Subgroups — C₁₃₉×#36443 #48031039

Order 35584.

2416 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2852×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2601×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2599×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2468×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2466×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2461×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2459×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2451×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2429×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2427×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2407×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2367×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2363×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2362×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	#556×C₁₃₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₄×#41×C₁₃₉	—	2	8	no	—
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×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×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
53	#398×C₁₃₉	C₂²	1	2	yes	—
54	#398×C₁₃₉	C₂²	1	2	yes	—
55	#397×C₁₃₉	C₂²	1	2	yes	—
56	#396×C₁₃₉	C₂²	1	2	yes	—
57	#396×C₁₃₉	C₂²	1	2	yes	—
58	#395×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#394×C₁₃₉	C₂²	1	2	yes	—
61	#394×C₁₃₉	C₂²	1	2	yes	—
62	#394×C₁₃₉	C₂²	1	2	yes	—
63	#393×C₁₃₉	C₂²	1	2	yes	—
64	#392×C₁₃₉	C₂²	1	2	yes	—
65	#391×C₁₃₉	C₂²	1	2	yes	—
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic
67	#391×C₁₃₉	C₂²	1	1	yes	characteristic
68	#391×C₁₃₉	C₂²	1	1	yes	characteristic
69	#391×C₁₃₉	C₂²	1	1	yes	characteristic
70	#390×C₁₃₉	C₂²	1	2	yes	—
71	#390×C₁₃₉	C₂²	1	1	yes	characteristic
72	#390×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	2	yes	—
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic
76	#389×C₁₃₉	C₂²	1	2	yes	—
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic
78	#389×C₁₃₉	C₂²	1	1	yes	characteristic
79	#388×C₁₃₉	C₂²	1	1	yes	characteristic
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	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	#387×C₁₃₉	C₂²	1	1	yes	characteristic
90	#387×C₁₃₉	C₂²	1	1	yes	characteristic
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	#387×C₁₃₉	C₂²	1	2	yes	—
97	#386×C₁₃₉	C₂²	1	1	yes	characteristic
98	#386×C₁₃₉	C₂²	1	2	yes	—
99	#386×C₁₃₉	C₂²	1	2	yes	—
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#385×C₁₃₉	C₂²	1	1	yes	characteristic
102	#385×C₁₃₉	C₂²	1	2	yes	—
103	#385×C₁₃₉	C₂²	1	2	yes	—
104	#385×C₁₃₉	C₂²	1	2	yes	—
105	#385×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#383×C₁₃₉	C₂²	1	2	yes	—
109	#381×C₁₃₉	C₂²	1	1	yes	characteristic
110	#381×C₁₃₉	C₂²	1	2	yes	—
111	#380×C₁₃₉	C₂²	1	2	yes	—
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
124	C₄×C₂²⋊C₄×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×Q₈×C₁₃₉	C₂³	1	2	yes	—
130	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
143	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
144	#126×C₁₃₉	—	2	8	no	—
145	#126×C₁₃₉	—	2	8	no	—
146	#124×C₁₃₉	—	2	4	no	—
147	#124×C₁₃₉	—	2	8	no	—
148	#123×C₁₃₉	—	2	4	no	—
149	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
153	#121×C₁₃₉	—	2	4	no	—
154	C₄×Q₈×C₁₃₉	—	2	4	no	—
155	C₄×Q₈×C₁₃₉	—	2	4	no	—
156	C₄×Q₈×C₁₃₉	—	2	4	no	—
157	C₄×Q₈×C₁₃₉	—	2	8	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	8	no	—
162	C₄×D₄×C₁₃₉	—	2	8	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	#117×C₁₃₉	—	2	8	no	—
165	#117×C₁₃₉	D₄	1	8	yes	complemented
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	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃₉	—	2	4	no	—
213	C₂×C₄²×C₁₃₉	—	2	8	no	—
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	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	1	yes	characteristic
222	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
244	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
249	#95×C₁₃₉	C₂³	1	1	yes	characteristic
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	#95×C₁₃₉	C₂³	1	1	yes	characteristic
253	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
256	#41×C₁₃₉	—	2	32	no	—
257	C₂×Q₈×C₁₃₉	—	2	2	no	—
258	C₂×Q₈×C₁₃₉	—	2	2	no	—
259	C₂×Q₈×C₁₃₉	—	2	4	no	—
260	C₂×Q₈×C₁₃₉	—	2	2	no	—
261	C₂×Q₈×C₁₃₉	—	2	4	no	—
262	C₂×Q₈×C₁₃₉	—	2	2	no	—
263	C₂×Q₈×C₁₃₉	—	2	2	no	—
264	C₂×Q₈×C₁₃₉	—	4	2	no	—
265	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
266	C₂×D₄×C₁₃₉	—	2	4	no	—
267	C₂×D₄×C₁₃₉	—	2	4	no	—
268	C₂×D₄×C₁₃₉	—	2	2	no	—
269	C₂×D₄×C₁₃₉	—	2	4	no	—
270	C₂×D₄×C₁₃₉	—	2	2	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	1	no	—
275	C₂×D₄×C₁₃₉	—	4	2	no	—
276	C₂×D₄×C₁₃₉	—	4	2	no	—
277	C₂×D₄×C₁₃₉	#41	1	4	yes	—
278	C₂²×C₄×C₁₃₉	—	2	4	no	—
279	C₂²×C₄×C₁₃₉	—	2	4	no	—
280	C₂²×C₄×C₁₃₉	—	2	4	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	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	4	no	—
286	C₂²×C₄×C₁₃₉	—	2	4	no	—
287	C₂²×C₄×C₁₃₉	—	2	2	no	—
288	C₂²×C₄×C₁₃₉	—	2	2	no	—
289	C₂²×C₄×C₁₃₉	—	2	4	no	—
290	C₂²×C₄×C₁₃₉	—	2	2	no	—
291	C₂²×C₄×C₁₃₉	—	2	2	no	—
292	C₂²×C₄×C₁₃₉	—	2	4	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	4	2	no	—
295	C₂²×C₄×C₁₃₉	—	4	2	no	—
296	C₂²×C₄×C₁₃₉	—	4	1	no	—
297	C₂²×C₄×C₁₃₉	—	4	1	no	—
298	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	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	1	yes	characteristic
303	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
329	C₄⋊C₄×C₁₃₉	—	2	2	no	—
330	C₄⋊C₄×C₁₃₉	—	2	4	no	—
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	no	—
333	C₄⋊C₄×C₁₃₉	—	2	4	no	—
334	C₄⋊C₄×C₁₃₉	—	2	4	no	—
335	C₄⋊C₄×C₁₃₉	—	2	2	no	—
336	C₄⋊C₄×C₁₃₉	—	4	1	no	—
337	C₄⋊C₄×C₁₃₉	—	4	2	no	—
338	C₄⋊C₄×C₁₃₉	—	4	2	no	—
339	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
340	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
341	C₄⋊C₄×C₁₃₉	#41	1	4	yes	complemented
342	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
344	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	2	4	no	—
349	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
350	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
360	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
363	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
364	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
365	C₄²×C₁₃₉	—	2	2	no	—
366	C₄²×C₁₃₉	—	2	2	no	—
367	C₄²×C₁₃₉	—	2	4	no	—
368	C₄²×C₁₃₉	—	2	4	no	—
369	C₄²×C₁₃₉	—	2	2	no	—
370	C₄²×C₁₃₉	—	2	2	no	—
371	C₄²×C₁₃₉	—	2	4	no	—
372	C₄²×C₁₃₉	—	2	2	no	—
373	C₄²×C₁₃₉	—	2	4	no	—
374	C₄²×C₁₃₉	—	2	2	no	—
375	C₄²×C₁₃₉	—	2	2	no	—
376	C₄²×C₁₃₉	—	4	2	no	—
377	C₄²×C₁₃₉	—	4	2	no	—
378	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
379	C₂³×C₁₃₉	—	2	2	no	—
380	C₂³×C₁₃₉	—	2	2	no	—
381	C₂³×C₁₃₉	—	2	1	no	—
382	C₂³×C₁₃₉	—	2	1	no	—
383	C₂³×C₁₃₉	—	2	1	no	—
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	2	no	—
390	C₂³×C₁₃₉	—	2	2	no	—
391	C₂³×C₁₃₉	—	2	1	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	1	no	—
395	C₂³×C₁₃₉	—	2	1	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	1	no	—
398	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
399	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
400	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
401	Q₈×C₁₃₉	—	2	8	no	—
402	Q₈×C₁₃₉	—	4	8	no	—
403	Q₈×C₁₃₉	—	4	4	no	—
404	D₄×C₁₃₉	—	2	16	no	—
405	D₄×C₁₃₉	—	2	8	no	—
406	D₄×C₁₃₉	—	4	4	no	—
407	D₄×C₁₃₉	—	8	4	no	—
408	C₂×C₄×C₁₃₉	—	2	16	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	1	no	—
414	C₂×C₄×C₁₃₉	—	2	2	no	—
415	C₂×C₄×C₁₃₉	—	2	1	no	—
416	C₂×C₄×C₁₃₉	—	2	1	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	2	no	—
419	C₂×C₄×C₁₃₉	—	2	1	no	—
420	C₂×C₄×C₁₃₉	—	2	2	no	—
421	C₂×C₄×C₁₃₉	—	2	2	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	8	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	1	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	1	no	—
435	C₂×C₄×C₁₃₉	—	2	1	no	—
436	C₂×C₄×C₁₃₉	—	2	1	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	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	2	no	—
445	C₂×C₄×C₁₃₉	—	2	1	no	—
446	C₂×C₄×C₁₃₉	—	2	1	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	1	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	2	no	—
451	C₂×C₄×C₁₃₉	—	2	2	no	—
452	C₂×C₄×C₁₃₉	—	2	1	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	2	1	no	—
455	C₂×C₄×C₁₃₉	—	2	1	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	1	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	4	8	no	—
460	C₂×C₄×C₁₃₉	—	4	8	no	—
461	C₂×C₄×C₁₃₉	—	4	4	no	—
462	C₂×C₄×C₁₃₉	—	4	4	no	—
463	C₂×C₄×C₁₃₉	—	4	4	no	—
464	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
465	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
467	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
469	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
470	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
471	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
472	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
473	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
474	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
475	C₂²×C₁₃₉	—	2	2	no	—
476	C₂²×C₁₃₉	—	2	4	no	—
477	C₂²×C₁₃₉	—	2	2	no	—
478	C₂²×C₁₃₉	—	2	4	no	—
479	C₂²×C₁₃₉	—	2	2	no	—
480	C₂²×C₁₃₉	—	2	4	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	2	no	—
486	C₂²×C₁₃₉	—	4	1	no	—
487	C₂²×C₁₃₉	—	4	2	no	—
488	C₂²×C₁₃₉	—	4	1	no	—
489	C₂²×C₁₃₉	—	4	1	no	—
490	C₂²×C₁₃₉	—	4	1	no	—
491	C₂²×C₁₃₉	—	4	1	no	—
492	C₂²×C₁₃₉	—	4	1	no	—
493	C₂²×C₁₃₉	—	4	1	no	—
494	C₂²×C₁₃₉	—	4	1	no	—
495	C₂²×C₁₃₉	—	4	1	no	—
496	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
497	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₂²×C₁₃₉	#585	1	1	yes	characteristic
502	C₂²×C₁₃₉	#585	1	1	yes	characteristic
503	C₄×C₁₃₉	—	2	2	no	—
504	C₄×C₁₃₉	—	2	4	no	—
505	C₄×C₁₃₉	—	2	2	no	—
506	C₄×C₁₃₉	—	2	4	no	—
507	C₄×C₁₃₉	—	2	2	no	—
508	C₄×C₁₃₉	—	2	2	no	—
509	C₄×C₁₃₉	—	2	2	no	—
510	C₄×C₁₃₉	—	2	4	no	—
511	C₄×C₁₃₉	—	4	1	no	—
512	C₄×C₁₃₉	—	4	2	no	—
513	C₄×C₁₃₉	—	4	1	no	—
514	C₄×C₁₃₉	—	4	2	no	—
515	C₄×C₁₃₉	—	4	2	no	—
516	C₄×C₁₃₉	—	4	1	no	—
517	C₄×C₁₃₉	—	4	1	no	—
518	C₄×C₁₃₉	—	4	1	no	—
519	C₄×C₁₃₉	—	4	1	no	—
520	C₄×C₁₃₉	—	4	1	no	—
521	C₄×C₁₃₉	—	4	2	no	—
522	C₄×C₁₃₉	#525	1	4	yes	—
523	C₂×C₁₃₉	—	4	2	no	—
524	C₂×C₁₃₉	—	4	4	no	—
525	C₂×C₁₃₉	—	8	1	no	—
526	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
527	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
528	C₂×C₁₃₉	#3480	1	1	yes	characteristic
529	C₂×C₁₃₉	#3482	1	1	yes	characteristic
530	C₂×C₁₃₉	#3489	1	1	yes	characteristic
531	C₂×C₁₃₉	#3518	1	1	yes	characteristic
532	C₂×C₁₃₉	#3521	1	1	yes	characteristic
533	#36443	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
534	C₁₃₉	#36443	1	1	yes	characteristic, direct product factor, Sylow
535	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
536	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	#2852	C₂×C₁₃₉	1	2	yes	complemented
539	#2601	C₂×C₁₃₉	1	2	yes	complemented
540	#2599	C₂×C₁₃₉	1	2	yes	complemented
541	#2468	C₂×C₁₃₉	1	2	yes	complemented
542	#2466	C₂×C₁₃₉	1	2	yes	complemented
543	#2461	C₂×C₁₃₉	1	2	yes	complemented
544	#2459	C₂×C₁₃₉	1	2	yes	complemented
545	#2452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
546	#2451	C₂×C₁₃₉	1	1	yes	characteristic, complemented
547	#2432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
548	#2429	C₂×C₁₃₉	1	1	yes	characteristic, complemented
549	#2427	C₂×C₁₃₉	1	1	yes	characteristic, complemented
550	#2407	C₂×C₁₃₉	1	1	yes	characteristic
551	#2367	C₂×C₁₃₉	1	1	yes	characteristic, complemented
552	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
553	#2363	C₂×C₁₃₉	1	1	yes	characteristic, complemented
554	#2362	C₂×C₁₃₉	1	1	yes	characteristic, complemented
555	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
556	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
557	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
558	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
559	#556	—	2	8	no	—
560	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
563	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
564	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
566	C₂×#123	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×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
571	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
572	C₄×#41	—	2	8	no	—
573	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
574	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄×Q₈	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×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
580	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
581	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
583	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
585	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
586	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
587	#398	C₂²×C₁₃₉	1	2	yes	—
588	#398	C₂²×C₁₃₉	1	2	yes	—
589	#397	C₂²×C₁₃₉	1	2	yes	—
590	#396	C₂²×C₁₃₉	1	2	yes	—
591	#396	C₂²×C₁₃₉	1	2	yes	—
592	#395	C₂²×C₁₃₉	1	2	yes	—
593	#394	C₂²×C₁₃₉	1	2	yes	—
594	#394	C₂²×C₁₃₉	1	2	yes	—
595	#394	C₂²×C₁₃₉	1	2	yes	—
596	#394	C₂²×C₁₃₉	1	2	yes	—
597	#393	C₂²×C₁₃₉	1	2	yes	—
598	#392	C₂²×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
603	#391	C₂²×C₁₃₉	1	2	yes	—
604	#390	C₂²×C₁₃₉	1	2	yes	—
605	#390	C₂²×C₁₃₉	1	1	yes	characteristic
606	#390	C₂²×C₁₃₉	1	1	yes	characteristic
607	#389	C₂²×C₁₃₉	1	1	yes	characteristic
608	#389	C₂²×C₁₃₉	1	1	yes	characteristic
609	#389	C₂²×C₁₃₉	1	2	yes	—
610	#389	C₂²×C₁₃₉	1	1	yes	characteristic
611	#389	C₂²×C₁₃₉	1	1	yes	characteristic
612	#389	C₂²×C₁₃₉	1	2	yes	—
613	#388	C₂²×C₁₃₉	1	1	yes	characteristic
614	#388	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	1	yes	characteristic
619	#388	C₂²×C₁₃₉	1	2	yes	—
620	#388	C₂²×C₁₃₉	1	2	yes	—
621	#388	C₂²×C₁₃₉	1	2	yes	—
622	#388	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	1	yes	characteristic
627	#387	C₂²×C₁₃₉	1	2	yes	—
628	#387	C₂²×C₁₃₉	1	2	yes	—
629	#387	C₂²×C₁₃₉	1	2	yes	—
630	#387	C₂²×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
635	#385	C₂²×C₁₃₉	1	2	yes	—
636	#385	C₂²×C₁₃₉	1	2	yes	—
637	#385	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	1	yes	characteristic
642	#383	C₂²×C₁₃₉	1	2	yes	—
643	#381	C₂²×C₁₃₉	1	2	yes	—
644	#381	C₂²×C₁₃₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
649	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
650	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
651	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
652	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
653	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
654	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
655	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
656	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
657	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
658	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
659	C₂×#41	—	2	4	no	—
660	C₂×#41	—	2	4	no	—
661	C₂×#41	—	2	4	no	—
662	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
663	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
664	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
666	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
668	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
669	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
671	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
672	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₄⋊Q₈	—	2	4	no	—
677	C₄⋊Q₈	—	2	4	no	—
678	#126	—	2	8	no	—
679	#126	—	2	8	no	—
680	#124	—	2	4	no	—
681	#124	—	2	8	no	—
682	#123	—	2	4	no	—
683	C₂²⋊Q₈	—	2	4	no	—
684	C₂²⋊Q₈	—	2	4	no	—
685	C₂²⋊Q₈	—	2	4	no	—
686	C₂²⋊Q₈	—	2	8	no	—
687	#121	—	2	4	no	—
688	C₄×Q₈	—	2	4	no	—
689	C₄×Q₈	—	2	4	no	—
690	C₄×Q₈	—	2	4	no	—
691	C₄×Q₈	—	2	8	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	8	no	—
697	#117	—	2	4	no	—
698	#117	—	2	8	no	—
699	#117	D₄×C₁₃₉	1	8	yes	complemented
700	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₄²	—	2	4	no	—
747	C₂×C₄²	—	2	8	no	—
748	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
750	C₂×C₄²	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	2	yes	—
754	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
756	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
760	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
761	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
762	#95	C₂³×C₁₃₉	1	1	yes	characteristic
763	#95	C₂³×C₁₃₉	1	1	yes	characteristic
764	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
771	#95	C₂³×C₁₃₉	1	2	yes	—
772	#95	C₂³×C₁₃₉	1	2	yes	—
773	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
786	#95	C₂³×C₁₃₉	1	2	yes	—
787	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
788	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
789	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
790	#41	—	2	32	no	—
791	C₂×Q₈	—	2	2	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	4	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	4	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	4	2	no	—
799	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	4	1	no	—
809	C₂×D₄	—	4	2	no	—
810	C₂×D₄	—	4	2	no	—
811	C₂×D₄	#41×C₁₃₉	1	4	yes	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	4	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	4	no	—
820	C₂²×C₄	—	2	4	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	4	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	1	no	—
831	C₂²×C₄	—	4	1	no	—
832	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
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	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
844	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	4	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	4	1	no	—
871	C₄⋊C₄	—	4	2	no	—
872	C₄⋊C₄	—	4	2	no	—
873	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
874	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
875	C₄⋊C₄	#41×C₁₃₉	1	4	yes	complemented
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	4	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	4	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	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	4	1	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	1	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	4	no	—
902	C₄²	—	2	4	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	4	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	4	2	no	—
911	C₄²	—	4	2	no	—
912	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
933	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
934	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
935	Q₈	—	2	8	no	—
936	Q₈	—	4	8	no	—
937	Q₈	—	4	4	no	—
938	D₄	—	2	16	no	—
939	D₄	—	2	8	no	—
940	D₄	—	4	4	no	—
941	D₄	—	8	4	no	—
942	C₂×C₄	—	2	16	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	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	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	8	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	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	4	8	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	4	4	no	—
998	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
999	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1001	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1002	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1003	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1004	C₂×C₄	C₂×#41×C₁₃₉	1	4	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	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	—	4	1	no	—
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	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1034	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1035	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1036	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	4	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	1	no	—
1056	C₄	#525×C₁₃₉	1	4	yes	—
1057	C₂	—	4	2	no	—
1058	C₂	—	4	4	no	—
1059	C₂	—	8	1	no	—
1060	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1061	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1062	C₂	#3480×C₁₃₉	1	1	yes	characteristic
1063	C₂	#3482×C₁₃₉	1	1	yes	characteristic
1064	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1065	C₂	#3518×C₁₃₉	1	1	yes	characteristic
1066	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2407×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×#556×C₁₃₉	C₂	semidirect
2. C₂×C₄×#41×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2852×C₁₃₉	C₂	semidirect
5. #2601×C₁₃₉	C₂	semidirect
6. #2599×C₁₃₉	C₂	semidirect
7. #2468×C₁₃₉	C₂	semidirect
8. #2466×C₁₃₉	C₂	semidirect
9. #2461×C₁₃₉	C₂	semidirect
10. #2459×C₁₃₉	C₂	semidirect
11. #2452×C₁₃₉	C₂	semidirect
12. #2451×C₁₃₉	C₂	semidirect
13. #2432×C₁₃₉	C₂	semidirect
14. #2429×C₁₃₉	C₂	semidirect
15. #2427×C₁₃₉	C₂	semidirect
17. #2367×C₁₃₉	C₂	semidirect
18. #2365×C₁₃₉	C₂	semidirect
19. #2363×C₁₃₉	C₂	semidirect
20. #2362×C₁₃₉	C₂	semidirect
21. #2347×C₁₃₉	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
23. C₄×#123×C₁₃₉	C₂	semidirect
165. #117×C₁₃₉	D₄	semidirect
341. C₄⋊C₄×C₁₃₉	#41	semidirect
533. #36443	C₁₃₉	direct (N × H)
534. C₁₃₉	#36443	direct (N × H)
535. C₂×#556	C₂×C₁₃₉	semidirect
536. C₂×C₄×#41	C₂×C₁₃₉	semidirect
537. #2855	C₂×C₁₃₉	semidirect
538. #2852	C₂×C₁₃₉	semidirect
539. #2601	C₂×C₁₃₉	semidirect
540. #2599	C₂×C₁₃₉	semidirect
541. #2468	C₂×C₁₃₉	semidirect
542. #2466	C₂×C₁₃₉	semidirect
543. #2461	C₂×C₁₃₉	semidirect
544. #2459	C₂×C₁₃₉	semidirect
545. #2452	C₂×C₁₃₉	semidirect
546. #2451	C₂×C₁₃₉	semidirect
547. #2432	C₂×C₁₃₉	semidirect
548. #2429	C₂×C₁₃₉	semidirect
549. #2427	C₂×C₁₃₉	semidirect
551. #2367	C₂×C₁₃₉	semidirect
552. #2365	C₂×C₁₃₉	semidirect
553. #2363	C₂×C₁₃₉	semidirect
554. #2362	C₂×C₁₃₉	semidirect
555. #2347	C₂×C₁₃₉	semidirect
556. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
557. C₄×#123	C₂×C₁₃₉	semidirect
699. #117	D₄×C₁₃₉	semidirect
875. C₄⋊C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2855×C₁₃₉	2
#2852×C₁₃₉	2
#2601×C₁₃₉	2
#2599×C₁₃₉	2
#2468×C₁₃₉	2
#2466×C₁₃₉	2
#2461×C₁₃₉	2
#2459×C₁₃₉	2
#2452×C₁₃₉	2
#2451×C₁₃₉	2
#2432×C₁₃₉	2
#2429×C₁₃₉	2
#2427×C₁₃₉	2
#2407×C₁₃₉	2
#2367×C₁₃₉	2
#2365×C₁₃₉	2
#2363×C₁₃₉	2
#2362×C₁₃₉	2
#2347×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#123×C₁₃₉	2
#36443	139

Subgroups — C139×#36443 #48031039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36443 #48031039