Subgroups — C₁₃₉×#36317 #48030913

Order 35584.

2980 conjugacy classes of subgroups.

The subgroup lattice has 1150 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2583×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2579×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2482×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2468×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2466×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2461×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2455×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2425×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2411×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2410×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2405×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
20	#2342×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#385×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	#551×C₁₃₉	—	2	8	no	—
28	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#126×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
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, complemented
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
39	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
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, complemented
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	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×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
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	1	yes	characteristic
59	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
60	#399×C₁₃₉	C₂²	1	2	yes	complemented
61	#398×C₁₃₉	C₂²	1	2	yes	complemented
62	#398×C₁₃₉	C₂²	1	2	yes	complemented
63	#397×C₁₃₉	C₂²	1	2	yes	complemented
64	#396×C₁₃₉	C₂²	1	2	yes	complemented
65	#396×C₁₃₉	C₂²	1	2	yes	complemented
66	#395×C₁₃₉	C₂²	1	2	yes	complemented
67	#394×C₁₃₉	C₂²	1	2	yes	—
68	#394×C₁₃₉	C₂²	1	2	yes	—
69	#394×C₁₃₉	C₂²	1	2	yes	—
70	#394×C₁₃₉	C₂²	1	2	yes	complemented
71	#392×C₁₃₉	C₂²	1	2	yes	—
72	#390×C₁₃₉	C₂²	1	2	yes	complemented
73	#389×C₁₃₉	C₂²	1	2	yes	complemented
74	#389×C₁₃₉	C₂²	1	2	yes	complemented
75	#389×C₁₃₉	C₂²	1	2	yes	complemented
76	#389×C₁₃₉	C₂²	1	2	yes	complemented
77	#388×C₁₃₉	C₂²	1	2	yes	complemented
78	#388×C₁₃₉	C₂²	1	2	yes	complemented
79	#388×C₁₃₉	C₂²	1	2	yes	complemented
80	#388×C₁₃₉	C₂²	1	2	yes	complemented
81	#388×C₁₃₉	C₂²	1	2	yes	complemented
82	#388×C₁₃₉	C₂²	1	2	yes	complemented
83	#388×C₁₃₉	C₂²	1	2	yes	complemented
84	#387×C₁₃₉	C₂²	1	2	yes	complemented
85	#387×C₁₃₉	C₂²	1	2	yes	complemented
86	#387×C₁₃₉	C₂²	1	2	yes	complemented
87	#386×C₁₃₉	C₂²	1	1	yes	characteristic
88	#386×C₁₃₉	C₂²	1	1	yes	characteristic
89	#386×C₁₃₉	C₂²	1	1	yes	characteristic
90	#386×C₁₃₉	C₂²	1	2	yes	—
91	#386×C₁₃₉	C₂²	1	2	yes	—
92	#386×C₁₃₉	C₂²	1	2	yes	complemented
93	#386×C₁₃₉	C₂²	1	2	yes	complemented
94	#385×C₁₃₉	C₂²	1	1	yes	characteristic
95	#385×C₁₃₉	C₂²	1	1	yes	characteristic
96	#385×C₁₃₉	C₂²	1	1	yes	characteristic
97	#385×C₁₃₉	C₂²	1	1	yes	characteristic
98	#385×C₁₃₉	C₂²	1	1	yes	characteristic
99	#385×C₁₃₉	C₂²	1	1	yes	characteristic
100	#385×C₁₃₉	C₂²	1	1	yes	characteristic
101	#385×C₁₃₉	C₂²	1	1	yes	characteristic
102	#385×C₁₃₉	C₂²	1	1	yes	characteristic
103	#385×C₁₃₉	C₂²	1	2	yes	complemented
104	#385×C₁₃₉	C₂²	1	2	yes	complemented
105	#385×C₁₃₉	C₂²	1	2	yes	complemented
106	#385×C₁₃₉	C₂²	1	2	yes	complemented
107	#385×C₁₃₉	C₂²	1	2	yes	complemented
108	#385×C₁₃₉	C₂²	1	2	yes	complemented
109	#385×C₁₃₉	C₂²	1	2	yes	complemented
110	#385×C₁₃₉	C₂²	1	2	yes	complemented
111	#381×C₁₃₉	C₂²	1	1	yes	characteristic
112	#381×C₁₃₉	C₂²	1	2	yes	complemented
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic
114	#380×C₁₃₉	C₂²	1	2	yes	complemented
115	#379×C₁₃₉	C₂²	1	1	yes	characteristic
116	#379×C₁₃₉	C₂²	1	1	yes	characteristic
117	#379×C₁₃₉	C₂²	1	1	yes	characteristic
118	#379×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
120	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃₉	—	2	4	no	—
129	C₂²×D₄×C₁₃₉	—	2	8	no	—
130	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
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	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	—	2	4	no	—
137	C₂³×C₄×C₁₃₉	—	2	4	no	—
138	C₂³×C₄×C₁₃₉	—	4	4	no	—
139	C₂³×C₄×C₁₃₉	—	4	4	no	—
140	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	#126×C₁₃₉	—	2	4	no	—
154	#126×C₁₃₉	—	2	4	no	—
155	#124×C₁₃₉	—	2	4	no	—
156	#123×C₁₃₉	—	2	8	no	—
157	#123×C₁₃₉	—	2	4	no	—
158	#123×C₁₃₉	—	2	4	no	—
159	#123×C₁₃₉	—	2	4	no	—
160	#123×C₁₃₉	—	4	4	no	—
161	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
162	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
163	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
164	#121×C₁₃₉	—	2	8	no	—
165	#120×C₁₃₉	—	2	4	no	—
166	#120×C₁₃₉	—	2	4	no	—
167	C₄×D₄×C₁₃₉	—	2	4	no	—
168	C₄×D₄×C₁₃₉	—	2	8	no	—
169	C₄×D₄×C₁₃₉	—	2	8	no	—
170	C₄×D₄×C₁₃₉	—	2	8	no	—
171	C₄×D₄×C₁₃₉	—	2	8	no	—
172	C₄×D₄×C₁₃₉	—	2	4	no	—
173	C₄×D₄×C₁₃₉	—	4	4	no	—
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	2	yes	—
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×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	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
201	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
233	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₁₃₉	—	2	4	no	—
238	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
239	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
243	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	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	#95×C₁₃₉	C₂³	1	2	yes	—
260	#95×C₁₃₉	C₂³	1	2	yes	—
261	C₂⁴×C₁₃₉	—	2	2	no	—
262	C₂⁴×C₁₃₉	—	2	2	no	—
263	C₂⁴×C₁₃₉	—	2	4	no	—
264	C₂⁴×C₁₃₉	—	2	4	no	—
265	C₂⁴×C₁₃₉	—	2	2	no	—
266	C₂⁴×C₁₃₉	—	2	2	no	—
267	C₂⁴×C₁₃₉	—	2	2	no	—
268	C₂⁴×C₁₃₉	—	4	2	no	—
269	C₂⁴×C₁₃₉	—	4	2	no	—
270	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
271	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
274	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂×Q₈×C₁₃₉	—	2	2	no	—
277	C₂×Q₈×C₁₃₉	—	4	2	no	—
278	C₂×D₄×C₁₃₉	—	2	32	no	—
279	C₂×D₄×C₁₃₉	—	2	4	no	—
280	C₂×D₄×C₁₃₉	—	2	4	no	—
281	C₂×D₄×C₁₃₉	—	2	4	no	—
282	C₂×D₄×C₁₃₉	—	2	4	no	—
283	C₂×D₄×C₁₃₉	—	2	2	no	—
284	C₂×D₄×C₁₃₉	—	2	2	no	—
285	C₂×D₄×C₁₃₉	—	2	2	no	—
286	C₂×D₄×C₁₃₉	—	2	4	no	—
287	C₂×D₄×C₁₃₉	—	2	4	no	—
288	C₂×D₄×C₁₃₉	—	2	2	no	—
289	C₂×D₄×C₁₃₉	—	2	2	no	—
290	C₂×D₄×C₁₃₉	—	2	4	no	—
291	C₂×D₄×C₁₃₉	—	2	4	no	—
292	C₂×D₄×C₁₃₉	—	4	2	no	—
293	C₂×D₄×C₁₃₉	—	4	2	no	—
294	C₂×D₄×C₁₃₉	#41	1	8	yes	—
295	C₂²×C₄×C₁₃₉	—	2	2	no	—
296	C₂²×C₄×C₁₃₉	—	2	2	no	—
297	C₂²×C₄×C₁₃₉	—	2	2	no	—
298	C₂²×C₄×C₁₃₉	—	2	2	no	—
299	C₂²×C₄×C₁₃₉	—	2	4	no	—
300	C₂²×C₄×C₁₃₉	—	2	4	no	—
301	C₂²×C₄×C₁₃₉	—	2	2	no	—
302	C₂²×C₄×C₁₃₉	—	2	2	no	—
303	C₂²×C₄×C₁₃₉	—	2	4	no	—
304	C₂²×C₄×C₁₃₉	—	2	4	no	—
305	C₂²×C₄×C₁₃₉	—	2	4	no	—
306	C₂²×C₄×C₁₃₉	—	2	4	no	—
307	C₂²×C₄×C₁₃₉	—	2	2	no	—
308	C₂²×C₄×C₁₃₉	—	2	4	no	—
309	C₂²×C₄×C₁₃₉	—	2	4	no	—
310	C₂²×C₄×C₁₃₉	—	2	4	no	—
311	C₂²×C₄×C₁₃₉	—	2	4	no	—
312	C₂²×C₄×C₁₃₉	—	2	4	no	—
313	C₂²×C₄×C₁₃₉	—	2	4	no	—
314	C₂²×C₄×C₁₃₉	—	2	4	no	—
315	C₂²×C₄×C₁₃₉	—	2	2	no	—
316	C₂²×C₄×C₁₃₉	—	4	2	no	—
317	C₂²×C₄×C₁₃₉	—	4	2	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	16	no	—
326	C₂²×C₄×C₁₃₉	—	4	16	no	—
327	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
328	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
329	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
342	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₁₃₉	—	2	4	no	—
348	C₄⋊C₄×C₁₃₉	—	2	4	no	—
349	C₄⋊C₄×C₁₃₉	—	2	2	no	—
350	C₄⋊C₄×C₁₃₉	—	2	2	no	—
351	C₄⋊C₄×C₁₃₉	—	2	2	no	—
352	C₄⋊C₄×C₁₃₉	—	2	2	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	—	2	4	no	—
363	C₄⋊C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
370	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
373	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
374	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
378	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
379	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
380	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
381	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
382	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
383	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
384	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
385	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
386	C₂²⋊C₄×C₁₃₉	—	2	2	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	C₂×D₄	1	4	yes	—
397	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
398	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
399	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
400	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
401	C₄²×C₁₃₉	—	2	4	no	—
402	C₄²×C₁₃₉	—	2	4	no	—
403	C₄²×C₁₃₉	—	2	2	no	—
404	C₄²×C₁₃₉	—	2	2	no	—
405	C₄²×C₁₃₉	—	2	2	no	—
406	C₄²×C₁₃₉	—	2	4	no	—
407	C₄²×C₁₃₉	—	4	2	no	—
408	C₂³×C₁₃₉	—	2	1	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	—	2	8	no	—
414	C₂³×C₁₃₉	—	2	8	no	—
415	C₂³×C₁₃₉	—	2	8	no	—
416	C₂³×C₁₃₉	—	2	2	no	—
417	C₂³×C₁₃₉	—	2	1	no	—
418	C₂³×C₁₃₉	—	2	2	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	1	no	—
425	C₂³×C₁₃₉	—	2	2	no	—
426	C₂³×C₁₃₉	—	2	1	no	—
427	C₂³×C₁₃₉	—	2	2	no	—
428	C₂³×C₁₃₉	—	2	1	no	—
429	C₂³×C₁₃₉	—	2	2	no	—
430	C₂³×C₁₃₉	—	2	1	no	—
431	C₂³×C₁₃₉	—	4	4	no	—
432	C₂³×C₁₃₉	—	4	8	no	—
433	C₂³×C₁₃₉	—	4	8	no	—
434	C₂³×C₁₃₉	—	4	8	no	—
435	C₂³×C₁₃₉	—	4	8	no	—
436	C₂³×C₁₃₉	—	4	4	no	—
437	C₂³×C₁₃₉	—	4	4	no	—
438	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
439	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
440	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
441	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
442	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
443	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
444	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
445	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
446	Q₈×C₁₃₉	—	8	2	no	—
447	D₄×C₁₃₉	—	2	16	no	—
448	D₄×C₁₃₉	—	2	16	no	—
449	D₄×C₁₃₉	—	4	8	no	—
450	D₄×C₁₃₉	—	4	4	no	—
451	D₄×C₁₃₉	—	4	4	no	—
452	D₄×C₁₃₉	—	8	2	no	—
453	C₂×C₄×C₁₃₉	—	2	8	no	—
454	C₂×C₄×C₁₃₉	—	2	8	no	—
455	C₂×C₄×C₁₃₉	—	2	8	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	1	no	—
459	C₂×C₄×C₁₃₉	—	2	1	no	—
460	C₂×C₄×C₁₃₉	—	2	2	no	—
461	C₂×C₄×C₁₃₉	—	2	2	no	—
462	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
467	C₂×C₄×C₁₃₉	—	2	1	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	1	no	—
470	C₂×C₄×C₁₃₉	—	2	1	no	—
471	C₂×C₄×C₁₃₉	—	2	1	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	2	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	1	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	1	no	—
495	C₂×C₄×C₁₃₉	—	4	4	no	—
496	C₂×C₄×C₁₃₉	—	4	8	no	—
497	C₂×C₄×C₁₃₉	—	4	8	no	—
498	C₂×C₄×C₁₃₉	—	4	8	no	—
499	C₂×C₄×C₁₃₉	—	4	8	no	—
500	C₂×C₄×C₁₃₉	—	4	8	no	—
501	C₂×C₄×C₁₃₉	—	4	4	no	—
502	C₂×C₄×C₁₃₉	—	4	4	no	—
503	C₂×C₄×C₁₃₉	—	8	2	no	—
504	C₂×C₄×C₁₃₉	—	8	2	no	—
505	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
510	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
511	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
512	C₂²×C₁₃₉	—	2	2	no	—
513	C₂²×C₁₃₉	—	2	2	no	—
514	C₂²×C₁₃₉	—	2	4	no	—
515	C₂²×C₁₃₉	—	2	4	no	—
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	4	no	—
522	C₂²×C₁₃₉	—	2	2	no	—
523	C₂²×C₁₃₉	—	2	4	no	—
524	C₂²×C₁₃₉	—	2	2	no	—
525	C₂²×C₁₃₉	—	2	4	no	—
526	C₂²×C₁₃₉	—	4	16	no	—
527	C₂²×C₁₃₉	—	4	16	no	—
528	C₂²×C₁₃₉	—	4	2	no	—
529	C₂²×C₁₃₉	—	4	2	no	—
530	C₂²×C₁₃₉	—	4	2	no	—
531	C₂²×C₁₃₉	—	4	2	no	—
532	C₂²×C₁₃₉	—	4	2	no	—
533	C₂²×C₁₃₉	—	4	2	no	—
534	C₂²×C₁₃₉	—	4	1	no	—
535	C₂²×C₁₃₉	—	4	1	no	—
536	C₂²×C₁₃₉	—	4	2	no	—
537	C₂²×C₁₃₉	—	4	1	no	—
538	C₂²×C₁₃₉	—	4	2	no	—
539	C₂²×C₁₃₉	#525	1	4	yes	—
540	C₂²×C₁₃₉	#547	1	4	yes	—
541	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
542	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
543	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
545	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
546	C₄×C₁₃₉	—	2	4	no	—
547	C₄×C₁₃₉	—	2	2	no	—
548	C₄×C₁₃₉	—	2	2	no	—
549	C₄×C₁₃₉	—	2	4	no	—
550	C₄×C₁₃₉	—	2	4	no	—
551	C₄×C₁₃₉	—	2	2	no	—
552	C₄×C₁₃₉	—	2	2	no	—
553	C₄×C₁₃₉	—	4	1	no	—
554	C₄×C₁₃₉	—	4	1	no	—
555	C₄×C₁₃₉	—	4	1	no	—
556	C₄×C₁₃₉	—	4	1	no	—
557	C₄×C₁₃₉	—	4	2	no	—
558	C₄×C₁₃₉	—	4	2	no	—
559	C₄×C₁₃₉	—	4	2	no	—
560	C₄×C₁₃₉	—	4	1	no	—
561	C₄×C₁₃₉	—	4	1	no	—
562	C₄×C₁₃₉	—	4	1	no	—
563	C₄×C₁₃₉	—	4	2	no	—
564	C₂×C₁₃₉	—	2	4	no	—
565	C₂×C₁₃₉	—	2	4	no	—
566	C₂×C₁₃₉	—	4	2	no	—
567	C₂×C₁₃₉	—	4	4	no	—
568	C₂×C₁₃₉	—	8	1	no	—
569	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
570	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
571	C₂×C₁₃₉	#3481	1	2	yes	—
572	C₂×C₁₃₉	#3484	1	1	yes	characteristic
573	C₂×C₁₃₉	#3520	1	2	yes	—
574	#36317	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
575	C₁₃₉	#36317	1	1	yes	characteristic, direct product factor, Sylow
576	C₂×#551	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
578	#2853	C₂×C₁₃₉	1	1	yes	characteristic, complemented
579	#2849	C₂×C₁₃₉	1	1	yes	characteristic, complemented
580	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
581	#2583	C₂×C₁₃₉	1	1	yes	characteristic, complemented
582	#2579	C₂×C₁₃₉	1	1	yes	characteristic, complemented
583	#2482	C₂×C₁₃₉	1	1	yes	characteristic, complemented
584	#2468	C₂×C₁₃₉	1	2	yes	complemented
585	#2466	C₂×C₁₃₉	1	2	yes	complemented
586	#2461	C₂×C₁₃₉	1	2	yes	complemented
587	#2455	C₂×C₁₃₉	1	2	yes	complemented
588	#2449	C₂×C₁₃₉	1	2	yes	complemented
589	#2425	C₂×C₁₃₉	1	2	yes	complemented
590	#2411	C₂×C₁₃₉	1	1	yes	characteristic, complemented
591	#2410	C₂×C₁₃₉	1	1	yes	characteristic
592	#2405	C₂×C₁₃₉	1	1	yes	characteristic, complemented
593	#2361	C₂×C₁₃₉	1	2	yes	complemented
594	#2359	C₂×C₁₃₉	1	2	yes	complemented
595	#2342	C₂×C₁₃₉	1	1	yes	characteristic, complemented
596	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic, complemented
597	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
598	C₂×#385	C₂×C₁₃₉	1	1	yes	characteristic, complemented
599	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
600	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
602	#551	—	2	8	no	—
603	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
604	C₂×#126	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
605	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
606	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
607	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
608	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
609	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
610	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
611	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
612	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
613	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
614	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
615	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
616	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
617	C₂×C₄×D₄	—	2	8	no	—
618	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
620	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
621	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
622	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
623	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
624	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
625	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
626	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
627	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
628	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
629	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
630	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
631	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
633	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
634	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
635	#399	C₂²×C₁₃₉	1	2	yes	complemented
636	#398	C₂²×C₁₃₉	1	2	yes	complemented
637	#398	C₂²×C₁₃₉	1	2	yes	complemented
638	#397	C₂²×C₁₃₉	1	2	yes	complemented
639	#396	C₂²×C₁₃₉	1	2	yes	complemented
640	#396	C₂²×C₁₃₉	1	2	yes	complemented
641	#395	C₂²×C₁₃₉	1	2	yes	complemented
642	#394	C₂²×C₁₃₉	1	2	yes	—
643	#394	C₂²×C₁₃₉	1	2	yes	—
644	#394	C₂²×C₁₃₉	1	2	yes	—
645	#394	C₂²×C₁₃₉	1	2	yes	complemented
646	#392	C₂²×C₁₃₉	1	2	yes	—
647	#390	C₂²×C₁₃₉	1	2	yes	complemented
648	#389	C₂²×C₁₃₉	1	2	yes	complemented
649	#389	C₂²×C₁₃₉	1	2	yes	complemented
650	#389	C₂²×C₁₃₉	1	2	yes	complemented
651	#389	C₂²×C₁₃₉	1	2	yes	complemented
652	#388	C₂²×C₁₃₉	1	2	yes	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	#387	C₂²×C₁₃₉	1	2	yes	complemented
660	#387	C₂²×C₁₃₉	1	2	yes	complemented
661	#387	C₂²×C₁₃₉	1	2	yes	complemented
662	#386	C₂²×C₁₃₉	1	1	yes	characteristic
663	#386	C₂²×C₁₃₉	1	1	yes	characteristic
664	#386	C₂²×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
670	#385	C₂²×C₁₃₉	1	1	yes	characteristic
671	#385	C₂²×C₁₃₉	1	1	yes	characteristic
672	#385	C₂²×C₁₃₉	1	1	yes	characteristic
673	#385	C₂²×C₁₃₉	1	1	yes	characteristic
674	#385	C₂²×C₁₃₉	1	1	yes	characteristic
675	#385	C₂²×C₁₃₉	1	1	yes	characteristic
676	#385	C₂²×C₁₃₉	1	1	yes	characteristic
677	#385	C₂²×C₁₃₉	1	1	yes	characteristic
678	#385	C₂²×C₁₃₉	1	2	yes	complemented
679	#385	C₂²×C₁₃₉	1	2	yes	complemented
680	#385	C₂²×C₁₃₉	1	2	yes	complemented
681	#385	C₂²×C₁₃₉	1	2	yes	complemented
682	#385	C₂²×C₁₃₉	1	2	yes	complemented
683	#385	C₂²×C₁₃₉	1	2	yes	complemented
684	#385	C₂²×C₁₃₉	1	2	yes	complemented
685	#385	C₂²×C₁₃₉	1	2	yes	complemented
686	#381	C₂²×C₁₃₉	1	1	yes	characteristic
687	#381	C₂²×C₁₃₉	1	2	yes	complemented
688	#380	C₂²×C₁₃₉	1	1	yes	characteristic
689	#380	C₂²×C₁₃₉	1	2	yes	complemented
690	#379	C₂²×C₁₃₉	1	1	yes	characteristic
691	#379	C₂²×C₁₃₉	1	1	yes	characteristic
692	#379	C₂²×C₁₃₉	1	1	yes	characteristic
693	#379	C₂²×C₁₃₉	1	1	yes	characteristic
694	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
695	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
696	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
697	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
698	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
699	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
700	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
701	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
702	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
703	C₂²×D₄	—	2	4	no	—
704	C₂²×D₄	—	2	8	no	—
705	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
706	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
709	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
710	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₂³×C₄	—	2	4	no	—
712	C₂³×C₄	—	2	4	no	—
713	C₂³×C₄	—	4	4	no	—
714	C₂³×C₄	—	4	4	no	—
715	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
719	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
728	#126	—	2	4	no	—
729	#126	—	2	4	no	—
730	#124	—	2	4	no	—
731	#123	—	2	8	no	—
732	#123	—	2	4	no	—
733	#123	—	2	4	no	—
734	#123	—	2	4	no	—
735	#123	—	4	4	no	—
736	C₂²⋊Q₈	—	2	4	no	—
737	C₂²⋊Q₈	—	2	4	no	—
738	C₂²⋊Q₈	—	4	4	no	—
739	#121	—	2	8	no	—
740	#120	—	2	4	no	—
741	#120	—	2	4	no	—
742	C₄×D₄	—	2	4	no	—
743	C₄×D₄	—	2	8	no	—
744	C₄×D₄	—	2	8	no	—
745	C₄×D₄	—	2	8	no	—
746	C₄×D₄	—	2	8	no	—
747	C₄×D₄	—	2	4	no	—
748	C₄×D₄	—	4	4	no	—
749	#117	—	2	4	no	—
750	#117	—	2	4	no	—
751	#117	—	2	4	no	—
752	C₂×C₄⋊C₄	—	2	4	no	—
753	C₂×C₄⋊C₄	—	4	4	no	—
754	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
765	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
768	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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×C₂²⋊C₄	—	2	4	no	—
776	C₂×C₂²⋊C₄	—	2	4	no	—
777	C₂×C₂²⋊C₄	—	2	4	no	—
778	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
808	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
810	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
812	C₂×C₄²	—	2	4	no	—
813	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
816	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
817	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
818	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
819	C₂×C₄²	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	#95	C₂³×C₁₃₉	1	2	yes	—
824	#95	C₂³×C₁₃₉	1	2	yes	—
825	#95	C₂³×C₁₃₉	1	2	yes	—
826	#95	C₂³×C₁₃₉	1	2	yes	—
827	#95	C₂³×C₁₃₉	1	2	yes	—
828	#95	C₂³×C₁₃₉	1	2	yes	—
829	#95	C₂³×C₁₃₉	1	2	yes	—
830	#95	C₂³×C₁₃₉	1	2	yes	—
831	#95	C₂³×C₁₃₉	1	2	yes	—
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	C₂⁴	—	2	2	no	—
837	C₂⁴	—	2	2	no	—
838	C₂⁴	—	2	4	no	—
839	C₂⁴	—	2	4	no	—
840	C₂⁴	—	2	2	no	—
841	C₂⁴	—	2	2	no	—
842	C₂⁴	—	2	2	no	—
843	C₂⁴	—	4	2	no	—
844	C₂⁴	—	4	2	no	—
845	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
846	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
847	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
848	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
849	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
850	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	4	2	no	—
853	C₂×D₄	—	2	32	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	4	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	4	no	—
866	C₂×D₄	—	2	4	no	—
867	C₂×D₄	—	4	2	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	#41×C₁₃₉	1	8	yes	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	4	no	—
879	C₂²×C₄	—	2	4	no	—
880	C₂²×C₄	—	2	4	no	—
881	C₂²×C₄	—	2	4	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	4	no	—
884	C₂²×C₄	—	2	4	no	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	2	4	no	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	2	4	no	—
889	C₂²×C₄	—	2	4	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	4	2	no	—
892	C₂²×C₄	—	4	2	no	—
893	C₂²×C₄	—	4	2	no	—
894	C₂²×C₄	—	4	2	no	—
895	C₂²×C₄	—	4	2	no	—
896	C₂²×C₄	—	4	2	no	—
897	C₂²×C₄	—	4	2	no	—
898	C₂²×C₄	—	4	2	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	16	no	—
901	C₂²×C₄	—	4	16	no	—
902	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
903	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
904	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
922	C₄⋊C₄	—	2	4	no	—
923	C₄⋊C₄	—	2	4	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	4	no	—
933	C₄⋊C₄	—	2	4	no	—
934	C₄⋊C₄	—	2	4	no	—
935	C₄⋊C₄	—	2	4	no	—
936	C₄⋊C₄	—	2	4	no	—
937	C₄⋊C₄	—	2	4	no	—
938	C₄⋊C₄	—	2	4	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	2	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	4	no	—
963	C₂²⋊C₄	—	2	4	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	2	4	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
972	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
973	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
974	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
975	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
976	C₄²	—	2	4	no	—
977	C₄²	—	2	4	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	4	no	—
982	C₄²	—	4	2	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	8	no	—
989	C₂³	—	2	8	no	—
990	C₂³	—	2	8	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	4	4	no	—
1007	C₂³	—	4	8	no	—
1008	C₂³	—	4	8	no	—
1009	C₂³	—	4	8	no	—
1010	C₂³	—	4	8	no	—
1011	C₂³	—	4	4	no	—
1012	C₂³	—	4	4	no	—
1013	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1014	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1015	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1016	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
1017	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
1018	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1019	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1020	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1021	Q₈	—	8	2	no	—
1022	D₄	—	2	16	no	—
1023	D₄	—	2	16	no	—
1024	D₄	—	4	8	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	4	no	—
1027	D₄	—	8	2	no	—
1028	C₂×C₄	—	2	8	no	—
1029	C₂×C₄	—	2	8	no	—
1030	C₂×C₄	—	2	8	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	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	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	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	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	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	1	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	8	no	—
1072	C₂×C₄	—	4	8	no	—
1073	C₂×C₄	—	4	8	no	—
1074	C₂×C₄	—	4	8	no	—
1075	C₂×C₄	—	4	8	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1084	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1085	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1086	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	4	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	4	no	—
1094	C₂²	—	2	4	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	4	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	4	no	—
1101	C₂²	—	4	16	no	—
1102	C₂²	—	4	16	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	#525×C₁₃₉	1	4	yes	—
1115	C₂²	#547×C₁₃₉	1	4	yes	—
1116	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1117	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
1118	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1119	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1120	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1121	C₄	—	2	4	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	4	no	—
1125	C₄	—	2	4	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₂	—	2	4	no	—
1140	C₂	—	2	4	no	—
1141	C₂	—	4	2	no	—
1142	C₂	—	4	4	no	—
1143	C₂	—	8	1	no	—
1144	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1145	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
1146	C₂	#3481×C₁₃₉	1	2	yes	—
1147	C₂	#3484×C₁₃₉	1	1	yes	characteristic
1148	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2410×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. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2848×C₁₃₉	C₂	semidirect
6. #2583×C₁₃₉	C₂	semidirect
7. #2579×C₁₃₉	C₂	semidirect
8. #2482×C₁₃₉	C₂	semidirect
9. #2468×C₁₃₉	C₂	semidirect
10. #2466×C₁₃₉	C₂	semidirect
11. #2461×C₁₃₉	C₂	semidirect
12. #2455×C₁₃₉	C₂	semidirect
13. #2449×C₁₃₉	C₂	semidirect
14. #2425×C₁₃₉	C₂	semidirect
15. #2411×C₁₃₉	C₂	semidirect
17. #2405×C₁₃₉	C₂	semidirect
18. #2361×C₁₃₉	C₂	semidirect
19. #2359×C₁₃₉	C₂	semidirect
20. #2342×C₁₃₉	C₂	semidirect
21. C₄×#120×C₁₃₉	C₂	semidirect
22. #2296×C₁₃₉	C₂	semidirect
23. C₂×#385×C₁₃₉	C₂	semidirect
28. C₂×#126×C₁₃₉	C₂²	semidirect
29. C₂×#126×C₁₃₉	C₂²	semidirect
30. C₂×#124×C₁₃₉	C₂²	semidirect
33. C₂×#123×C₁₃₉	C₂²	semidirect
34. C₂×#123×C₁₃₉	C₂²	semidirect
35. C₂×#123×C₁₃₉	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
52. C₂×#117×C₁₃₉	C₂²	semidirect
54. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
60. #399×C₁₃₉	C₂²	semidirect
61. #398×C₁₃₉	C₂²	semidirect
62. #398×C₁₃₉	C₂²	semidirect
63. #397×C₁₃₉	C₂²	semidirect
64. #396×C₁₃₉	C₂²	semidirect
65. #396×C₁₃₉	C₂²	semidirect
66. #395×C₁₃₉	C₂²	semidirect
70. #394×C₁₃₉	C₂²	semidirect
72. #390×C₁₃₉	C₂²	semidirect
73. #389×C₁₃₉	C₂²	semidirect
74. #389×C₁₃₉	C₂²	semidirect
75. #389×C₁₃₉	C₂²	semidirect
76. #389×C₁₃₉	C₂²	semidirect
77. #388×C₁₃₉	C₂²	semidirect
78. #388×C₁₃₉	C₂²	semidirect
79. #388×C₁₃₉	C₂²	semidirect
80. #388×C₁₃₉	C₂²	semidirect
81. #388×C₁₃₉	C₂²	semidirect
82. #388×C₁₃₉	C₂²	semidirect
83. #388×C₁₃₉	C₂²	semidirect
84. #387×C₁₃₉	C₂²	semidirect
85. #387×C₁₃₉	C₂²	semidirect
86. #387×C₁₃₉	C₂²	semidirect
92. #386×C₁₃₉	C₂²	semidirect
93. #386×C₁₃₉	C₂²	semidirect
103. #385×C₁₃₉	C₂²	semidirect
104. #385×C₁₃₉	C₂²	semidirect
105. #385×C₁₃₉	C₂²	semidirect
106. #385×C₁₃₉	C₂²	semidirect
107. #385×C₁₃₉	C₂²	semidirect
108. #385×C₁₃₉	C₂²	semidirect
109. #385×C₁₃₉	C₂²	semidirect
110. #385×C₁₃₉	C₂²	semidirect
112. #381×C₁₃₉	C₂²	semidirect
114. #380×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
203. C₂×C₂²⋊C₄×C₁₃₉	D₄	semidirect
574. #36317	C₁₃₉	direct (N × H)
575. C₁₃₉	#36317	direct (N × H)
576. C₂×#551	C₂×C₁₃₉	semidirect
577. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
578. #2853	C₂×C₁₃₉	semidirect
579. #2849	C₂×C₁₃₉	semidirect
580. #2848	C₂×C₁₃₉	semidirect
581. #2583	C₂×C₁₃₉	semidirect
582. #2579	C₂×C₁₃₉	semidirect
583. #2482	C₂×C₁₃₉	semidirect
584. #2468	C₂×C₁₃₉	semidirect
585. #2466	C₂×C₁₃₉	semidirect
586. #2461	C₂×C₁₃₉	semidirect
587. #2455	C₂×C₁₃₉	semidirect
588. #2449	C₂×C₁₃₉	semidirect
589. #2425	C₂×C₁₃₉	semidirect
590. #2411	C₂×C₁₃₉	semidirect
592. #2405	C₂×C₁₃₉	semidirect
593. #2361	C₂×C₁₃₉	semidirect
594. #2359	C₂×C₁₃₉	semidirect
595. #2342	C₂×C₁₃₉	semidirect
596. C₄×#120	C₂×C₁₃₉	semidirect
597. #2296	C₂×C₁₃₉	semidirect
598. C₂×#385	C₂×C₁₃₉	semidirect
603. C₂×#126	C₂²×C₁₃₉	semidirect
604. C₂×#126	C₂²×C₁₃₉	semidirect
605. C₂×#124	C₂²×C₁₃₉	semidirect
608. C₂×#123	C₂²×C₁₃₉	semidirect
609. C₂×#123	C₂²×C₁₃₉	semidirect
610. C₂×#123	C₂²×C₁₃₉	semidirect
612. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
613. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
623. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
624. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
627. C₂×#117	C₂²×C₁₃₉	semidirect
629. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
635. #399	C₂²×C₁₃₉	semidirect
636. #398	C₂²×C₁₃₉	semidirect
637. #398	C₂²×C₁₃₉	semidirect
638. #397	C₂²×C₁₃₉	semidirect
639. #396	C₂²×C₁₃₉	semidirect
640. #396	C₂²×C₁₃₉	semidirect
641. #395	C₂²×C₁₃₉	semidirect
645. #394	C₂²×C₁₃₉	semidirect
647. #390	C₂²×C₁₃₉	semidirect
648. #389	C₂²×C₁₃₉	semidirect
649. #389	C₂²×C₁₃₉	semidirect
650. #389	C₂²×C₁₃₉	semidirect
651. #389	C₂²×C₁₃₉	semidirect
652. #388	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. #387	C₂²×C₁₃₉	semidirect
660. #387	C₂²×C₁₃₉	semidirect
661. #387	C₂²×C₁₃₉	semidirect
667. #386	C₂²×C₁₃₉	semidirect
668. #386	C₂²×C₁₃₉	semidirect
678. #385	C₂²×C₁₃₉	semidirect
679. #385	C₂²×C₁₃₉	semidirect
680. #385	C₂²×C₁₃₉	semidirect
681. #385	C₂²×C₁₃₉	semidirect
682. #385	C₂²×C₁₃₉	semidirect
683. #385	C₂²×C₁₃₉	semidirect
684. #385	C₂²×C₁₃₉	semidirect
685. #385	C₂²×C₁₃₉	semidirect
687. #381	C₂²×C₁₃₉	semidirect
689. #380	C₂²×C₁₃₉	semidirect
694. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
695. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
697. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
698. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
699. C₂×#95	C₂²×C₁₃₉	semidirect
778. C₂×C₂²⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2853×C₁₃₉	2
#2849×C₁₃₉	2
#2848×C₁₃₉	2
#2583×C₁₃₉	2
#2579×C₁₃₉	2
#2482×C₁₃₉	2
#2468×C₁₃₉	2
#2466×C₁₃₉	2
#2461×C₁₃₉	2
#2455×C₁₃₉	2
#2449×C₁₃₉	2
#2425×C₁₃₉	2
#2411×C₁₃₉	2
#2410×C₁₃₉	2
#2405×C₁₃₉	2
#2361×C₁₃₉	2
#2359×C₁₃₉	2
#2342×C₁₃₉	2
C₄×#120×C₁₃₉	2
#2296×C₁₃₉	2
C₂×#385×C₁₃₉	2
#36317	139

Subgroups — C139×#36317 #48030913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36317 #48030913