Subgroups — C₁₃₉×#35850 #48030446

Order 35584.

2418 conjugacy classes of subgroups.

The subgroup lattice has 1098 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×#551×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2664×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2661×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2639×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2611×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2603×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2560×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2557×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2543×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2539×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2498×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2425×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2424×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2358×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#553×C₁₃₉	—	2	8	no	—
25	#551×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
41	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
43	C₂×#120×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	2	yes	—
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	2	yes	—
57	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#399×C₁₃₉	C₂²	1	1	yes	characteristic
60	#399×C₁₃₉	C₂²	1	1	yes	characteristic
61	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#398×C₁₃₉	C₂²	1	2	yes	complemented
63	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
64	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
65	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	#397×C₁₃₉	C₂²	1	2	yes	—
67	#397×C₁₃₉	C₂²	1	1	yes	characteristic
68	#397×C₁₃₉	C₂²	1	2	yes	—
69	#397×C₁₃₉	C₂²	1	1	yes	characteristic
70	#397×C₁₃₉	C₂²	1	1	yes	characteristic
71	#397×C₁₃₉	C₂²	1	1	yes	characteristic
72	#397×C₁₃₉	C₂²	1	2	yes	complemented
73	#397×C₁₃₉	C₂²	1	2	yes	complemented
74	#396×C₁₃₉	C₂²	1	2	yes	—
75	#396×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	1	yes	characteristic, complemented
79	#394×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#394×C₁₃₉	C₂²	1	2	yes	complemented
81	#393×C₁₃₉	C₂²	1	2	yes	complemented
82	#392×C₁₃₉	C₂²	1	1	yes	characteristic
83	#392×C₁₃₉	C₂²	1	1	yes	characteristic
84	#392×C₁₃₉	C₂²	1	2	yes	—
85	#391×C₁₃₉	C₂²	1	2	yes	complemented
86	#390×C₁₃₉	C₂²	1	2	yes	—
87	#390×C₁₃₉	C₂²	1	2	yes	—
88	#390×C₁₃₉	C₂²	1	2	yes	—
89	#390×C₁₃₉	C₂²	1	2	yes	—
90	#389×C₁₃₉	C₂²	1	2	yes	complemented
91	#389×C₁₃₉	C₂²	1	2	yes	complemented
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	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	—
105	#386×C₁₃₉	C₂²	1	2	yes	complemented
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	complemented
110	#384×C₁₃₉	C₂²	1	2	yes	complemented
111	#380×C₁₃₉	C₂²	1	2	yes	complemented
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
121	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
124	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	#126×C₁₃₉	—	2	4	no	—
145	#126×C₁₃₉	—	2	8	no	—
146	#126×C₁₃₉	—	2	4	no	—
147	#125×C₁₃₉	—	2	4	no	—
148	#124×C₁₃₉	—	2	4	no	—
149	#123×C₁₃₉	—	2	4	no	—
150	#123×C₁₃₉	—	2	4	no	—
151	#123×C₁₃₉	—	2	4	no	—
152	#123×C₁₃₉	—	2	8	no	—
153	#123×C₁₃₉	—	2	8	no	—
154	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
155	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
156	#121×C₁₃₉	—	2	8	no	—
157	#121×C₁₃₉	—	2	4	no	—
158	#121×C₁₃₉	—	2	4	no	—
159	#121×C₁₃₉	—	4	4	no	—
160	#120×C₁₃₉	—	2	4	no	—
161	#120×C₁₃₉	—	2	8	no	—
162	C₄×D₄×C₁₃₉	—	2	4	no	—
163	C₄×D₄×C₁₃₉	—	2	8	no	—
164	C₄×D₄×C₁₃₉	—	2	8	no	—
165	C₄×D₄×C₁₃₉	—	2	4	no	—
166	C₄×D₄×C₁₃₉	—	4	4	no	—
167	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
168	#117×C₁₃₉	—	2	4	no	—
169	#117×C₁₃₉	—	2	4	no	—
170	#117×C₁₃₉	—	2	4	no	—
171	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
194	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
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	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
233	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
234	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
235	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	1	yes	characteristic
242	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
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	C₂⁴×C₁₃₉	—	2	2	no	—
256	C₂⁴×C₁₃₉	—	2	2	no	—
257	C₂⁴×C₁₃₉	—	2	4	no	—
258	C₂⁴×C₁₃₉	—	4	2	no	—
259	C₂⁴×C₁₃₉	—	4	1	no	—
260	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂×Q₈×C₁₃₉	—	2	2	no	—
266	C₂×Q₈×C₁₃₉	—	4	2	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	4	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	2	no	—
275	C₂×D₄×C₁₃₉	—	2	4	no	—
276	C₂×D₄×C₁₃₉	—	2	2	no	—
277	C₂×D₄×C₁₃₉	—	2	4	no	—
278	C₂×D₄×C₁₃₉	—	2	4	no	—
279	C₂×D₄×C₁₃₉	—	4	2	no	—
280	C₂×D₄×C₁₃₉	—	4	2	no	—
281	C₂×D₄×C₁₃₉	—	4	1	no	—
282	C₂×D₄×C₁₃₉	—	4	2	no	—
283	C₂×D₄×C₁₃₉	—	4	2	no	—
284	C₂×D₄×C₁₃₉	—	4	2	no	—
285	C₂×D₄×C₁₃₉	—	4	2	no	—
286	C₂×D₄×C₁₃₉	—	4	2	no	—
287	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	4	no	—
292	C₂²×C₄×C₁₃₉	—	2	4	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	2	2	no	—
295	C₂²×C₄×C₁₃₉	—	2	4	no	—
296	C₂²×C₄×C₁₃₉	—	2	4	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	—	4	2	no	—
299	C₂²×C₄×C₁₃₉	—	4	1	no	—
300	C₂²×C₄×C₁₃₉	—	4	2	no	—
301	C₂²×C₄×C₁₃₉	—	4	2	no	—
302	C₂²×C₄×C₁₃₉	—	4	2	no	—
303	C₂²×C₄×C₁₃₉	—	4	2	no	—
304	C₂²×C₄×C₁₃₉	—	4	2	no	—
305	C₂²×C₄×C₁₃₉	—	4	2	no	—
306	C₂²×C₄×C₁₃₉	—	4	2	no	—
307	C₂²×C₄×C₁₃₉	—	4	2	no	—
308	C₂²×C₄×C₁₃₉	—	4	2	no	—
309	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
310	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	1	yes	characteristic
316	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
329	C₄⋊C₄×C₁₃₉	—	2	2	no	—
330	C₄⋊C₄×C₁₃₉	—	2	2	no	—
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	no	—
333	C₄⋊C₄×C₁₃₉	—	2	2	no	—
334	C₄⋊C₄×C₁₃₉	—	2	2	no	—
335	C₄⋊C₄×C₁₃₉	—	2	2	no	—
336	C₄⋊C₄×C₁₃₉	—	2	2	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	4	no	—
339	C₄⋊C₄×C₁₃₉	—	2	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	2	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	no	—
342	C₄⋊C₄×C₁₃₉	—	2	4	no	—
343	C₄⋊C₄×C₁₃₉	—	2	4	no	—
344	C₄⋊C₄×C₁₃₉	—	2	4	no	—
345	C₄⋊C₄×C₁₃₉	—	4	2	no	—
346	C₄⋊C₄×C₁₃₉	—	4	2	no	—
347	C₄⋊C₄×C₁₃₉	—	4	2	no	—
348	C₄⋊C₄×C₁₃₉	—	4	2	no	—
349	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
350	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
368	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
374	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
378	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
379	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
380	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
381	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	—
382	C₄²×C₁₃₉	—	2	2	no	—
383	C₄²×C₁₃₉	—	2	2	no	—
384	C₄²×C₁₃₉	—	2	4	no	—
385	C₄²×C₁₃₉	—	2	4	no	—
386	C₄²×C₁₃₉	—	4	2	no	—
387	C₄²×C₁₃₉	—	4	2	no	—
388	C₄²×C₁₃₉	—	4	2	no	—
389	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
390	C₂³×C₁₃₉	—	2	1	no	—
391	C₂³×C₁₃₉	—	2	2	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	2	no	—
395	C₂³×C₁₃₉	—	2	2	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	2	1	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	1	no	—
401	C₂³×C₁₃₉	—	2	1	no	—
402	C₂³×C₁₃₉	—	2	2	no	—
403	C₂³×C₁₃₉	—	2	2	no	—
404	C₂³×C₁₃₉	—	2	2	no	—
405	C₂³×C₁₃₉	—	2	2	no	—
406	C₂³×C₁₃₉	—	2	1	no	—
407	C₂³×C₁₃₉	—	2	2	no	—
408	C₂³×C₁₃₉	—	2	2	no	—
409	C₂³×C₁₃₉	—	2	2	no	—
410	C₂³×C₁₃₉	—	2	2	no	—
411	C₂³×C₁₃₉	—	2	2	no	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	4	4	no	—
414	C₂³×C₁₃₉	—	4	8	no	—
415	C₂³×C₁₃₉	—	4	4	no	—
416	C₂³×C₁₃₉	—	8	2	no	—
417	C₂³×C₁₃₉	—	8	4	no	—
418	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
419	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
420	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
421	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
422	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
423	Q₈×C₁₃₉	—	8	2	no	—
424	D₄×C₁₃₉	—	2	8	no	—
425	D₄×C₁₃₉	—	4	8	no	—
426	D₄×C₁₃₉	—	4	4	no	—
427	D₄×C₁₃₉	—	4	4	no	—
428	D₄×C₁₃₉	—	4	8	no	—
429	D₄×C₁₃₉	—	8	4	no	—
430	D₄×C₁₃₉	—	8	2	no	—
431	D₄×C₁₃₉	—	8	4	no	—
432	C₂×C₄×C₁₃₉	—	2	2	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	2	no	—
435	C₂×C₄×C₁₃₉	—	2	2	no	—
436	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
443	C₂×C₄×C₁₃₉	—	2	2	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	1	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	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	2	no	—
453	C₂×C₄×C₁₃₉	—	2	2	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	2	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	2	no	—
461	C₂×C₄×C₁₃₉	—	2	1	no	—
462	C₂×C₄×C₁₃₉	—	2	1	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	2	no	—
465	C₂×C₄×C₁₃₉	—	2	2	no	—
466	C₂×C₄×C₁₃₉	—	2	2	no	—
467	C₂×C₄×C₁₃₉	—	2	1	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	2	no	—
470	C₂×C₄×C₁₃₉	—	2	2	no	—
471	C₂×C₄×C₁₃₉	—	4	4	no	—
472	C₂×C₄×C₁₃₉	—	4	4	no	—
473	C₂×C₄×C₁₃₉	—	4	4	no	—
474	C₂×C₄×C₁₃₉	—	4	4	no	—
475	C₂×C₄×C₁₃₉	—	8	2	no	—
476	C₂×C₄×C₁₃₉	—	8	4	no	—
477	C₂×C₄×C₁₃₉	—	8	4	no	—
478	C₂×C₄×C₁₃₉	—	8	4	no	—
479	C₂×C₄×C₁₃₉	—	8	4	no	—
480	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
486	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
487	C₂²×C₁₃₉	—	2	2	no	—
488	C₂²×C₁₃₉	—	2	2	no	—
489	C₂²×C₁₃₉	—	2	4	no	—
490	C₂²×C₁₃₉	—	2	4	no	—
491	C₂²×C₁₃₉	—	2	2	no	—
492	C₂²×C₁₃₉	—	2	2	no	—
493	C₂²×C₁₃₉	—	2	2	no	—
494	C₂²×C₁₃₉	—	2	2	no	—
495	C₂²×C₁₃₉	—	2	4	no	—
496	C₂²×C₁₃₉	—	4	1	no	—
497	C₂²×C₁₃₉	—	4	1	no	—
498	C₂²×C₁₃₉	—	4	2	no	—
499	C₂²×C₁₃₉	—	4	2	no	—
500	C₂²×C₁₃₉	—	4	2	no	—
501	C₂²×C₁₃₉	—	4	2	no	—
502	C₂²×C₁₃₉	—	4	1	no	—
503	C₂²×C₁₃₉	—	4	2	no	—
504	C₂²×C₁₃₉	—	4	1	no	—
505	C₂²×C₁₃₉	—	4	2	no	—
506	C₂²×C₁₃₉	—	4	1	no	—
507	C₂²×C₁₃₉	—	4	2	no	—
508	C₂²×C₁₃₉	—	4	2	no	—
509	C₂²×C₁₃₉	—	4	2	no	—
510	C₂²×C₁₃₉	—	4	2	no	—
511	C₂²×C₁₃₉	—	4	2	no	—
512	C₂²×C₁₃₉	—	4	2	no	—
513	C₂²×C₁₃₉	—	8	8	no	—
514	C₂²×C₁₃₉	#532	1	4	yes	—
515	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
516	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
517	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₁₃₉	#585	1	2	yes	—
519	C₂²×C₁₃₉	#585	1	1	yes	characteristic
520	C₄×C₁₃₉	—	2	2	no	—
521	C₄×C₁₃₉	—	2	2	no	—
522	C₄×C₁₃₉	—	2	2	no	—
523	C₄×C₁₃₉	—	2	2	no	—
524	C₄×C₁₃₉	—	2	2	no	—
525	C₄×C₁₃₉	—	2	4	no	—
526	C₄×C₁₃₉	—	2	4	no	—
527	C₄×C₁₃₉	—	4	1	no	—
528	C₄×C₁₃₉	—	4	1	no	—
529	C₄×C₁₃₉	—	4	2	no	—
530	C₄×C₁₃₉	—	4	1	no	—
531	C₄×C₁₃₉	—	4	1	no	—
532	C₄×C₁₃₉	—	4	1	no	—
533	C₄×C₁₃₉	—	4	2	no	—
534	C₄×C₁₃₉	—	4	2	no	—
535	C₄×C₁₃₉	—	4	1	no	—
536	C₄×C₁₃₉	—	4	2	no	—
537	C₄×C₁₃₉	—	4	2	no	—
538	C₂×C₁₃₉	—	2	4	no	—
539	C₂×C₁₃₉	—	4	2	no	—
540	C₂×C₁₃₉	—	4	2	no	—
541	C₂×C₁₃₉	—	8	2	no	—
542	C₂×C₁₃₉	—	8	1	no	—
543	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
544	C₂×C₁₃₉	#3485	1	1	yes	characteristic
545	C₂×C₁₃₉	#3488	1	1	yes	characteristic
546	C₂×C₁₃₉	#3513	1	2	yes	—
547	C₂×C₁₃₉	#3521	1	2	yes	—
548	#35850	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
549	C₁₃₉	#35850	1	1	yes	characteristic, direct product factor, Sylow
550	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
551	C₂×#551	C₂×C₁₃₉	1	1	yes	characteristic, complemented
552	#2664	C₂×C₁₃₉	1	1	yes	characteristic, complemented
553	#2661	C₂×C₁₃₉	1	1	yes	characteristic, complemented
554	#2639	C₂×C₁₃₉	1	1	yes	characteristic, complemented
555	#2611	C₂×C₁₃₉	1	1	yes	characteristic, complemented
556	#2603	C₂×C₁₃₉	1	1	yes	characteristic, complemented
557	#2560	C₂×C₁₃₉	1	2	yes	complemented
558	#2557	C₂×C₁₃₉	1	2	yes	complemented
559	#2543	C₂×C₁₃₉	1	1	yes	characteristic, complemented
560	#2539	C₂×C₁₃₉	1	1	yes	characteristic, complemented
561	#2512	C₂×C₁₃₉	1	2	yes	complemented
562	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
563	#2498	C₂×C₁₃₉	1	1	yes	characteristic, complemented
564	#2425	C₂×C₁₃₉	1	2	yes	complemented
565	#2424	C₂×C₁₃₉	1	2	yes	complemented
566	#2422	C₂×C₁₃₉	1	2	yes	complemented
567	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
568	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
569	C₂×#397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
570	#2359	C₂×C₁₃₉	1	2	yes	complemented
571	#2358	C₂×C₁₃₉	1	2	yes	complemented
572	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
573	#553	—	2	8	no	—
574	#551	—	2	8	no	—
575	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
578	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
579	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
581	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
583	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
585	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
586	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
588	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
589	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
590	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
591	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
592	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
594	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
596	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
597	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
599	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
600	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
602	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
603	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
604	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
605	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
606	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
607	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
608	#399	C₂²×C₁₃₉	1	1	yes	characteristic
609	#399	C₂²×C₁₃₉	1	1	yes	characteristic
610	#398	C₂²×C₁₃₉	1	2	yes	complemented
611	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
612	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
613	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
614	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
615	#397	C₂²×C₁₃₉	1	2	yes	—
616	#397	C₂²×C₁₃₉	1	1	yes	characteristic
617	#397	C₂²×C₁₃₉	1	1	yes	characteristic
618	#397	C₂²×C₁₃₉	1	1	yes	characteristic
619	#397	C₂²×C₁₃₉	1	1	yes	characteristic
620	#397	C₂²×C₁₃₉	1	2	yes	—
621	#397	C₂²×C₁₃₉	1	2	yes	complemented
622	#397	C₂²×C₁₃₉	1	2	yes	complemented
623	#396	C₂²×C₁₃₉	1	2	yes	—
624	#396	C₂²×C₁₃₉	1	2	yes	complemented
625	#394	C₂²×C₁₃₉	1	2	yes	—
626	#394	C₂²×C₁₃₉	1	2	yes	—
627	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
628	#394	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
629	#394	C₂²×C₁₃₉	1	2	yes	complemented
630	#393	C₂²×C₁₃₉	1	2	yes	complemented
631	#392	C₂²×C₁₃₉	1	1	yes	characteristic
632	#392	C₂²×C₁₃₉	1	1	yes	characteristic
633	#392	C₂²×C₁₃₉	1	2	yes	—
634	#391	C₂²×C₁₃₉	1	2	yes	complemented
635	#390	C₂²×C₁₃₉	1	2	yes	—
636	#390	C₂²×C₁₃₉	1	2	yes	—
637	#390	C₂²×C₁₃₉	1	2	yes	—
638	#390	C₂²×C₁₃₉	1	2	yes	—
639	#389	C₂²×C₁₃₉	1	2	yes	complemented
640	#389	C₂²×C₁₃₉	1	2	yes	complemented
641	#388	C₂²×C₁₃₉	1	2	yes	—
642	#388	C₂²×C₁₃₉	1	2	yes	—
643	#388	C₂²×C₁₃₉	1	2	yes	—
644	#388	C₂²×C₁₃₉	1	2	yes	complemented
645	#388	C₂²×C₁₃₉	1	2	yes	complemented
646	#388	C₂²×C₁₃₉	1	2	yes	complemented
647	#387	C₂²×C₁₃₉	1	2	yes	complemented
648	#387	C₂²×C₁₃₉	1	2	yes	complemented
649	#386	C₂²×C₁₃₉	1	2	yes	—
650	#386	C₂²×C₁₃₉	1	2	yes	—
651	#386	C₂²×C₁₃₉	1	2	yes	—
652	#386	C₂²×C₁₃₉	1	2	yes	—
653	#386	C₂²×C₁₃₉	1	2	yes	—
654	#386	C₂²×C₁₃₉	1	2	yes	complemented
655	#385	C₂²×C₁₃₉	1	2	yes	—
656	#385	C₂²×C₁₃₉	1	2	yes	—
657	#385	C₂²×C₁₃₉	1	2	yes	—
658	#385	C₂²×C₁₃₉	1	2	yes	complemented
659	#384	C₂²×C₁₃₉	1	2	yes	complemented
660	#380	C₂²×C₁₃₉	1	2	yes	complemented
661	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
662	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
663	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
664	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
665	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
666	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
668	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
669	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
670	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
671	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
672	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
673	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
674	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
677	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
678	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
679	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
683	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
684	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
687	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
689	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
690	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
691	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
693	#126	—	2	4	no	—
694	#126	—	2	8	no	—
695	#126	—	2	4	no	—
696	#125	—	2	4	no	—
697	#124	—	2	4	no	—
698	#123	—	2	4	no	—
699	#123	—	2	4	no	—
700	#123	—	2	4	no	—
701	#123	—	2	8	no	—
702	#123	—	2	8	no	—
703	C₂²⋊Q₈	—	2	4	no	—
704	C₂²⋊Q₈	—	2	4	no	—
705	#121	—	2	8	no	—
706	#121	—	2	4	no	—
707	#121	—	2	4	no	—
708	#121	—	4	4	no	—
709	#120	—	2	4	no	—
710	#120	—	2	8	no	—
711	C₄×D₄	—	2	4	no	—
712	C₄×D₄	—	2	8	no	—
713	C₄×D₄	—	2	8	no	—
714	C₄×D₄	—	2	4	no	—
715	C₄×D₄	—	4	4	no	—
716	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
717	#117	—	2	4	no	—
718	#117	—	2	4	no	—
719	#117	—	2	4	no	—
720	C₂×C₄⋊C₄	—	2	4	no	—
721	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	—	2	4	no	—
743	C₂×C₂²⋊C₄	—	2	4	no	—
744	C₂×C₂²⋊C₄	—	4	4	no	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
754	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
780	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
784	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
785	#95	C₂³×C₁₃₉	1	1	yes	characteristic
786	#95	C₂³×C₁₃₉	1	2	yes	—
787	#95	C₂³×C₁₃₉	1	1	yes	characteristic
788	#95	C₂³×C₁₃₉	1	2	yes	—
789	#95	C₂³×C₁₃₉	1	2	yes	—
790	#95	C₂³×C₁₃₉	1	2	yes	—
791	#95	C₂³×C₁₃₉	1	2	yes	—
792	#95	C₂³×C₁₃₉	1	2	yes	—
793	#95	C₂³×C₁₃₉	1	1	yes	characteristic
794	#95	C₂³×C₁₃₉	1	2	yes	—
795	#95	C₂³×C₁₃₉	1	1	yes	characteristic
796	#95	C₂³×C₁₃₉	1	2	yes	—
797	#95	C₂³×C₁₃₉	1	2	yes	—
798	#95	C₂³×C₁₃₉	1	2	yes	—
799	#95	C₂³×C₁₃₉	1	2	yes	—
800	#95	C₂³×C₁₃₉	1	2	yes	—
801	#95	C₂³×C₁₃₉	1	2	yes	—
802	#95	C₂³×C₁₃₉	1	2	yes	—
803	#95	C₂³×C₁₃₉	1	2	yes	—
804	C₂⁴	—	2	2	no	—
805	C₂⁴	—	2	2	no	—
806	C₂⁴	—	2	4	no	—
807	C₂⁴	—	4	2	no	—
808	C₂⁴	—	4	1	no	—
809	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
810	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
811	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
812	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
813	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
814	C₂×Q₈	—	2	2	no	—
815	C₂×Q₈	—	4	2	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	1	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
859	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
860	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
867	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
869	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	4	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
929	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
930	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	4	no	—
934	C₄²	—	2	4	no	—
935	C₄²	—	4	2	no	—
936	C₄²	—	4	2	no	—
937	C₄²	—	4	2	no	—
938	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	4	4	no	—
963	C₂³	—	4	8	no	—
964	C₂³	—	4	4	no	—
965	C₂³	—	8	2	no	—
966	C₂³	—	8	4	no	—
967	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
968	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
969	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
970	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
971	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
972	Q₈	—	8	2	no	—
973	D₄	—	2	8	no	—
974	D₄	—	4	8	no	—
975	D₄	—	4	4	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	8	no	—
978	D₄	—	8	4	no	—
979	D₄	—	8	2	no	—
980	D₄	—	8	4	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	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	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	4	no	—
1026	C₂×C₄	—	8	4	no	—
1027	C₂×C₄	—	8	4	no	—
1028	C₂×C₄	—	8	4	no	—
1029	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1034	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1035	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	4	no	—
1039	C₂²	—	2	4	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	8	8	no	—
1063	C₂²	#532×C₁₃₉	1	4	yes	—
1064	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1065	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
1066	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1067	C₂²	#585×C₁₃₉	1	2	yes	—
1068	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	4	no	—
1075	C₄	—	2	4	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	2	no	—
1087	C₂	—	2	4	no	—
1088	C₂	—	4	2	no	—
1089	C₂	—	4	2	no	—
1090	C₂	—	8	1	no	—
1091	C₂	—	8	2	no	—
1092	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
1093	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1094	C₂	#3488×C₁₃₉	1	1	yes	characteristic
1095	C₂	#3513×C₁₃₉	1	2	yes	—
1096	C₂	#3521×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×#551×C₁₃₉	C₂	semidirect
3. #2664×C₁₃₉	C₂	semidirect
4. #2661×C₁₃₉	C₂	semidirect
5. #2639×C₁₃₉	C₂	semidirect
6. #2611×C₁₃₉	C₂	semidirect
7. #2603×C₁₃₉	C₂	semidirect
8. #2560×C₁₃₉	C₂	semidirect
9. #2557×C₁₃₉	C₂	semidirect
10. #2543×C₁₃₉	C₂	semidirect
11. #2539×C₁₃₉	C₂	semidirect
12. #2512×C₁₃₉	C₂	semidirect
13. #2502×C₁₃₉	C₂	semidirect
14. #2498×C₁₃₉	C₂	semidirect
15. #2425×C₁₃₉	C₂	semidirect
16. #2424×C₁₃₉	C₂	semidirect
17. #2422×C₁₃₉	C₂	semidirect
18. #2395×C₁₃₉	C₂	semidirect
19. #2392×C₁₃₉	C₂	semidirect
20. C₂×#397×C₁₃₉	C₂	semidirect
21. #2359×C₁₃₉	C₂	semidirect
22. #2358×C₁₃₉	C₂	semidirect
23. #2275×C₁₃₉	C₂	semidirect
28. C₂×#126×C₁₃₉	C₂²	semidirect
29. C₂×#125×C₁₃₉	C₂²	semidirect
35. C₂×#123×C₁₃₉	C₂²	semidirect
41. C₂×#121×C₁₃₉	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
52. C₂×#117×C₁₃₉	C₂²	semidirect
57. #400×C₁₃₉	C₂²	semidirect
58. #400×C₁₃₉	C₂²	semidirect
61. #398×C₁₃₉	C₂²	semidirect
62. #398×C₁₃₉	C₂²	semidirect
63. #398×C₁₃₉	C₂²	semidirect
64. #398×C₁₃₉	C₂²	semidirect
65. #398×C₁₃₉	C₂²	semidirect
72. #397×C₁₃₉	C₂²	semidirect
73. #397×C₁₃₉	C₂²	semidirect
75. #396×C₁₃₉	C₂²	semidirect
78. #394×C₁₃₉	C₂²	semidirect
79. #394×C₁₃₉	C₂²	semidirect
80. #394×C₁₃₉	C₂²	semidirect
81. #393×C₁₃₉	C₂²	semidirect
85. #391×C₁₃₉	C₂²	semidirect
90. #389×C₁₃₉	C₂²	semidirect
91. #389×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
105. #386×C₁₃₉	C₂²	semidirect
109. #385×C₁₃₉	C₂²	semidirect
110. #384×C₁₃₉	C₂²	semidirect
111. #380×C₁₃₉	C₂²	semidirect
112. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
113. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
114. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
121. #376×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
167. C₄×D₄×C₁₃₉	D₄	semidirect
548. #35850	C₁₃₉	direct (N × H)
549. C₁₃₉	#35850	direct (N × H)
550. C₂×#553	C₂×C₁₃₉	semidirect
551. C₂×#551	C₂×C₁₃₉	semidirect
552. #2664	C₂×C₁₃₉	semidirect
553. #2661	C₂×C₁₃₉	semidirect
554. #2639	C₂×C₁₃₉	semidirect
555. #2611	C₂×C₁₃₉	semidirect
556. #2603	C₂×C₁₃₉	semidirect
557. #2560	C₂×C₁₃₉	semidirect
558. #2557	C₂×C₁₃₉	semidirect
559. #2543	C₂×C₁₃₉	semidirect
560. #2539	C₂×C₁₃₉	semidirect
561. #2512	C₂×C₁₃₉	semidirect
562. #2502	C₂×C₁₃₉	semidirect
563. #2498	C₂×C₁₃₉	semidirect
564. #2425	C₂×C₁₃₉	semidirect
565. #2424	C₂×C₁₃₉	semidirect
566. #2422	C₂×C₁₃₉	semidirect
567. #2395	C₂×C₁₃₉	semidirect
568. #2392	C₂×C₁₃₉	semidirect
569. C₂×#397	C₂×C₁₃₉	semidirect
570. #2359	C₂×C₁₃₉	semidirect
571. #2358	C₂×C₁₃₉	semidirect
572. #2275	C₂×C₁₃₉	semidirect
577. C₂×#126	C₂²×C₁₃₉	semidirect
578. C₂×#125	C₂²×C₁₃₉	semidirect
584. C₂×#123	C₂²×C₁₃₉	semidirect
590. C₂×#121	C₂²×C₁₃₉	semidirect
598. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
601. C₂×#117	C₂²×C₁₃₉	semidirect
606. #400	C₂²×C₁₃₉	semidirect
607. #400	C₂²×C₁₃₉	semidirect
610. #398	C₂²×C₁₃₉	semidirect
611. #398	C₂²×C₁₃₉	semidirect
612. #398	C₂²×C₁₃₉	semidirect
613. #398	C₂²×C₁₃₉	semidirect
614. #398	C₂²×C₁₃₉	semidirect
621. #397	C₂²×C₁₃₉	semidirect
622. #397	C₂²×C₁₃₉	semidirect
624. #396	C₂²×C₁₃₉	semidirect
627. #394	C₂²×C₁₃₉	semidirect
628. #394	C₂²×C₁₃₉	semidirect
629. #394	C₂²×C₁₃₉	semidirect
630. #393	C₂²×C₁₃₉	semidirect
634. #391	C₂²×C₁₃₉	semidirect
639. #389	C₂²×C₁₃₉	semidirect
640. #389	C₂²×C₁₃₉	semidirect
644. #388	C₂²×C₁₃₉	semidirect
645. #388	C₂²×C₁₃₉	semidirect
646. #388	C₂²×C₁₃₉	semidirect
647. #387	C₂²×C₁₃₉	semidirect
648. #387	C₂²×C₁₃₉	semidirect
654. #386	C₂²×C₁₃₉	semidirect
658. #385	C₂²×C₁₃₉	semidirect
659. #384	C₂²×C₁₃₉	semidirect
660. #380	C₂²×C₁₃₉	semidirect
661. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
662. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
663. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
667. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
668. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
669. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
670. #376	C₂²×C₁₃₉	semidirect
673. C₂×#95	C₂²×C₁₃₉	semidirect
716. 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×#551×C₁₃₉	2
#2664×C₁₃₉	2
#2661×C₁₃₉	2
#2639×C₁₃₉	2
#2611×C₁₃₉	2
#2603×C₁₃₉	2
#2560×C₁₃₉	2
#2557×C₁₃₉	2
#2543×C₁₃₉	2
#2539×C₁₃₉	2
#2512×C₁₃₉	2
#2502×C₁₃₉	2
#2498×C₁₃₉	2
#2425×C₁₃₉	2
#2424×C₁₃₉	2
#2422×C₁₃₉	2
#2395×C₁₃₉	2
#2392×C₁₃₉	2
C₂×#397×C₁₃₉	2
#2359×C₁₃₉	2
#2358×C₁₃₉	2
#2275×C₁₃₉	2
#35850	139

Subgroups — C139×#35850 #48030446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35850 #48030446