Subgroups — C₁₃₉×#36262 #48030858

Order 35584.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2601×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2560×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2557×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2534×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2512×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2491×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2422×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2342×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2293×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#390×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#551×C₁₃₉	—	2	16	no	—
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
35	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	complemented
44	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
45	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	#398×C₁₃₉	C₂²	1	2	yes	complemented
53	#397×C₁₃₉	C₂²	1	2	yes	complemented
54	#397×C₁₃₉	C₂²	1	2	yes	complemented
55	#397×C₁₃₉	C₂²	1	2	yes	complemented
56	#396×C₁₃₉	C₂²	1	2	yes	complemented
57	#396×C₁₃₉	C₂²	1	2	yes	complemented
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	complemented
60	#394×C₁₃₉	C₂²	1	2	yes	complemented
61	#393×C₁₃₉	C₂²	1	2	yes	complemented
62	#393×C₁₃₉	C₂²	1	2	yes	complemented
63	#392×C₁₃₉	C₂²	1	2	yes	—
64	#391×C₁₃₉	C₂²	1	2	yes	complemented
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#390×C₁₃₉	C₂²	1	1	yes	characteristic
68	#390×C₁₃₉	C₂²	1	1	yes	characteristic
69	#390×C₁₃₉	C₂²	1	2	yes	—
70	#390×C₁₃₉	C₂²	1	1	yes	characteristic
71	#390×C₁₃₉	C₂²	1	2	yes	—
72	#390×C₁₃₉	C₂²	1	1	yes	characteristic
73	#390×C₁₃₉	C₂²	1	1	yes	characteristic
74	#390×C₁₃₉	C₂²	1	1	yes	characteristic
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
78	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#389×C₁₃₉	C₂²	1	2	yes	complemented
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	#388×C₁₃₉	C₂²	1	2	yes	complemented
83	#388×C₁₃₉	C₂²	1	2	yes	complemented
84	#388×C₁₃₉	C₂²	1	2	yes	complemented
85	#388×C₁₃₉	C₂²	1	2	yes	complemented
86	#388×C₁₃₉	C₂²	1	2	yes	complemented
87	#388×C₁₃₉	C₂²	1	2	yes	complemented
88	#388×C₁₃₉	C₂²	1	2	yes	complemented
89	#388×C₁₃₉	C₂²	1	2	yes	complemented
90	#388×C₁₃₉	C₂²	1	2	yes	complemented
91	#388×C₁₃₉	C₂²	1	2	yes	complemented
92	#387×C₁₃₉	C₂²	1	2	yes	complemented
93	#387×C₁₃₉	C₂²	1	2	yes	complemented
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#386×C₁₃₉	C₂²	1	2	yes	complemented
97	#386×C₁₃₉	C₂²	1	2	yes	complemented
98	#385×C₁₃₉	C₂²	1	2	yes	complemented
99	#385×C₁₃₉	C₂²	1	2	yes	complemented
100	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
101	#381×C₁₃₉	C₂²	1	2	yes	—
102	#381×C₁₃₉	C₂²	1	2	yes	—
103	#380×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	1	yes	characteristic
105	#380×C₁₃₉	C₂²	1	1	yes	characteristic
106	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
108	#379×C₁₃₉	C₂²	1	2	yes	—
109	#379×C₁₃₉	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, 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	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃₉	—	2	4	no	—
127	C₂²×D₄×C₁₃₉	—	2	4	no	—
128	C₂²×D₄×C₁₃₉	—	4	2	no	—
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
145	#126×C₁₃₉	—	2	8	no	—
146	#126×C₁₃₉	—	2	8	no	—
147	#124×C₁₃₉	—	2	8	no	—
148	#123×C₁₃₉	—	2	8	no	—
149	#123×C₁₃₉	—	2	8	no	—
150	#123×C₁₃₉	—	2	8	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
152	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
153	#121×C₁₃₉	—	2	4	no	—
154	#121×C₁₃₉	—	4	2	no	—
155	#120×C₁₃₉	—	2	8	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	8	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	C₄×D₄×C₁₃₉	—	4	2	no	—
161	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
162	#117×C₁₃₉	—	2	8	no	—
163	#117×C₁₃₉	—	2	8	no	—
164	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	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	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
185	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
186	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
187	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	2	yes	—
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
212	C₂×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×C₄²×C₁₃₉	—	4	2	no	—
218	C₂×C₄²×C₁₃₉	—	4	2	no	—
219	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
234	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	1	yes	characteristic
245	#95×C₁₃₉	C₂³	1	1	yes	characteristic
246	#95×C₁₃₉	C₂³	1	1	yes	characteristic
247	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
252	C₂⁴×C₁₃₉	—	2	4	no	—
253	C₂⁴×C₁₃₉	—	2	4	no	—
254	C₂⁴×C₁₃₉	—	2	4	no	—
255	C₂⁴×C₁₃₉	—	2	4	no	—
256	C₂⁴×C₁₃₉	—	4	2	no	—
257	C₂⁴×C₁₃₉	—	4	2	no	—
258	C₂⁴×C₁₃₉	—	4	2	no	—
259	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂×Q₈×C₁₃₉	—	2	4	no	—
264	C₂×Q₈×C₁₃₉	—	4	2	no	—
265	C₂×Q₈×C₁₃₉	—	4	2	no	—
266	C₂×D₄×C₁₃₉	—	2	2	no	—
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	4	no	—
271	C₂×D₄×C₁₃₉	—	2	4	no	—
272	C₂×D₄×C₁₃₉	—	2	2	no	—
273	C₂×D₄×C₁₃₉	—	2	4	no	—
274	C₂×D₄×C₁₃₉	—	2	2	no	—
275	C₂×D₄×C₁₃₉	—	2	2	no	—
276	C₂×D₄×C₁₃₉	—	2	2	no	—
277	C₂×D₄×C₁₃₉	—	2	2	no	—
278	C₂×D₄×C₁₃₉	—	4	16	no	—
279	C₂×D₄×C₁₃₉	—	4	2	no	—
280	C₂×D₄×C₁₃₉	—	4	2	no	—
281	C₂×D₄×C₁₃₉	—	4	2	no	—
282	C₂×D₄×C₁₃₉	—	4	2	no	—
283	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
284	C₂×D₄×C₁₃₉	#41	1	4	yes	—
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	—	2	4	no	—
291	C₂²×C₄×C₁₃₉	—	2	4	no	—
292	C₂²×C₄×C₁₃₉	—	2	2	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	2	2	no	—
295	C₂²×C₄×C₁₃₉	—	2	2	no	—
296	C₂²×C₄×C₁₃₉	—	2	4	no	—
297	C₂²×C₄×C₁₃₉	—	4	1	no	—
298	C₂²×C₄×C₁₃₉	—	4	1	no	—
299	C₂²×C₄×C₁₃₉	—	4	1	no	—
300	C₂²×C₄×C₁₃₉	—	4	1	no	—
301	C₂²×C₄×C₁₃₉	—	4	1	no	—
302	C₂²×C₄×C₁₃₉	—	4	1	no	—
303	C₂²×C₄×C₁₃₉	—	4	1	no	—
304	C₂²×C₄×C₁₃₉	—	4	1	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	C₂×D₄	1	4	yes	—
309	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
310	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
311	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
312	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	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	2	yes	—
319	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
328	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
338	C₄⋊C₄×C₁₃₉	—	2	4	no	—
339	C₄⋊C₄×C₁₃₉	—	2	2	no	—
340	C₄⋊C₄×C₁₃₉	—	2	2	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	no	—
342	C₄⋊C₄×C₁₃₉	—	2	2	no	—
343	C₄⋊C₄×C₁₃₉	—	2	2	no	—
344	C₄⋊C₄×C₁₃₉	—	2	2	no	—
345	C₄⋊C₄×C₁₃₉	—	2	2	no	—
346	C₄⋊C₄×C₁₃₉	—	2	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	complemented
350	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
351	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
352	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
353	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
355	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	4	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	2	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₃₉	—	4	2	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	C₂×D₄	1	4	yes	—
379	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
380	C₄²×C₁₃₉	—	2	4	no	—
381	C₄²×C₁₃₉	—	2	4	no	—
382	C₄²×C₁₃₉	—	2	2	no	—
383	C₄²×C₁₃₉	—	2	2	no	—
384	C₄²×C₁₃₉	—	2	2	no	—
385	C₄²×C₁₃₉	—	2	2	no	—
386	C₄²×C₁₃₉	—	2	2	no	—
387	C₄²×C₁₃₉	—	2	2	no	—
388	C₄²×C₁₃₉	—	4	1	no	—
389	C₄²×C₁₃₉	—	4	1	no	—
390	C₄²×C₁₃₉	—	4	1	no	—
391	C₄²×C₁₃₉	—	4	1	no	—
392	C₄²×C₁₃₉	—	4	1	no	—
393	C₄²×C₁₃₉	—	4	1	no	—
394	C₄²×C₁₃₉	C₂×D₄	1	4	yes	complemented
395	C₂³×C₁₃₉	—	2	1	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	1	no	—
398	C₂³×C₁₃₉	—	2	1	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	2	no	—
401	C₂³×C₁₃₉	—	2	1	no	—
402	C₂³×C₁₃₉	—	2	1	no	—
403	C₂³×C₁₃₉	—	2	1	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	1	no	—
409	C₂³×C₁₃₉	—	2	1	no	—
410	C₂³×C₁₃₉	—	2	2	no	—
411	C₂³×C₁₃₉	—	2	2	no	—
412	C₂³×C₁₃₉	—	2	2	no	—
413	C₂³×C₁₃₉	—	2	2	no	—
414	C₂³×C₁₃₉	—	2	2	no	—
415	C₂³×C₁₃₉	—	2	2	no	—
416	C₂³×C₁₃₉	—	2	2	no	—
417	C₂³×C₁₃₉	—	2	2	no	—
418	C₂³×C₁₃₉	—	4	8	no	—
419	C₂³×C₁₃₉	—	4	8	no	—
420	C₂³×C₁₃₉	—	4	8	no	—
421	C₂³×C₁₃₉	—	4	8	no	—
422	C₂³×C₁₃₉	—	8	4	no	—
423	C₂³×C₁₃₉	—	8	4	no	—
424	C₂³×C₁₃₉	—	8	4	no	—
425	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
426	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
427	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
428	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
429	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
430	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
431	Q₈×C₁₃₉	—	8	4	no	—
432	D₄×C₁₃₉	—	2	8	no	—
433	D₄×C₁₃₉	—	2	8	no	—
434	D₄×C₁₃₉	—	4	8	no	—
435	D₄×C₁₃₉	—	4	8	no	—
436	D₄×C₁₃₉	—	4	4	no	—
437	D₄×C₁₃₉	—	8	4	no	—
438	C₂×C₄×C₁₃₉	—	2	1	no	—
439	C₂×C₄×C₁₃₉	—	2	1	no	—
440	C₂×C₄×C₁₃₉	—	2	1	no	—
441	C₂×C₄×C₁₃₉	—	2	1	no	—
442	C₂×C₄×C₁₃₉	—	2	1	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
452	C₂×C₄×C₁₃₉	—	2	1	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	2	8	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	1	no	—
464	C₂×C₄×C₁₃₉	—	2	2	no	—
465	C₂×C₄×C₁₃₉	—	2	2	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	2	2	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	1	no	—
470	C₂×C₄×C₁₃₉	—	2	2	no	—
471	C₂×C₄×C₁₃₉	—	2	2	no	—
472	C₂×C₄×C₁₃₉	—	2	2	no	—
473	C₂×C₄×C₁₃₉	—	2	1	no	—
474	C₂×C₄×C₁₃₉	—	2	1	no	—
475	C₂×C₄×C₁₃₉	—	2	2	no	—
476	C₂×C₄×C₁₃₉	—	2	2	no	—
477	C₂×C₄×C₁₃₉	—	2	1	no	—
478	C₂×C₄×C₁₃₉	—	2	1	no	—
479	C₂×C₄×C₁₃₉	—	2	1	no	—
480	C₂×C₄×C₁₃₉	—	2	1	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	—	4	4	no	—
486	C₂×C₄×C₁₃₉	—	4	4	no	—
487	C₂×C₄×C₁₃₉	—	4	4	no	—
488	C₂×C₄×C₁₃₉	—	4	8	no	—
489	C₂×C₄×C₁₃₉	—	4	4	no	—
490	C₂×C₄×C₁₃₉	—	4	8	no	—
491	C₂×C₄×C₁₃₉	—	4	4	no	—
492	C₂×C₄×C₁₃₉	—	8	4	no	—
493	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
499	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
500	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
501	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
502	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
503	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
504	C₂²×C₁₃₉	—	2	2	no	—
505	C₂²×C₁₃₉	—	2	2	no	—
506	C₂²×C₁₃₉	—	2	2	no	—
507	C₂²×C₁₃₉	—	2	2	no	—
508	C₂²×C₁₃₉	—	2	2	no	—
509	C₂²×C₁₃₉	—	2	2	no	—
510	C₂²×C₁₃₉	—	2	2	no	—
511	C₂²×C₁₃₉	—	2	4	no	—
512	C₂²×C₁₃₉	—	2	2	no	—
513	C₂²×C₁₃₉	—	2	4	no	—
514	C₂²×C₁₃₉	—	2	4	no	—
515	C₂²×C₁₃₉	—	2	2	no	—
516	C₂²×C₁₃₉	—	4	2	no	—
517	C₂²×C₁₃₉	—	4	1	no	—
518	C₂²×C₁₃₉	—	4	1	no	—
519	C₂²×C₁₃₉	—	4	2	no	—
520	C₂²×C₁₃₉	—	4	1	no	—
521	C₂²×C₁₃₉	—	4	2	no	—
522	C₂²×C₁₃₉	—	4	1	no	—
523	C₂²×C₁₃₉	—	4	2	no	—
524	C₂²×C₁₃₉	—	4	2	no	—
525	C₂²×C₁₃₉	—	4	2	no	—
526	C₂²×C₁₃₉	—	4	2	no	—
527	C₂²×C₁₃₉	—	4	2	no	—
528	C₂²×C₁₃₉	—	4	2	no	—
529	C₂²×C₁₃₉	—	4	2	no	—
530	C₂²×C₁₃₉	—	4	2	no	—
531	C₂²×C₁₃₉	—	8	16	no	—
532	C₂²×C₁₃₉	#532	1	4	yes	—
533	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
534	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
535	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
536	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
537	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²×C₁₃₉	#585	1	1	yes	characteristic
539	C₂²×C₁₃₉	#585	1	1	yes	characteristic
540	C₄×C₁₃₉	—	2	2	no	—
541	C₄×C₁₃₉	—	2	2	no	—
542	C₄×C₁₃₉	—	2	2	no	—
543	C₄×C₁₃₉	—	2	2	no	—
544	C₄×C₁₃₉	—	2	2	no	—
545	C₄×C₁₃₉	—	2	2	no	—
546	C₄×C₁₃₉	—	2	2	no	—
547	C₄×C₁₃₉	—	2	2	no	—
548	C₄×C₁₃₉	—	4	2	no	—
549	C₄×C₁₃₉	—	4	2	no	—
550	C₄×C₁₃₉	—	4	2	no	—
551	C₄×C₁₃₉	—	4	2	no	—
552	C₄×C₁₃₉	—	4	1	no	—
553	C₄×C₁₃₉	—	4	1	no	—
554	C₄×C₁₃₉	—	4	2	no	—
555	C₄×C₁₃₉	—	4	2	no	—
556	C₄×C₁₃₉	—	4	1	no	—
557	C₄×C₁₃₉	—	4	1	no	—
558	C₄×C₁₃₉	#551	1	4	yes	complemented
559	C₂×C₁₃₉	—	2	4	no	—
560	C₂×C₁₃₉	—	4	2	no	—
561	C₂×C₁₃₉	—	4	4	no	—
562	C₂×C₁₃₉	—	8	2	no	—
563	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
564	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
565	C₂×C₁₃₉	C₂×#551	1	1	yes	characteristic
566	C₂×C₁₃₉	#3475	1	1	yes	characteristic
567	C₂×C₁₃₉	#3496	1	1	yes	characteristic
568	C₂×C₁₃₉	#3505	1	1	yes	characteristic
569	C₂×C₁₃₉	#3510	1	1	yes	characteristic
570	#36262	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
571	C₁₃₉	#36262	1	1	yes	characteristic, direct product factor, Sylow
572	C₂×#551	C₂×C₁₃₉	1	2	yes	complemented
573	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
574	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
575	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
576	#2602	C₂×C₁₃₉	1	2	yes	complemented
577	#2601	C₂×C₁₃₉	1	2	yes	complemented
578	#2561	C₂×C₁₃₉	1	2	yes	complemented
579	#2560	C₂×C₁₃₉	1	2	yes	complemented
580	#2557	C₂×C₁₃₉	1	2	yes	complemented
581	#2534	C₂×C₁₃₉	1	2	yes	complemented
582	#2512	C₂×C₁₃₉	1	1	yes	characteristic, complemented
583	#2491	C₂×C₁₃₉	1	1	yes	characteristic, complemented
584	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
585	#2452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
586	#2422	C₂×C₁₃₉	1	1	yes	characteristic, complemented
587	#2408	C₂×C₁₃₉	1	1	yes	characteristic
588	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
589	#2342	C₂×C₁₃₉	1	2	yes	complemented
590	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
591	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
592	#2293	C₂×C₁₃₉	1	1	yes	characteristic, complemented
593	C₂×#390	C₂×C₁₃₉	1	1	yes	characteristic, complemented
594	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
595	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
596	#551	—	2	16	no	—
597	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
598	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
599	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
600	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
601	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
602	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
603	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
604	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
605	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
606	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
607	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
608	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
609	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
615	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
616	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
617	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
618	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
619	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
620	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
621	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
623	#398	C₂²×C₁₃₉	1	2	yes	complemented
624	#397	C₂²×C₁₃₉	1	2	yes	complemented
625	#397	C₂²×C₁₃₉	1	2	yes	complemented
626	#397	C₂²×C₁₃₉	1	2	yes	complemented
627	#396	C₂²×C₁₃₉	1	2	yes	complemented
628	#396	C₂²×C₁₃₉	1	2	yes	complemented
629	#394	C₂²×C₁₃₉	1	2	yes	—
630	#394	C₂²×C₁₃₉	1	2	yes	complemented
631	#394	C₂²×C₁₃₉	1	2	yes	complemented
632	#393	C₂²×C₁₃₉	1	2	yes	complemented
633	#393	C₂²×C₁₃₉	1	2	yes	complemented
634	#392	C₂²×C₁₃₉	1	2	yes	—
635	#391	C₂²×C₁₃₉	1	2	yes	complemented
636	#390	C₂²×C₁₃₉	1	2	yes	—
637	#390	C₂²×C₁₃₉	1	1	yes	characteristic
638	#390	C₂²×C₁₃₉	1	1	yes	characteristic
639	#390	C₂²×C₁₃₉	1	1	yes	characteristic
640	#390	C₂²×C₁₃₉	1	2	yes	—
641	#390	C₂²×C₁₃₉	1	1	yes	characteristic
642	#390	C₂²×C₁₃₉	1	1	yes	characteristic
643	#390	C₂²×C₁₃₉	1	1	yes	characteristic
644	#390	C₂²×C₁₃₉	1	1	yes	characteristic
645	#390	C₂²×C₁₃₉	1	1	yes	characteristic
646	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
647	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
648	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
649	#389	C₂²×C₁₃₉	1	2	yes	complemented
650	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
651	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
652	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
653	#388	C₂²×C₁₃₉	1	2	yes	complemented
654	#388	C₂²×C₁₃₉	1	2	yes	complemented
655	#388	C₂²×C₁₃₉	1	2	yes	complemented
656	#388	C₂²×C₁₃₉	1	2	yes	complemented
657	#388	C₂²×C₁₃₉	1	2	yes	complemented
658	#388	C₂²×C₁₃₉	1	2	yes	complemented
659	#388	C₂²×C₁₃₉	1	2	yes	complemented
660	#388	C₂²×C₁₃₉	1	2	yes	complemented
661	#388	C₂²×C₁₃₉	1	2	yes	complemented
662	#388	C₂²×C₁₃₉	1	2	yes	complemented
663	#387	C₂²×C₁₃₉	1	2	yes	complemented
664	#387	C₂²×C₁₃₉	1	2	yes	complemented
665	#386	C₂²×C₁₃₉	1	2	yes	—
666	#386	C₂²×C₁₃₉	1	2	yes	—
667	#386	C₂²×C₁₃₉	1	2	yes	complemented
668	#386	C₂²×C₁₃₉	1	2	yes	complemented
669	#385	C₂²×C₁₃₉	1	2	yes	complemented
670	#385	C₂²×C₁₃₉	1	2	yes	complemented
671	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
672	#381	C₂²×C₁₃₉	1	2	yes	—
673	#381	C₂²×C₁₃₉	1	2	yes	—
674	#380	C₂²×C₁₃₉	1	1	yes	characteristic
675	#380	C₂²×C₁₃₉	1	2	yes	—
676	#380	C₂²×C₁₃₉	1	1	yes	characteristic
677	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
678	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
679	#379	C₂²×C₁₃₉	1	2	yes	—
680	#379	C₂²×C₁₃₉	1	2	yes	—
681	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
682	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
683	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
684	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
685	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
686	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
687	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
689	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
690	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
691	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
692	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
693	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
694	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
695	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
696	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
697	C₂²×D₄	—	2	4	no	—
698	C₂²×D₄	—	2	4	no	—
699	C₂²×D₄	—	4	2	no	—
700	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
701	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
702	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
703	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
706	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
707	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
708	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
709	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
711	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
713	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
714	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
715	C₄⋊Q₈	—	4	2	no	—
716	#126	—	2	8	no	—
717	#126	—	2	8	no	—
718	#124	—	2	8	no	—
719	#123	—	2	8	no	—
720	#123	—	2	8	no	—
721	#123	—	2	8	no	—
722	C₂²⋊Q₈	—	2	8	no	—
723	C₂²⋊Q₈	—	2	8	no	—
724	#121	—	2	4	no	—
725	#121	—	4	2	no	—
726	#120	—	2	8	no	—
727	C₄×D₄	—	2	4	no	—
728	C₄×D₄	—	2	8	no	—
729	C₄×D₄	—	2	4	no	—
730	C₄×D₄	—	2	4	no	—
731	C₄×D₄	—	4	2	no	—
732	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
733	#117	—	2	8	no	—
734	#117	—	2	8	no	—
735	C₂×C₄⋊C₄	—	2	4	no	—
736	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	—	2	8	no	—
756	C₂×C₂²⋊C₄	—	2	8	no	—
757	C₂×C₂²⋊C₄	—	2	8	no	—
758	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
788	C₂×C₄²	—	4	2	no	—
789	C₂×C₄²	—	4	2	no	—
790	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
791	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
792	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
805	#95	C₂³×C₁₃₉	1	1	yes	characteristic
806	#95	C₂³×C₁₃₉	1	1	yes	characteristic
807	#95	C₂³×C₁₃₉	1	1	yes	characteristic
808	#95	C₂³×C₁₃₉	1	1	yes	characteristic
809	#95	C₂³×C₁₃₉	1	1	yes	characteristic
810	#95	C₂³×C₁₃₉	1	1	yes	characteristic
811	#95	C₂³×C₁₃₉	1	2	yes	—
812	#95	C₂³×C₁₃₉	1	2	yes	—
813	#95	C₂³×C₁₃₉	1	2	yes	—
814	#95	C₂³×C₁₃₉	1	2	yes	—
815	#95	C₂³×C₁₃₉	1	2	yes	—
816	#95	C₂³×C₁₃₉	1	2	yes	—
817	#95	C₂³×C₁₃₉	1	2	yes	—
818	#95	C₂³×C₁₃₉	1	2	yes	—
819	#95	C₂³×C₁₃₉	1	2	yes	—
820	#95	C₂³×C₁₃₉	1	2	yes	—
821	#95	C₂³×C₁₃₉	1	2	yes	—
822	#95	C₂³×C₁₃₉	1	2	yes	—
823	C₂⁴	—	2	4	no	—
824	C₂⁴	—	2	4	no	—
825	C₂⁴	—	2	4	no	—
826	C₂⁴	—	2	4	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	—	4	2	no	—
829	C₂⁴	—	4	2	no	—
830	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
831	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
832	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
833	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
834	C₂×Q₈	—	2	4	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	4	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	4	16	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
855	C₂×D₄	#41×C₁₃₉	1	4	yes	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	4	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	4	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	1	no	—
871	C₂²×C₄	—	4	1	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	1	no	—
874	C₂²×C₄	—	4	1	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
880	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
881	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
882	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
883	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	4	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	4	no	—
908	C₄⋊C₄	—	2	4	no	—
909	C₄⋊C₄	—	2	4	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
950	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
951	C₄²	—	2	4	no	—
952	C₄²	—	2	4	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	4	1	no	—
960	C₄²	—	4	1	no	—
961	C₄²	—	4	1	no	—
962	C₄²	—	4	1	no	—
963	C₄²	—	4	1	no	—
964	C₄²	—	4	1	no	—
965	C₄²	C₂×D₄×C₁₃₉	1	4	yes	complemented
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	4	8	no	—
990	C₂³	—	4	8	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	8	4	no	—
994	C₂³	—	8	4	no	—
995	C₂³	—	8	4	no	—
996	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
997	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
998	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
999	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1000	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1001	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1002	Q₈	—	8	4	no	—
1003	D₄	—	2	8	no	—
1004	D₄	—	2	8	no	—
1005	D₄	—	4	8	no	—
1006	D₄	—	4	8	no	—
1007	D₄	—	4	4	no	—
1008	D₄	—	8	4	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	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	1	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	—	4	4	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	8	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	8	no	—
1062	C₂×C₄	—	4	4	no	—
1063	C₂×C₄	—	8	4	no	—
1064	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1069	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1070	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1071	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1072	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1073	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1074	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	4	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	8	16	no	—
1103	C₂²	#532×C₁₃₉	1	4	yes	—
1104	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1105	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1106	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1107	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1108	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1109	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1110	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1111	C₄	—	2	2	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	2	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	#551×C₁₃₉	1	4	yes	complemented
1130	C₂	—	2	4	no	—
1131	C₂	—	4	4	no	—
1132	C₂	—	4	2	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
1135	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1136	C₂	C₂×#551×C₁₃₉	1	1	yes	characteristic
1137	C₂	#3475×C₁₃₉	1	1	yes	characteristic
1138	C₂	#3496×C₁₃₉	1	1	yes	characteristic
1139	C₂	#3505×C₁₃₉	1	1	yes	characteristic
1140	C₂	#3510×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2408×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×#551×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2602×C₁₃₉	C₂	semidirect
6. #2601×C₁₃₉	C₂	semidirect
7. #2561×C₁₃₉	C₂	semidirect
8. #2560×C₁₃₉	C₂	semidirect
9. #2557×C₁₃₉	C₂	semidirect
10. #2534×C₁₃₉	C₂	semidirect
11. #2512×C₁₃₉	C₂	semidirect
12. #2491×C₁₃₉	C₂	semidirect
13. #2486×C₁₃₉	C₂	semidirect
14. #2452×C₁₃₉	C₂	semidirect
15. #2422×C₁₃₉	C₂	semidirect
17. #2344×C₁₃₉	C₂	semidirect
18. #2342×C₁₃₉	C₂	semidirect
19. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
20. C₄×#121×C₁₃₉	C₂	semidirect
21. #2293×C₁₃₉	C₂	semidirect
22. C₂×#390×C₁₃₉	C₂	semidirect
23. C₄²×D₄×C₁₃₉	C₂	semidirect
26. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×#126×C₁₃₉	C₂²	semidirect
28. C₂×#126×C₁₃₉	C₂²	semidirect
29. C₂×#124×C₁₃₉	C₂²	semidirect
31. C₂×#123×C₁₃₉	C₂²	semidirect
32. C₂×#123×C₁₃₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
45. C₂×#117×C₁₃₉	C₂²	semidirect
51. C₂²×C₄²×C₁₃₉	C₂²	semidirect
52. #398×C₁₃₉	C₂²	semidirect
53. #397×C₁₃₉	C₂²	semidirect
54. #397×C₁₃₉	C₂²	semidirect
55. #397×C₁₃₉	C₂²	semidirect
56. #396×C₁₃₉	C₂²	semidirect
57. #396×C₁₃₉	C₂²	semidirect
59. #394×C₁₃₉	C₂²	semidirect
60. #394×C₁₃₉	C₂²	semidirect
61. #393×C₁₃₉	C₂²	semidirect
62. #393×C₁₃₉	C₂²	semidirect
64. #391×C₁₃₉	C₂²	semidirect
75. #389×C₁₃₉	C₂²	semidirect
76. #389×C₁₃₉	C₂²	semidirect
77. #389×C₁₃₉	C₂²	semidirect
78. #389×C₁₃₉	C₂²	semidirect
79. #389×C₁₃₉	C₂²	semidirect
80. #389×C₁₃₉	C₂²	semidirect
81. #389×C₁₃₉	C₂²	semidirect
82. #388×C₁₃₉	C₂²	semidirect
83. #388×C₁₃₉	C₂²	semidirect
84. #388×C₁₃₉	C₂²	semidirect
85. #388×C₁₃₉	C₂²	semidirect
86. #388×C₁₃₉	C₂²	semidirect
87. #388×C₁₃₉	C₂²	semidirect
88. #388×C₁₃₉	C₂²	semidirect
89. #388×C₁₃₉	C₂²	semidirect
90. #388×C₁₃₉	C₂²	semidirect
91. #388×C₁₃₉	C₂²	semidirect
92. #387×C₁₃₉	C₂²	semidirect
93. #387×C₁₃₉	C₂²	semidirect
96. #386×C₁₃₉	C₂²	semidirect
97. #386×C₁₃₉	C₂²	semidirect
98. #385×C₁₃₉	C₂²	semidirect
99. #385×C₁₃₉	C₂²	semidirect
100. #384×C₁₃₉	C₂²	semidirect
106. #380×C₁₃₉	C₂²	semidirect
107. #380×C₁₃₉	C₂²	semidirect
110. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
111. C₄×C₄⋊C₄×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. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. C₄³×C₁₃₉	C₂²	semidirect
161. C₄×D₄×C₁₃₉	D₄	semidirect
309. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
349. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
379. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
394. C₄²×C₁₃₉	C₂×D₄	semidirect
558. C₄×C₁₃₉	#551	semidirect
570. #36262	C₁₃₉	direct (N × H)
571. C₁₃₉	#36262	direct (N × H)
572. C₂×#551	C₂×C₁₃₉	semidirect
573. #2860	C₂×C₁₃₉	semidirect
574. #2857	C₂×C₁₃₉	semidirect
575. #2854	C₂×C₁₃₉	semidirect
576. #2602	C₂×C₁₃₉	semidirect
577. #2601	C₂×C₁₃₉	semidirect
578. #2561	C₂×C₁₃₉	semidirect
579. #2560	C₂×C₁₃₉	semidirect
580. #2557	C₂×C₁₃₉	semidirect
581. #2534	C₂×C₁₃₉	semidirect
582. #2512	C₂×C₁₃₉	semidirect
583. #2491	C₂×C₁₃₉	semidirect
584. #2486	C₂×C₁₃₉	semidirect
585. #2452	C₂×C₁₃₉	semidirect
586. #2422	C₂×C₁₃₉	semidirect
588. #2344	C₂×C₁₃₉	semidirect
589. #2342	C₂×C₁₃₉	semidirect
590. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
591. C₄×#121	C₂×C₁₃₉	semidirect
592. #2293	C₂×C₁₃₉	semidirect
593. C₂×#390	C₂×C₁₃₉	semidirect
594. C₄²×D₄	C₂×C₁₃₉	semidirect
597. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
598. C₂×#126	C₂²×C₁₃₉	semidirect
599. C₂×#126	C₂²×C₁₃₉	semidirect
600. C₂×#124	C₂²×C₁₃₉	semidirect
602. C₂×#123	C₂²×C₁₃₉	semidirect
603. C₂×#123	C₂²×C₁₃₉	semidirect
605. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
614. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
616. C₂×#117	C₂²×C₁₃₉	semidirect
622. C₂²×C₄²	C₂²×C₁₃₉	semidirect
623. #398	C₂²×C₁₃₉	semidirect
624. #397	C₂²×C₁₃₉	semidirect
625. #397	C₂²×C₁₃₉	semidirect
626. #397	C₂²×C₁₃₉	semidirect
627. #396	C₂²×C₁₃₉	semidirect
628. #396	C₂²×C₁₃₉	semidirect
630. #394	C₂²×C₁₃₉	semidirect
631. #394	C₂²×C₁₃₉	semidirect
632. #393	C₂²×C₁₃₉	semidirect
633. #393	C₂²×C₁₃₉	semidirect
635. #391	C₂²×C₁₃₉	semidirect
646. #389	C₂²×C₁₃₉	semidirect
647. #389	C₂²×C₁₃₉	semidirect
648. #389	C₂²×C₁₃₉	semidirect
649. #389	C₂²×C₁₃₉	semidirect
650. #389	C₂²×C₁₃₉	semidirect
651. #389	C₂²×C₁₃₉	semidirect
652. #389	C₂²×C₁₃₉	semidirect
653. #388	C₂²×C₁₃₉	semidirect
654. #388	C₂²×C₁₃₉	semidirect
655. #388	C₂²×C₁₃₉	semidirect
656. #388	C₂²×C₁₃₉	semidirect
657. #388	C₂²×C₁₃₉	semidirect
658. #388	C₂²×C₁₃₉	semidirect
659. #388	C₂²×C₁₃₉	semidirect
660. #388	C₂²×C₁₃₉	semidirect
661. #388	C₂²×C₁₃₉	semidirect
662. #388	C₂²×C₁₃₉	semidirect
663. #387	C₂²×C₁₃₉	semidirect
664. #387	C₂²×C₁₃₉	semidirect
667. #386	C₂²×C₁₃₉	semidirect
668. #386	C₂²×C₁₃₉	semidirect
669. #385	C₂²×C₁₃₉	semidirect
670. #385	C₂²×C₁₃₉	semidirect
671. #384	C₂²×C₁₃₉	semidirect
677. #380	C₂²×C₁₃₉	semidirect
678. #380	C₂²×C₁₃₉	semidirect
681. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
682. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
683. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
684. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
685. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
690. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
691. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
692. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
693. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
694. C₄³	C₂²×C₁₃₉	semidirect
732. C₄×D₄	D₄×C₁₃₉	semidirect
880. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
920. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
950. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
965. C₄²	C₂×D₄×C₁₃₉	semidirect
1129. C₄	#551×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₁₃₉	2
#2860×C₁₃₉	2
#2857×C₁₃₉	2
#2854×C₁₃₉	2
#2602×C₁₃₉	2
#2601×C₁₃₉	2
#2561×C₁₃₉	2
#2560×C₁₃₉	2
#2557×C₁₃₉	2
#2534×C₁₃₉	2
#2512×C₁₃₉	2
#2491×C₁₃₉	2
#2486×C₁₃₉	2
#2452×C₁₃₉	2
#2422×C₁₃₉	2
#2408×C₁₃₉	2
#2344×C₁₃₉	2
#2342×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#121×C₁₃₉	2
#2293×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36262	139

Subgroups — C139×#36262 #48030858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36262 #48030858