Subgroups — C₁₃₉×#35636 #48030232

Order 35584.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2564×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2557×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2553×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2535×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2521×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2499×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2496×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2492×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2489×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2427×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2427×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2327×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2323×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2290×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#542×C₁₃₉	—	2	8	no	—
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	#529×C₁₃₉	—	2	8	no	—
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
41	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
53	#400×C₁₃₉	C₂²	1	2	yes	—
54	#400×C₁₃₉	C₂²	1	2	yes	—
55	#399×C₁₃₉	C₂²	1	2	yes	—
56	#399×C₁₃₉	C₂²	1	2	yes	—
57	#398×C₁₃₉	C₂²	1	2	yes	—
58	#397×C₁₃₉	C₂²	1	2	yes	—
59	#397×C₁₃₉	C₂²	1	2	yes	—
60	#397×C₁₃₉	C₂²	1	2	yes	—
61	#397×C₁₃₉	C₂²	1	2	yes	—
62	#397×C₁₃₉	C₂²	1	2	yes	—
63	#397×C₁₃₉	C₂²	1	2	yes	—
64	#395×C₁₃₉	C₂²	1	2	yes	—
65	#394×C₁₃₉	C₂²	1	2	yes	—
66	#394×C₁₃₉	C₂²	1	2	yes	—
67	#393×C₁₃₉	C₂²	1	2	yes	—
68	#392×C₁₃₉	C₂²	1	2	yes	—
69	#391×C₁₃₉	C₂²	1	2	yes	—
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic
71	#391×C₁₃₉	C₂²	1	1	yes	characteristic
72	#391×C₁₃₉	C₂²	1	2	yes	—
73	#391×C₁₃₉	C₂²	1	1	yes	characteristic
74	#391×C₁₃₉	C₂²	1	1	yes	characteristic
75	#390×C₁₃₉	C₂²	1	2	yes	—
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic
78	#389×C₁₃₉	C₂²	1	2	yes	—
79	#389×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	1	yes	characteristic
81	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
88	#387×C₁₃₉	C₂²	1	1	yes	characteristic
89	#387×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	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#386×C₁₃₉	C₂²	1	1	yes	characteristic
97	#386×C₁₃₉	C₂²	1	1	yes	characteristic
98	#386×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	1	yes	characteristic
101	#385×C₁₃₉	C₂²	1	1	yes	characteristic
102	#385×C₁₃₉	C₂²	1	2	yes	—
103	#384×C₁₃₉	C₂²	1	2	yes	—
104	#382×C₁₃₉	C₂²	1	1	yes	characteristic
105	#382×C₁₃₉	C₂²	1	2	yes	—
106	#380×C₁₃₉	C₂²	1	2	yes	—
107	#380×C₁₃₉	C₂²	1	1	yes	characteristic
108	#380×C₁₃₉	C₂²	1	1	yes	characteristic
109	#380×C₁₃₉	C₂²	1	2	yes	—
110	#380×C₁₃₉	C₂²	1	2	yes	—
111	#380×C₁₃₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊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	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
123	#376×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
125	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
140	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
141	#126×C₁₃₉	—	2	8	no	—
142	#126×C₁₃₉	—	2	8	no	—
143	#125×C₁₃₉	—	2	4	no	—
144	#124×C₁₃₉	—	2	4	no	—
145	#124×C₁₃₉	—	2	4	no	—
146	#124×C₁₃₉	—	2	8	no	—
147	#123×C₁₃₉	—	2	8	no	—
148	#123×C₁₃₉	—	2	8	no	—
149	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
153	C₂²⋊Q₈×C₁₃₉	—	2	4	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	8	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	D₄	1	8	yes	complemented
163	#117×C₁₃₉	—	2	8	no	—
164	#117×C₁₃₉	—	2	4	no	—
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	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	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	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃₉	—	2	4	no	—
212	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
219	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
228	#95×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	#95×C₁₃₉	C₂³	1	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	2	yes	—
236	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	1	yes	characteristic
244	#95×C₁₃₉	C₂³	1	1	yes	characteristic
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	1	yes	characteristic
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	1	yes	characteristic
249	#95×C₁₃₉	C₂³	1	1	yes	characteristic
250	#95×C₁₃₉	C₂³	1	1	yes	characteristic
251	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂×Q₈×C₁₃₉	—	2	2	no	—
255	C₂×Q₈×C₁₃₉	—	2	2	no	—
256	C₂×Q₈×C₁₃₉	—	2	4	no	—
257	C₂×Q₈×C₁₃₉	—	2	2	no	—
258	C₂×Q₈×C₁₃₉	—	2	2	no	—
259	C₂×Q₈×C₁₃₉	—	2	2	no	—
260	C₂×Q₈×C₁₃₉	—	2	2	no	—
261	C₂×Q₈×C₁₃₉	—	4	2	no	—
262	C₂×Q₈×C₁₃₉	—	4	2	no	—
263	C₂×D₄×C₁₃₉	—	2	4	no	—
264	C₂×D₄×C₁₃₉	—	2	2	no	—
265	C₂×D₄×C₁₃₉	—	2	4	no	—
266	C₂×D₄×C₁₃₉	—	2	4	no	—
267	C₂×D₄×C₁₃₉	—	2	2	no	—
268	C₂×D₄×C₁₃₉	—	2	2	no	—
269	C₂×D₄×C₁₃₉	—	2	2	no	—
270	C₂×D₄×C₁₃₉	—	4	1	no	—
271	C₂×D₄×C₁₃₉	—	4	2	no	—
272	C₂×D₄×C₁₃₉	—	4	2	no	—
273	C₂×D₄×C₁₃₉	—	4	2	no	—
274	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
275	C₂²×C₄×C₁₃₉	—	2	2	no	—
276	C₂²×C₄×C₁₃₉	—	2	2	no	—
277	C₂²×C₄×C₁₃₉	—	2	2	no	—
278	C₂²×C₄×C₁₃₉	—	2	2	no	—
279	C₂²×C₄×C₁₃₉	—	2	2	no	—
280	C₂²×C₄×C₁₃₉	—	2	2	no	—
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	4	no	—
285	C₂²×C₄×C₁₃₉	—	2	4	no	—
286	C₂²×C₄×C₁₃₉	—	4	1	no	—
287	C₂²×C₄×C₁₃₉	—	4	2	no	—
288	C₂²×C₄×C₁₃₉	—	4	2	no	—
289	C₂²×C₄×C₁₃₉	—	4	1	no	—
290	C₂²×C₄×C₁₃₉	—	4	1	no	—
291	C₂²×C₄×C₁₃₉	—	4	2	no	—
292	C₂²×C₄×C₁₃₉	—	4	2	no	—
293	C₂²×C₄×C₁₃₉	—	4	2	no	—
294	C₂²×C₄×C₁₃₉	—	4	2	no	—
295	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
296	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₁₃₉	—	2	2	no	—
317	C₄⋊C₄×C₁₃₉	—	2	4	no	—
318	C₄⋊C₄×C₁₃₉	—	2	4	no	—
319	C₄⋊C₄×C₁₃₉	—	2	2	no	—
320	C₄⋊C₄×C₁₃₉	—	2	4	no	—
321	C₄⋊C₄×C₁₃₉	—	2	2	no	—
322	C₄⋊C₄×C₁₃₉	—	2	2	no	—
323	C₄⋊C₄×C₁₃₉	—	2	4	no	—
324	C₄⋊C₄×C₁₃₉	—	2	4	no	—
325	C₄⋊C₄×C₁₃₉	—	2	4	no	—
326	C₄⋊C₄×C₁₃₉	—	2	4	no	—
327	C₄⋊C₄×C₁₃₉	—	2	2	no	—
328	C₄⋊C₄×C₁₃₉	—	2	2	no	—
329	C₄⋊C₄×C₁₃₉	—	2	4	no	—
330	C₄⋊C₄×C₁₃₉	—	2	4	no	—
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	2	4	no	—
333	C₄⋊C₄×C₁₃₉	—	4	2	no	—
334	C₄⋊C₄×C₁₃₉	—	4	2	no	—
335	C₄⋊C₄×C₁₃₉	—	4	1	no	—
336	C₄⋊C₄×C₁₃₉	—	4	1	no	—
337	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
338	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
339	C₂²⋊C₄×C₁₃₉	—	2	4	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	4	no	—
345	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
349	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
350	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
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	—	4	1	no	—
357	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
358	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
360	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
361	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
362	C₄²×C₁₃₉	—	2	2	no	—
363	C₄²×C₁₃₉	—	2	2	no	—
364	C₄²×C₁₃₉	—	2	2	no	—
365	C₄²×C₁₃₉	—	2	4	no	—
366	C₄²×C₁₃₉	—	2	2	no	—
367	C₄²×C₁₃₉	—	2	4	no	—
368	C₄²×C₁₃₉	—	2	2	no	—
369	C₄²×C₁₃₉	—	4	2	no	—
370	C₄²×C₁₃₉	—	4	2	no	—
371	C₄²×C₁₃₉	—	4	2	no	—
372	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
373	C₄²×C₁₃₉	#41	1	4	yes	—
374	C₂³×C₁₃₉	—	2	1	no	—
375	C₂³×C₁₃₉	—	2	1	no	—
376	C₂³×C₁₃₉	—	2	2	no	—
377	C₂³×C₁₃₉	—	2	2	no	—
378	C₂³×C₁₃₉	—	2	1	no	—
379	C₂³×C₁₃₉	—	2	2	no	—
380	C₂³×C₁₃₉	—	2	1	no	—
381	C₂³×C₁₃₉	—	2	1	no	—
382	C₂³×C₁₃₉	—	2	2	no	—
383	C₂³×C₁₃₉	—	2	2	no	—
384	C₂³×C₁₃₉	—	2	2	no	—
385	C₂³×C₁₃₉	—	2	1	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	1	no	—
391	C₂³×C₁₃₉	—	2	1	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
394	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
395	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
396	Q₈×C₁₃₉	—	4	4	no	—
397	Q₈×C₁₃₉	—	4	4	no	—
398	Q₈×C₁₃₉	—	8	4	no	—
399	D₄×C₁₃₉	—	2	8	no	—
400	D₄×C₁₃₉	—	4	4	no	—
401	D₄×C₁₃₉	—	4	8	no	—
402	D₄×C₁₃₉	—	8	4	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	2	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	1	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	1	no	—
419	C₂×C₄×C₁₃₉	—	2	2	no	—
420	C₂×C₄×C₁₃₉	—	2	2	no	—
421	C₂×C₄×C₁₃₉	—	2	1	no	—
422	C₂×C₄×C₁₃₉	—	2	2	no	—
423	C₂×C₄×C₁₃₉	—	2	2	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	1	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	1	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	2	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	2	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	1	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	1	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	1	no	—
451	C₂×C₄×C₁₃₉	—	2	1	no	—
452	C₂×C₄×C₁₃₉	—	2	2	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	4	8	no	—
455	C₂×C₄×C₁₃₉	—	4	4	no	—
456	C₂×C₄×C₁₃₉	—	4	4	no	—
457	C₂×C₄×C₁₃₉	—	4	4	no	—
458	C₂×C₄×C₁₃₉	—	4	4	no	—
459	C₂×C₄×C₁₃₉	—	8	4	no	—
460	C₂×C₄×C₁₃₉	—	8	4	no	—
461	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
464	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
466	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
467	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
468	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
469	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
470	C₂²×C₁₃₉	—	2	4	no	—
471	C₂²×C₁₃₉	—	2	4	no	—
472	C₂²×C₁₃₉	—	2	2	no	—
473	C₂²×C₁₃₉	—	2	4	no	—
474	C₂²×C₁₃₉	—	2	2	no	—
475	C₂²×C₁₃₉	—	2	2	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	1	no	—
481	C₂²×C₁₃₉	—	4	2	no	—
482	C₂²×C₁₃₉	—	4	2	no	—
483	C₂²×C₁₃₉	—	4	1	no	—
484	C₂²×C₁₃₉	—	4	1	no	—
485	C₂²×C₁₃₉	—	4	1	no	—
486	C₂²×C₁₃₉	—	4	1	no	—
487	C₂²×C₁₃₉	—	4	1	no	—
488	C₂²×C₁₃₉	—	4	1	no	—
489	C₂²×C₁₃₉	—	4	1	no	—
490	C₂²×C₁₃₉	—	4	1	no	—
491	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
492	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
493	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
494	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
495	C₂²×C₁₃₉	#585	1	1	yes	characteristic
496	C₂²×C₁₃₉	#585	1	1	yes	characteristic
497	C₂²×C₁₃₉	#585	1	1	yes	characteristic
498	C₄×C₁₃₉	—	2	2	no	—
499	C₄×C₁₃₉	—	2	4	no	—
500	C₄×C₁₃₉	—	2	2	no	—
501	C₄×C₁₃₉	—	2	2	no	—
502	C₄×C₁₃₉	—	2	2	no	—
503	C₄×C₁₃₉	—	2	4	no	—
504	C₄×C₁₃₉	—	4	1	no	—
505	C₄×C₁₃₉	—	4	1	no	—
506	C₄×C₁₃₉	—	4	2	no	—
507	C₄×C₁₃₉	—	4	2	no	—
508	C₄×C₁₃₉	—	4	1	no	—
509	C₄×C₁₃₉	—	4	2	no	—
510	C₄×C₁₃₉	—	4	1	no	—
511	C₄×C₁₃₉	—	4	1	no	—
512	C₄×C₁₃₉	—	4	1	no	—
513	C₄×C₁₃₉	—	4	2	no	—
514	C₄×C₁₃₉	—	4	2	no	—
515	C₄×C₁₃₉	—	4	1	no	—
516	C₄×C₁₃₉	—	4	1	no	—
517	C₄×C₁₃₉	#532	1	4	yes	—
518	C₂×C₁₃₉	—	4	4	no	—
519	C₂×C₁₃₉	—	4	2	no	—
520	C₂×C₁₃₉	—	8	1	no	—
521	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
522	C₂×C₁₃₉	#3485	1	1	yes	characteristic
523	C₂×C₁₃₉	#3489	1	1	yes	characteristic
524	C₂×C₁₃₉	#3495	1	1	yes	characteristic
525	C₂×C₁₃₉	#3510	1	1	yes	characteristic
526	C₂×C₁₃₉	#3516	1	1	yes	characteristic
527	C₂×C₁₃₉	#3521	1	1	yes	characteristic
528	#35636	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
529	C₁₃₉	#35636	1	1	yes	characteristic, direct product factor, Sylow
530	C₂×#542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
531	C₂×#529	C₂×C₁₃₉	1	1	yes	characteristic, complemented
532	#2602	C₂×C₁₃₉	1	2	yes	complemented
533	#2564	C₂×C₁₃₉	1	2	yes	complemented
534	#2557	C₂×C₁₃₉	1	2	yes	complemented
535	#2553	C₂×C₁₃₉	1	2	yes	complemented
536	#2550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
539	#2535	C₂×C₁₃₉	1	1	yes	characteristic
540	#2521	C₂×C₁₃₉	1	2	yes	complemented
541	#2499	C₂×C₁₃₉	1	2	yes	complemented
542	#2498	C₂×C₁₃₉	1	2	yes	complemented
543	#2496	C₂×C₁₃₉	1	2	yes	complemented
544	#2492	C₂×C₁₃₉	1	1	yes	characteristic, complemented
545	#2489	C₂×C₁₃₉	1	1	yes	characteristic, complemented
546	#2427	C₂×C₁₃₉	1	1	yes	characteristic, complemented
547	#2427	C₂×C₁₃₉	1	1	yes	characteristic, complemented
548	#2327	C₂×C₁₃₉	1	1	yes	characteristic, complemented
549	#2323	C₂×C₁₃₉	1	1	yes	characteristic, complemented
550	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
551	#2290	C₂×C₁₃₉	1	1	yes	characteristic, complemented
552	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
553	#542	—	2	8	no	—
554	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
555	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
556	#529	—	2	8	no	—
557	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
558	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
559	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
560	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
561	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
563	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
564	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
566	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
568	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
570	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
571	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
573	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
575	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
578	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
581	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
582	#400	C₂²×C₁₃₉	1	2	yes	—
583	#400	C₂²×C₁₃₉	1	2	yes	—
584	#399	C₂²×C₁₃₉	1	2	yes	—
585	#399	C₂²×C₁₃₉	1	2	yes	—
586	#398	C₂²×C₁₃₉	1	2	yes	—
587	#397	C₂²×C₁₃₉	1	2	yes	—
588	#397	C₂²×C₁₃₉	1	2	yes	—
589	#397	C₂²×C₁₃₉	1	2	yes	—
590	#397	C₂²×C₁₃₉	1	2	yes	—
591	#397	C₂²×C₁₃₉	1	2	yes	—
592	#397	C₂²×C₁₃₉	1	2	yes	—
593	#395	C₂²×C₁₃₉	1	2	yes	—
594	#394	C₂²×C₁₃₉	1	2	yes	—
595	#394	C₂²×C₁₃₉	1	2	yes	—
596	#393	C₂²×C₁₃₉	1	2	yes	—
597	#392	C₂²×C₁₃₉	1	2	yes	—
598	#391	C₂²×C₁₃₉	1	1	yes	characteristic
599	#391	C₂²×C₁₃₉	1	1	yes	characteristic
600	#391	C₂²×C₁₃₉	1	1	yes	characteristic
601	#391	C₂²×C₁₃₉	1	1	yes	characteristic
602	#391	C₂²×C₁₃₉	1	2	yes	—
603	#391	C₂²×C₁₃₉	1	2	yes	—
604	#390	C₂²×C₁₃₉	1	2	yes	—
605	#389	C₂²×C₁₃₉	1	1	yes	characteristic
606	#389	C₂²×C₁₃₉	1	2	yes	—
607	#389	C₂²×C₁₃₉	1	2	yes	—
608	#389	C₂²×C₁₃₉	1	1	yes	characteristic
609	#388	C₂²×C₁₃₉	1	2	yes	—
610	#388	C₂²×C₁₃₉	1	2	yes	—
611	#388	C₂²×C₁₃₉	1	2	yes	—
612	#388	C₂²×C₁₃₉	1	2	yes	—
613	#388	C₂²×C₁₃₉	1	1	yes	characteristic
614	#388	C₂²×C₁₃₉	1	1	yes	characteristic
615	#387	C₂²×C₁₃₉	1	2	yes	—
616	#387	C₂²×C₁₃₉	1	2	yes	—
617	#387	C₂²×C₁₃₉	1	2	yes	—
618	#387	C₂²×C₁₃₉	1	2	yes	—
619	#387	C₂²×C₁₃₉	1	2	yes	—
620	#387	C₂²×C₁₃₉	1	1	yes	characteristic
621	#387	C₂²×C₁₃₉	1	2	yes	—
622	#387	C₂²×C₁₃₉	1	1	yes	characteristic
623	#386	C₂²×C₁₃₉	1	2	yes	—
624	#386	C₂²×C₁₃₉	1	2	yes	—
625	#386	C₂²×C₁₃₉	1	1	yes	characteristic
626	#386	C₂²×C₁₃₉	1	2	yes	—
627	#386	C₂²×C₁₃₉	1	2	yes	—
628	#386	C₂²×C₁₃₉	1	1	yes	characteristic
629	#385	C₂²×C₁₃₉	1	1	yes	characteristic
630	#385	C₂²×C₁₃₉	1	2	yes	—
631	#385	C₂²×C₁₃₉	1	1	yes	characteristic
632	#384	C₂²×C₁₃₉	1	2	yes	—
633	#382	C₂²×C₁₃₉	1	1	yes	characteristic
634	#382	C₂²×C₁₃₉	1	2	yes	—
635	#380	C₂²×C₁₃₉	1	2	yes	—
636	#380	C₂²×C₁₃₉	1	2	yes	—
637	#380	C₂²×C₁₃₉	1	1	yes	characteristic
638	#380	C₂²×C₁₃₉	1	2	yes	—
639	#380	C₂²×C₁₃₉	1	1	yes	characteristic
640	#380	C₂²×C₁₃₉	1	2	yes	—
641	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
642	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
643	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
644	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
645	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
647	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
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	#376	C₂²×C₁₃₉	1	1	yes	characteristic
653	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
654	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
656	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
657	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
661	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
662	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
666	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
667	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
668	C₄⋊Q₈	—	2	4	no	—
669	C₄⋊Q₈	—	2	4	no	—
670	#126	—	2	8	no	—
671	#126	—	2	8	no	—
672	#125	—	2	4	no	—
673	#124	—	2	4	no	—
674	#124	—	2	4	no	—
675	#124	—	2	8	no	—
676	#123	—	2	8	no	—
677	#123	—	2	8	no	—
678	C₂²⋊Q₈	—	2	8	no	—
679	C₂²⋊Q₈	—	2	4	no	—
680	C₂²⋊Q₈	—	2	4	no	—
681	C₂²⋊Q₈	—	2	4	no	—
682	C₂²⋊Q₈	—	2	4	no	—
683	#121	—	2	4	no	—
684	#121	—	2	4	no	—
685	C₄×Q₈	—	2	4	no	—
686	C₄×Q₈	—	2	4	no	—
687	C₄×D₄	—	2	8	no	—
688	C₄×D₄	—	2	4	no	—
689	C₄×D₄	—	2	4	no	—
690	C₄×D₄	—	2	4	no	—
691	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
692	#117	—	2	8	no	—
693	#117	—	2	4	no	—
694	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₄²	—	2	4	no	—
741	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
749	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
750	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
751	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
753	#95	C₂³×C₁₃₉	1	1	yes	characteristic
754	#95	C₂³×C₁₃₉	1	2	yes	—
755	#95	C₂³×C₁₃₉	1	2	yes	—
756	#95	C₂³×C₁₃₉	1	2	yes	—
757	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
764	#95	C₂³×C₁₃₉	1	2	yes	—
765	#95	C₂³×C₁₃₉	1	1	yes	characteristic
766	#95	C₂³×C₁₃₉	1	2	yes	—
767	#95	C₂³×C₁₃₉	1	2	yes	—
768	#95	C₂³×C₁₃₉	1	1	yes	characteristic
769	#95	C₂³×C₁₃₉	1	1	yes	characteristic
770	#95	C₂³×C₁₃₉	1	2	yes	—
771	#95	C₂³×C₁₃₉	1	2	yes	—
772	#95	C₂³×C₁₃₉	1	2	yes	—
773	#95	C₂³×C₁₃₉	1	2	yes	—
774	#95	C₂³×C₁₃₉	1	2	yes	—
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	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
781	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
782	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	2	4	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	4	1	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	2	no	—
803	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	4	1	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
825	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
844	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	4	no	—
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	4	no	—
862	C₄⋊C₄	—	4	2	no	—
863	C₄⋊C₄	—	4	2	no	—
864	C₄⋊C₄	—	4	1	no	—
865	C₄⋊C₄	—	4	1	no	—
866	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
867	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	4	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	4	1	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₂²⋊C₄	—	4	1	no	—
889	C₂²⋊C₄	—	4	1	no	—
890	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	4	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	4	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	—	4	2	no	—
900	C₄²	—	4	2	no	—
901	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
902	C₄²	#41×C₁₃₉	1	4	yes	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
923	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
924	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
925	Q₈	—	4	4	no	—
926	Q₈	—	4	4	no	—
927	Q₈	—	8	4	no	—
928	D₄	—	2	8	no	—
929	D₄	—	4	4	no	—
930	D₄	—	4	8	no	—
931	D₄	—	8	4	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	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	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	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	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	1	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	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	4	8	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	4	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	8	4	no	—
989	C₂×C₄	—	8	4	no	—
990	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
991	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
992	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
993	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
994	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
995	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
996	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
997	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
998	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1021	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1022	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1023	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1024	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1025	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1026	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1027	C₄	—	2	2	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	4	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	1	no	—
1046	C₄	#532×C₁₃₉	1	4	yes	—
1047	C₂	—	4	4	no	—
1048	C₂	—	4	2	no	—
1049	C₂	—	8	1	no	—
1050	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
1051	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1052	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1053	C₂	#3495×C₁₃₉	1	1	yes	characteristic
1054	C₂	#3510×C₁₃₉	1	1	yes	characteristic
1055	C₂	#3516×C₁₃₉	1	1	yes	characteristic
1056	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2535×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×#542×C₁₃₉	C₂	semidirect
2. C₂×#529×C₁₃₉	C₂	semidirect
3. #2602×C₁₃₉	C₂	semidirect
4. #2564×C₁₃₉	C₂	semidirect
5. #2557×C₁₃₉	C₂	semidirect
6. #2553×C₁₃₉	C₂	semidirect
7. #2550×C₁₃₉	C₂	semidirect
8. #2547×C₁₃₉	C₂	semidirect
9. #2542×C₁₃₉	C₂	semidirect
11. #2521×C₁₃₉	C₂	semidirect
12. #2499×C₁₃₉	C₂	semidirect
13. #2498×C₁₃₉	C₂	semidirect
14. #2496×C₁₃₉	C₂	semidirect
15. #2492×C₁₃₉	C₂	semidirect
16. #2489×C₁₃₉	C₂	semidirect
17. #2427×C₁₃₉	C₂	semidirect
18. #2427×C₁₃₉	C₂	semidirect
19. #2327×C₁₃₉	C₂	semidirect
20. #2323×C₁₃₉	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
22. #2290×C₁₃₉	C₂	semidirect
23. #2275×C₁₃₉	C₂	semidirect
162. C₄×D₄×C₁₃₉	D₄	semidirect
528. #35636	C₁₃₉	direct (N × H)
529. C₁₃₉	#35636	direct (N × H)
530. C₂×#542	C₂×C₁₃₉	semidirect
531. C₂×#529	C₂×C₁₃₉	semidirect
532. #2602	C₂×C₁₃₉	semidirect
533. #2564	C₂×C₁₃₉	semidirect
534. #2557	C₂×C₁₃₉	semidirect
535. #2553	C₂×C₁₃₉	semidirect
536. #2550	C₂×C₁₃₉	semidirect
537. #2547	C₂×C₁₃₉	semidirect
538. #2542	C₂×C₁₃₉	semidirect
540. #2521	C₂×C₁₃₉	semidirect
541. #2499	C₂×C₁₃₉	semidirect
542. #2498	C₂×C₁₃₉	semidirect
543. #2496	C₂×C₁₃₉	semidirect
544. #2492	C₂×C₁₃₉	semidirect
545. #2489	C₂×C₁₃₉	semidirect
546. #2427	C₂×C₁₃₉	semidirect
547. #2427	C₂×C₁₃₉	semidirect
548. #2327	C₂×C₁₃₉	semidirect
549. #2323	C₂×C₁₃₉	semidirect
550. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
551. #2290	C₂×C₁₃₉	semidirect
552. #2275	C₂×C₁₃₉	semidirect
691. 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×#542×C₁₃₉	2
C₂×#529×C₁₃₉	2
#2602×C₁₃₉	2
#2564×C₁₃₉	2
#2557×C₁₃₉	2
#2553×C₁₃₉	2
#2550×C₁₃₉	2
#2547×C₁₃₉	2
#2542×C₁₃₉	2
#2535×C₁₃₉	2
#2521×C₁₃₉	2
#2499×C₁₃₉	2
#2498×C₁₃₉	2
#2496×C₁₃₉	2
#2492×C₁₃₉	2
#2489×C₁₃₉	2
#2427×C₁₃₉	2
#2327×C₁₃₉	2
#2323×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#2290×C₁₃₉	2
#2275×C₁₃₉	2
#35636	139

Subgroups — C139×#35636 #48030232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35636 #48030232