Subgroups — C₁₃₉×#35840 #48030436

Order 35584.

2726 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2635×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2633×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2617×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2611×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2598×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2543×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2539×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2482×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2479×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2467×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2455×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2443×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2418×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2410×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2358×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#553×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
36	#518×C₁₃₉	—	2	8	no	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
54	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
59	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#399×C₁₃₉	C₂²	1	1	yes	characteristic
62	#399×C₁₃₉	C₂²	1	1	yes	characteristic
63	#399×C₁₃₉	C₂²	1	2	yes	—
64	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
65	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	#399×C₁₃₉	C₂²	1	2	yes	complemented
68	#399×C₁₃₉	C₂²	1	2	yes	complemented
69	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
70	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
71	#398×C₁₃₉	C₂²	1	2	yes	complemented
72	#397×C₁₃₉	C₂²	1	1	yes	characteristic
73	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#397×C₁₃₉	C₂²	1	2	yes	complemented
76	#394×C₁₃₉	C₂²	1	2	yes	—
77	#394×C₁₃₉	C₂²	1	2	yes	—
78	#394×C₁₃₉	C₂²	1	2	yes	—
79	#394×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#394×C₁₃₉	C₂²	1	2	yes	complemented
81	#394×C₁₃₉	C₂²	1	2	yes	complemented
82	#392×C₁₃₉	C₂²	1	1	yes	characteristic
83	#392×C₁₃₉	C₂²	1	2	yes	—
84	#392×C₁₃₉	C₂²	1	2	yes	—
85	#392×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	#392×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
87	#390×C₁₃₉	C₂²	1	2	yes	—
88	#390×C₁₃₉	C₂²	1	2	yes	complemented
89	#389×C₁₃₉	C₂²	1	2	yes	complemented
90	#389×C₁₃₉	C₂²	1	2	yes	complemented
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	2	yes	—
93	#388×C₁₃₉	C₂²	1	2	yes	complemented
94	#388×C₁₃₉	C₂²	1	2	yes	complemented
95	#388×C₁₃₉	C₂²	1	2	yes	complemented
96	#388×C₁₃₉	C₂²	1	2	yes	complemented
97	#388×C₁₃₉	C₂²	1	2	yes	complemented
98	#387×C₁₃₉	C₂²	1	2	yes	complemented
99	#387×C₁₃₉	C₂²	1	2	yes	complemented
100	#386×C₁₃₉	C₂²	1	2	yes	—
101	#386×C₁₃₉	C₂²	1	2	yes	—
102	#386×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#386×C₁₃₉	C₂²	1	2	yes	complemented
105	#386×C₁₃₉	C₂²	1	2	yes	complemented
106	#386×C₁₃₉	C₂²	1	2	yes	complemented
107	#386×C₁₃₉	C₂²	1	2	yes	complemented
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#385×C₁₃₉	C₂²	1	2	yes	complemented
110	#385×C₁₃₉	C₂²	1	2	yes	complemented
111	#385×C₁₃₉	C₂²	1	2	yes	complemented
112	#385×C₁₃₉	C₂²	1	2	yes	complemented
113	#385×C₁₃₉	C₂²	1	2	yes	complemented
114	#383×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
115	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
116	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
117	#380×C₁₃₉	C₂²	1	2	yes	complemented
118	#379×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
123	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	—	2	4	no	—
128	C₂²×D₄×C₁₃₉	—	2	4	no	—
129	C₂²×D₄×C₁₃₉	—	2	4	no	—
130	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	#126×C₁₃₉	—	2	8	no	—
153	#125×C₁₃₉	—	2	4	no	—
154	#123×C₁₃₉	—	2	8	no	—
155	#123×C₁₃₉	—	4	4	no	—
156	#121×C₁₃₉	—	2	8	no	—
157	#121×C₁₃₉	—	2	8	no	—
158	#121×C₁₃₉	—	2	4	no	—
159	#121×C₁₃₉	—	2	4	no	—
160	#120×C₁₃₉	—	2	8	no	—
161	#120×C₁₃₉	—	4	4	no	—
162	C₄×D₄×C₁₃₉	—	2	4	no	—
163	C₄×D₄×C₁₃₉	—	2	4	no	—
164	C₄×D₄×C₁₃₉	—	2	4	no	—
165	C₄×D₄×C₁₃₉	—	2	4	no	—
166	C₄×D₄×C₁₃₉	—	2	4	no	—
167	C₄×D₄×C₁₃₉	—	2	4	no	—
168	C₄×D₄×C₁₃₉	—	2	8	no	—
169	C₄×D₄×C₁₃₉	—	2	4	no	—
170	C₄×D₄×C₁₃₉	—	2	4	no	—
171	C₄×D₄×C₁₃₉	—	4	4	no	—
172	C₄×D₄×C₁₃₉	—	4	4	no	—
173	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
174	#117×C₁₃₉	—	2	4	no	—
175	#117×C₁₃₉	—	2	4	no	—
176	#117×C₁₃₉	—	2	4	no	—
177	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
178	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
198	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
200	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
201	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
239	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
241	C₂×C₄²×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	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	1	yes	characteristic
248	#95×C₁₃₉	C₂³	1	1	yes	characteristic
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	1	yes	characteristic
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	2	yes	—
255	#95×C₁₃₉	C₂³	1	2	yes	—
256	#95×C₁₃₉	C₂³	1	2	yes	—
257	#95×C₁₃₉	C₂³	1	2	yes	—
258	#95×C₁₃₉	C₂³	1	2	yes	—
259	C₂⁴×C₁₃₉	—	2	2	no	—
260	C₂⁴×C₁₃₉	—	2	2	no	—
261	C₂⁴×C₁₃₉	—	2	2	no	—
262	C₂⁴×C₁₃₉	—	2	2	no	—
263	C₂⁴×C₁₃₉	—	2	2	no	—
264	C₂⁴×C₁₃₉	—	4	2	no	—
265	C₂⁴×C₁₃₉	—	4	2	no	—
266	C₂⁴×C₁₃₉	—	4	2	no	—
267	C₂⁴×C₁₃₉	—	4	2	no	—
268	C₂⁴×C₁₃₉	#41	1	4	yes	—
269	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
270	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂×D₄×C₁₃₉	—	2	32	no	—
276	C₂×D₄×C₁₃₉	—	2	2	no	—
277	C₂×D₄×C₁₃₉	—	2	2	no	—
278	C₂×D₄×C₁₃₉	—	2	2	no	—
279	C₂×D₄×C₁₃₉	—	2	2	no	—
280	C₂×D₄×C₁₃₉	—	2	2	no	—
281	C₂×D₄×C₁₃₉	—	2	2	no	—
282	C₂×D₄×C₁₃₉	—	2	2	no	—
283	C₂×D₄×C₁₃₉	—	2	2	no	—
284	C₂×D₄×C₁₃₉	—	2	4	no	—
285	C₂×D₄×C₁₃₉	—	2	4	no	—
286	C₂×D₄×C₁₃₉	—	2	4	no	—
287	C₂×D₄×C₁₃₉	—	2	4	no	—
288	C₂×D₄×C₁₃₉	—	2	4	no	—
289	C₂×D₄×C₁₃₉	—	2	4	no	—
290	C₂×D₄×C₁₃₉	—	2	4	no	—
291	C₂×D₄×C₁₃₉	—	2	2	no	—
292	C₂×D₄×C₁₃₉	—	2	2	no	—
293	C₂×D₄×C₁₃₉	—	2	2	no	—
294	C₂×D₄×C₁₃₉	—	2	4	no	—
295	C₂×D₄×C₁₃₉	—	4	2	no	—
296	C₂×D₄×C₁₃₉	—	4	2	no	—
297	C₂×D₄×C₁₃₉	—	4	2	no	—
298	C₂×D₄×C₁₃₉	—	4	2	no	—
299	C₂×D₄×C₁₃₉	—	4	2	no	—
300	C₂×D₄×C₁₃₉	—	4	2	no	—
301	C₂×D₄×C₁₃₉	—	4	2	no	—
302	C₂×D₄×C₁₃₉	—	4	2	no	—
303	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
304	C₂×D₄×C₁₃₉	#41	1	4	yes	—
305	C₂²×C₄×C₁₃₉	—	2	2	no	—
306	C₂²×C₄×C₁₃₉	—	2	2	no	—
307	C₂²×C₄×C₁₃₉	—	2	2	no	—
308	C₂²×C₄×C₁₃₉	—	2	4	no	—
309	C₂²×C₄×C₁₃₉	—	2	2	no	—
310	C₂²×C₄×C₁₃₉	—	2	2	no	—
311	C₂²×C₄×C₁₃₉	—	2	4	no	—
312	C₂²×C₄×C₁₃₉	—	2	4	no	—
313	C₂²×C₄×C₁₃₉	—	2	2	no	—
314	C₂²×C₄×C₁₃₉	—	2	2	no	—
315	C₂²×C₄×C₁₃₉	—	2	2	no	—
316	C₂²×C₄×C₁₃₉	—	2	2	no	—
317	C₂²×C₄×C₁₃₉	—	2	4	no	—
318	C₂²×C₄×C₁₃₉	—	4	2	no	—
319	C₂²×C₄×C₁₃₉	—	4	2	no	—
320	C₂²×C₄×C₁₃₉	—	4	2	no	—
321	C₂²×C₄×C₁₃₉	—	4	2	no	—
322	C₂²×C₄×C₁₃₉	—	4	2	no	—
323	C₂²×C₄×C₁₃₉	—	4	2	no	—
324	C₂²×C₄×C₁₃₉	—	4	2	no	—
325	C₂²×C₄×C₁₃₉	—	4	2	no	—
326	C₂²×C₄×C₁₃₉	—	4	2	no	—
327	C₂²×C₄×C₁₃₉	—	4	2	no	—
328	C₂²×C₄×C₁₃₉	—	4	2	no	—
329	C₂²×C₄×C₁₃₉	—	4	2	no	—
330	C₂²×C₄×C₁₃₉	—	4	2	no	—
331	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
332	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
333	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₁₃₉	—	2	2	no	—
351	C₄⋊C₄×C₁₃₉	—	2	2	no	—
352	C₄⋊C₄×C₁₃₉	—	2	4	no	—
353	C₄⋊C₄×C₁₃₉	—	2	2	no	—
354	C₄⋊C₄×C₁₃₉	—	2	2	no	—
355	C₄⋊C₄×C₁₃₉	—	2	2	no	—
356	C₄⋊C₄×C₁₃₉	—	2	2	no	—
357	C₄⋊C₄×C₁₃₉	—	2	4	no	—
358	C₄⋊C₄×C₁₃₉	—	2	4	no	—
359	C₄⋊C₄×C₁₃₉	—	2	4	no	—
360	C₄⋊C₄×C₁₃₉	—	2	4	no	—
361	C₄⋊C₄×C₁₃₉	—	2	4	no	—
362	C₄⋊C₄×C₁₃₉	—	4	2	no	—
363	C₄⋊C₄×C₁₃₉	—	4	2	no	—
364	C₄⋊C₄×C₁₃₉	—	4	2	no	—
365	C₄⋊C₄×C₁₃₉	—	4	2	no	—
366	C₄⋊C₄×C₁₃₉	—	4	2	no	—
367	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
368	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
370	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
372	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
373	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
374	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
375	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
378	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
379	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
383	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
384	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
385	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
386	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
387	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
388	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
389	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
390	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
391	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
392	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
393	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
394	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
395	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
396	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
397	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
398	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
399	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
400	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
401	C₄²×C₁₃₉	—	2	2	no	—
402	C₄²×C₁₃₉	—	2	2	no	—
403	C₄²×C₁₃₉	—	2	2	no	—
404	C₄²×C₁₃₉	—	2	4	no	—
405	C₄²×C₁₃₉	—	2	4	no	—
406	C₄²×C₁₃₉	—	4	2	no	—
407	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
408	C₂³×C₁₃₉	—	2	2	no	—
409	C₂³×C₁₃₉	—	2	2	no	—
410	C₂³×C₁₃₉	—	2	8	no	—
411	C₂³×C₁₃₉	—	2	1	no	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	2	1	no	—
414	C₂³×C₁₃₉	—	2	1	no	—
415	C₂³×C₁₃₉	—	2	1	no	—
416	C₂³×C₁₃₉	—	2	1	no	—
417	C₂³×C₁₃₉	—	2	1	no	—
418	C₂³×C₁₃₉	—	2	1	no	—
419	C₂³×C₁₃₉	—	2	2	no	—
420	C₂³×C₁₃₉	—	2	2	no	—
421	C₂³×C₁₃₉	—	2	2	no	—
422	C₂³×C₁₃₉	—	2	2	no	—
423	C₂³×C₁₃₉	—	2	2	no	—
424	C₂³×C₁₃₉	—	2	2	no	—
425	C₂³×C₁₃₉	—	2	2	no	—
426	C₂³×C₁₃₉	—	2	2	no	—
427	C₂³×C₁₃₉	—	2	8	no	—
428	C₂³×C₁₃₉	—	2	2	no	—
429	C₂³×C₁₃₉	—	2	2	no	—
430	C₂³×C₁₃₉	—	2	2	no	—
431	C₂³×C₁₃₉	—	2	2	no	—
432	C₂³×C₁₃₉	—	2	2	no	—
433	C₂³×C₁₃₉	—	2	2	no	—
434	C₂³×C₁₃₉	—	2	2	no	—
435	C₂³×C₁₃₉	—	4	8	no	—
436	C₂³×C₁₃₉	—	8	2	no	—
437	C₂³×C₁₃₉	—	8	2	no	—
438	C₂³×C₁₃₉	—	8	4	no	—
439	C₂³×C₁₃₉	—	8	2	no	—
440	C₂³×C₁₃₉	—	8	2	no	—
441	C₂³×C₁₃₉	—	8	4	no	—
442	C₂³×C₁₃₉	—	8	4	no	—
443	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
444	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
445	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
446	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
447	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
448	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
449	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
450	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
451	D₄×C₁₃₉	—	2	8	no	—
452	D₄×C₁₃₉	—	2	8	no	—
453	D₄×C₁₃₉	—	2	8	no	—
454	D₄×C₁₃₉	—	2	8	no	—
455	D₄×C₁₃₉	—	4	8	no	—
456	D₄×C₁₃₉	—	4	4	no	—
457	D₄×C₁₃₉	—	4	8	no	—
458	D₄×C₁₃₉	—	4	8	no	—
459	D₄×C₁₃₉	—	8	4	no	—
460	D₄×C₁₃₉	—	8	4	no	—
461	C₂×C₄×C₁₃₉	—	2	8	no	—
462	C₂×C₄×C₁₃₉	—	2	1	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	1	no	—
465	C₂×C₄×C₁₃₉	—	2	1	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	2	2	no	—
468	C₂×C₄×C₁₃₉	—	2	2	no	—
469	C₂×C₄×C₁₃₉	—	2	2	no	—
470	C₂×C₄×C₁₃₉	—	2	2	no	—
471	C₂×C₄×C₁₃₉	—	2	2	no	—
472	C₂×C₄×C₁₃₉	—	2	1	no	—
473	C₂×C₄×C₁₃₉	—	2	1	no	—
474	C₂×C₄×C₁₃₉	—	2	1	no	—
475	C₂×C₄×C₁₃₉	—	2	1	no	—
476	C₂×C₄×C₁₃₉	—	2	2	no	—
477	C₂×C₄×C₁₃₉	—	2	2	no	—
478	C₂×C₄×C₁₃₉	—	2	2	no	—
479	C₂×C₄×C₁₃₉	—	2	2	no	—
480	C₂×C₄×C₁₃₉	—	2	2	no	—
481	C₂×C₄×C₁₃₉	—	2	2	no	—
482	C₂×C₄×C₁₃₉	—	2	2	no	—
483	C₂×C₄×C₁₃₉	—	2	2	no	—
484	C₂×C₄×C₁₃₉	—	2	2	no	—
485	C₂×C₄×C₁₃₉	—	2	2	no	—
486	C₂×C₄×C₁₃₉	—	2	2	no	—
487	C₂×C₄×C₁₃₉	—	2	2	no	—
488	C₂×C₄×C₁₃₉	—	2	2	no	—
489	C₂×C₄×C₁₃₉	—	2	2	no	—
490	C₂×C₄×C₁₃₉	—	2	2	no	—
491	C₂×C₄×C₁₃₉	—	2	2	no	—
492	C₂×C₄×C₁₃₉	—	2	2	no	—
493	C₂×C₄×C₁₃₉	—	2	2	no	—
494	C₂×C₄×C₁₃₉	—	2	2	no	—
495	C₂×C₄×C₁₃₉	—	2	2	no	—
496	C₂×C₄×C₁₃₉	—	2	2	no	—
497	C₂×C₄×C₁₃₉	—	2	2	no	—
498	C₂×C₄×C₁₃₉	—	4	4	no	—
499	C₂×C₄×C₁₃₉	—	4	4	no	—
500	C₂×C₄×C₁₃₉	—	4	8	no	—
501	C₂×C₄×C₁₃₉	—	8	2	no	—
502	C₂×C₄×C₁₃₉	—	8	2	no	—
503	C₂×C₄×C₁₃₉	—	8	2	no	—
504	C₂×C₄×C₁₃₉	—	8	2	no	—
505	C₂×C₄×C₁₃₉	—	8	4	no	—
506	C₂×C₄×C₁₃₉	—	8	2	no	—
507	C₂×C₄×C₁₃₉	—	8	2	no	—
508	C₂×C₄×C₁₃₉	—	8	4	no	—
509	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
515	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
516	C₂²×C₁₃₉	—	2	2	no	—
517	C₂²×C₁₃₉	—	2	2	no	—
518	C₂²×C₁₃₉	—	2	4	no	—
519	C₂²×C₁₃₉	—	2	4	no	—
520	C₂²×C₁₃₉	—	2	2	no	—
521	C₂²×C₁₃₉	—	2	2	no	—
522	C₂²×C₁₃₉	—	2	2	no	—
523	C₂²×C₁₃₉	—	2	2	no	—
524	C₂²×C₁₃₉	—	2	2	no	—
525	C₂²×C₁₃₉	—	2	2	no	—
526	C₂²×C₁₃₉	—	2	4	no	—
527	C₂²×C₁₃₉	—	2	4	no	—
528	C₂²×C₁₃₉	—	2	4	no	—
529	C₂²×C₁₃₉	—	4	1	no	—
530	C₂²×C₁₃₉	—	4	1	no	—
531	C₂²×C₁₃₉	—	4	1	no	—
532	C₂²×C₁₃₉	—	4	1	no	—
533	C₂²×C₁₃₉	—	4	1	no	—
534	C₂²×C₁₃₉	—	4	1	no	—
535	C₂²×C₁₃₉	—	4	2	no	—
536	C₂²×C₁₃₉	—	4	2	no	—
537	C₂²×C₁₃₉	—	4	2	no	—
538	C₂²×C₁₃₉	—	4	2	no	—
539	C₂²×C₁₃₉	—	4	2	no	—
540	C₂²×C₁₃₉	—	4	2	no	—
541	C₂²×C₁₃₉	—	4	2	no	—
542	C₂²×C₁₃₉	—	4	2	no	—
543	C₂²×C₁₃₉	—	4	2	no	—
544	C₂²×C₁₃₉	—	4	2	no	—
545	C₂²×C₁₃₉	—	4	2	no	—
546	C₂²×C₁₃₉	—	4	2	no	—
547	C₂²×C₁₃₉	—	8	8	no	—
548	C₂²×C₁₃₉	—	8	8	no	—
549	C₂²×C₁₃₉	#525	1	4	yes	—
550	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
551	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
552	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
553	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
554	C₂²×C₁₃₉	#585	1	2	yes	—
555	C₄×C₁₃₉	—	2	2	no	—
556	C₄×C₁₃₉	—	2	2	no	—
557	C₄×C₁₃₉	—	2	2	no	—
558	C₄×C₁₃₉	—	2	2	no	—
559	C₄×C₁₃₉	—	2	2	no	—
560	C₄×C₁₃₉	—	2	2	no	—
561	C₄×C₁₃₉	—	2	4	no	—
562	C₄×C₁₃₉	—	4	2	no	—
563	C₄×C₁₃₉	—	4	1	no	—
564	C₄×C₁₃₉	—	4	1	no	—
565	C₄×C₁₃₉	—	4	1	no	—
566	C₄×C₁₃₉	—	4	1	no	—
567	C₄×C₁₃₉	—	4	2	no	—
568	C₄×C₁₃₉	—	4	2	no	—
569	C₄×C₁₃₉	—	4	2	no	—
570	C₄×C₁₃₉	—	4	2	no	—
571	C₄×C₁₃₉	—	4	2	no	—
572	C₂×C₁₃₉	—	2	4	no	—
573	C₂×C₁₃₉	—	4	2	no	—
574	C₂×C₁₃₉	—	4	2	no	—
575	C₂×C₁₃₉	—	4	2	no	—
576	C₂×C₁₃₉	—	4	2	no	—
577	C₂×C₁₃₉	—	8	2	no	—
578	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
579	C₂×C₁₃₉	#3485	1	1	yes	characteristic
580	C₂×C₁₃₉	#3498	1	1	yes	characteristic
581	C₂×C₁₃₉	#3505	1	2	yes	—
582	C₂×C₁₃₉	#3513	1	2	yes	—
583	#35840	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
584	C₁₃₉	#35840	1	1	yes	characteristic, direct product factor, Sylow
585	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
586	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
587	#2635	C₂×C₁₃₉	1	1	yes	characteristic, complemented
588	#2633	C₂×C₁₃₉	1	1	yes	characteristic, complemented
589	#2617	C₂×C₁₃₉	1	1	yes	characteristic, complemented
590	#2611	C₂×C₁₃₉	1	1	yes	characteristic, complemented
591	#2598	C₂×C₁₃₉	1	1	yes	characteristic, complemented
592	#2543	C₂×C₁₃₉	1	1	yes	characteristic, complemented
593	#2539	C₂×C₁₃₉	1	1	yes	characteristic, complemented
594	#2487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
595	#2482	C₂×C₁₃₉	1	1	yes	characteristic, complemented
596	#2479	C₂×C₁₃₉	1	2	yes	complemented
597	#2467	C₂×C₁₃₉	1	2	yes	complemented
598	#2455	C₂×C₁₃₉	1	2	yes	complemented
599	#2443	C₂×C₁₃₉	1	2	yes	complemented
600	#2418	C₂×C₁₃₉	1	2	yes	complemented
601	#2410	C₂×C₁₃₉	1	2	yes	complemented
602	#2397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
603	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
604	C₂×#399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
605	#2361	C₂×C₁₃₉	1	2	yes	complemented
606	#2358	C₂×C₁₃₉	1	2	yes	complemented
607	#2353	C₂×C₁₃₉	1	1	yes	characteristic, complemented
608	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
609	#553	—	2	8	no	—
610	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
611	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
612	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
613	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
614	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
615	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
616	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
617	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
618	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
619	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
620	#518	—	2	8	no	—
621	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
625	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
628	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
629	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
630	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
631	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
632	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
633	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
634	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
635	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
636	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
637	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
638	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
640	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
641	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
642	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
643	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
644	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
645	#399	C₂²×C₁₃₉	1	1	yes	characteristic
646	#399	C₂²×C₁₃₉	1	1	yes	characteristic
647	#399	C₂²×C₁₃₉	1	2	yes	—
648	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
649	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
650	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
651	#399	C₂²×C₁₃₉	1	2	yes	complemented
652	#399	C₂²×C₁₃₉	1	2	yes	complemented
653	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
654	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
655	#398	C₂²×C₁₃₉	1	2	yes	complemented
656	#397	C₂²×C₁₃₉	1	1	yes	characteristic
657	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
658	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
659	#397	C₂²×C₁₃₉	1	2	yes	complemented
660	#394	C₂²×C₁₃₉	1	2	yes	—
661	#394	C₂²×C₁₃₉	1	2	yes	—
662	#394	C₂²×C₁₃₉	1	2	yes	—
663	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
664	#394	C₂²×C₁₃₉	1	2	yes	complemented
665	#394	C₂²×C₁₃₉	1	2	yes	complemented
666	#392	C₂²×C₁₃₉	1	1	yes	characteristic
667	#392	C₂²×C₁₃₉	1	2	yes	—
668	#392	C₂²×C₁₃₉	1	2	yes	—
669	#392	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
670	#392	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
671	#390	C₂²×C₁₃₉	1	2	yes	—
672	#390	C₂²×C₁₃₉	1	2	yes	complemented
673	#389	C₂²×C₁₃₉	1	2	yes	complemented
674	#389	C₂²×C₁₃₉	1	2	yes	complemented
675	#388	C₂²×C₁₃₉	1	2	yes	—
676	#388	C₂²×C₁₃₉	1	2	yes	—
677	#388	C₂²×C₁₃₉	1	2	yes	complemented
678	#388	C₂²×C₁₃₉	1	2	yes	complemented
679	#388	C₂²×C₁₃₉	1	2	yes	complemented
680	#388	C₂²×C₁₃₉	1	2	yes	complemented
681	#388	C₂²×C₁₃₉	1	2	yes	complemented
682	#387	C₂²×C₁₃₉	1	2	yes	complemented
683	#387	C₂²×C₁₃₉	1	2	yes	complemented
684	#386	C₂²×C₁₃₉	1	2	yes	—
685	#386	C₂²×C₁₃₉	1	2	yes	—
686	#386	C₂²×C₁₃₉	1	2	yes	—
687	#386	C₂²×C₁₃₉	1	2	yes	—
688	#386	C₂²×C₁₃₉	1	2	yes	complemented
689	#386	C₂²×C₁₃₉	1	2	yes	complemented
690	#386	C₂²×C₁₃₉	1	2	yes	complemented
691	#386	C₂²×C₁₃₉	1	2	yes	complemented
692	#385	C₂²×C₁₃₉	1	2	yes	—
693	#385	C₂²×C₁₃₉	1	2	yes	complemented
694	#385	C₂²×C₁₃₉	1	2	yes	complemented
695	#385	C₂²×C₁₃₉	1	2	yes	complemented
696	#385	C₂²×C₁₃₉	1	2	yes	complemented
697	#385	C₂²×C₁₃₉	1	2	yes	complemented
698	#383	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
699	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
700	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
701	#380	C₂²×C₁₃₉	1	2	yes	complemented
702	#379	C₂²×C₁₃₉	1	2	yes	—
703	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
704	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
705	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
706	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
707	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
708	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
709	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₂²×D₄	—	2	4	no	—
712	C₂²×D₄	—	2	4	no	—
713	C₂²×D₄	—	2	4	no	—
714	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
715	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
718	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
719	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
720	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
728	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
729	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
731	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
732	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
733	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
734	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	#126	—	2	8	no	—
737	#125	—	2	4	no	—
738	#123	—	2	8	no	—
739	#123	—	4	4	no	—
740	#121	—	2	8	no	—
741	#121	—	2	8	no	—
742	#121	—	2	4	no	—
743	#121	—	2	4	no	—
744	#120	—	2	8	no	—
745	#120	—	4	4	no	—
746	C₄×D₄	—	2	4	no	—
747	C₄×D₄	—	2	4	no	—
748	C₄×D₄	—	2	4	no	—
749	C₄×D₄	—	2	4	no	—
750	C₄×D₄	—	2	4	no	—
751	C₄×D₄	—	2	4	no	—
752	C₄×D₄	—	2	8	no	—
753	C₄×D₄	—	2	4	no	—
754	C₄×D₄	—	2	4	no	—
755	C₄×D₄	—	4	4	no	—
756	C₄×D₄	—	4	4	no	—
757	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
758	#117	—	2	4	no	—
759	#117	—	2	4	no	—
760	#117	—	2	4	no	—
761	C₂×C₄⋊C₄	—	2	4	no	—
762	C₂×C₄⋊C₄	—	4	4	no	—
763	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
766	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
776	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	—	2	4	no	—
782	C₂×C₂²⋊C₄	—	2	4	no	—
783	C₂×C₂²⋊C₄	—	2	4	no	—
784	C₂×C₂²⋊C₄	—	2	4	no	—
785	C₂×C₂²⋊C₄	—	4	4	no	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
790	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
792	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
796	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
821	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
823	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
824	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
825	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
826	#95	C₂³×C₁₃₉	1	1	yes	characteristic
827	#95	C₂³×C₁₃₉	1	1	yes	characteristic
828	#95	C₂³×C₁₃₉	1	2	yes	—
829	#95	C₂³×C₁₃₉	1	1	yes	characteristic
830	#95	C₂³×C₁₃₉	1	2	yes	—
831	#95	C₂³×C₁₃₉	1	1	yes	characteristic
832	#95	C₂³×C₁₃₉	1	2	yes	—
833	#95	C₂³×C₁₃₉	1	2	yes	—
834	#95	C₂³×C₁₃₉	1	2	yes	—
835	#95	C₂³×C₁₃₉	1	2	yes	—
836	#95	C₂³×C₁₃₉	1	2	yes	—
837	#95	C₂³×C₁₃₉	1	2	yes	—
838	#95	C₂³×C₁₃₉	1	2	yes	—
839	#95	C₂³×C₁₃₉	1	2	yes	—
840	#95	C₂³×C₁₃₉	1	2	yes	—
841	#95	C₂³×C₁₃₉	1	2	yes	—
842	#95	C₂³×C₁₃₉	1	2	yes	—
843	C₂⁴	—	2	2	no	—
844	C₂⁴	—	2	2	no	—
845	C₂⁴	—	2	2	no	—
846	C₂⁴	—	2	2	no	—
847	C₂⁴	—	2	2	no	—
848	C₂⁴	—	4	2	no	—
849	C₂⁴	—	4	2	no	—
850	C₂⁴	—	4	2	no	—
851	C₂⁴	—	4	2	no	—
852	C₂⁴	#41×C₁₃₉	1	4	yes	—
853	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
854	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
855	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
856	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
857	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
858	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
859	C₂×D₄	—	2	32	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	4	no	—
872	C₂×D₄	—	2	4	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	4	no	—
879	C₂×D₄	—	4	2	no	—
880	C₂×D₄	—	4	2	no	—
881	C₂×D₄	—	4	2	no	—
882	C₂×D₄	—	4	2	no	—
883	C₂×D₄	—	4	2	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	2	no	—
887	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
888	C₂×D₄	#41×C₁₃₉	1	4	yes	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	4	no	—
902	C₂²×C₄	—	4	2	no	—
903	C₂²×C₄	—	4	2	no	—
904	C₂²×C₄	—	4	2	no	—
905	C₂²×C₄	—	4	2	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	—	4	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
916	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
917	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
927	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	4	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	4	no	—
942	C₄⋊C₄	—	2	4	no	—
943	C₄⋊C₄	—	2	4	no	—
944	C₄⋊C₄	—	2	4	no	—
945	C₄⋊C₄	—	2	4	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	2	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	4	no	—
968	C₂²⋊C₄	—	2	4	no	—
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
984	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	4	no	—
989	C₄²	—	2	4	no	—
990	C₄²	—	4	2	no	—
991	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	8	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	8	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	4	8	no	—
1020	C₂³	—	8	2	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	—	8	4	no	—
1023	C₂³	—	8	2	no	—
1024	C₂³	—	8	2	no	—
1025	C₂³	—	8	4	no	—
1026	C₂³	—	8	4	no	—
1027	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1028	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1029	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1030	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1031	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1032	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1033	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1034	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1035	D₄	—	2	8	no	—
1036	D₄	—	2	8	no	—
1037	D₄	—	2	8	no	—
1038	D₄	—	2	8	no	—
1039	D₄	—	4	8	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	8	no	—
1042	D₄	—	4	8	no	—
1043	D₄	—	8	4	no	—
1044	D₄	—	8	4	no	—
1045	C₂×C₄	—	2	8	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	4	4	no	—
1083	C₂×C₄	—	4	4	no	—
1084	C₂×C₄	—	4	8	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	4	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	4	no	—
1093	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1094	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1098	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1099	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	4	no	—
1103	C₂²	—	2	4	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	4	no	—
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	4	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	8	8	no	—
1132	C₂²	—	8	8	no	—
1133	C₂²	#525×C₁₃₉	1	4	yes	—
1134	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1135	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1136	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1137	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1138	C₂²	#585×C₁₃₉	1	2	yes	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	2	no	—
1145	C₄	—	2	4	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	2	no	—
1156	C₂	—	2	4	no	—
1157	C₂	—	4	2	no	—
1158	C₂	—	4	2	no	—
1159	C₂	—	4	2	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1163	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1164	C₂	#3498×C₁₃₉	1	1	yes	characteristic
1165	C₂	#3505×C₁₃₉	1	2	yes	—
1166	C₂	#3513×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#553×C₁₃₉	C₂	semidirect
2. C₂×#518×C₁₃₉	C₂	semidirect
3. #2635×C₁₃₉	C₂	semidirect
4. #2633×C₁₃₉	C₂	semidirect
5. #2617×C₁₃₉	C₂	semidirect
6. #2611×C₁₃₉	C₂	semidirect
7. #2598×C₁₃₉	C₂	semidirect
8. #2543×C₁₃₉	C₂	semidirect
9. #2539×C₁₃₉	C₂	semidirect
10. #2487×C₁₃₉	C₂	semidirect
11. #2482×C₁₃₉	C₂	semidirect
12. #2479×C₁₃₉	C₂	semidirect
13. #2467×C₁₃₉	C₂	semidirect
14. #2455×C₁₃₉	C₂	semidirect
15. #2443×C₁₃₉	C₂	semidirect
16. #2418×C₁₃₉	C₂	semidirect
17. #2410×C₁₃₉	C₂	semidirect
18. #2397×C₁₃₉	C₂	semidirect
19. #2395×C₁₃₉	C₂	semidirect
20. C₂×#399×C₁₃₉	C₂	semidirect
21. #2361×C₁₃₉	C₂	semidirect
22. #2358×C₁₃₉	C₂	semidirect
23. #2353×C₁₃₉	C₂	semidirect
26. C₂×#126×C₁₃₉	C₂²	semidirect
27. C₂×#125×C₁₃₉	C₂²	semidirect
28. C₂×#123×C₁₃₉	C₂²	semidirect
29. C₂×#123×C₁₃₉	C₂²	semidirect
32. C₂×#121×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
47. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
51. C₂×#117×C₁₃₉	C₂²	semidirect
52. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
53. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
59. #400×C₁₃₉	C₂²	semidirect
60. #400×C₁₃₉	C₂²	semidirect
64. #399×C₁₃₉	C₂²	semidirect
65. #399×C₁₃₉	C₂²	semidirect
66. #399×C₁₃₉	C₂²	semidirect
67. #399×C₁₃₉	C₂²	semidirect
68. #399×C₁₃₉	C₂²	semidirect
69. #399×C₁₃₉	C₂²	semidirect
70. #398×C₁₃₉	C₂²	semidirect
71. #398×C₁₃₉	C₂²	semidirect
73. #397×C₁₃₉	C₂²	semidirect
74. #397×C₁₃₉	C₂²	semidirect
75. #397×C₁₃₉	C₂²	semidirect
79. #394×C₁₃₉	C₂²	semidirect
80. #394×C₁₃₉	C₂²	semidirect
81. #394×C₁₃₉	C₂²	semidirect
85. #392×C₁₃₉	C₂²	semidirect
86. #392×C₁₃₉	C₂²	semidirect
88. #390×C₁₃₉	C₂²	semidirect
89. #389×C₁₃₉	C₂²	semidirect
90. #389×C₁₃₉	C₂²	semidirect
93. #388×C₁₃₉	C₂²	semidirect
94. #388×C₁₃₉	C₂²	semidirect
95. #388×C₁₃₉	C₂²	semidirect
96. #388×C₁₃₉	C₂²	semidirect
97. #388×C₁₃₉	C₂²	semidirect
98. #387×C₁₃₉	C₂²	semidirect
99. #387×C₁₃₉	C₂²	semidirect
104. #386×C₁₃₉	C₂²	semidirect
105. #386×C₁₃₉	C₂²	semidirect
106. #386×C₁₃₉	C₂²	semidirect
107. #386×C₁₃₉	C₂²	semidirect
109. #385×C₁₃₉	C₂²	semidirect
110. #385×C₁₃₉	C₂²	semidirect
111. #385×C₁₃₉	C₂²	semidirect
112. #385×C₁₃₉	C₂²	semidirect
113. #385×C₁₃₉	C₂²	semidirect
114. #383×C₁₃₉	C₂²	semidirect
115. #381×C₁₃₉	C₂²	semidirect
116. #380×C₁₃₉	C₂²	semidirect
117. #380×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. #376×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
173. C₄×D₄×C₁₃₉	D₄	semidirect
583. #35840	C₁₃₉	direct (N × H)
584. C₁₃₉	#35840	direct (N × H)
585. C₂×#553	C₂×C₁₃₉	semidirect
586. C₂×#518	C₂×C₁₃₉	semidirect
587. #2635	C₂×C₁₃₉	semidirect
588. #2633	C₂×C₁₃₉	semidirect
589. #2617	C₂×C₁₃₉	semidirect
590. #2611	C₂×C₁₃₉	semidirect
591. #2598	C₂×C₁₃₉	semidirect
592. #2543	C₂×C₁₃₉	semidirect
593. #2539	C₂×C₁₃₉	semidirect
594. #2487	C₂×C₁₃₉	semidirect
595. #2482	C₂×C₁₃₉	semidirect
596. #2479	C₂×C₁₃₉	semidirect
597. #2467	C₂×C₁₃₉	semidirect
598. #2455	C₂×C₁₃₉	semidirect
599. #2443	C₂×C₁₃₉	semidirect
600. #2418	C₂×C₁₃₉	semidirect
601. #2410	C₂×C₁₃₉	semidirect
602. #2397	C₂×C₁₃₉	semidirect
603. #2395	C₂×C₁₃₉	semidirect
604. C₂×#399	C₂×C₁₃₉	semidirect
605. #2361	C₂×C₁₃₉	semidirect
606. #2358	C₂×C₁₃₉	semidirect
607. #2353	C₂×C₁₃₉	semidirect
610. C₂×#126	C₂²×C₁₃₉	semidirect
611. C₂×#125	C₂²×C₁₃₉	semidirect
612. C₂×#123	C₂²×C₁₃₉	semidirect
613. C₂×#123	C₂²×C₁₃₉	semidirect
616. C₂×#121	C₂²×C₁₃₉	semidirect
617. C₂×#121	C₂²×C₁₃₉	semidirect
629. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
630. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
631. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
632. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
635. C₂×#117	C₂²×C₁₃₉	semidirect
636. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
637. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
643. #400	C₂²×C₁₃₉	semidirect
644. #400	C₂²×C₁₃₉	semidirect
648. #399	C₂²×C₁₃₉	semidirect
649. #399	C₂²×C₁₃₉	semidirect
650. #399	C₂²×C₁₃₉	semidirect
651. #399	C₂²×C₁₃₉	semidirect
652. #399	C₂²×C₁₃₉	semidirect
653. #399	C₂²×C₁₃₉	semidirect
654. #398	C₂²×C₁₃₉	semidirect
655. #398	C₂²×C₁₃₉	semidirect
657. #397	C₂²×C₁₃₉	semidirect
658. #397	C₂²×C₁₃₉	semidirect
659. #397	C₂²×C₁₃₉	semidirect
663. #394	C₂²×C₁₃₉	semidirect
664. #394	C₂²×C₁₃₉	semidirect
665. #394	C₂²×C₁₃₉	semidirect
669. #392	C₂²×C₁₃₉	semidirect
670. #392	C₂²×C₁₃₉	semidirect
672. #390	C₂²×C₁₃₉	semidirect
673. #389	C₂²×C₁₃₉	semidirect
674. #389	C₂²×C₁₃₉	semidirect
677. #388	C₂²×C₁₃₉	semidirect
678. #388	C₂²×C₁₃₉	semidirect
679. #388	C₂²×C₁₃₉	semidirect
680. #388	C₂²×C₁₃₉	semidirect
681. #388	C₂²×C₁₃₉	semidirect
682. #387	C₂²×C₁₃₉	semidirect
683. #387	C₂²×C₁₃₉	semidirect
688. #386	C₂²×C₁₃₉	semidirect
689. #386	C₂²×C₁₃₉	semidirect
690. #386	C₂²×C₁₃₉	semidirect
691. #386	C₂²×C₁₃₉	semidirect
693. #385	C₂²×C₁₃₉	semidirect
694. #385	C₂²×C₁₃₉	semidirect
695. #385	C₂²×C₁₃₉	semidirect
696. #385	C₂²×C₁₃₉	semidirect
697. #385	C₂²×C₁₃₉	semidirect
698. #383	C₂²×C₁₃₉	semidirect
699. #381	C₂²×C₁₃₉	semidirect
700. #380	C₂²×C₁₃₉	semidirect
701. #380	C₂²×C₁₃₉	semidirect
703. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
704. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
705. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
706. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
707. #376	C₂²×C₁₃₉	semidirect
708. C₂×#95	C₂²×C₁₃₉	semidirect
757. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2635×C₁₃₉	2
#2633×C₁₃₉	2
#2617×C₁₃₉	2
#2611×C₁₃₉	2
#2598×C₁₃₉	2
#2543×C₁₃₉	2
#2539×C₁₃₉	2
#2487×C₁₃₉	2
#2482×C₁₃₉	2
#2479×C₁₃₉	2
#2467×C₁₃₉	2
#2455×C₁₃₉	2
#2443×C₁₃₉	2
#2418×C₁₃₉	2
#2410×C₁₃₉	2
#2397×C₁₃₉	2
#2395×C₁₃₉	2
C₂×#399×C₁₃₉	2
#2361×C₁₃₉	2
#2358×C₁₃₉	2
#2353×C₁₃₉	2
#35840	139

Subgroups — C139×#35840 #48030436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35840 #48030436