2	no	—
196	C₂×C₄×C₁₃₉	—	2	2	no	—
197	C₂×C₄×C₁₃₉	—	2	2	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	2	2	no	—
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₄×C₁₃₉	—	2	4	no	—
209	C₂×C₄×C₁₃₉	—	2	4	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	4	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	2	4	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	4	8	no	—
218	C₂×C₄×C₁₃₉	—	4	8	no	—
219	C₂×C₄×C₁₃₉	—	4	8	no	—
220	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
221	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
222	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
223	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
227	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
228	C₂²×C₁₃₉	—	2	4	no	—
229	C₂²×C₁₃₉	—	2	4	no	—
230	C₂²×C₁₃₉	—	2	4	no	—
231	C₂²×C₁₃₉	—	4	2	no	—
232	C₂²×C₁₃₉	—	4	2	no	—
233	C₂²×C₁₃₉	—	4	2	no	—
234	C₂²×C₁₃₉	—	4	2	no	—
235	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
236	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
237	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
238	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
239	C₂²×C₁₃₉	#585	1	2	yes	—
240	C₄×C₁₃₉	—	2	2	no	—
241	C₄×C₁₃₉	—	2	4	no	—
242	C₄×C₁₃₉	—	2	4	no	—
243	C₄×C₁₃₉	—	2	2	no	—
244	C₄×C₁₃₉	—	2	4	no	—
245	C₄×C₁₃₉	—	4	4	no	—
246	C₄×C₁₃₉	—	4	2	no	—
247	C₄×C₁₃₉	—	4	4	no	—
248	C₄×C₁₃₉	—	4	2	no	—
249	C₄×C₁₃₉	—	4	4	no	—
250	C₄×C₁₃₉	—	4	4	no	—
251	C₄×C₁₃₉	#556	1	4	yes	—
252	C₂×C₁₃₉	—	4	4	no	—
253	C₂×C₁₃₉	#3444	1	1	yes	characteristic
254	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
255	C₂×C₁₃₉	#3475	1	2	yes	—
256	C₂×C₁₃₉	#3512	1	1	yes	characteristic
257	C₂×C₁₃₉	#3515	1	2	yes	—
258	#36196	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₁₃₉	#36196	1	1	yes	characteristic, direct product factor, Sylow
260	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
261	#2851	C₂×C₁₃₉	1	2	yes	complemented
262	#2573	C₂×C₁₃₉	1	4	yes	complemented
263	#2562	C₂×C₁₃₉	1	2	yes	—
264	#2533	C₂×C₁₃₉	1	4	yes	complemented
265	#2497	C₂×C₁₃₉	1	2	yes	complemented
266	#2496	C₂×C₁₃₉	1	2	yes	complemented
267	#2466	C₂×C₁₃₉	1	4	yes	—
268	#2373	C₂×C₁₃₉	1	4	yes	complemented
269	#2370	C₂×C₁₃₉	1	2	yes	complemented
270	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
271	#2283	C₂×C₁₃₉	1	2	yes	complemented
272	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
273	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
274	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
275	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
276	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
278	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
279	#400	C₂²×C₁₃₉	1	4	yes	—
280	#400	C₂²×C₁₃₉	1	4	yes	—
281	#400	C₂²×C₁₃₉	1	4	yes	—
282	#397	C₂²×C₁₃₉	1	4	yes	—
283	#396	C₂²×C₁₃₉	1	4	yes	—
284	#394	C₂²×C₁₃₉	1	4	yes	—
285	#389	C₂²×C₁₃₉	1	2	yes	—
286	#389	C₂²×C₁₃₉	1	4	yes	—
287	#389	C₂²×C₁₃₉	1	2	yes	—
288	#389	C₂²×C₁₃₉	1	2	yes	—
289	#389	C₂²×C₁₃₉	1	4	yes	—
290	#389	C₂²×C₁₃₉	1	4	yes	—
291	#388	C₂²×C₁₃₉	1	4	yes	—
292	#388	C₂²×C₁₃₉	1	4	yes	—
293	#388	C₂²×C₁₃₉	1	4	yes	—
294	#387	C₂²×C₁₃₉	1	4	yes	—
295	#387	C₂²×C₁₃₉	1	4	yes	—
296	#387	C₂²×C₁₃₉	1	4	yes	—
297	#387	C₂²×C₁₃₉	1	4	yes	—
298	#387	C₂²×C₁₃₉	1	4	yes	—
299	#387	C₂²×C₁₃₉	1	4	yes	—
300	#387	C₂²×C₁₃₉	1	4	yes	—
301	#385	C₂²×C₁₃₉	1	4	yes	—
302	#385	C₂²×C₁₃₉	1	4	yes	—
303	#384	C₂²×C₁₃₉	1	1	yes	characteristic
304	#384	C₂²×C₁₃₉	1	1	yes	characteristic
305	#383	C₂²×C₁₃₉	1	4	yes	—
306	#382	C₂²×C₁₃₉	1	1	yes	characteristic
307	#382	C₂²×C₁₃₉	1	2	yes	—
308	#381	C₂²×C₁₃₉	1	4	yes	—
309	#380	C₂²×C₁₃₉	1	2	yes	—
310	#380	C₂²×C₁₃₉	1	2	yes	—
311	#380	C₂²×C₁₃₉	1	2	yes	—
312	#380	C₂²×C₁₃₉	1	2	yes	—
313	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
315	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
317	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
318	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
319	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
320	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
321	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
323	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
324	#376	C₂²×C₁₃₉	1	4	yes	—
325	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
328	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
329	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
330	#126	—	2	16	no	—
331	#125	—	2	4	no	—
332	#125	—	2	8	no	—
333	C₄×D₄	—	2	8	no	—
334	C₄×D₄	—	2	4	no	—
335	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
356	C₂×C₄²	—	2	8	no	—
357	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
358	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
359	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
361	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
362	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
363	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
365	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
366	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
368	#95	C₂³×C₁₃₉	1	4	yes	—
369	#95	C₂³×C₁₃₉	1	4	yes	—
370	#95	C₂³×C₁₃₉	1	4	yes	—
371	#95	C₂³×C₁₃₉	1	4	yes	—
372	#95	C₂³×C₁₃₉	1	1	yes	characteristic
373	#95	C₂³×C₁₃₉	1	2	yes	—
374	#95	C₂³×C₁₃₉	1	1	yes	characteristic
375	#95	C₂³×C₁₃₉	1	2	yes	—
376	#95	C₂³×C₁₃₉	1	4	yes	—
377	#95	C₂³×C₁₃₉	1	4	yes	—
378	#95	C₂³×C₁₃₉	1	4	yes	—
379	#95	C₂³×C₁₃₉	1	4	yes	—
380	#95	C₂³×C₁₃₉	1	4	yes	—
381	#95	C₂³×C₁₃₉	1	4	yes	—
382	#95	C₂³×C₁₃₉	1	4	yes	—
383	#95	C₂³×C₁₃₉	1	4	yes	—
384	#95	C₂³×C₁₃₉	1	4	yes	—
385	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	4	4	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	—
430	C₄²	—	2	4	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	8	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	4	2	no	—
437	C₄²	—	4	4	no	—
438	C₄²	—	4	4	no	—
439	C₄²	#41×C₁₃₉	1	4	yes	—
440	C₄²	#41×C₁₃₉	1	4	yes	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
448	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
449	D₄	—	2	8	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
480	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
481	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
482	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
483	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
484	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
485	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
486	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
495	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
496	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
497	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
498	C₂²	#585×C₁₃₉	1	2	yes	—
499	C₄	—	2	2	no	—
500	C₄	—	2	4	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	4	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	#556×C₁₃₉	1	4	yes	—
511	C₂	—	4	4	no	—
512	C₂	#3444×C₁₃₉	1	1	yes	characteristic
513	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
514	C₂	#3475×C₁₃₉	1	2	yes	—
515	C₂	#3512×C₁₃₉	1	1	yes	characteristic
516	C₂	#3515×C₁₃₉	1	2	yes	—

	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. #2859×C₁₃₉	C₂	semidirect
2. #2851×C₁₃₉	C₂	semidirect
3. #2573×C₁₃₉	C₂	semidirect
5. #2533×C₁₃₉	C₂	semidirect
6. #2497×C₁₃₉	C₂	semidirect
7. #2496×C₁₃₉	C₂	semidirect
9. #2373×C₁₃₉	C₂	semidirect
10. #2370×C₁₃₉	C₂	semidirect
11. C₄×#125×C₁₃₉	C₂	semidirect
12. #2283×C₁₃₉	C₂	semidirect
258. #36196	C₁₃₉	direct (N × H)
259. C₁₃₉	#36196	direct (N × H)
260. #2859	C₂×C₁₃₉	semidirect
261. #2851	C₂×C₁₃₉	semidirect
262. #2573	C₂×C₁₃₉	semidirect
264. #2533	C₂×C₁₃₉	semidirect
265. #2497	C₂×C₁₃₉	semidirect
266. #2496	C₂×C₁₃₉	semidirect
268. #2373	C₂×C₁₃₉	semidirect
269. #2370	C₂×C₁₃₉	semidirect
270. C₄×#125	C₂×C₁₃₉	semidirect
271. #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
#2859×C₁₃₉	2
#2851×C₁₃₉	2
#2573×C₁₃₉	2
#2562×C₁₃₉	2
#2533×C₁₃₉	2
#2497×C₁₃₉	2
#2496×C₁₃₉	2
#2466×C₁₃₉	2
#2373×C₁₃₉	2
#2370×C₁₃₉	2
C₄×#125×C₁₃₉	2
#2283×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36196	139

Subgroups — C139×#36196 #48030792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36196 #48030792