Subgroups — C₁₃₉×#36118 #48030714

Order 35584.

2334 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2512×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2506×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2496×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2491×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2475×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2474×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2468×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2450×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2444×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2440×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2416×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2361×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2361×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	#529×C₁₃₉	—	2	16	no	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
49	#400×C₁₃₉	C₂²	1	2	yes	—
50	#400×C₁₃₉	C₂²	1	2	yes	—
51	#398×C₁₃₉	C₂²	1	2	yes	—
52	#398×C₁₃₉	C₂²	1	2	yes	—
53	#397×C₁₃₉	C₂²	1	2	yes	—
54	#397×C₁₃₉	C₂²	1	2	yes	—
55	#396×C₁₃₉	C₂²	1	2	yes	—
56	#396×C₁₃₉	C₂²	1	2	yes	—
57	#395×C₁₃₉	C₂²	1	2	yes	—
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#393×C₁₃₉	C₂²	1	2	yes	—
61	#391×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×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	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	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	1	yes	characteristic
75	#388×C₁₃₉	C₂²	1	1	yes	characteristic
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	#387×C₁₃₉	C₂²	1	1	yes	characteristic
84	#387×C₁₃₉	C₂²	1	1	yes	characteristic
85	#387×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	#387×C₁₃₉	C₂²	1	2	yes	—
91	#386×C₁₃₉	C₂²	1	1	yes	characteristic
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	1	yes	characteristic
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	2	yes	—
101	#385×C₁₃₉	C₂²	1	2	yes	—
102	#384×C₁₃₉	C₂²	1	1	yes	characteristic
103	#384×C₁₃₉	C₂²	1	1	yes	characteristic
104	#381×C₁₃₉	C₂²	1	1	yes	characteristic
105	#381×C₁₃₉	C₂²	1	2	yes	—
106	#380×C₁₃₉	C₂²	1	1	yes	characteristic
107	#380×C₁₃₉	C₂²	1	1	yes	characteristic
108	#380×C₁₃₉	C₂²	1	1	yes	characteristic
109	#380×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	—
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
124	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
138	#126×C₁₃₉	—	2	8	no	—
139	#126×C₁₃₉	—	2	8	no	—
140	#125×C₁₃₉	—	2	8	no	—
141	#124×C₁₃₉	—	2	8	no	—
142	#123×C₁₃₉	—	2	8	no	—
143	#123×C₁₃₉	D₄	1	8	yes	complemented
144	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
145	#121×C₁₃₉	—	2	8	no	—
146	#121×C₁₃₉	—	2	4	no	—
147	#121×C₁₃₉	—	2	4	no	—
148	C₄×Q₈×C₁₃₉	—	2	8	no	—
149	C₄×D₄×C₁₃₉	—	2	8	no	—
150	C₄×D₄×C₁₃₉	—	2	4	no	—
151	C₄×D₄×C₁₃₉	—	2	4	no	—
152	C₄×D₄×C₁₃₉	—	2	8	no	—
153	C₄×D₄×C₁₃₉	—	2	8	no	—
154	#117×C₁₃₉	—	2	8	no	—
155	#117×C₁₃₉	—	2	8	no	—
156	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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×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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
207	C₂×C₄²×C₁₃₉	—	2	8	no	—
208	C₂×C₄²×C₁₃₉	—	2	4	no	—
209	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
212	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	1	yes	characteristic
242	#95×C₁₃₉	C₂³	1	1	yes	characteristic
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	1	yes	characteristic
246	#95×C₁₃₉	C₂³	1	1	yes	characteristic
247	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂×Q₈×C₁₃₉	—	2	4	no	—
251	C₂×Q₈×C₁₃₉	—	2	4	no	—
252	C₂×Q₈×C₁₃₉	—	4	2	no	—
253	C₂×D₄×C₁₃₉	—	2	2	no	—
254	C₂×D₄×C₁₃₉	—	2	2	no	—
255	C₂×D₄×C₁₃₉	—	2	4	no	—
256	C₂×D₄×C₁₃₉	—	2	4	no	—
257	C₂×D₄×C₁₃₉	—	2	4	no	—
258	C₂×D₄×C₁₃₉	—	2	4	no	—
259	C₂×D₄×C₁₃₉	—	2	2	no	—
260	C₂×D₄×C₁₃₉	—	2	4	no	—
261	C₂×D₄×C₁₃₉	—	2	2	no	—
262	C₂×D₄×C₁₃₉	—	2	2	no	—
263	C₂×D₄×C₁₃₉	—	4	2	no	—
264	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
265	C₂²×C₄×C₁₃₉	—	2	2	no	—
266	C₂²×C₄×C₁₃₉	—	2	2	no	—
267	C₂²×C₄×C₁₃₉	—	2	2	no	—
268	C₂²×C₄×C₁₃₉	—	2	2	no	—
269	C₂²×C₄×C₁₃₉	—	2	4	no	—
270	C₂²×C₄×C₁₃₉	—	2	4	no	—
271	C₂²×C₄×C₁₃₉	—	2	4	no	—
272	C₂²×C₄×C₁₃₉	—	2	2	no	—
273	C₂²×C₄×C₁₃₉	—	2	4	no	—
274	C₂²×C₄×C₁₃₉	—	2	4	no	—
275	C₂²×C₄×C₁₃₉	—	2	4	no	—
276	C₂²×C₄×C₁₃₉	—	2	4	no	—
277	C₂²×C₄×C₁₃₉	—	2	2	no	—
278	C₂²×C₄×C₁₃₉	—	2	4	no	—
279	C₂²×C₄×C₁₃₉	—	2	2	no	—
280	C₂²×C₄×C₁₃₉	—	2	2	no	—
281	C₂²×C₄×C₁₃₉	—	4	2	no	—
282	C₂²×C₄×C₁₃₉	—	4	2	no	—
283	C₂²×C₄×C₁₃₉	—	4	2	no	—
284	C₂²×C₄×C₁₃₉	—	4	2	no	—
285	C₂²×C₄×C₁₃₉	—	4	1	no	—
286	C₂²×C₄×C₁₃₉	—	4	1	no	—
287	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
288	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
289	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₁₃₉	—	2	4	no	—
310	C₄⋊C₄×C₁₃₉	—	2	4	no	—
311	C₄⋊C₄×C₁₃₉	—	2	4	no	—
312	C₄⋊C₄×C₁₃₉	—	2	4	no	—
313	C₄⋊C₄×C₁₃₉	—	2	4	no	—
314	C₄⋊C₄×C₁₃₉	—	2	4	no	—
315	C₄⋊C₄×C₁₃₉	—	2	4	no	—
316	C₄⋊C₄×C₁₃₉	—	2	4	no	—
317	C₄⋊C₄×C₁₃₉	—	2	4	no	—
318	C₄⋊C₄×C₁₃₉	—	2	4	no	—
319	C₄⋊C₄×C₁₃₉	—	2	4	no	—
320	C₄⋊C₄×C₁₃₉	—	2	2	no	—
321	C₄⋊C₄×C₁₃₉	—	2	2	no	—
322	C₄⋊C₄×C₁₃₉	—	2	2	no	—
323	C₄⋊C₄×C₁₃₉	—	2	2	no	—
324	C₄⋊C₄×C₁₃₉	—	2	2	no	—
325	C₄⋊C₄×C₁₃₉	—	2	4	no	—
326	C₄⋊C₄×C₁₃₉	—	2	2	no	—
327	C₄⋊C₄×C₁₃₉	—	4	1	no	—
328	C₄⋊C₄×C₁₃₉	—	4	1	no	—
329	C₄⋊C₄×C₁₃₉	—	4	2	no	—
330	C₄⋊C₄×C₁₃₉	—	4	2	no	—
331	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
332	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
333	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
334	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
335	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
336	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
337	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
338	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
339	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
340	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
341	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
342	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
343	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
344	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
346	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
348	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
349	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
350	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
351	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
352	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
353	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
354	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
355	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
356	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
357	C₄²×C₁₃₉	—	2	4	no	—
358	C₄²×C₁₃₉	—	2	4	no	—
359	C₄²×C₁₃₉	—	2	4	no	—
360	C₄²×C₁₃₉	—	2	4	no	—
361	C₄²×C₁₃₉	—	2	4	no	—
362	C₄²×C₁₃₉	—	2	4	no	—
363	C₄²×C₁₃₉	—	2	2	no	—
364	C₄²×C₁₃₉	—	2	2	no	—
365	C₄²×C₁₃₉	—	2	2	no	—
366	C₄²×C₁₃₉	—	2	2	no	—
367	C₄²×C₁₃₉	—	2	2	no	—
368	C₄²×C₁₃₉	—	2	2	no	—
369	C₄²×C₁₃₉	—	2	2	no	—
370	C₂³×C₁₃₉	—	2	1	no	—
371	C₂³×C₁₃₉	—	2	1	no	—
372	C₂³×C₁₃₉	—	2	1	no	—
373	C₂³×C₁₃₉	—	2	1	no	—
374	C₂³×C₁₃₉	—	2	1	no	—
375	C₂³×C₁₃₉	—	2	1	no	—
376	C₂³×C₁₃₉	—	2	1	no	—
377	C₂³×C₁₃₉	—	2	1	no	—
378	C₂³×C₁₃₉	—	2	1	no	—
379	C₂³×C₁₃₉	—	2	1	no	—
380	C₂³×C₁₃₉	—	2	2	no	—
381	C₂³×C₁₃₉	—	2	2	no	—
382	C₂³×C₁₃₉	—	2	2	no	—
383	C₂³×C₁₃₉	—	2	2	no	—
384	C₂³×C₁₃₉	—	2	2	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	2	no	—
387	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
388	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
389	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
390	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
391	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
392	Q₈×C₁₃₉	—	4	8	no	—
393	D₄×C₁₃₉	—	2	8	no	—
394	D₄×C₁₃₉	—	4	8	no	—
395	D₄×C₁₃₉	—	4	8	no	—
396	D₄×C₁₃₉	—	4	4	no	—
397	C₂×C₄×C₁₃₉	—	2	8	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	2	no	—
400	C₂×C₄×C₁₃₉	—	2	1	no	—
401	C₂×C₄×C₁₃₉	—	2	1	no	—
402	C₂×C₄×C₁₃₉	—	2	1	no	—
403	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
409	C₂×C₄×C₁₃₉	—	2	1	no	—
410	C₂×C₄×C₁₃₉	—	2	1	no	—
411	C₂×C₄×C₁₃₉	—	2	1	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	2	2	no	—
414	C₂×C₄×C₁₃₉	—	2	8	no	—
415	C₂×C₄×C₁₃₉	—	2	2	no	—
416	C₂×C₄×C₁₃₉	—	2	2	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
427	C₂×C₄×C₁₃₉	—	2	2	no	—
428	C₂×C₄×C₁₃₉	—	2	1	no	—
429	C₂×C₄×C₁₃₉	—	2	2	no	—
430	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
436	C₂×C₄×C₁₃₉	—	2	1	no	—
437	C₂×C₄×C₁₃₉	—	2	1	no	—
438	C₂×C₄×C₁₃₉	—	2	1	no	—
439	C₂×C₄×C₁₃₉	—	2	1	no	—
440	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
445	C₂×C₄×C₁₃₉	—	2	1	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	4	8	no	—
449	C₂×C₄×C₁₃₉	—	4	8	no	—
450	C₂×C₄×C₁₃₉	—	4	8	no	—
451	C₂×C₄×C₁₃₉	—	4	8	no	—
452	C₂×C₄×C₁₃₉	—	4	4	no	—
453	C₂×C₄×C₁₃₉	—	4	4	no	—
454	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
460	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
461	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
462	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
463	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
464	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
465	C₂²×C₁₃₉	—	2	2	no	—
466	C₂²×C₁₃₉	—	2	2	no	—
467	C₂²×C₁₃₉	—	2	2	no	—
468	C₂²×C₁₃₉	—	2	2	no	—
469	C₂²×C₁₃₉	—	2	2	no	—
470	C₂²×C₁₃₉	—	2	2	no	—
471	C₂²×C₁₃₉	—	2	2	no	—
472	C₂²×C₁₃₉	—	2	2	no	—
473	C₂²×C₁₃₉	—	2	2	no	—
474	C₂²×C₁₃₉	—	4	1	no	—
475	C₂²×C₁₃₉	—	4	1	no	—
476	C₂²×C₁₃₉	—	4	1	no	—
477	C₂²×C₁₃₉	—	4	1	no	—
478	C₂²×C₁₃₉	—	4	2	no	—
479	C₂²×C₁₃₉	—	4	2	no	—
480	C₂²×C₁₃₉	—	4	2	no	—
481	C₂²×C₁₃₉	—	4	2	no	—
482	C₂²×C₁₃₉	—	4	2	no	—
483	C₂²×C₁₃₉	—	4	2	no	—
484	C₂²×C₁₃₉	—	4	2	no	—
485	C₂²×C₁₃₉	#547	1	4	yes	—
486	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
487	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
488	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
489	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂²×C₁₃₉	#585	1	1	yes	characteristic
492	C₂²×C₁₃₉	#585	1	1	yes	characteristic
493	C₄×C₁₃₉	—	2	2	no	—
494	C₄×C₁₃₉	—	2	2	no	—
495	C₄×C₁₃₉	—	2	2	no	—
496	C₄×C₁₃₉	—	2	2	no	—
497	C₄×C₁₃₉	—	2	4	no	—
498	C₄×C₁₃₉	—	2	2	no	—
499	C₄×C₁₃₉	—	2	4	no	—
500	C₄×C₁₃₉	—	2	2	no	—
501	C₄×C₁₃₉	—	4	1	no	—
502	C₄×C₁₃₉	—	4	2	no	—
503	C₄×C₁₃₉	—	4	2	no	—
504	C₄×C₁₃₉	—	4	2	no	—
505	C₄×C₁₃₉	—	4	2	no	—
506	C₄×C₁₃₉	—	4	2	no	—
507	C₄×C₁₃₉	—	4	1	no	—
508	C₄×C₁₃₉	—	4	1	no	—
509	C₄×C₁₃₉	—	4	1	no	—
510	C₄×C₁₃₉	—	4	1	no	—
511	C₄×C₁₃₉	—	4	1	no	—
512	C₄×C₁₃₉	#529	1	4	yes	complemented
513	C₂×C₁₃₉	—	2	4	no	—
514	C₂×C₁₃₉	—	4	2	no	—
515	C₂×C₁₃₉	—	8	2	no	—
516	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
517	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
518	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
519	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
520	C₂×C₁₃₉	#3493	1	1	yes	characteristic
521	C₂×C₁₃₉	#3516	1	1	yes	characteristic
522	C₂×C₁₃₉	#3516	1	1	yes	characteristic
523	#36118	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
524	C₁₃₉	#36118	1	1	yes	characteristic, direct product factor, Sylow
525	C₂×#529	C₂×C₁₃₉	1	2	yes	complemented
526	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
527	#2853	C₂×C₁₃₉	1	2	yes	complemented
528	#2512	C₂×C₁₃₉	1	1	yes	characteristic, complemented
529	#2506	C₂×C₁₃₉	1	1	yes	characteristic, complemented
530	#2496	C₂×C₁₃₉	1	1	yes	characteristic, complemented
531	#2491	C₂×C₁₃₉	1	1	yes	characteristic, complemented
532	#2475	C₂×C₁₃₉	1	2	yes	complemented
533	#2474	C₂×C₁₃₉	1	2	yes	complemented
534	#2469	C₂×C₁₃₉	1	2	yes	complemented
535	#2468	C₂×C₁₃₉	1	2	yes	complemented
536	#2450	C₂×C₁₃₉	1	2	yes	complemented
537	#2444	C₂×C₁₃₉	1	2	yes	complemented
538	#2440	C₂×C₁₃₉	1	1	yes	characteristic, complemented
539	#2416	C₂×C₁₃₉	1	1	yes	characteristic
540	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
541	#2361	C₂×C₁₃₉	1	1	yes	characteristic, complemented
542	#2361	C₂×C₁₃₉	1	1	yes	characteristic, complemented
543	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
544	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
545	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
546	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
547	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
548	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
549	#529	—	2	16	no	—
550	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
551	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
552	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
553	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
554	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
555	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
556	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
557	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
558	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
559	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
560	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
561	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
562	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
565	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
566	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
567	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
568	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
571	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
572	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
573	#400	C₂²×C₁₃₉	1	2	yes	—
574	#400	C₂²×C₁₃₉	1	2	yes	—
575	#398	C₂²×C₁₃₉	1	2	yes	—
576	#398	C₂²×C₁₃₉	1	2	yes	—
577	#397	C₂²×C₁₃₉	1	2	yes	—
578	#397	C₂²×C₁₃₉	1	2	yes	—
579	#396	C₂²×C₁₃₉	1	2	yes	—
580	#396	C₂²×C₁₃₉	1	2	yes	—
581	#395	C₂²×C₁₃₉	1	2	yes	—
582	#394	C₂²×C₁₃₉	1	2	yes	—
583	#394	C₂²×C₁₃₉	1	2	yes	—
584	#393	C₂²×C₁₃₉	1	2	yes	—
585	#391	C₂²×C₁₃₉	1	2	yes	—
586	#390	C₂²×C₁₃₉	1	1	yes	characteristic
587	#390	C₂²×C₁₃₉	1	1	yes	characteristic
588	#390	C₂²×C₁₃₉	1	1	yes	characteristic
589	#390	C₂²×C₁₃₉	1	1	yes	characteristic
590	#389	C₂²×C₁₃₉	1	1	yes	characteristic
591	#389	C₂²×C₁₃₉	1	1	yes	characteristic
592	#389	C₂²×C₁₃₉	1	1	yes	characteristic
593	#389	C₂²×C₁₃₉	1	2	yes	—
594	#389	C₂²×C₁₃₉	1	1	yes	characteristic
595	#389	C₂²×C₁₃₉	1	1	yes	characteristic
596	#389	C₂²×C₁₃₉	1	1	yes	characteristic
597	#388	C₂²×C₁₃₉	1	2	yes	—
598	#388	C₂²×C₁₃₉	1	2	yes	—
599	#388	C₂²×C₁₃₉	1	2	yes	—
600	#388	C₂²×C₁₃₉	1	2	yes	—
601	#388	C₂²×C₁₃₉	1	2	yes	—
602	#388	C₂²×C₁₃₉	1	2	yes	—
603	#388	C₂²×C₁₃₉	1	2	yes	—
604	#388	C₂²×C₁₃₉	1	2	yes	—
605	#388	C₂²×C₁₃₉	1	1	yes	characteristic
606	#388	C₂²×C₁₃₉	1	1	yes	characteristic
607	#387	C₂²×C₁₃₉	1	2	yes	—
608	#387	C₂²×C₁₃₉	1	2	yes	—
609	#387	C₂²×C₁₃₉	1	2	yes	—
610	#387	C₂²×C₁₃₉	1	2	yes	—
611	#387	C₂²×C₁₃₉	1	2	yes	—
612	#387	C₂²×C₁₃₉	1	2	yes	—
613	#387	C₂²×C₁₃₉	1	1	yes	characteristic
614	#387	C₂²×C₁₃₉	1	1	yes	characteristic
615	#386	C₂²×C₁₃₉	1	2	yes	—
616	#386	C₂²×C₁₃₉	1	2	yes	—
617	#386	C₂²×C₁₃₉	1	2	yes	—
618	#386	C₂²×C₁₃₉	1	2	yes	—
619	#386	C₂²×C₁₃₉	1	1	yes	characteristic
620	#385	C₂²×C₁₃₉	1	2	yes	—
621	#385	C₂²×C₁₃₉	1	2	yes	—
622	#385	C₂²×C₁₃₉	1	2	yes	—
623	#385	C₂²×C₁₃₉	1	2	yes	—
624	#385	C₂²×C₁₃₉	1	2	yes	—
625	#385	C₂²×C₁₃₉	1	1	yes	characteristic
626	#384	C₂²×C₁₃₉	1	1	yes	characteristic
627	#384	C₂²×C₁₃₉	1	1	yes	characteristic
628	#381	C₂²×C₁₃₉	1	1	yes	characteristic
629	#381	C₂²×C₁₃₉	1	2	yes	—
630	#380	C₂²×C₁₃₉	1	1	yes	characteristic
631	#380	C₂²×C₁₃₉	1	1	yes	characteristic
632	#380	C₂²×C₁₃₉	1	1	yes	characteristic
633	#380	C₂²×C₁₃₉	1	2	yes	—
634	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
638	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
640	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
641	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
642	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
643	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
645	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
647	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
648	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
649	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
650	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
661	C₄⋊Q₈	—	2	4	no	—
662	#126	—	2	8	no	—
663	#126	—	2	8	no	—
664	#125	—	2	8	no	—
665	#124	—	2	8	no	—
666	#123	—	2	8	no	—
667	#123	D₄×C₁₃₉	1	8	yes	complemented
668	C₂²⋊Q₈	—	2	8	no	—
669	#121	—	2	8	no	—
670	#121	—	2	4	no	—
671	#121	—	2	4	no	—
672	C₄×Q₈	—	2	8	no	—
673	C₄×D₄	—	2	8	no	—
674	C₄×D₄	—	2	4	no	—
675	C₄×D₄	—	2	4	no	—
676	C₄×D₄	—	2	8	no	—
677	C₄×D₄	—	2	8	no	—
678	#117	—	2	8	no	—
679	#117	—	2	8	no	—
680	C₂×C₄⋊C₄	—	2	4	no	—
681	C₂×C₄⋊C₄	—	2	4	no	—
682	C₂×C₄⋊C₄	—	2	4	no	—
683	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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×C₄²	—	2	8	no	—
732	C₂×C₄²	—	2	4	no	—
733	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
734	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
735	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
736	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
737	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
746	#95	C₂³×C₁₃₉	1	2	yes	—
747	#95	C₂³×C₁₃₉	1	2	yes	—
748	#95	C₂³×C₁₃₉	1	2	yes	—
749	#95	C₂³×C₁₃₉	1	2	yes	—
750	#95	C₂³×C₁₃₉	1	1	yes	characteristic
751	#95	C₂³×C₁₃₉	1	1	yes	characteristic
752	#95	C₂³×C₁₃₉	1	1	yes	characteristic
753	#95	C₂³×C₁₃₉	1	1	yes	characteristic
754	#95	C₂³×C₁₃₉	1	1	yes	characteristic
755	#95	C₂³×C₁₃₉	1	1	yes	characteristic
756	#95	C₂³×C₁₃₉	1	2	yes	—
757	#95	C₂³×C₁₃₉	1	2	yes	—
758	#95	C₂³×C₁₃₉	1	1	yes	characteristic
759	#95	C₂³×C₁₃₉	1	1	yes	characteristic
760	#95	C₂³×C₁₃₉	1	1	yes	characteristic
761	#95	C₂³×C₁₃₉	1	1	yes	characteristic
762	#95	C₂³×C₁₃₉	1	2	yes	—
763	#95	C₂³×C₁₃₉	1	2	yes	—
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	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
772	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
774	C₂×Q₈	—	2	4	no	—
775	C₂×Q₈	—	2	4	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
812	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
813	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	4	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	4	1	no	—
852	C₄⋊C₄	—	4	1	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
856	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
857	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
858	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	4	1	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	1	no	—
878	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
879	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
880	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
881	C₄²	—	2	4	no	—
882	C₄²	—	2	4	no	—
883	C₄²	—	2	4	no	—
884	C₄²	—	2	4	no	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
912	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
913	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
914	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
915	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
916	Q₈	—	4	8	no	—
917	D₄	—	2	8	no	—
918	D₄	—	4	8	no	—
919	D₄	—	4	8	no	—
920	D₄	—	4	4	no	—
921	C₂×C₄	—	2	8	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	8	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	4	8	no	—
973	C₂×C₄	—	4	8	no	—
974	C₂×C₄	—	4	8	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
983	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
984	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
985	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
986	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
987	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
988	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	#547×C₁₃₉	1	4	yes	—
1010	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1011	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1012	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1013	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1014	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1015	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1016	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	4	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	4	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	2	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	#529×C₁₃₉	1	4	yes	complemented
1037	C₂	—	2	4	no	—
1038	C₂	—	4	2	no	—
1039	C₂	—	8	2	no	—
1040	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
1041	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
1042	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1043	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1044	C₂	#3493×C₁₃₉	1	1	yes	characteristic
1045	C₂	#3516×C₁₃₉	1	1	yes	characteristic
1046	C₂	#3516×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. C₂×#529×C₁₃₉	C₂	semidirect
2. #2854×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2512×C₁₃₉	C₂	semidirect
5. #2506×C₁₃₉	C₂	semidirect
6. #2496×C₁₃₉	C₂	semidirect
7. #2491×C₁₃₉	C₂	semidirect
8. #2475×C₁₃₉	C₂	semidirect
9. #2474×C₁₃₉	C₂	semidirect
10. #2469×C₁₃₉	C₂	semidirect
11. #2468×C₁₃₉	C₂	semidirect
12. #2450×C₁₃₉	C₂	semidirect
13. #2444×C₁₃₉	C₂	semidirect
14. #2440×C₁₃₉	C₂	semidirect
16. #2365×C₁₃₉	C₂	semidirect
17. #2361×C₁₃₉	C₂	semidirect
18. #2361×C₁₃₉	C₂	semidirect
19. #2354×C₁₃₉	C₂	semidirect
20. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
21. #2344×C₁₃₉	C₂	semidirect
22. C₄×#123×C₁₃₉	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
143. #123×C₁₃₉	D₄	semidirect
512. C₄×C₁₃₉	#529	semidirect
523. #36118	C₁₃₉	direct (N × H)
524. C₁₃₉	#36118	direct (N × H)
525. C₂×#529	C₂×C₁₃₉	semidirect
526. #2854	C₂×C₁₃₉	semidirect
527. #2853	C₂×C₁₃₉	semidirect
528. #2512	C₂×C₁₃₉	semidirect
529. #2506	C₂×C₁₃₉	semidirect
530. #2496	C₂×C₁₃₉	semidirect
531. #2491	C₂×C₁₃₉	semidirect
532. #2475	C₂×C₁₃₉	semidirect
533. #2474	C₂×C₁₃₉	semidirect
534. #2469	C₂×C₁₃₉	semidirect
535. #2468	C₂×C₁₃₉	semidirect
536. #2450	C₂×C₁₃₉	semidirect
537. #2444	C₂×C₁₃₉	semidirect
538. #2440	C₂×C₁₃₉	semidirect
540. #2365	C₂×C₁₃₉	semidirect
541. #2361	C₂×C₁₃₉	semidirect
542. #2361	C₂×C₁₃₉	semidirect
543. #2354	C₂×C₁₃₉	semidirect
544. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
545. #2344	C₂×C₁₃₉	semidirect
546. C₄×#123	C₂×C₁₃₉	semidirect
547. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
667. #123	D₄×C₁₃₉	semidirect
1036. C₄	#529×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₉	2
#2854×C₁₃₉	2
#2853×C₁₃₉	2
#2512×C₁₃₉	2
#2506×C₁₃₉	2
#2496×C₁₃₉	2
#2491×C₁₃₉	2
#2475×C₁₃₉	2
#2474×C₁₃₉	2
#2469×C₁₃₉	2
#2468×C₁₃₉	2
#2450×C₁₃₉	2
#2444×C₁₃₉	2
#2440×C₁₃₉	2
#2416×C₁₃₉	2
#2365×C₁₃₉	2
#2361×C₁₃₉	2
#2354×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36118	139

Subgroups — C139×#36118 #48030714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36118 #48030714