Subgroups — C₁₃₉×#35858 #48030454

Order 35584.

1836 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2647×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2646×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2570×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2569×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2508×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2507×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2506×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2505×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2442×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2402×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#398×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
21	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
22	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#400×C₁₃₉	C₂²	1	1	yes	characteristic
40	#400×C₁₃₉	C₂²	1	2	yes	—
41	#400×C₁₃₉	C₂²	1	2	yes	—
42	#400×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	1	yes	characteristic
44	#400×C₁₃₉	C₂²	1	1	yes	characteristic
45	#400×C₁₃₉	C₂²	1	1	yes	characteristic
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	1	yes	characteristic
49	#398×C₁₃₉	C₂²	1	2	yes	—
50	#398×C₁₃₉	C₂²	1	2	yes	—
51	#398×C₁₃₉	C₂²	1	2	yes	—
52	#398×C₁₃₉	C₂²	1	2	yes	—
53	#398×C₁₃₉	C₂²	1	1	yes	characteristic
54	#398×C₁₃₉	C₂²	1	2	yes	—
55	#398×C₁₃₉	C₂²	1	2	yes	—
56	#398×C₁₃₉	C₂²	1	2	yes	—
57	#398×C₁₃₉	C₂²	1	2	yes	—
58	#398×C₁₃₉	C₂²	1	2	yes	—
59	#398×C₁₃₉	C₂²	1	1	yes	characteristic
60	#398×C₁₃₉	C₂²	1	1	yes	characteristic
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	1	yes	characteristic
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic
74	#389×C₁₃₉	C₂²	1	2	yes	—
75	#389×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#385×C₁₃₉	C₂²	1	2	yes	—
83	#385×C₁₃₉	C₂²	1	2	yes	—
84	#385×C₁₃₉	C₂²	1	2	yes	—
85	#385×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#385×C₁₃₉	C₂²	1	2	yes	—
88	#385×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#384×C₁₃₉	C₂²	1	1	yes	characteristic
95	#384×C₁₃₉	C₂²	1	1	yes	characteristic
96	#384×C₁₃₉	C₂²	1	1	yes	characteristic
97	#384×C₁₃₉	C₂²	1	1	yes	characteristic
98	#382×C₁₃₉	C₂²	1	1	yes	characteristic
99	#382×C₁₃₉	C₂²	1	1	yes	characteristic
100	#382×C₁₃₉	C₂²	1	2	yes	—
101	#380×C₁₃₉	C₂²	1	2	yes	—
102	#380×C₁₃₉	C₂²	1	2	yes	—
103	#380×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	2	yes	—
105	#380×C₁₃₉	C₂²	1	2	yes	—
106	#380×C₁₃₉	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	#376×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
121	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
122	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
123	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
131	#125×C₁₃₉	—	4	4	no	—
132	#125×C₁₃₉	—	4	4	no	—
133	C₄×D₄×C₁₃₉	—	2	4	no	—
134	C₄×D₄×C₁₃₉	—	2	4	no	—
135	C₄×D₄×C₁₃₉	—	2	4	no	—
136	C₄×D₄×C₁₃₉	—	2	4	no	—
137	C₄×D₄×C₁₃₉	—	2	4	no	—
138	C₄×D₄×C₁₃₉	—	2	4	no	—
139	C₄×D₄×C₁₃₉	Q₈	1	8	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
141	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
142	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
143	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	#95×C₁₃₉	C₂³	1	1	yes	characteristic
201	#95×C₁₃₉	C₂³	1	1	yes	characteristic
202	#95×C₁₃₉	C₂³	1	1	yes	characteristic
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	1	yes	characteristic
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	1	yes	characteristic
210	#95×C₁₃₉	C₂³	1	1	yes	characteristic
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	1	yes	characteristic
216	#95×C₁₃₉	C₂³	1	1	yes	characteristic
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	1	yes	characteristic
219	#95×C₁₃₉	C₂³	1	1	yes	characteristic
220	#95×C₁₃₉	C₂³	1	1	yes	characteristic
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	2	yes	—
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	2	yes	—
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	#95×C₁₃₉	C₂³	1	2	yes	—
235	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
237	C₂×D₄×C₁₃₉	#41	1	4	yes	—
238	C₂×D₄×C₁₃₉	#41	1	4	yes	—
239	C₂²×C₄×C₁₃₉	—	2	4	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	2	4	no	—
243	C₂²×C₄×C₁₃₉	—	2	4	no	—
244	C₂²×C₄×C₁₃₉	—	2	4	no	—
245	C₂²×C₄×C₁₃₉	—	2	4	no	—
246	C₂²×C₄×C₁₃₉	—	2	4	no	—
247	C₂²×C₄×C₁₃₉	—	2	4	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	2	no	—
250	C₂²×C₄×C₁₃₉	—	4	2	no	—
251	C₂²×C₄×C₁₃₉	—	4	2	no	—
252	C₂²×C₄×C₁₃₉	—	4	2	no	—
253	C₂²×C₄×C₁₃₉	—	4	2	no	—
254	C₂²×C₄×C₁₃₉	—	4	2	no	—
255	C₂²×C₄×C₁₃₉	—	4	2	no	—
256	C₂²×C₄×C₁₃₉	—	4	2	no	—
257	C₂²×C₄×C₁₃₉	—	4	2	no	—
258	C₂²×C₄×C₁₃₉	—	4	2	no	—
259	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
282	C₄⋊C₄×C₁₃₉	—	2	2	no	—
283	C₄⋊C₄×C₁₃₉	—	2	2	no	—
284	C₄⋊C₄×C₁₃₉	—	2	2	no	—
285	C₄⋊C₄×C₁₃₉	—	2	2	no	—
286	C₄⋊C₄×C₁₃₉	—	2	2	no	—
287	C₄⋊C₄×C₁₃₉	—	2	2	no	—
288	C₄⋊C₄×C₁₃₉	—	2	2	no	—
289	C₄⋊C₄×C₁₃₉	—	2	2	no	—
290	C₄⋊C₄×C₁₃₉	—	2	2	no	—
291	C₄⋊C₄×C₁₃₉	—	2	2	no	—
292	C₄⋊C₄×C₁₃₉	—	2	4	no	—
293	C₄⋊C₄×C₁₃₉	—	2	4	no	—
294	C₄⋊C₄×C₁₃₉	—	2	4	no	—
295	C₄⋊C₄×C₁₃₉	—	2	4	no	—
296	C₄⋊C₄×C₁₃₉	—	2	2	no	—
297	C₄⋊C₄×C₁₃₉	—	2	2	no	—
298	C₄⋊C₄×C₁₃₉	—	2	2	no	—
299	C₄⋊C₄×C₁₃₉	—	2	2	no	—
300	C₄⋊C₄×C₁₃₉	—	2	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	2	no	—
302	C₄⋊C₄×C₁₃₉	—	4	2	no	—
303	C₄⋊C₄×C₁₃₉	—	4	2	no	—
304	C₄⋊C₄×C₁₃₉	—	4	2	no	—
305	C₄⋊C₄×C₁₃₉	—	4	2	no	—
306	C₄⋊C₄×C₁₃₉	—	4	2	no	—
307	C₄⋊C₄×C₁₃₉	—	4	2	no	—
308	C₄⋊C₄×C₁₃₉	—	4	2	no	—
309	C₄⋊C₄×C₁₃₉	—	4	2	no	—
310	C₄⋊C₄×C₁₃₉	—	4	1	no	—
311	C₄⋊C₄×C₁₃₉	—	4	1	no	—
312	C₄⋊C₄×C₁₃₉	—	4	2	no	—
313	C₄⋊C₄×C₁₃₉	—	4	1	no	—
314	C₄⋊C₄×C₁₃₉	—	4	2	no	—
315	C₄⋊C₄×C₁₃₉	—	4	2	no	—
316	C₄⋊C₄×C₁₃₉	—	4	2	no	—
317	C₄⋊C₄×C₁₃₉	—	4	2	no	—
318	C₄⋊C₄×C₁₃₉	—	4	2	no	—
319	C₄⋊C₄×C₁₃₉	—	4	2	no	—
320	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
321	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
322	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
323	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
324	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
325	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
326	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
327	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
328	C₄²×C₁₃₉	—	2	2	no	—
329	C₄²×C₁₃₉	—	2	2	no	—
330	C₄²×C₁₃₉	—	2	2	no	—
331	C₄²×C₁₃₉	—	2	2	no	—
332	C₄²×C₁₃₉	—	2	2	no	—
333	C₄²×C₁₃₉	—	2	2	no	—
334	C₄²×C₁₃₉	—	4	2	no	—
335	C₄²×C₁₃₉	—	4	2	no	—
336	C₄²×C₁₃₉	—	4	2	no	—
337	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	2	no	—
342	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
343	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
344	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
345	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
346	D₄×C₁₃₉	#125	1	16	yes	complemented
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	1	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	1	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	1	no	—
388	C₂×C₄×C₁₃₉	—	2	1	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	1	no	—
392	C₂×C₄×C₁₃₉	—	2	1	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	1	no	—
395	C₂×C₄×C₁₃₉	—	2	1	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	1	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	1	no	—
400	C₂×C₄×C₁₃₉	—	2	1	no	—
401	C₂×C₄×C₁₃₉	—	2	1	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	1	no	—
404	C₂×C₄×C₁₃₉	—	4	8	no	—
405	C₂×C₄×C₁₃₉	—	4	8	no	—
406	C₂×C₄×C₁₃₉	—	4	8	no	—
407	C₂×C₄×C₁₃₉	—	4	8	no	—
408	C₂×C₄×C₁₃₉	—	8	4	no	—
409	C₂×C₄×C₁₃₉	—	8	4	no	—
410	C₂×C₄×C₁₃₉	—	8	4	no	—
411	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
412	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
413	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
414	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
415	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
416	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
417	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
420	C₂²×C₁₃₉	—	2	4	no	—
421	C₂²×C₁₃₉	—	2	4	no	—
422	C₂²×C₁₃₉	—	2	4	no	—
423	C₂²×C₁₃₉	—	2	4	no	—
424	C₂²×C₁₃₉	—	2	4	no	—
425	C₂²×C₁₃₉	—	2	4	no	—
426	C₂²×C₁₃₉	C₂×#125	1	8	yes	—
427	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
428	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂²×C₁₃₉	#585	1	1	yes	characteristic
434	C₄×C₁₃₉	—	2	2	no	—
435	C₄×C₁₃₉	—	2	4	no	—
436	C₄×C₁₃₉	—	2	2	no	—
437	C₄×C₁₃₉	—	2	2	no	—
438	C₄×C₁₃₉	—	2	2	no	—
439	C₄×C₁₃₉	—	2	2	no	—
440	C₄×C₁₃₉	—	4	1	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	2	no	—
443	C₄×C₁₃₉	—	4	1	no	—
444	C₄×C₁₃₉	—	4	1	no	—
445	C₄×C₁₃₉	—	4	1	no	—
446	C₄×C₁₃₉	—	4	1	no	—
447	C₄×C₁₃₉	—	4	2	no	—
448	C₄×C₁₃₉	—	4	2	no	—
449	C₄×C₁₃₉	—	4	2	no	—
450	C₄×C₁₃₉	—	4	1	no	—
451	C₄×C₁₃₉	—	4	1	no	—
452	C₄×C₁₃₉	—	4	1	no	—
453	C₄×C₁₃₉	—	4	1	no	—
454	C₄×C₁₃₉	—	4	2	no	—
455	C₄×C₁₃₉	C₂×#125	1	4	yes	—
456	C₂×C₁₃₉	—	2	8	no	—
457	C₂×C₁₃₉	C₂²×#125	1	1	yes	characteristic
458	C₂×C₁₃₉	#3501	1	1	yes	characteristic
459	C₂×C₁₃₉	#3503	1	1	yes	characteristic
460	C₂×C₁₃₉	#3513	1	1	yes	characteristic
461	C₂×C₁₃₉	#3515	1	1	yes	characteristic
462	C₂×C₁₃₉	#3519	1	1	yes	characteristic
463	C₂×C₁₃₉	#3520	1	1	yes	characteristic
464	#35858	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₁₃₉	#35858	1	1	yes	characteristic, direct product factor, Sylow
466	#2647	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	#2646	C₂×C₁₃₉	1	2	yes	complemented
468	#2570	C₂×C₁₃₉	1	1	yes	characteristic, complemented
469	#2569	C₂×C₁₃₉	1	2	yes	complemented
470	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
471	#2508	C₂×C₁₃₉	1	1	yes	characteristic, complemented
472	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
473	#2507	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2506	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2505	C₂×C₁₃₉	1	2	yes	complemented
476	#2473	C₂×C₁₃₉	1	2	yes	complemented
477	#2473	C₂×C₁₃₉	1	2	yes	complemented
478	#2473	C₂×C₁₃₉	1	2	yes	complemented
479	#2442	C₂×C₁₃₉	1	2	yes	complemented
480	#2402	C₂×C₁₃₉	1	1	yes	characteristic, complemented
481	C₂×#398	C₂×C₁₃₉	1	2	yes	complemented
482	#2349	C₂×C₁₃₉	1	1	yes	characteristic
483	#2349	C₂×C₁₃₉	1	1	yes	characteristic
484	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
485	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
486	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
487	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
488	#2275	C₂×C₁₃₉	1	1	yes	characteristic
489	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
490	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
491	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
499	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
500	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
501	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
502	#400	C₂²×C₁₃₉	1	2	yes	—
503	#400	C₂²×C₁₃₉	1	2	yes	—
504	#400	C₂²×C₁₃₉	1	1	yes	characteristic
505	#400	C₂²×C₁₃₉	1	2	yes	—
506	#400	C₂²×C₁₃₉	1	2	yes	—
507	#400	C₂²×C₁₃₉	1	2	yes	—
508	#400	C₂²×C₁₃₉	1	1	yes	characteristic
509	#400	C₂²×C₁₃₉	1	1	yes	characteristic
510	#400	C₂²×C₁₃₉	1	1	yes	characteristic
511	#398	C₂²×C₁₃₉	1	1	yes	characteristic
512	#398	C₂²×C₁₃₉	1	2	yes	—
513	#398	C₂²×C₁₃₉	1	2	yes	—
514	#398	C₂²×C₁₃₉	1	2	yes	—
515	#398	C₂²×C₁₃₉	1	2	yes	—
516	#398	C₂²×C₁₃₉	1	2	yes	—
517	#398	C₂²×C₁₃₉	1	2	yes	—
518	#398	C₂²×C₁₃₉	1	1	yes	characteristic
519	#398	C₂²×C₁₃₉	1	2	yes	—
520	#398	C₂²×C₁₃₉	1	2	yes	—
521	#398	C₂²×C₁₃₉	1	2	yes	—
522	#398	C₂²×C₁₃₉	1	2	yes	—
523	#398	C₂²×C₁₃₉	1	2	yes	—
524	#398	C₂²×C₁₃₉	1	1	yes	characteristic
525	#398	C₂²×C₁₃₉	1	1	yes	characteristic
526	#389	C₂²×C₁₃₉	1	1	yes	characteristic
527	#389	C₂²×C₁₃₉	1	1	yes	characteristic
528	#389	C₂²×C₁₃₉	1	1	yes	characteristic
529	#389	C₂²×C₁₃₉	1	1	yes	characteristic
530	#389	C₂²×C₁₃₉	1	1	yes	characteristic
531	#389	C₂²×C₁₃₉	1	1	yes	characteristic
532	#389	C₂²×C₁₃₉	1	1	yes	characteristic
533	#389	C₂²×C₁₃₉	1	1	yes	characteristic
534	#389	C₂²×C₁₃₉	1	1	yes	characteristic
535	#389	C₂²×C₁₃₉	1	1	yes	characteristic
536	#389	C₂²×C₁₃₉	1	1	yes	characteristic
537	#389	C₂²×C₁₃₉	1	1	yes	characteristic
538	#389	C₂²×C₁₃₉	1	2	yes	—
539	#389	C₂²×C₁₃₉	1	2	yes	—
540	#389	C₂²×C₁₃₉	1	2	yes	—
541	#387	C₂²×C₁₃₉	1	2	yes	—
542	#387	C₂²×C₁₃₉	1	2	yes	—
543	#387	C₂²×C₁₃₉	1	2	yes	—
544	#387	C₂²×C₁₃₉	1	2	yes	—
545	#387	C₂²×C₁₃₉	1	2	yes	—
546	#387	C₂²×C₁₃₉	1	2	yes	—
547	#385	C₂²×C₁₃₉	1	2	yes	—
548	#385	C₂²×C₁₃₉	1	2	yes	—
549	#385	C₂²×C₁₃₉	1	2	yes	—
550	#385	C₂²×C₁₃₉	1	2	yes	—
551	#385	C₂²×C₁₃₉	1	2	yes	—
552	#385	C₂²×C₁₃₉	1	2	yes	—
553	#385	C₂²×C₁₃₉	1	2	yes	—
554	#385	C₂²×C₁₃₉	1	2	yes	—
555	#385	C₂²×C₁₃₉	1	2	yes	—
556	#385	C₂²×C₁₃₉	1	2	yes	—
557	#385	C₂²×C₁₃₉	1	2	yes	—
558	#385	C₂²×C₁₃₉	1	2	yes	—
559	#384	C₂²×C₁₃₉	1	1	yes	characteristic
560	#384	C₂²×C₁₃₉	1	1	yes	characteristic
561	#384	C₂²×C₁₃₉	1	1	yes	characteristic
562	#384	C₂²×C₁₃₉	1	1	yes	characteristic
563	#382	C₂²×C₁₃₉	1	1	yes	characteristic
564	#382	C₂²×C₁₃₉	1	1	yes	characteristic
565	#382	C₂²×C₁₃₉	1	2	yes	—
566	#380	C₂²×C₁₃₉	1	2	yes	—
567	#380	C₂²×C₁₃₉	1	2	yes	—
568	#380	C₂²×C₁₃₉	1	2	yes	—
569	#380	C₂²×C₁₃₉	1	2	yes	—
570	#380	C₂²×C₁₃₉	1	2	yes	—
571	#380	C₂²×C₁₃₉	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
584	#376	C₂²×C₁₃₉	1	1	yes	characteristic
585	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
586	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
587	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
588	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
596	#125	—	4	4	no	—
597	#125	—	4	4	no	—
598	C₄×D₄	—	2	4	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	4	no	—
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	Q₈×C₁₃₉	1	8	yes	—
605	C₂×C₄⋊C₄	—	4	4	no	—
606	C₂×C₄⋊C₄	—	4	4	no	—
607	C₂×C₄⋊C₄	—	4	4	no	—
608	C₂×C₄⋊C₄	—	4	4	no	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
663	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
664	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
665	#95	C₂³×C₁₃₉	1	1	yes	characteristic
666	#95	C₂³×C₁₃₉	1	1	yes	characteristic
667	#95	C₂³×C₁₃₉	1	1	yes	characteristic
668	#95	C₂³×C₁₃₉	1	2	yes	—
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	#95	C₂³×C₁₃₉	1	2	yes	—
673	#95	C₂³×C₁₃₉	1	2	yes	—
674	#95	C₂³×C₁₃₉	1	2	yes	—
675	#95	C₂³×C₁₃₉	1	2	yes	—
676	#95	C₂³×C₁₃₉	1	2	yes	—
677	#95	C₂³×C₁₃₉	1	1	yes	characteristic
678	#95	C₂³×C₁₃₉	1	1	yes	characteristic
679	#95	C₂³×C₁₃₉	1	1	yes	characteristic
680	#95	C₂³×C₁₃₉	1	1	yes	characteristic
681	#95	C₂³×C₁₃₉	1	1	yes	characteristic
682	#95	C₂³×C₁₃₉	1	1	yes	characteristic
683	#95	C₂³×C₁₃₉	1	1	yes	characteristic
684	#95	C₂³×C₁₃₉	1	1	yes	characteristic
685	#95	C₂³×C₁₃₉	1	1	yes	characteristic
686	#95	C₂³×C₁₃₉	1	1	yes	characteristic
687	#95	C₂³×C₁₃₉	1	1	yes	characteristic
688	#95	C₂³×C₁₃₉	1	1	yes	characteristic
689	#95	C₂³×C₁₃₉	1	1	yes	characteristic
690	#95	C₂³×C₁₃₉	1	2	yes	—
691	#95	C₂³×C₁₃₉	1	2	yes	—
692	#95	C₂³×C₁₃₉	1	2	yes	—
693	#95	C₂³×C₁₃₉	1	2	yes	—
694	#95	C₂³×C₁₃₉	1	2	yes	—
695	#95	C₂³×C₁₃₉	1	2	yes	—
696	#95	C₂³×C₁₃₉	1	2	yes	—
697	#95	C₂³×C₁₃₉	1	2	yes	—
698	#95	C₂³×C₁₃₉	1	2	yes	—
699	#95	C₂³×C₁₃₉	1	2	yes	—
700	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
701	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
702	C₂×D₄	#41×C₁₃₉	1	4	yes	—
703	C₂×D₄	#41×C₁₃₉	1	4	yes	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
725	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	—	4	2	no	—
802	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
808	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
809	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
810	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
811	D₄	#125×C₁₃₉	1	16	yes	complemented
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
877	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
878	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
879	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
880	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
881	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
882	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
883	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
884	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	4	no	—
891	C₂²	C₂×#125×C₁₃₉	1	8	yes	—
892	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
893	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
894	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
895	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
896	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
897	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
898	C₂²	#585×C₁₃₉	1	1	yes	characteristic
899	C₄	—	2	2	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	C₂×#125×C₁₃₉	1	4	yes	—
921	C₂	—	2	8	no	—
922	C₂	C₂²×#125×C₁₃₉	1	1	yes	characteristic
923	C₂	#3501×C₁₃₉	1	1	yes	characteristic
924	C₂	#3503×C₁₃₉	1	1	yes	characteristic
925	C₂	#3513×C₁₃₉	1	1	yes	characteristic
926	C₂	#3515×C₁₃₉	1	1	yes	characteristic
927	C₂	#3519×C₁₃₉	1	1	yes	characteristic
928	C₂	#3520×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. #2647×C₁₃₉	C₂	semidirect
2. #2646×C₁₃₉	C₂	semidirect
3. #2570×C₁₃₉	C₂	semidirect
4. #2569×C₁₃₉	C₂	semidirect
5. #2552×C₁₃₉	C₂	semidirect
6. #2508×C₁₃₉	C₂	semidirect
7. #2507×C₁₃₉	C₂	semidirect
8. #2507×C₁₃₉	C₂	semidirect
9. #2506×C₁₃₉	C₂	semidirect
10. #2505×C₁₃₉	C₂	semidirect
11. #2473×C₁₃₉	C₂	semidirect
12. #2473×C₁₃₉	C₂	semidirect
13. #2473×C₁₃₉	C₂	semidirect
14. #2442×C₁₃₉	C₂	semidirect
15. #2402×C₁₃₉	C₂	semidirect
16. C₂×#398×C₁₃₉	C₂	semidirect
346. D₄×C₁₃₉	#125	semidirect
464. #35858	C₁₃₉	direct (N × H)
465. C₁₃₉	#35858	direct (N × H)
466. #2647	C₂×C₁₃₉	semidirect
467. #2646	C₂×C₁₃₉	semidirect
468. #2570	C₂×C₁₃₉	semidirect
469. #2569	C₂×C₁₃₉	semidirect
470. #2552	C₂×C₁₃₉	semidirect
471. #2508	C₂×C₁₃₉	semidirect
472. #2507	C₂×C₁₃₉	semidirect
473. #2507	C₂×C₁₃₉	semidirect
474. #2506	C₂×C₁₃₉	semidirect
475. #2505	C₂×C₁₃₉	semidirect
476. #2473	C₂×C₁₃₉	semidirect
477. #2473	C₂×C₁₃₉	semidirect
478. #2473	C₂×C₁₃₉	semidirect
479. #2442	C₂×C₁₃₉	semidirect
480. #2402	C₂×C₁₃₉	semidirect
481. C₂×#398	C₂×C₁₃₉	semidirect
811. D₄	#125×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2647×C₁₃₉	2
#2646×C₁₃₉	2
#2570×C₁₃₉	2
#2569×C₁₃₉	2
#2552×C₁₃₉	2
#2508×C₁₃₉	2
#2507×C₁₃₉	2
#2506×C₁₃₉	2
#2505×C₁₃₉	2
#2473×C₁₃₉	2
#2442×C₁₃₉	2
#2402×C₁₃₉	2
C₂×#398×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35858	139

Subgroups — C139×#35858 #48030454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35858 #48030454