Subgroups — C₁₃₉×#36073 #48030669

Order 35584.

1742 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2651×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2624×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2576×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2559×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2531×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2516×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2512×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2506×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2494×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2490×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2442×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2416×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2401×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2370×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2363×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2363×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2346×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	#401×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	#399×C₁₃₉	C₂²	1	2	yes	—
41	#399×C₁₃₉	C₂²	1	1	yes	characteristic
42	#398×C₁₃₉	C₂²	1	1	yes	characteristic
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#397×C₁₃₉	C₂²	1	2	yes	—
46	#397×C₁₃₉	C₂²	1	1	yes	characteristic
47	#397×C₁₃₉	C₂²	1	1	yes	characteristic
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	1	yes	characteristic
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#394×C₁₃₉	C₂²	1	1	yes	characteristic
57	#394×C₁₃₉	C₂²	1	2	yes	—
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	1	yes	characteristic
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	2	yes	—
65	#390×C₁₃₉	C₂²	1	2	yes	—
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#390×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	2	yes	—
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	1	yes	characteristic
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	2	yes	—
81	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#386×C₁₃₉	C₂²	1	2	yes	—
91	#386×C₁₃₉	C₂²	1	2	yes	—
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#384×C₁₃₉	C₂²	1	1	yes	characteristic
95	#382×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	1	yes	characteristic
97	#381×C₁₃₉	C₂²	1	2	yes	—
98	#380×C₁₃₉	C₂²	1	2	yes	—
99	#380×C₁₃₉	C₂²	1	1	yes	characteristic
100	#380×C₁₃₉	C₂²	1	1	yes	characteristic
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	—
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	#376×C₁₃₉	C₂²	1	2	yes	—
123	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
131	#126×C₁₃₉	—	4	4	no	—
132	#125×C₁₃₉	—	2	4	no	—
133	#125×C₁₃₉	—	4	4	no	—
134	#121×C₁₃₉	—	2	4	no	—
135	#121×C₁₃₉	—	2	4	no	—
136	#121×C₁₃₉	—	4	4	no	—
137	C₄×D₄×C₁₃₉	—	2	4	no	—
138	C₄×D₄×C₁₃₉	—	2	4	no	—
139	#117×C₁₃₉	—	2	4	no	—
140	#117×C₁₃₉	—	2	4	no	—
141	#117×C₁₃₉	—	2	4	no	—
142	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
213	#95×C₁₃₉	C₂³	1	1	yes	characteristic
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	1	yes	characteristic
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	1	yes	characteristic
221	#95×C₁₃₉	C₂³	1	1	yes	characteristic
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	2	yes	—
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂×D₄×C₁₃₉	—	2	2	no	—
238	C₂×D₄×C₁₃₉	—	2	4	no	—
239	C₂×D₄×C₁₃₉	—	2	2	no	—
240	C₂×D₄×C₁₃₉	—	2	2	no	—
241	C₂×D₄×C₁₃₉	—	2	2	no	—
242	C₂×D₄×C₁₃₉	—	2	4	no	—
243	C₂×D₄×C₁₃₉	—	2	2	no	—
244	C₂×D₄×C₁₃₉	—	4	1	no	—
245	C₂×D₄×C₁₃₉	—	4	2	no	—
246	C₂×D₄×C₁₃₉	—	4	2	no	—
247	C₂×D₄×C₁₃₉	—	4	2	no	—
248	C₂×D₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	2	2	no	—
250	C₂²×C₄×C₁₃₉	—	2	2	no	—
251	C₂²×C₄×C₁₃₉	—	2	2	no	—
252	C₂²×C₄×C₁₃₉	—	2	2	no	—
253	C₂²×C₄×C₁₃₉	—	2	2	no	—
254	C₂²×C₄×C₁₃₉	—	2	4	no	—
255	C₂²×C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
260	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
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	1	yes	characteristic
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	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	4	no	—
290	C₄⋊C₄×C₁₃₉	—	2	4	no	—
291	C₄⋊C₄×C₁₃₉	—	2	2	no	—
292	C₄⋊C₄×C₁₃₉	—	2	4	no	—
293	C₄⋊C₄×C₁₃₉	—	2	2	no	—
294	C₄⋊C₄×C₁₃₉	—	2	4	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	4	1	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	2	no	—
299	C₄⋊C₄×C₁₃₉	—	4	1	no	—
300	C₄⋊C₄×C₁₃₉	—	4	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	#41	1	4	yes	—
305	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
306	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
316	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
317	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
318	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
319	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
320	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
321	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
322	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
323	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
324	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
325	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
326	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
327	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
328	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
329	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
330	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
331	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
332	C₄²×C₁₃₉	—	2	4	no	—
333	C₄²×C₁₃₉	—	2	4	no	—
334	C₄²×C₁₃₉	—	2	2	no	—
335	C₄²×C₁₃₉	—	2	2	no	—
336	C₄²×C₁₃₉	—	2	2	no	—
337	C₄²×C₁₃₉	—	2	2	no	—
338	C₄²×C₁₃₉	—	2	2	no	—
339	C₄²×C₁₃₉	—	4	2	no	—
340	C₄²×C₁₃₉	—	4	2	no	—
341	C₄²×C₁₃₉	—	4	2	no	—
342	C₄²×C₁₃₉	—	4	2	no	—
343	C₄²×C₁₃₉	—	4	2	no	—
344	C₄²×C₁₃₉	—	4	2	no	—
345	C₂³×C₁₃₉	—	2	1	no	—
346	C₂³×C₁₃₉	—	2	1	no	—
347	C₂³×C₁₃₉	—	2	1	no	—
348	C₂³×C₁₃₉	—	2	1	no	—
349	C₂³×C₁₃₉	—	2	1	no	—
350	C₂³×C₁₃₉	—	2	1	no	—
351	C₂³×C₁₃₉	—	2	1	no	—
352	C₂³×C₁₃₉	—	2	1	no	—
353	C₂³×C₁₃₉	—	2	2	no	—
354	C₂³×C₁₃₉	—	2	2	no	—
355	C₂³×C₁₃₉	—	2	2	no	—
356	C₂³×C₁₃₉	—	2	1	no	—
357	C₂³×C₁₃₉	—	2	2	no	—
358	C₂³×C₁₃₉	—	2	1	no	—
359	C₂³×C₁₃₉	—	2	1	no	—
360	C₂³×C₁₃₉	—	2	2	no	—
361	C₂³×C₁₃₉	—	2	1	no	—
362	C₂³×C₁₃₉	—	2	2	no	—
363	C₂³×C₁₃₉	—	2	2	no	—
364	C₂³×C₁₃₉	—	2	1	no	—
365	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
366	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
367	D₄×C₁₃₉	—	4	4	no	—
368	D₄×C₁₃₉	—	4	4	no	—
369	D₄×C₁₃₉	—	8	4	no	—
370	D₄×C₁₃₉	—	8	4	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	1	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	8	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	1	no	—
383	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	1	no	—
390	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
395	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
401	C₂×C₄×C₁₃₉	—	2	1	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	2	no	—
404	C₂×C₄×C₁₃₉	—	2	1	no	—
405	C₂×C₄×C₁₃₉	—	2	1	no	—
406	C₂×C₄×C₁₃₉	—	2	1	no	—
407	C₂×C₄×C₁₃₉	—	2	1	no	—
408	C₂×C₄×C₁₃₉	—	2	2	no	—
409	C₂×C₄×C₁₃₉	—	2	2	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	1	no	—
412	C₂×C₄×C₁₃₉	—	2	1	no	—
413	C₂×C₄×C₁₃₉	—	2	1	no	—
414	C₂×C₄×C₁₃₉	—	2	2	no	—
415	C₂×C₄×C₁₃₉	—	2	1	no	—
416	C₂×C₄×C₁₃₉	—	2	1	no	—
417	C₂×C₄×C₁₃₉	—	2	1	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	2	1	no	—
420	C₂×C₄×C₁₃₉	—	2	2	no	—
421	C₂×C₄×C₁₃₉	—	2	1	no	—
422	C₂×C₄×C₁₃₉	—	2	1	no	—
423	C₂×C₄×C₁₃₉	—	2	1	no	—
424	C₂×C₄×C₁₃₉	—	2	1	no	—
425	C₂×C₄×C₁₃₉	—	4	4	no	—
426	C₂×C₄×C₁₃₉	—	8	4	no	—
427	C₂×C₄×C₁₃₉	—	8	4	no	—
428	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
429	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
430	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
431	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
432	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
433	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
434	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
435	C₂²×C₁₃₉	—	2	2	no	—
436	C₂²×C₁₃₉	—	2	2	no	—
437	C₂²×C₁₃₉	—	2	2	no	—
438	C₂²×C₁₃₉	—	4	1	no	—
439	C₂²×C₁₃₉	—	4	1	no	—
440	C₂²×C₁₃₉	—	4	1	no	—
441	C₂²×C₁₃₉	—	4	1	no	—
442	C₂²×C₁₃₉	—	4	1	no	—
443	C₂²×C₁₃₉	—	4	2	no	—
444	C₂²×C₁₃₉	—	4	1	no	—
445	C₂²×C₁₃₉	—	4	2	no	—
446	C₂²×C₁₃₉	—	4	1	no	—
447	C₂²×C₁₃₉	—	4	2	no	—
448	C₂²×C₁₃₉	—	4	1	no	—
449	C₂²×C₁₃₉	—	4	2	no	—
450	C₂²×C₁₃₉	—	4	1	no	—
451	C₂²×C₁₃₉	—	4	2	no	—
452	C₂²×C₁₃₉	—	4	2	no	—
453	C₂²×C₁₃₉	—	4	1	no	—
454	C₂²×C₁₃₉	—	4	2	no	—
455	C₂²×C₁₃₉	—	4	1	no	—
456	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
457	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂²×C₁₃₉	#585	1	1	yes	characteristic
461	C₂²×C₁₃₉	#585	1	1	yes	characteristic
462	C₂²×C₁₃₉	#585	1	1	yes	characteristic
463	C₄×C₁₃₉	—	2	2	no	—
464	C₄×C₁₃₉	—	2	2	no	—
465	C₄×C₁₃₉	—	2	4	no	—
466	C₄×C₁₃₉	—	2	4	no	—
467	C₄×C₁₃₉	—	4	1	no	—
468	C₄×C₁₃₉	—	4	1	no	—
469	C₄×C₁₃₉	—	4	1	no	—
470	C₄×C₁₃₉	—	4	2	no	—
471	C₄×C₁₃₉	—	4	1	no	—
472	C₄×C₁₃₉	—	4	1	no	—
473	C₄×C₁₃₉	—	4	1	no	—
474	C₄×C₁₃₉	—	4	1	no	—
475	C₄×C₁₃₉	—	4	2	no	—
476	C₄×C₁₃₉	—	4	1	no	—
477	C₄×C₁₃₉	—	4	2	no	—
478	C₄×C₁₃₉	—	4	2	no	—
479	C₄×C₁₃₉	—	4	1	no	—
480	C₄×C₁₃₉	—	4	1	no	—
481	C₄×C₁₃₉	—	4	2	no	—
482	C₄×C₁₃₉	#529	1	4	yes	—
483	C₂×C₁₃₉	—	4	2	no	—
484	C₂×C₁₃₉	—	8	1	no	—
485	C₂×C₁₃₉	—	8	2	no	—
486	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
487	C₂×C₁₃₉	#3494	1	1	yes	characteristic
488	C₂×C₁₃₉	#3512	1	1	yes	characteristic
489	C₂×C₁₃₉	#3514	1	1	yes	characteristic
490	C₂×C₁₃₉	#3517	1	1	yes	characteristic
491	C₂×C₁₃₉	#3521	1	1	yes	characteristic
492	C₂×C₁₃₉	#3524	1	1	yes	characteristic
493	#36073	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
494	C₁₃₉	#36073	1	1	yes	characteristic, direct product factor, Sylow
495	#2651	C₂×C₁₃₉	1	2	yes	complemented
496	#2624	C₂×C₁₃₉	1	1	yes	characteristic, complemented
497	#2576	C₂×C₁₃₉	1	2	yes	complemented
498	#2559	C₂×C₁₃₉	1	2	yes	complemented
499	#2531	C₂×C₁₃₉	1	2	yes	complemented
500	#2519	C₂×C₁₃₉	1	2	yes	complemented
501	#2516	C₂×C₁₃₉	1	2	yes	complemented
502	#2512	C₂×C₁₃₉	1	1	yes	characteristic, complemented
503	#2506	C₂×C₁₃₉	1	1	yes	characteristic, complemented
504	#2494	C₂×C₁₃₉	1	1	yes	characteristic, complemented
505	#2490	C₂×C₁₃₉	1	1	yes	characteristic, complemented
506	#2490	C₂×C₁₃₉	1	2	yes	complemented
507	#2442	C₂×C₁₃₉	1	1	yes	characteristic, complemented
508	#2416	C₂×C₁₃₉	1	1	yes	characteristic
509	#2401	C₂×C₁₃₉	1	2	yes	complemented
510	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
511	#2370	C₂×C₁₃₉	1	1	yes	characteristic, complemented
512	#2363	C₂×C₁₃₉	1	1	yes	characteristic, complemented
513	#2363	C₂×C₁₃₉	1	1	yes	characteristic, complemented
514	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
515	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
516	#2346	C₂×C₁₃₉	1	1	yes	characteristic, complemented
517	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
518	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
519	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
520	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
521	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
522	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
523	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
524	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
526	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
529	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
530	#401	C₂²×C₁₃₉	1	2	yes	—
531	#400	C₂²×C₁₃₉	1	1	yes	characteristic
532	#400	C₂²×C₁₃₉	1	2	yes	—
533	#400	C₂²×C₁₃₉	1	2	yes	—
534	#399	C₂²×C₁₃₉	1	2	yes	—
535	#399	C₂²×C₁₃₉	1	1	yes	characteristic
536	#398	C₂²×C₁₃₉	1	1	yes	characteristic
537	#398	C₂²×C₁₃₉	1	2	yes	—
538	#398	C₂²×C₁₃₉	1	2	yes	—
539	#397	C₂²×C₁₃₉	1	1	yes	characteristic
540	#397	C₂²×C₁₃₉	1	2	yes	—
541	#397	C₂²×C₁₃₉	1	1	yes	characteristic
542	#397	C₂²×C₁₃₉	1	1	yes	characteristic
543	#397	C₂²×C₁₃₉	1	2	yes	—
544	#397	C₂²×C₁₃₉	1	2	yes	—
545	#397	C₂²×C₁₃₉	1	2	yes	—
546	#396	C₂²×C₁₃₉	1	2	yes	—
547	#396	C₂²×C₁₃₉	1	2	yes	—
548	#394	C₂²×C₁₃₉	1	2	yes	—
549	#394	C₂²×C₁₃₉	1	2	yes	—
550	#394	C₂²×C₁₃₉	1	1	yes	characteristic
551	#394	C₂²×C₁₃₉	1	1	yes	characteristic
552	#394	C₂²×C₁₃₉	1	2	yes	—
553	#394	C₂²×C₁₃₉	1	2	yes	—
554	#390	C₂²×C₁₃₉	1	2	yes	—
555	#390	C₂²×C₁₃₉	1	1	yes	characteristic
556	#390	C₂²×C₁₃₉	1	1	yes	characteristic
557	#390	C₂²×C₁₃₉	1	1	yes	characteristic
558	#390	C₂²×C₁₃₉	1	2	yes	—
559	#390	C₂²×C₁₃₉	1	1	yes	characteristic
560	#390	C₂²×C₁₃₉	1	2	yes	—
561	#390	C₂²×C₁₃₉	1	2	yes	—
562	#389	C₂²×C₁₃₉	1	1	yes	characteristic
563	#389	C₂²×C₁₃₉	1	1	yes	characteristic
564	#389	C₂²×C₁₃₉	1	1	yes	characteristic
565	#389	C₂²×C₁₃₉	1	1	yes	characteristic
566	#389	C₂²×C₁₃₉	1	1	yes	characteristic
567	#389	C₂²×C₁₃₉	1	1	yes	characteristic
568	#389	C₂²×C₁₃₉	1	2	yes	—
569	#388	C₂²×C₁₃₉	1	2	yes	—
570	#388	C₂²×C₁₃₉	1	2	yes	—
571	#388	C₂²×C₁₃₉	1	2	yes	—
572	#388	C₂²×C₁₃₉	1	2	yes	—
573	#388	C₂²×C₁₃₉	1	2	yes	—
574	#388	C₂²×C₁₃₉	1	2	yes	—
575	#388	C₂²×C₁₃₉	1	2	yes	—
576	#388	C₂²×C₁₃₉	1	2	yes	—
577	#388	C₂²×C₁₃₉	1	2	yes	—
578	#388	C₂²×C₁₃₉	1	2	yes	—
579	#388	C₂²×C₁₃₉	1	2	yes	—
580	#387	C₂²×C₁₃₉	1	2	yes	—
581	#387	C₂²×C₁₃₉	1	2	yes	—
582	#387	C₂²×C₁₃₉	1	2	yes	—
583	#387	C₂²×C₁₃₉	1	2	yes	—
584	#386	C₂²×C₁₃₉	1	2	yes	—
585	#386	C₂²×C₁₃₉	1	2	yes	—
586	#386	C₂²×C₁₃₉	1	2	yes	—
587	#385	C₂²×C₁₃₉	1	2	yes	—
588	#384	C₂²×C₁₃₉	1	1	yes	characteristic
589	#382	C₂²×C₁₃₉	1	2	yes	—
590	#382	C₂²×C₁₃₉	1	1	yes	characteristic
591	#381	C₂²×C₁₃₉	1	2	yes	—
592	#380	C₂²×C₁₃₉	1	1	yes	characteristic
593	#380	C₂²×C₁₃₉	1	1	yes	characteristic
594	#380	C₂²×C₁₃₉	1	1	yes	characteristic
595	#380	C₂²×C₁₃₉	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
600	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
604	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
605	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
608	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
611	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
615	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
616	#376	C₂²×C₁₃₉	1	2	yes	—
617	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
625	#126	—	4	4	no	—
626	#125	—	2	4	no	—
627	#125	—	4	4	no	—
628	#121	—	2	4	no	—
629	#121	—	2	4	no	—
630	#121	—	4	4	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	#117	—	2	4	no	—
634	#117	—	2	4	no	—
635	#117	—	2	4	no	—
636	C₂×C₄⋊C₄	—	2	4	no	—
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
688	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
689	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
690	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
696	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
697	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
698	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
699	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
700	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
701	#95	C₂³×C₁₃₉	1	1	yes	characteristic
702	#95	C₂³×C₁₃₉	1	2	yes	—
703	#95	C₂³×C₁₃₉	1	2	yes	—
704	#95	C₂³×C₁₃₉	1	2	yes	—
705	#95	C₂³×C₁₃₉	1	1	yes	characteristic
706	#95	C₂³×C₁₃₉	1	1	yes	characteristic
707	#95	C₂³×C₁₃₉	1	1	yes	characteristic
708	#95	C₂³×C₁₃₉	1	2	yes	—
709	#95	C₂³×C₁₃₉	1	2	yes	—
710	#95	C₂³×C₁₃₉	1	2	yes	—
711	#95	C₂³×C₁₃₉	1	2	yes	—
712	#95	C₂³×C₁₃₉	1	2	yes	—
713	#95	C₂³×C₁₃₉	1	1	yes	characteristic
714	#95	C₂³×C₁₃₉	1	2	yes	—
715	#95	C₂³×C₁₃₉	1	2	yes	—
716	#95	C₂³×C₁₃₉	1	1	yes	characteristic
717	#95	C₂³×C₁₃₉	1	1	yes	characteristic
718	#95	C₂³×C₁₃₉	1	1	yes	characteristic
719	#95	C₂³×C₁₃₉	1	2	yes	—
720	#95	C₂³×C₁₃₉	1	2	yes	—
721	#95	C₂³×C₁₃₉	1	1	yes	characteristic
722	#95	C₂³×C₁₃₉	1	2	yes	—
723	#95	C₂³×C₁₃₉	1	2	yes	—
724	#95	C₂³×C₁₃₉	1	1	yes	characteristic
725	#95	C₂³×C₁₃₉	1	2	yes	—
726	#95	C₂³×C₁₃₉	1	2	yes	—
727	#95	C₂³×C₁₃₉	1	2	yes	—
728	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
729	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
730	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	4	1	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	1	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
799	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	4	1	no	—
811	C₂²⋊C₄	—	4	1	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	1	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	1	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	1	no	—
822	C₂²⋊C₄	—	4	1	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	4	2	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	2	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
860	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
861	D₄	—	4	4	no	—
862	D₄	—	4	4	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	4	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	8	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	—	8	4	no	—
922	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
923	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
924	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
925	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
926	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
927	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
928	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	1	no	—
950	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
951	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
952	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
953	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
954	C₂²	#585×C₁₃₉	1	1	yes	characteristic
955	C₂²	#585×C₁₃₉	1	1	yes	characteristic
956	C₂²	#585×C₁₃₉	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	4	no	—
960	C₄	—	2	4	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	2	no	—
976	C₄	#529×C₁₃₉	1	4	yes	—
977	C₂	—	4	2	no	—
978	C₂	—	8	1	no	—
979	C₂	—	8	2	no	—
980	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
981	C₂	#3494×C₁₃₉	1	1	yes	characteristic
982	C₂	#3512×C₁₃₉	1	1	yes	characteristic
983	C₂	#3514×C₁₃₉	1	1	yes	characteristic
984	C₂	#3517×C₁₃₉	1	1	yes	characteristic
985	C₂	#3521×C₁₃₉	1	1	yes	characteristic
986	C₂	#3524×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2416×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. #2651×C₁₃₉	C₂	semidirect
2. #2624×C₁₃₉	C₂	semidirect
3. #2576×C₁₃₉	C₂	semidirect
4. #2559×C₁₃₉	C₂	semidirect
5. #2531×C₁₃₉	C₂	semidirect
6. #2519×C₁₃₉	C₂	semidirect
7. #2516×C₁₃₉	C₂	semidirect
8. #2512×C₁₃₉	C₂	semidirect
9. #2506×C₁₃₉	C₂	semidirect
10. #2494×C₁₃₉	C₂	semidirect
11. #2490×C₁₃₉	C₂	semidirect
12. #2490×C₁₃₉	C₂	semidirect
13. #2442×C₁₃₉	C₂	semidirect
15. #2401×C₁₃₉	C₂	semidirect
16. #2395×C₁₃₉	C₂	semidirect
17. #2370×C₁₃₉	C₂	semidirect
18. #2363×C₁₃₉	C₂	semidirect
19. #2363×C₁₃₉	C₂	semidirect
20. #2357×C₁₃₉	C₂	semidirect
21. #2354×C₁₃₉	C₂	semidirect
22. #2346×C₁₃₉	C₂	semidirect
23. #2274×C₁₃₉	C₂	semidirect
493. #36073	C₁₃₉	direct (N × H)
494. C₁₃₉	#36073	direct (N × H)
495. #2651	C₂×C₁₃₉	semidirect
496. #2624	C₂×C₁₃₉	semidirect
497. #2576	C₂×C₁₃₉	semidirect
498. #2559	C₂×C₁₃₉	semidirect
499. #2531	C₂×C₁₃₉	semidirect
500. #2519	C₂×C₁₃₉	semidirect
501. #2516	C₂×C₁₃₉	semidirect
502. #2512	C₂×C₁₃₉	semidirect
503. #2506	C₂×C₁₃₉	semidirect
504. #2494	C₂×C₁₃₉	semidirect
505. #2490	C₂×C₁₃₉	semidirect
506. #2490	C₂×C₁₃₉	semidirect
507. #2442	C₂×C₁₃₉	semidirect
509. #2401	C₂×C₁₃₉	semidirect
510. #2395	C₂×C₁₃₉	semidirect
511. #2370	C₂×C₁₃₉	semidirect
512. #2363	C₂×C₁₃₉	semidirect
513. #2363	C₂×C₁₃₉	semidirect
514. #2357	C₂×C₁₃₉	semidirect
515. #2354	C₂×C₁₃₉	semidirect
516. #2346	C₂×C₁₃₉	semidirect
517. #2274	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2651×C₁₃₉	2
#2624×C₁₃₉	2
#2576×C₁₃₉	2
#2559×C₁₃₉	2
#2531×C₁₃₉	2
#2519×C₁₃₉	2
#2516×C₁₃₉	2
#2512×C₁₃₉	2
#2506×C₁₃₉	2
#2494×C₁₃₉	2
#2490×C₁₃₉	2
#2442×C₁₃₉	2
#2416×C₁₃₉	2
#2401×C₁₃₉	2
#2395×C₁₃₉	2
#2370×C₁₃₉	2
#2363×C₁₃₉	2
#2357×C₁₃₉	2
#2354×C₁₃₉	2
#2346×C₁₃₉	2
#2274×C₁₃₉	2
#36073	139

Subgroups — C139×#36073 #48030669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36073 #48030669