Subgroups — C₁₃₉×#36032 #48030628

Order 35584.

2370 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2635×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2634×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2618×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2611×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2598×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2591×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2543×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2484×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2481×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2470×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2457×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2444×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2430×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#400×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2364×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	#553×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	#520×C₁₃₉	—	2	8	no	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	#400×C₁₃₉	C₂²	1	1	yes	characteristic
54	#400×C₁₃₉	C₂²	1	1	yes	characteristic
55	#400×C₁₃₉	C₂²	1	1	yes	characteristic
56	#400×C₁₃₉	C₂²	1	1	yes	characteristic
57	#400×C₁₃₉	C₂²	1	2	yes	—
58	#400×C₁₃₉	C₂²	1	1	yes	characteristic
59	#400×C₁₃₉	C₂²	1	2	yes	—
60	#400×C₁₃₉	C₂²	1	2	yes	—
61	#400×C₁₃₉	C₂²	1	1	yes	characteristic
62	#399×C₁₃₉	C₂²	1	1	yes	characteristic
63	#399×C₁₃₉	C₂²	1	1	yes	characteristic
64	#398×C₁₃₉	C₂²	1	1	yes	characteristic
65	#398×C₁₃₉	C₂²	1	1	yes	characteristic
66	#398×C₁₃₉	C₂²	1	1	yes	characteristic
67	#397×C₁₃₉	C₂²	1	1	yes	characteristic
68	#397×C₁₃₉	C₂²	1	2	yes	—
69	#397×C₁₃₉	C₂²	1	2	yes	—
70	#396×C₁₃₉	C₂²	1	2	yes	—
71	#396×C₁₃₉	C₂²	1	2	yes	—
72	#395×C₁₃₉	C₂²	1	2	yes	—
73	#394×C₁₃₉	C₂²	1	1	yes	characteristic
74	#394×C₁₃₉	C₂²	1	1	yes	characteristic
75	#394×C₁₃₉	C₂²	1	1	yes	characteristic
76	#394×C₁₃₉	C₂²	1	2	yes	—
77	#394×C₁₃₉	C₂²	1	2	yes	—
78	#393×C₁₃₉	C₂²	1	2	yes	—
79	#392×C₁₃₉	C₂²	1	1	yes	characteristic
80	#392×C₁₃₉	C₂²	1	2	yes	—
81	#389×C₁₃₉	C₂²	1	2	yes	—
82	#389×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	#388×C₁₃₉	C₂²	1	2	yes	—
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#387×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#386×C₁₃₉	C₂²	1	2	yes	—
97	#386×C₁₃₉	C₂²	1	2	yes	—
98	#386×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#386×C₁₃₉	C₂²	1	2	yes	—
102	#386×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#386×C₁₃₉	C₂²	1	2	yes	—
105	#386×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#385×C₁₃₉	C₂²	1	2	yes	—
110	#383×C₁₃₉	C₂²	1	1	yes	characteristic
111	#381×C₁₃₉	C₂²	1	1	yes	characteristic
112	#381×C₁₃₉	C₂²	1	2	yes	—
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic
114	#380×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
125	C₂×#41×C₁₃₉	—	2	4	no	—
126	C₂×#41×C₁₃₉	—	2	4	no	—
127	C₂×#41×C₁₃₉	—	2	4	no	—
128	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	#126×C₁₃₉	—	2	8	no	—
149	#125×C₁₃₉	—	2	4	no	—
150	#123×C₁₃₉	—	2	8	no	—
151	#123×C₁₃₉	—	2	8	no	—
152	#121×C₁₃₉	—	2	8	no	—
153	#121×C₁₃₉	—	2	8	no	—
154	#121×C₁₃₉	—	2	4	no	—
155	#121×C₁₃₉	—	2	4	no	—
156	C₄×Q₈×C₁₃₉	—	2	4	no	—
157	C₄×Q₈×C₁₃₉	—	2	4	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	C₄×D₄×C₁₃₉	—	2	4	no	—
161	C₄×D₄×C₁₃₉	—	2	4	no	—
162	C₄×D₄×C₁₃₉	—	2	4	no	—
163	C₄×D₄×C₁₃₉	—	2	8	no	—
164	C₄×D₄×C₁₃₉	—	2	4	no	—
165	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
166	#117×C₁₃₉	—	2	4	no	—
167	#117×C₁₃₉	—	2	4	no	—
168	#117×C₁₃₉	—	2	4	no	—
169	#117×C₁₃₉	—	2	4	no	—
170	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
172	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
173	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	#95×C₁₃₉	C₂³	1	2	yes	—
235	#95×C₁₃₉	C₂³	1	1	yes	characteristic
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	1	yes	characteristic
239	#95×C₁₃₉	C₂³	1	1	yes	characteristic
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	#41×C₁₃₉	—	2	32	no	—
258	C₂×Q₈×C₁₃₉	—	2	2	no	—
259	C₂×Q₈×C₁₃₉	—	2	2	no	—
260	C₂×Q₈×C₁₃₉	—	2	2	no	—
261	C₂×D₄×C₁₃₉	—	2	2	no	—
262	C₂×D₄×C₁₃₉	—	2	2	no	—
263	C₂×D₄×C₁₃₉	—	2	2	no	—
264	C₂×D₄×C₁₃₉	—	2	2	no	—
265	C₂×D₄×C₁₃₉	—	2	2	no	—
266	C₂×D₄×C₁₃₉	—	2	2	no	—
267	C₂×D₄×C₁₃₉	—	2	4	no	—
268	C₂×D₄×C₁₃₉	—	2	4	no	—
269	C₂×D₄×C₁₃₉	—	2	4	no	—
270	C₂×D₄×C₁₃₉	—	2	4	no	—
271	C₂×D₄×C₁₃₉	—	2	4	no	—
272	C₂×D₄×C₁₃₉	—	2	2	no	—
273	C₂×D₄×C₁₃₉	—	2	2	no	—
274	C₂×D₄×C₁₃₉	—	4	2	no	—
275	C₂×D₄×C₁₃₉	—	4	2	no	—
276	C₂×D₄×C₁₃₉	—	4	2	no	—
277	C₂×D₄×C₁₃₉	—	4	2	no	—
278	C₂×D₄×C₁₃₉	—	4	2	no	—
279	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
280	C₂×D₄×C₁₃₉	#41	1	4	yes	—
281	C₂²×C₄×C₁₃₉	—	2	2	no	—
282	C₂²×C₄×C₁₃₉	—	2	2	no	—
283	C₂²×C₄×C₁₃₉	—	2	2	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	2	no	—
287	C₂²×C₄×C₁₃₉	—	2	2	no	—
288	C₂²×C₄×C₁₃₉	—	2	2	no	—
289	C₂²×C₄×C₁₃₉	—	2	2	no	—
290	C₂²×C₄×C₁₃₉	—	2	2	no	—
291	C₂²×C₄×C₁₃₉	—	2	4	no	—
292	C₂²×C₄×C₁₃₉	—	2	4	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	2	2	no	—
295	C₂²×C₄×C₁₃₉	—	2	4	no	—
296	C₂²×C₄×C₁₃₉	—	4	2	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	—	4	2	no	—
299	C₂²×C₄×C₁₃₉	—	4	2	no	—
300	C₂²×C₄×C₁₃₉	—	4	2	no	—
301	C₂²×C₄×C₁₃₉	—	4	2	no	—
302	C₂²×C₄×C₁₃₉	—	4	2	no	—
303	C₂²×C₄×C₁₃₉	—	4	2	no	—
304	C₂²×C₄×C₁₃₉	—	4	2	no	—
305	C₂²×C₄×C₁₃₉	—	4	2	no	—
306	C₂²×C₄×C₁₃₉	—	4	2	no	—
307	C₂²×C₄×C₁₃₉	—	4	2	no	—
308	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
309	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
310	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
311	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
330	C₄⋊C₄×C₁₃₉	—	2	2	no	—
331	C₄⋊C₄×C₁₃₉	—	2	2	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	no	—
333	C₄⋊C₄×C₁₃₉	—	2	2	no	—
334	C₄⋊C₄×C₁₃₉	—	2	2	no	—
335	C₄⋊C₄×C₁₃₉	—	2	2	no	—
336	C₄⋊C₄×C₁₃₉	—	2	2	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	2	no	—
339	C₄⋊C₄×C₁₃₉	—	2	2	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	no	—
342	C₄⋊C₄×C₁₃₉	—	2	2	no	—
343	C₄⋊C₄×C₁₃₉	—	2	4	no	—
344	C₄⋊C₄×C₁₃₉	—	2	4	no	—
345	C₄⋊C₄×C₁₃₉	—	2	4	no	—
346	C₄⋊C₄×C₁₃₉	—	2	4	no	—
347	C₄⋊C₄×C₁₃₉	—	2	4	no	—
348	C₄⋊C₄×C₁₃₉	—	4	2	no	—
349	C₄⋊C₄×C₁₃₉	—	4	2	no	—
350	C₄⋊C₄×C₁₃₉	—	4	2	no	—
351	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
352	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
366	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
370	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
371	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
372	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
373	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
374	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
375	C₄²×C₁₃₉	—	2	2	no	—
376	C₄²×C₁₃₉	—	2	2	no	—
377	C₄²×C₁₃₉	—	2	2	no	—
378	C₄²×C₁₃₉	—	2	2	no	—
379	C₄²×C₁₃₉	—	2	2	no	—
380	C₄²×C₁₃₉	—	2	4	no	—
381	C₄²×C₁₃₉	—	4	2	no	—
382	C₄²×C₁₃₉	—	4	2	no	—
383	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
384	C₂³×C₁₃₉	—	2	2	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	1	no	—
387	C₂³×C₁₃₉	—	2	1	no	—
388	C₂³×C₁₃₉	—	2	1	no	—
389	C₂³×C₁₃₉	—	2	1	no	—
390	C₂³×C₁₃₉	—	2	2	no	—
391	C₂³×C₁₃₉	—	2	2	no	—
392	C₂³×C₁₃₉	—	2	2	no	—
393	C₂³×C₁₃₉	—	2	2	no	—
394	C₂³×C₁₃₉	—	2	2	no	—
395	C₂³×C₁₃₉	—	2	2	no	—
396	C₂³×C₁₃₉	—	2	2	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	2	2	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	2	no	—
401	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
402	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
403	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
404	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
405	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
406	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
407	Q₈×C₁₃₉	—	2	8	no	—
408	D₄×C₁₃₉	—	2	8	no	—
409	D₄×C₁₃₉	—	2	8	no	—
410	D₄×C₁₃₉	—	2	8	no	—
411	D₄×C₁₃₉	—	4	4	no	—
412	D₄×C₁₃₉	—	4	8	no	—
413	D₄×C₁₃₉	—	8	4	no	—
414	D₄×C₁₃₉	—	8	4	no	—
415	C₂×C₄×C₁₃₉	—	2	8	no	—
416	C₂×C₄×C₁₃₉	—	2	8	no	—
417	C₂×C₄×C₁₃₉	—	2	8	no	—
418	C₂×C₄×C₁₃₉	—	2	1	no	—
419	C₂×C₄×C₁₃₉	—	2	1	no	—
420	C₂×C₄×C₁₃₉	—	2	1	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	—	2	1	no	—
426	C₂×C₄×C₁₃₉	—	2	2	no	—
427	C₂×C₄×C₁₃₉	—	2	2	no	—
428	C₂×C₄×C₁₃₉	—	2	2	no	—
429	C₂×C₄×C₁₃₉	—	2	2	no	—
430	C₂×C₄×C₁₃₉	—	2	1	no	—
431	C₂×C₄×C₁₃₉	—	2	2	no	—
432	C₂×C₄×C₁₃₉	—	2	2	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	1	no	—
435	C₂×C₄×C₁₃₉	—	2	1	no	—
436	C₂×C₄×C₁₃₉	—	2	2	no	—
437	C₂×C₄×C₁₃₉	—	2	2	no	—
438	C₂×C₄×C₁₃₉	—	2	2	no	—
439	C₂×C₄×C₁₃₉	—	2	2	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	2	no	—
442	C₂×C₄×C₁₃₉	—	2	2	no	—
443	C₂×C₄×C₁₃₉	—	2	2	no	—
444	C₂×C₄×C₁₃₉	—	2	2	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	2	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	2	no	—
450	C₂×C₄×C₁₃₉	—	2	2	no	—
451	C₂×C₄×C₁₃₉	—	2	2	no	—
452	C₂×C₄×C₁₃₉	—	2	2	no	—
453	C₂×C₄×C₁₃₉	—	2	2	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	2	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	4	4	no	—
460	C₂×C₄×C₁₃₉	—	4	4	no	—
461	C₂×C₄×C₁₃₉	—	8	2	no	—
462	C₂×C₄×C₁₃₉	—	8	2	no	—
463	C₂×C₄×C₁₃₉	—	8	4	no	—
464	C₂×C₄×C₁₃₉	—	8	2	no	—
465	C₂×C₄×C₁₃₉	—	8	2	no	—
466	C₂×C₄×C₁₃₉	—	8	4	no	—
467	C₂×C₄×C₁₃₉	—	8	4	no	—
468	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
474	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
475	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
476	C₂²×C₁₃₉	—	2	2	no	—
477	C₂²×C₁₃₉	—	2	2	no	—
478	C₂²×C₁₃₉	—	2	4	no	—
479	C₂²×C₁₃₉	—	2	4	no	—
480	C₂²×C₁₃₉	—	2	2	no	—
481	C₂²×C₁₃₉	—	2	2	no	—
482	C₂²×C₁₃₉	—	2	2	no	—
483	C₂²×C₁₃₉	—	2	2	no	—
484	C₂²×C₁₃₉	—	2	4	no	—
485	C₂²×C₁₃₉	—	4	1	no	—
486	C₂²×C₁₃₉	—	4	1	no	—
487	C₂²×C₁₃₉	—	4	2	no	—
488	C₂²×C₁₃₉	—	4	2	no	—
489	C₂²×C₁₃₉	—	4	2	no	—
490	C₂²×C₁₃₉	—	4	2	no	—
491	C₂²×C₁₃₉	—	4	2	no	—
492	C₂²×C₁₃₉	—	4	2	no	—
493	C₂²×C₁₃₉	—	4	2	no	—
494	C₂²×C₁₃₉	—	4	2	no	—
495	C₂²×C₁₃₉	—	4	2	no	—
496	C₂²×C₁₃₉	—	4	2	no	—
497	C₂²×C₁₃₉	#525	1	4	yes	—
498	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
499	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
501	C₂²×C₁₃₉	#585	1	2	yes	—
502	C₂²×C₁₃₉	#585	1	2	yes	—
503	C₄×C₁₃₉	—	2	2	no	—
504	C₄×C₁₃₉	—	2	2	no	—
505	C₄×C₁₃₉	—	2	2	no	—
506	C₄×C₁₃₉	—	2	2	no	—
507	C₄×C₁₃₉	—	2	2	no	—
508	C₄×C₁₃₉	—	2	2	no	—
509	C₄×C₁₃₉	—	2	2	no	—
510	C₄×C₁₃₉	—	2	2	no	—
511	C₄×C₁₃₉	—	4	2	no	—
512	C₄×C₁₃₉	—	4	1	no	—
513	C₄×C₁₃₉	—	4	1	no	—
514	C₄×C₁₃₉	—	4	1	no	—
515	C₄×C₁₃₉	—	4	1	no	—
516	C₄×C₁₃₉	—	4	2	no	—
517	C₄×C₁₃₉	—	4	2	no	—
518	C₄×C₁₃₉	—	4	2	no	—
519	C₄×C₁₃₉	—	4	2	no	—
520	C₄×C₁₃₉	—	4	2	no	—
521	C₄×C₁₃₉	—	4	2	no	—
522	C₂×C₁₃₉	—	2	4	no	—
523	C₂×C₁₃₉	—	4	2	no	—
524	C₂×C₁₃₉	—	4	2	no	—
525	C₂×C₁₃₉	—	8	2	no	—
526	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
527	C₂×C₁₃₉	#3485	1	1	yes	characteristic
528	C₂×C₁₃₉	#3500	1	1	yes	characteristic
529	C₂×C₁₃₉	#3512	1	2	yes	—
530	C₂×C₁₃₉	#3521	1	2	yes	—
531	#36032	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
532	C₁₃₉	#36032	1	1	yes	characteristic, direct product factor, Sylow
533	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
534	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
535	#2635	C₂×C₁₃₉	1	1	yes	characteristic, complemented
536	#2634	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	#2618	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	#2611	C₂×C₁₃₉	1	1	yes	characteristic, complemented
539	#2598	C₂×C₁₃₉	1	1	yes	characteristic, complemented
540	#2591	C₂×C₁₃₉	1	1	yes	characteristic, complemented
541	#2543	C₂×C₁₃₉	1	1	yes	characteristic, complemented
542	#2487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
543	#2484	C₂×C₁₃₉	1	1	yes	characteristic, complemented
544	#2481	C₂×C₁₃₉	1	2	yes	complemented
545	#2470	C₂×C₁₃₉	1	2	yes	complemented
546	#2469	C₂×C₁₃₉	1	2	yes	complemented
547	#2457	C₂×C₁₃₉	1	2	yes	complemented
548	#2444	C₂×C₁₃₉	1	2	yes	complemented
549	#2430	C₂×C₁₃₉	1	2	yes	complemented
550	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
551	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
552	C₂×#400	C₂×C₁₃₉	1	1	yes	characteristic, complemented
553	#2364	C₂×C₁₃₉	1	2	yes	complemented
554	#2359	C₂×C₁₃₉	1	2	yes	complemented
555	#2353	C₂×C₁₃₉	1	1	yes	characteristic, complemented
556	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
557	#553	—	2	8	no	—
558	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
559	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
561	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
562	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
564	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
565	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
566	#520	—	2	8	no	—
567	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
568	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
570	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
571	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
573	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
578	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
583	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
585	#400	C₂²×C₁₃₉	1	1	yes	characteristic
586	#400	C₂²×C₁₃₉	1	1	yes	characteristic
587	#400	C₂²×C₁₃₉	1	1	yes	characteristic
588	#400	C₂²×C₁₃₉	1	1	yes	characteristic
589	#400	C₂²×C₁₃₉	1	2	yes	—
590	#400	C₂²×C₁₃₉	1	1	yes	characteristic
591	#400	C₂²×C₁₃₉	1	2	yes	—
592	#400	C₂²×C₁₃₉	1	2	yes	—
593	#400	C₂²×C₁₃₉	1	1	yes	characteristic
594	#399	C₂²×C₁₃₉	1	1	yes	characteristic
595	#399	C₂²×C₁₃₉	1	1	yes	characteristic
596	#398	C₂²×C₁₃₉	1	1	yes	characteristic
597	#398	C₂²×C₁₃₉	1	1	yes	characteristic
598	#398	C₂²×C₁₃₉	1	1	yes	characteristic
599	#397	C₂²×C₁₃₉	1	1	yes	characteristic
600	#397	C₂²×C₁₃₉	1	2	yes	—
601	#397	C₂²×C₁₃₉	1	2	yes	—
602	#396	C₂²×C₁₃₉	1	2	yes	—
603	#396	C₂²×C₁₃₉	1	2	yes	—
604	#395	C₂²×C₁₃₉	1	2	yes	—
605	#394	C₂²×C₁₃₉	1	1	yes	characteristic
606	#394	C₂²×C₁₃₉	1	1	yes	characteristic
607	#394	C₂²×C₁₃₉	1	1	yes	characteristic
608	#394	C₂²×C₁₃₉	1	2	yes	—
609	#394	C₂²×C₁₃₉	1	2	yes	—
610	#393	C₂²×C₁₃₉	1	2	yes	—
611	#392	C₂²×C₁₃₉	1	1	yes	characteristic
612	#392	C₂²×C₁₃₉	1	2	yes	—
613	#389	C₂²×C₁₃₉	1	2	yes	—
614	#389	C₂²×C₁₃₉	1	2	yes	—
615	#388	C₂²×C₁₃₉	1	2	yes	—
616	#388	C₂²×C₁₃₉	1	2	yes	—
617	#388	C₂²×C₁₃₉	1	2	yes	—
618	#388	C₂²×C₁₃₉	1	2	yes	—
619	#388	C₂²×C₁₃₉	1	2	yes	—
620	#388	C₂²×C₁₃₉	1	2	yes	—
621	#388	C₂²×C₁₃₉	1	2	yes	—
622	#387	C₂²×C₁₃₉	1	2	yes	—
623	#387	C₂²×C₁₃₉	1	2	yes	—
624	#387	C₂²×C₁₃₉	1	2	yes	—
625	#387	C₂²×C₁₃₉	1	2	yes	—
626	#387	C₂²×C₁₃₉	1	2	yes	—
627	#387	C₂²×C₁₃₉	1	2	yes	—
628	#386	C₂²×C₁₃₉	1	2	yes	—
629	#386	C₂²×C₁₃₉	1	2	yes	—
630	#386	C₂²×C₁₃₉	1	2	yes	—
631	#386	C₂²×C₁₃₉	1	2	yes	—
632	#386	C₂²×C₁₃₉	1	2	yes	—
633	#386	C₂²×C₁₃₉	1	2	yes	—
634	#386	C₂²×C₁₃₉	1	2	yes	—
635	#386	C₂²×C₁₃₉	1	2	yes	—
636	#386	C₂²×C₁₃₉	1	2	yes	—
637	#386	C₂²×C₁₃₉	1	2	yes	—
638	#385	C₂²×C₁₃₉	1	2	yes	—
639	#385	C₂²×C₁₃₉	1	2	yes	—
640	#385	C₂²×C₁₃₉	1	2	yes	—
641	#385	C₂²×C₁₃₉	1	2	yes	—
642	#383	C₂²×C₁₃₉	1	1	yes	characteristic
643	#381	C₂²×C₁₃₉	1	1	yes	characteristic
644	#381	C₂²×C₁₃₉	1	2	yes	—
645	#380	C₂²×C₁₃₉	1	1	yes	characteristic
646	#380	C₂²×C₁₃₉	1	2	yes	—
647	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
648	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
649	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
650	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
651	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
652	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
653	#376	C₂²×C₁₃₉	1	1	yes	characteristic
654	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
655	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
656	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
657	C₂×#41	—	2	4	no	—
658	C₂×#41	—	2	4	no	—
659	C₂×#41	—	2	4	no	—
660	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
663	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
666	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
667	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
674	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
676	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
677	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
678	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
680	#126	—	2	8	no	—
681	#125	—	2	4	no	—
682	#123	—	2	8	no	—
683	#123	—	2	8	no	—
684	#121	—	2	8	no	—
685	#121	—	2	8	no	—
686	#121	—	2	4	no	—
687	#121	—	2	4	no	—
688	C₄×Q₈	—	2	4	no	—
689	C₄×Q₈	—	2	4	no	—
690	C₄×D₄	—	2	4	no	—
691	C₄×D₄	—	2	4	no	—
692	C₄×D₄	—	2	4	no	—
693	C₄×D₄	—	2	4	no	—
694	C₄×D₄	—	2	4	no	—
695	C₄×D₄	—	2	8	no	—
696	C₄×D₄	—	2	4	no	—
697	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
698	#117	—	2	4	no	—
699	#117	—	2	4	no	—
700	#117	—	2	4	no	—
701	#117	—	2	4	no	—
702	C₂×C₄⋊C₄	—	2	4	no	—
703	C₂×C₄⋊C₄	—	2	4	no	—
704	C₂×C₄⋊C₄	—	2	4	no	—
705	C₂×C₄⋊C₄	—	2	4	no	—
706	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
758	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
759	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
760	#95	C₂³×C₁₃₉	1	1	yes	characteristic
761	#95	C₂³×C₁₃₉	1	2	yes	—
762	#95	C₂³×C₁₃₉	1	2	yes	—
763	#95	C₂³×C₁₃₉	1	1	yes	characteristic
764	#95	C₂³×C₁₃₉	1	2	yes	—
765	#95	C₂³×C₁₃₉	1	2	yes	—
766	#95	C₂³×C₁₃₉	1	2	yes	—
767	#95	C₂³×C₁₃₉	1	2	yes	—
768	#95	C₂³×C₁₃₉	1	2	yes	—
769	#95	C₂³×C₁₃₉	1	2	yes	—
770	#95	C₂³×C₁₃₉	1	2	yes	—
771	#95	C₂³×C₁₃₉	1	1	yes	characteristic
772	#95	C₂³×C₁₃₉	1	2	yes	—
773	#95	C₂³×C₁₃₉	1	2	yes	—
774	#95	C₂³×C₁₃₉	1	1	yes	characteristic
775	#95	C₂³×C₁₃₉	1	2	yes	—
776	#95	C₂³×C₁₃₉	1	2	yes	—
777	#95	C₂³×C₁₃₉	1	2	yes	—
778	#95	C₂³×C₁₃₉	1	2	yes	—
779	#95	C₂³×C₁₃₉	1	2	yes	—
780	#95	C₂³×C₁₃₉	1	2	yes	—
781	#95	C₂³×C₁₃₉	1	2	yes	—
782	#95	C₂³×C₁₃₉	1	2	yes	—
783	#95	C₂³×C₁₃₉	1	2	yes	—
784	#95	C₂³×C₁₃₉	1	2	yes	—
785	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
786	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
787	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
788	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
789	#41	—	2	32	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	4	2	no	—
808	C₂×D₄	—	4	2	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	—	4	2	no	—
811	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
812	C₂×D₄	#41×C₁₃₉	1	4	yes	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	4	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
841	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
842	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
843	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
844	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	4	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	4	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	4	no	—
879	C₄⋊C₄	—	2	4	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	2	no	—
882	C₄⋊C₄	—	4	2	no	—
883	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	2	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
906	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	4	no	—
913	C₄²	—	4	2	no	—
914	C₄²	—	4	2	no	—
915	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	2	no	—
933	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
934	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
935	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
936	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
937	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
938	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
939	Q₈	—	2	8	no	—
940	D₄	—	2	8	no	—
941	D₄	—	2	8	no	—
942	D₄	—	2	8	no	—
943	D₄	—	4	4	no	—
944	D₄	—	4	8	no	—
945	D₄	—	8	4	no	—
946	D₄	—	8	4	no	—
947	C₂×C₄	—	2	8	no	—
948	C₂×C₄	—	2	8	no	—
949	C₂×C₄	—	2	8	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	4	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	4	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1002	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1003	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1004	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1005	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1006	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1007	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	#525×C₁₃₉	1	4	yes	—
1030	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1031	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1032	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1033	C₂²	#585×C₁₃₉	1	2	yes	—
1034	C₂²	#585×C₁₃₉	1	2	yes	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₂	—	2	4	no	—
1055	C₂	—	4	2	no	—
1056	C₂	—	4	2	no	—
1057	C₂	—	8	2	no	—
1058	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1059	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1060	C₂	#3500×C₁₃₉	1	1	yes	characteristic
1061	C₂	#3512×C₁₃₉	1	2	yes	—
1062	C₂	#3521×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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. C₂×#553×C₁₃₉	C₂	semidirect
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2635×C₁₃₉	C₂	semidirect
4. #2634×C₁₃₉	C₂	semidirect
5. #2618×C₁₃₉	C₂	semidirect
6. #2611×C₁₃₉	C₂	semidirect
7. #2598×C₁₃₉	C₂	semidirect
8. #2591×C₁₃₉	C₂	semidirect
9. #2543×C₁₃₉	C₂	semidirect
10. #2487×C₁₃₉	C₂	semidirect
11. #2484×C₁₃₉	C₂	semidirect
12. #2481×C₁₃₉	C₂	semidirect
13. #2470×C₁₃₉	C₂	semidirect
14. #2469×C₁₃₉	C₂	semidirect
15. #2457×C₁₃₉	C₂	semidirect
16. #2444×C₁₃₉	C₂	semidirect
17. #2430×C₁₃₉	C₂	semidirect
18. #2398×C₁₃₉	C₂	semidirect
19. #2395×C₁₃₉	C₂	semidirect
20. C₂×#400×C₁₃₉	C₂	semidirect
21. #2364×C₁₃₉	C₂	semidirect
22. #2359×C₁₃₉	C₂	semidirect
23. #2353×C₁₃₉	C₂	semidirect
165. C₄×D₄×C₁₃₉	D₄	semidirect
531. #36032	C₁₃₉	direct (N × H)
532. C₁₃₉	#36032	direct (N × H)
533. C₂×#553	C₂×C₁₃₉	semidirect
534. C₂×#520	C₂×C₁₃₉	semidirect
535. #2635	C₂×C₁₃₉	semidirect
536. #2634	C₂×C₁₃₉	semidirect
537. #2618	C₂×C₁₃₉	semidirect
538. #2611	C₂×C₁₃₉	semidirect
539. #2598	C₂×C₁₃₉	semidirect
540. #2591	C₂×C₁₃₉	semidirect
541. #2543	C₂×C₁₃₉	semidirect
542. #2487	C₂×C₁₃₉	semidirect
543. #2484	C₂×C₁₃₉	semidirect
544. #2481	C₂×C₁₃₉	semidirect
545. #2470	C₂×C₁₃₉	semidirect
546. #2469	C₂×C₁₃₉	semidirect
547. #2457	C₂×C₁₃₉	semidirect
548. #2444	C₂×C₁₃₉	semidirect
549. #2430	C₂×C₁₃₉	semidirect
550. #2398	C₂×C₁₃₉	semidirect
551. #2395	C₂×C₁₃₉	semidirect
552. C₂×#400	C₂×C₁₃₉	semidirect
553. #2364	C₂×C₁₃₉	semidirect
554. #2359	C₂×C₁₃₉	semidirect
555. #2353	C₂×C₁₃₉	semidirect
697. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2635×C₁₃₉	2
#2634×C₁₃₉	2
#2618×C₁₃₉	2
#2611×C₁₃₉	2
#2598×C₁₃₉	2
#2591×C₁₃₉	2
#2543×C₁₃₉	2
#2487×C₁₃₉	2
#2484×C₁₃₉	2
#2481×C₁₃₉	2
#2470×C₁₃₉	2
#2469×C₁₃₉	2
#2457×C₁₃₉	2
#2444×C₁₃₉	2
#2430×C₁₃₉	2
#2398×C₁₃₉	2
#2395×C₁₃₉	2
C₂×#400×C₁₃₉	2
#2364×C₁₃₉	2
#2359×C₁₃₉	2
#2353×C₁₃₉	2
#36032	139

Subgroups — C139×#36032 #48030628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36032 #48030628