Subgroups — C₁₃₉×#35724 #48030320

Order 35584.

2412 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2638×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2625×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2600×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2477×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2475×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2451×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2429×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2427×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2407×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2367×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2361×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2360×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
25	#554×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×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
37	#520×C₁₃₉	—	2	8	no	—
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	—
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
50	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
51	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
54	#400×C₁₃₉	C₂²	1	2	yes	—
55	#400×C₁₃₉	C₂²	1	1	yes	characteristic
56	#399×C₁₃₉	C₂²	1	1	yes	characteristic
57	#398×C₁₃₉	C₂²	1	2	yes	—
58	#398×C₁₃₉	C₂²	1	2	yes	—
59	#398×C₁₃₉	C₂²	1	2	yes	—
60	#398×C₁₃₉	C₂²	1	1	yes	characteristic
61	#397×C₁₃₉	C₂²	1	2	yes	—
62	#397×C₁₃₉	C₂²	1	2	yes	—
63	#397×C₁₃₉	C₂²	1	1	yes	characteristic
64	#397×C₁₃₉	C₂²	1	2	yes	—
65	#397×C₁₃₉	C₂²	1	1	yes	characteristic
66	#397×C₁₃₉	C₂²	1	1	yes	characteristic
67	#396×C₁₃₉	C₂²	1	2	yes	—
68	#396×C₁₃₉	C₂²	1	2	yes	—
69	#395×C₁₃₉	C₂²	1	2	yes	—
70	#394×C₁₃₉	C₂²	1	1	yes	characteristic
71	#394×C₁₃₉	C₂²	1	2	yes	—
72	#394×C₁₃₉	C₂²	1	2	yes	—
73	#394×C₁₃₉	C₂²	1	1	yes	characteristic
74	#394×C₁₃₉	C₂²	1	2	yes	—
75	#394×C₁₃₉	C₂²	1	2	yes	—
76	#393×C₁₃₉	C₂²	1	2	yes	—
77	#392×C₁₃₉	C₂²	1	2	yes	—
78	#391×C₁₃₉	C₂²	1	1	yes	characteristic
79	#391×C₁₃₉	C₂²	1	1	yes	characteristic
80	#391×C₁₃₉	C₂²	1	1	yes	characteristic
81	#391×C₁₃₉	C₂²	1	1	yes	characteristic
82	#391×C₁₃₉	C₂²	1	2	yes	—
83	#390×C₁₃₉	C₂²	1	1	yes	characteristic
84	#390×C₁₃₉	C₂²	1	1	yes	characteristic
85	#389×C₁₃₉	C₂²	1	1	yes	characteristic
86	#389×C₁₃₉	C₂²	1	1	yes	characteristic
87	#389×C₁₃₉	C₂²	1	1	yes	characteristic
88	#389×C₁₃₉	C₂²	1	2	yes	—
89	#389×C₁₃₉	C₂²	1	1	yes	characteristic
90	#389×C₁₃₉	C₂²	1	2	yes	—
91	#389×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#388×C₁₃₉	C₂²	1	2	yes	—
94	#388×C₁₃₉	C₂²	1	2	yes	—
95	#388×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	2	yes	—
97	#387×C₁₃₉	C₂²	1	2	yes	—
98	#387×C₁₃₉	C₂²	1	2	yes	—
99	#387×C₁₃₉	C₂²	1	2	yes	—
100	#387×C₁₃₉	C₂²	1	2	yes	—
101	#387×C₁₃₉	C₂²	1	2	yes	—
102	#386×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#386×C₁₃₉	C₂²	1	2	yes	—
105	#385×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#385×C₁₃₉	C₂²	1	2	yes	—
110	#385×C₁₃₉	C₂²	1	2	yes	—
111	#385×C₁₃₉	C₂²	1	2	yes	—
112	#381×C₁₃₉	C₂²	1	2	yes	—
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic
114	#380×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	2	yes	—
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
130	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
143	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
144	#125×C₁₃₉	—	2	8	no	—
145	#124×C₁₃₉	—	2	4	no	—
146	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
147	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
148	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
149	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
152	#121×C₁₃₉	—	2	4	no	—
153	C₄×Q₈×C₁₃₉	—	2	4	no	—
154	C₄×Q₈×C₁₃₉	—	2	4	no	—
155	C₄×Q₈×C₁₃₉	—	2	4	no	—
156	C₄×D₄×C₁₃₉	—	2	8	no	—
157	C₄×D₄×C₁₃₉	—	2	8	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	—	4	4	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	#117×C₁₃₉	—	2	8	no	—
165	#117×C₁₃₉	—	4	4	no	—
166	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
167	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
219	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
224	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	#95×C₁₃₉	C₂³	1	1	yes	characteristic
235	#95×C₁₃₉	C₂³	1	2	yes	—
236	#95×C₁₃₉	C₂³	1	1	yes	characteristic
237	#95×C₁₃₉	C₂³	1	1	yes	characteristic
238	#95×C₁₃₉	C₂³	1	1	yes	characteristic
239	#95×C₁₃₉	C₂³	1	1	yes	characteristic
240	#95×C₁₃₉	C₂³	1	2	yes	—
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	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	1	yes	characteristic
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	#41×C₁₃₉	—	2	32	no	—
258	C₂×Q₈×C₁₃₉	—	2	2	no	—
259	C₂×Q₈×C₁₃₉	—	2	2	no	—
260	C₂×Q₈×C₁₃₉	—	2	4	no	—
261	C₂×Q₈×C₁₃₉	—	2	2	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	—	4	2	no	—
266	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
267	C₂×D₄×C₁₃₉	—	2	2	no	—
268	C₂×D₄×C₁₃₉	—	2	4	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	4	no	—
273	C₂×D₄×C₁₃₉	—	2	2	no	—
274	C₂×D₄×C₁₃₉	—	2	4	no	—
275	C₂×D₄×C₁₃₉	—	2	2	no	—
276	C₂×D₄×C₁₃₉	—	2	2	no	—
277	C₂×D₄×C₁₃₉	—	4	2	no	—
278	C₂×D₄×C₁₃₉	#41	1	4	yes	—
279	C₂²×C₄×C₁₃₉	—	2	4	no	—
280	C₂²×C₄×C₁₃₉	—	2	4	no	—
281	C₂²×C₄×C₁₃₉	—	2	4	no	—
282	C₂²×C₄×C₁₃₉	—	2	2	no	—
283	C₂²×C₄×C₁₃₉	—	2	2	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	2	no	—
287	C₂²×C₄×C₁₃₉	—	2	4	no	—
288	C₂²×C₄×C₁₃₉	—	2	4	no	—
289	C₂²×C₄×C₁₃₉	—	2	4	no	—
290	C₂²×C₄×C₁₃₉	—	4	2	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	—	4	2	no	—
296	C₂²×C₄×C₁₃₉	—	4	2	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
299	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	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	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	1	yes	characteristic
312	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₁₃₉	—	2	2	no	—
321	C₄⋊C₄×C₁₃₉	—	2	4	no	—
322	C₄⋊C₄×C₁₃₉	—	2	4	no	—
323	C₄⋊C₄×C₁₃₉	—	2	4	no	—
324	C₄⋊C₄×C₁₃₉	—	2	2	no	—
325	C₄⋊C₄×C₁₃₉	—	2	2	no	—
326	C₄⋊C₄×C₁₃₉	—	2	2	no	—
327	C₄⋊C₄×C₁₃₉	—	2	4	no	—
328	C₄⋊C₄×C₁₃₉	—	2	4	no	—
329	C₄⋊C₄×C₁₃₉	—	2	4	no	—
330	C₄⋊C₄×C₁₃₉	—	2	4	no	—
331	C₄⋊C₄×C₁₃₉	—	2	2	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	4	no	—
336	C₄⋊C₄×C₁₃₉	—	2	4	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	2	no	—
339	C₄⋊C₄×C₁₃₉	—	2	2	no	—
340	C₄⋊C₄×C₁₃₉	—	4	1	no	—
341	C₄⋊C₄×C₁₃₉	—	4	2	no	—
342	C₄⋊C₄×C₁₃₉	—	4	2	no	—
343	C₄⋊C₄×C₁₃₉	—	4	2	no	—
344	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
345	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
346	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
347	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	2	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	2	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
366	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
370	C₄²×C₁₃₉	—	2	4	no	—
371	C₄²×C₁₃₉	—	2	4	no	—
372	C₄²×C₁₃₉	—	2	2	no	—
373	C₄²×C₁₃₉	—	2	2	no	—
374	C₄²×C₁₃₉	—	2	4	no	—
375	C₄²×C₁₃₉	—	2	2	no	—
376	C₄²×C₁₃₉	—	2	2	no	—
377	C₄²×C₁₃₉	—	2	2	no	—
378	C₄²×C₁₃₉	—	2	4	no	—
379	C₄²×C₁₃₉	—	4	2	no	—
380	C₂³×C₁₃₉	—	2	1	no	—
381	C₂³×C₁₃₉	—	2	2	no	—
382	C₂³×C₁₃₉	—	2	1	no	—
383	C₂³×C₁₃₉	—	2	1	no	—
384	C₂³×C₁₃₉	—	2	1	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	1	no	—
387	C₂³×C₁₃₉	—	2	1	no	—
388	C₂³×C₁₃₉	—	2	2	no	—
389	C₂³×C₁₃₉	—	2	1	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	2	no	—
395	C₂³×C₁₃₉	—	2	1	no	—
396	C₂³×C₁₃₉	—	2	2	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	2₋¹⁺⁴	1	2	yes	—
401	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
402	Q₈×C₁₃₉	—	2	8	no	—
403	Q₈×C₁₃₉	—	4	4	no	—
404	Q₈×C₁₃₉	—	8	4	no	—
405	D₄×C₁₃₉	—	2	8	no	—
406	D₄×C₁₃₉	—	2	16	no	—
407	D₄×C₁₃₉	—	2	8	no	—
408	D₄×C₁₃₉	—	4	8	no	—
409	C₂×C₄×C₁₃₉	—	2	16	no	—
410	C₂×C₄×C₁₃₉	—	2	1	no	—
411	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
416	C₂×C₄×C₁₃₉	—	2	2	no	—
417	C₂×C₄×C₁₃₉	—	2	2	no	—
418	C₂×C₄×C₁₃₉	—	2	1	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	8	no	—
423	C₂×C₄×C₁₃₉	—	2	1	no	—
424	C₂×C₄×C₁₃₉	—	2	1	no	—
425	C₂×C₄×C₁₃₉	—	2	2	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	1	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	2	no	—
436	C₂×C₄×C₁₃₉	—	2	2	no	—
437	C₂×C₄×C₁₃₉	—	2	2	no	—
438	C₂×C₄×C₁₃₉	—	2	1	no	—
439	C₂×C₄×C₁₃₉	—	2	2	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	1	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	1	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	2	no	—
456	C₂×C₄×C₁₃₉	—	2	1	no	—
457	C₂×C₄×C₁₃₉	—	2	1	no	—
458	C₂×C₄×C₁₃₉	—	2	1	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	1	no	—
461	C₂×C₄×C₁₃₉	—	2	1	no	—
462	C₂×C₄×C₁₃₉	—	4	8	no	—
463	C₂×C₄×C₁₃₉	—	4	4	no	—
464	C₂×C₄×C₁₃₉	—	8	4	no	—
465	C₂×C₄×C₁₃₉	—	8	4	no	—
466	C₂×C₄×C₁₃₉	—	8	4	no	—
467	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
468	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
469	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
472	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
473	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
474	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
475	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
476	C₂²×C₁₃₉	—	2	2	no	—
477	C₂²×C₁₃₉	—	2	4	no	—
478	C₂²×C₁₃₉	—	2	2	no	—
479	C₂²×C₁₃₉	—	2	2	no	—
480	C₂²×C₁₃₉	—	2	2	no	—
481	C₂²×C₁₃₉	—	2	4	no	—
482	C₂²×C₁₃₉	—	2	2	no	—
483	C₂²×C₁₃₉	—	2	2	no	—
484	C₂²×C₁₃₉	—	2	4	no	—
485	C₂²×C₁₃₉	—	4	1	no	—
486	C₂²×C₁₃₉	—	4	2	no	—
487	C₂²×C₁₃₉	—	4	1	no	—
488	C₂²×C₁₃₉	—	4	2	no	—
489	C₂²×C₁₃₉	—	4	1	no	—
490	C₂²×C₁₃₉	—	4	1	no	—
491	C₂²×C₁₃₉	—	4	1	no	—
492	C₂²×C₁₃₉	—	4	2	no	—
493	C₂²×C₁₃₉	—	4	1	no	—
494	C₂²×C₁₃₉	—	4	1	no	—
495	C₂²×C₁₃₉	—	4	1	no	—
496	C₂²×C₁₃₉	—	4	2	no	—
497	C₂²×C₁₃₉	C₂³×D₄	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×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
502	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
503	C₂²×C₁₃₉	#585	1	1	yes	characteristic
504	C₄×C₁₃₉	—	2	2	no	—
505	C₄×C₁₃₉	—	2	4	no	—
506	C₄×C₁₃₉	—	2	2	no	—
507	C₄×C₁₃₉	—	2	4	no	—
508	C₄×C₁₃₉	—	2	4	no	—
509	C₄×C₁₃₉	—	2	2	no	—
510	C₄×C₁₃₉	—	4	1	no	—
511	C₄×C₁₃₉	—	4	2	no	—
512	C₄×C₁₃₉	—	4	1	no	—
513	C₄×C₁₃₉	—	4	1	no	—
514	C₄×C₁₃₉	—	4	1	no	—
515	C₄×C₁₃₉	—	4	1	no	—
516	C₄×C₁₃₉	—	4	2	no	—
517	C₄×C₁₃₉	—	4	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	—	4	2	no	—
523	C₄×C₁₃₉	#525	1	4	yes	—
524	C₂×C₁₃₉	—	4	2	no	—
525	C₂×C₁₃₉	—	4	4	no	—
526	C₂×C₁₃₉	—	4	2	no	—
527	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
528	C₂×C₁₃₉	#3486	1	1	yes	characteristic
529	C₂×C₁₃₉	#3496	1	1	yes	characteristic
530	C₂×C₁₃₉	#3515	1	1	yes	characteristic
531	C₂×C₁₃₉	#3516	1	1	yes	characteristic
532	C₂×C₁₃₉	#3520	1	1	yes	characteristic
533	C₂×C₁₃₉	#3522	1	1	yes	characteristic
534	#35724	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
535	C₁₃₉	#35724	1	1	yes	characteristic, direct product factor, Sylow
536	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
537	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
538	#2638	C₂×C₁₃₉	1	2	yes	complemented
539	#2625	C₂×C₁₃₉	1	1	yes	characteristic, complemented
540	#2600	C₂×C₁₃₉	1	2	yes	complemented
541	#2477	C₂×C₁₃₉	1	2	yes	complemented
542	#2475	C₂×C₁₃₉	1	2	yes	complemented
543	#2473	C₂×C₁₃₉	1	2	yes	complemented
544	#2452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
545	#2451	C₂×C₁₃₉	1	1	yes	characteristic, complemented
546	#2449	C₂×C₁₃₉	1	2	yes	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	#2415	C₂×C₁₃₉	1	2	yes	complemented
551	#2407	C₂×C₁₃₉	1	1	yes	characteristic
552	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
553	#2392	C₂×C₁₃₉	1	2	yes	complemented
554	#2367	C₂×C₁₃₉	1	1	yes	characteristic, complemented
555	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
556	#2361	C₂×C₁₃₉	1	1	yes	characteristic, complemented
557	#2360	C₂×C₁₃₉	1	1	yes	characteristic, complemented
558	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
559	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
560	#554	—	2	8	no	—
561	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
563	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
564	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
565	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
566	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
567	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
568	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
569	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
570	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
571	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
572	#520	—	2	8	no	—
573	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
577	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
581	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
583	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
585	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
586	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
588	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
589	#400	C₂²×C₁₃₉	1	2	yes	—
590	#400	C₂²×C₁₃₉	1	1	yes	characteristic
591	#399	C₂²×C₁₃₉	1	1	yes	characteristic
592	#398	C₂²×C₁₃₉	1	2	yes	—
593	#398	C₂²×C₁₃₉	1	2	yes	—
594	#398	C₂²×C₁₃₉	1	2	yes	—
595	#398	C₂²×C₁₃₉	1	1	yes	characteristic
596	#397	C₂²×C₁₃₉	1	2	yes	—
597	#397	C₂²×C₁₃₉	1	2	yes	—
598	#397	C₂²×C₁₃₉	1	1	yes	characteristic
599	#397	C₂²×C₁₃₉	1	2	yes	—
600	#397	C₂²×C₁₃₉	1	1	yes	characteristic
601	#397	C₂²×C₁₃₉	1	1	yes	characteristic
602	#396	C₂²×C₁₃₉	1	2	yes	—
603	#396	C₂²×C₁₃₉	1	2	yes	—
604	#395	C₂²×C₁₃₉	1	2	yes	—
605	#394	C₂²×C₁₃₉	1	1	yes	characteristic
606	#394	C₂²×C₁₃₉	1	2	yes	—
607	#394	C₂²×C₁₃₉	1	2	yes	—
608	#394	C₂²×C₁₃₉	1	1	yes	characteristic
609	#394	C₂²×C₁₃₉	1	2	yes	—
610	#394	C₂²×C₁₃₉	1	2	yes	—
611	#393	C₂²×C₁₃₉	1	2	yes	—
612	#392	C₂²×C₁₃₉	1	2	yes	—
613	#391	C₂²×C₁₃₉	1	1	yes	characteristic
614	#391	C₂²×C₁₃₉	1	1	yes	characteristic
615	#391	C₂²×C₁₃₉	1	1	yes	characteristic
616	#391	C₂²×C₁₃₉	1	1	yes	characteristic
617	#391	C₂²×C₁₃₉	1	2	yes	—
618	#390	C₂²×C₁₃₉	1	1	yes	characteristic
619	#390	C₂²×C₁₃₉	1	1	yes	characteristic
620	#389	C₂²×C₁₃₉	1	1	yes	characteristic
621	#389	C₂²×C₁₃₉	1	1	yes	characteristic
622	#389	C₂²×C₁₃₉	1	1	yes	characteristic
623	#389	C₂²×C₁₃₉	1	2	yes	—
624	#389	C₂²×C₁₃₉	1	1	yes	characteristic
625	#389	C₂²×C₁₃₉	1	2	yes	—
626	#389	C₂²×C₁₃₉	1	2	yes	—
627	#388	C₂²×C₁₃₉	1	2	yes	—
628	#388	C₂²×C₁₃₉	1	2	yes	—
629	#388	C₂²×C₁₃₉	1	2	yes	—
630	#388	C₂²×C₁₃₉	1	2	yes	—
631	#387	C₂²×C₁₃₉	1	2	yes	—
632	#387	C₂²×C₁₃₉	1	2	yes	—
633	#387	C₂²×C₁₃₉	1	2	yes	—
634	#387	C₂²×C₁₃₉	1	2	yes	—
635	#387	C₂²×C₁₃₉	1	2	yes	—
636	#387	C₂²×C₁₃₉	1	2	yes	—
637	#386	C₂²×C₁₃₉	1	2	yes	—
638	#386	C₂²×C₁₃₉	1	2	yes	—
639	#386	C₂²×C₁₃₉	1	2	yes	—
640	#385	C₂²×C₁₃₉	1	2	yes	—
641	#385	C₂²×C₁₃₉	1	2	yes	—
642	#385	C₂²×C₁₃₉	1	2	yes	—
643	#385	C₂²×C₁₃₉	1	2	yes	—
644	#385	C₂²×C₁₃₉	1	2	yes	—
645	#385	C₂²×C₁₃₉	1	2	yes	—
646	#385	C₂²×C₁₃₉	1	2	yes	—
647	#381	C₂²×C₁₃₉	1	2	yes	—
648	#380	C₂²×C₁₃₉	1	1	yes	characteristic
649	#380	C₂²×C₁₃₉	1	2	yes	—
650	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
655	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
656	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
657	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
658	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
659	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
660	C₂×#41	—	2	4	no	—
661	C₂×#41	—	2	4	no	—
662	C₂×#41	—	2	4	no	—
663	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
664	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
665	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
666	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
668	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
669	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
671	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
674	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
675	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
676	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
677	C₄⋊Q₈	—	2	4	no	—
678	C₄⋊Q₈	—	2	4	no	—
679	#125	—	2	8	no	—
680	#124	—	2	4	no	—
681	C₂²⋊Q₈	—	2	4	no	—
682	C₂²⋊Q₈	—	2	8	no	—
683	C₂²⋊Q₈	—	2	4	no	—
684	C₂²⋊Q₈	—	2	8	no	—
685	C₂²⋊Q₈	—	2	4	no	—
686	C₂²⋊Q₈	—	4	4	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×D₄	—	2	8	no	—
692	C₄×D₄	—	2	8	no	—
693	C₄×D₄	—	2	8	no	—
694	C₄×D₄	—	2	4	no	—
695	C₄×D₄	—	2	4	no	—
696	C₄×D₄	—	2	4	no	—
697	C₄×D₄	—	4	4	no	—
698	#117	—	2	4	no	—
699	#117	—	2	8	no	—
700	#117	—	4	4	no	—
701	C₂×C₄⋊C₄	—	2	8	no	—
702	C₂×C₄⋊C₄	—	2	4	no	—
703	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
704	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	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	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
753	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
754	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
758	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
759	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
760	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
764	#95	C₂³×C₁₃₉	1	1	yes	characteristic
765	#95	C₂³×C₁₃₉	1	1	yes	characteristic
766	#95	C₂³×C₁₃₉	1	1	yes	characteristic
767	#95	C₂³×C₁₃₉	1	1	yes	characteristic
768	#95	C₂³×C₁₃₉	1	1	yes	characteristic
769	#95	C₂³×C₁₃₉	1	2	yes	—
770	#95	C₂³×C₁₃₉	1	2	yes	—
771	#95	C₂³×C₁₃₉	1	1	yes	characteristic
772	#95	C₂³×C₁₃₉	1	2	yes	—
773	#95	C₂³×C₁₃₉	1	1	yes	characteristic
774	#95	C₂³×C₁₃₉	1	2	yes	—
775	#95	C₂³×C₁₃₉	1	2	yes	—
776	#95	C₂³×C₁₃₉	1	1	yes	characteristic
777	#95	C₂³×C₁₃₉	1	2	yes	—
778	#95	C₂³×C₁₃₉	1	1	yes	characteristic
779	#95	C₂³×C₁₃₉	1	2	yes	—
780	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
788	#95	C₂³×C₁₃₉	1	2	yes	—
789	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
791	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
792	#41	—	2	32	no	—
793	C₂×Q₈	—	2	2	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	—	2	2	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	#41×C₁₃₉	1	4	yes	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	4	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
834	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
835	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	4	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	4	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	4	1	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
880	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
881	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	4	1	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	1	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	4	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	4	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	4	no	—
914	C₄²	—	4	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	1	no	—
933	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
934	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
935	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
936	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
937	Q₈	—	2	8	no	—
938	Q₈	—	4	4	no	—
939	Q₈	—	8	4	no	—
940	D₄	—	2	16	no	—
941	D₄	—	2	8	no	—
942	D₄	—	2	8	no	—
943	D₄	—	4	8	no	—
944	C₂×C₄	—	2	16	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	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	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	8	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	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	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	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	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	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	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	4	8	no	—
998	C₂×C₄	—	4	4	no	—
999	C₂×C₄	—	8	4	no	—
1000	C₂×C₄	—	8	4	no	—
1001	C₂×C₄	—	8	4	no	—
1002	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1003	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1004	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1005	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1006	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1007	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1008	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1009	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1010	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	4	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1033	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1034	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1035	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1036	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1037	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1038	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1039	C₄	—	2	2	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	4	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	#525×C₁₃₉	1	4	yes	—
1059	C₂	—	4	2	no	—
1060	C₂	—	4	4	no	—
1061	C₂	—	4	2	no	—
1062	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1063	C₂	#3486×C₁₃₉	1	1	yes	characteristic
1064	C₂	#3496×C₁₃₉	1	1	yes	characteristic
1065	C₂	#3515×C₁₃₉	1	1	yes	characteristic
1066	C₂	#3516×C₁₃₉	1	1	yes	characteristic
1067	C₂	#3520×C₁₃₉	1	1	yes	characteristic
1068	C₂	#3522×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×#554×C₁₃₉	C₂	semidirect
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2638×C₁₃₉	C₂	semidirect
4. #2625×C₁₃₉	C₂	semidirect
5. #2600×C₁₃₉	C₂	semidirect
6. #2477×C₁₃₉	C₂	semidirect
7. #2475×C₁₃₉	C₂	semidirect
8. #2473×C₁₃₉	C₂	semidirect
9. #2452×C₁₃₉	C₂	semidirect
10. #2451×C₁₃₉	C₂	semidirect
11. #2449×C₁₃₉	C₂	semidirect
12. #2432×C₁₃₉	C₂	semidirect
13. #2429×C₁₃₉	C₂	semidirect
14. #2427×C₁₃₉	C₂	semidirect
15. #2415×C₁₃₉	C₂	semidirect
17. #2395×C₁₃₉	C₂	semidirect
18. #2392×C₁₃₉	C₂	semidirect
19. #2367×C₁₃₉	C₂	semidirect
20. #2365×C₁₃₉	C₂	semidirect
21. #2361×C₁₃₉	C₂	semidirect
22. #2360×C₁₃₉	C₂	semidirect
23. #2344×C₁₃₉	C₂	semidirect
168. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
534. #35724	C₁₃₉	direct (N × H)
535. C₁₃₉	#35724	direct (N × H)
536. C₂×#554	C₂×C₁₃₉	semidirect
537. C₂×#520	C₂×C₁₃₉	semidirect
538. #2638	C₂×C₁₃₉	semidirect
539. #2625	C₂×C₁₃₉	semidirect
540. #2600	C₂×C₁₃₉	semidirect
541. #2477	C₂×C₁₃₉	semidirect
542. #2475	C₂×C₁₃₉	semidirect
543. #2473	C₂×C₁₃₉	semidirect
544. #2452	C₂×C₁₃₉	semidirect
545. #2451	C₂×C₁₃₉	semidirect
546. #2449	C₂×C₁₃₉	semidirect
547. #2432	C₂×C₁₃₉	semidirect
548. #2429	C₂×C₁₃₉	semidirect
549. #2427	C₂×C₁₃₉	semidirect
550. #2415	C₂×C₁₃₉	semidirect
552. #2395	C₂×C₁₃₉	semidirect
553. #2392	C₂×C₁₃₉	semidirect
554. #2367	C₂×C₁₃₉	semidirect
555. #2365	C₂×C₁₃₉	semidirect
556. #2361	C₂×C₁₃₉	semidirect
557. #2360	C₂×C₁₃₉	semidirect
558. #2344	C₂×C₁₃₉	semidirect
703. C₂×C₄⋊C₄	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×#554×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2638×C₁₃₉	2
#2625×C₁₃₉	2
#2600×C₁₃₉	2
#2477×C₁₃₉	2
#2475×C₁₃₉	2
#2473×C₁₃₉	2
#2452×C₁₃₉	2
#2451×C₁₃₉	2
#2449×C₁₃₉	2
#2432×C₁₃₉	2
#2429×C₁₃₉	2
#2427×C₁₃₉	2
#2415×C₁₃₉	2
#2407×C₁₃₉	2
#2395×C₁₃₉	2
#2392×C₁₃₉	2
#2367×C₁₃₉	2
#2365×C₁₃₉	2
#2361×C₁₃₉	2
#2360×C₁₃₉	2
#2344×C₁₃₉	2
#35724	139

Subgroups — C139×#35724 #48030320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35724 #48030320