Subgroups — C₁₃₉×#36441 #48031037

Order 35584.

3004 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2600×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2472×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2459×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2455×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2447×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2445×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2418×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2367×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2366×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2361×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2360×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#120×C₁₃₉	C₂	1	2	yes	maximal, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
26	#559×C₁₃₉	—	2	8	no	—
27	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×#123×C₁₃₉	C₂²	1	2	yes	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
38	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
52	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
54	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
56	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
57	#399×C₁₃₉	C₂²	1	2	yes	complemented
58	#397×C₁₃₉	C₂²	1	2	yes	complemented
59	#397×C₁₃₉	C₂²	1	2	yes	complemented
60	#394×C₁₃₉	C₂²	1	2	yes	—
61	#394×C₁₃₉	C₂²	1	2	yes	—
62	#394×C₁₃₉	C₂²	1	2	yes	complemented
63	#394×C₁₃₉	C₂²	1	2	yes	complemented
64	#394×C₁₃₉	C₂²	1	2	yes	complemented
65	#394×C₁₃₉	C₂²	1	2	yes	complemented
66	#393×C₁₃₉	C₂²	1	2	yes	complemented
67	#392×C₁₃₉	C₂²	1	2	yes	—
68	#392×C₁₃₉	C₂²	1	2	yes	—
69	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
71	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
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	#390×C₁₃₉	C₂²	1	1	yes	characteristic
76	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
77	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
78	#390×C₁₃₉	C₂²	1	2	yes	complemented
79	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	#389×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	#387×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
91	#387×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
92	#387×C₁₃₉	C₂²	1	2	yes	complemented
93	#386×C₁₃₉	C₂²	1	2	yes	—
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	#386×C₁₃₉	C₂²	1	2	yes	complemented
99	#386×C₁₃₉	C₂²	1	2	yes	complemented
100	#386×C₁₃₉	C₂²	1	2	yes	complemented
101	#385×C₁₃₉	C₂²	1	1	yes	characteristic
102	#385×C₁₃₉	C₂²	1	1	yes	characteristic
103	#385×C₁₃₉	C₂²	1	2	yes	—
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	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
110	#381×C₁₃₉	C₂²	1	2	yes	complemented
111	#381×C₁₃₉	C₂²	1	2	yes	complemented
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic
113	#379×C₁₃₉	C₂²	1	2	yes	—
114	#379×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
124	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×Q₈×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	4	no	—
130	C₂²×D₄×C₁₃₉	—	2	4	no	—
131	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	—	2	8	no	—
141	C₂³×C₄×C₁₃₉	—	4	4	no	—
142	C₂³×C₄×C₁₃₉	—	4	4	no	—
143	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
152	#127×C₁₃₉	—	2	4	no	—
153	#127×C₁₃₉	—	2	4	no	—
154	#124×C₁₃₉	—	2	4	no	—
155	#124×C₁₃₉	—	2	4	no	—
156	#124×C₁₃₉	—	2	8	no	—
157	#124×C₁₃₉	—	2	4	no	—
158	#123×C₁₃₉	—	2	8	no	—
159	#123×C₁₃₉	—	2	8	no	—
160	#123×C₁₃₉	—	4	4	no	—
161	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
162	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
163	#121×C₁₃₉	—	2	4	no	—
164	#120×C₁₃₉	—	2	8	no	—
165	#120×C₁₃₉	—	4	4	no	—
166	C₄×Q₈×C₁₃₉	—	2	4	no	—
167	C₄×Q₈×C₁₃₉	—	2	4	no	—
168	C₄×D₄×C₁₃₉	—	2	4	no	—
169	C₄×D₄×C₁₃₉	—	2	8	no	—
170	C₄×D₄×C₁₃₉	—	2	8	no	—
171	C₄×D₄×C₁₃₉	—	2	4	no	—
172	C₄×D₄×C₁₃₉	—	2	4	no	—
173	C₄×D₄×C₁₃₉	—	2	8	no	—
174	C₄×D₄×C₁₃₉	—	2	4	no	—
175	C₄×D₄×C₁₃₉	—	4	4	no	—
176	C₄×D₄×C₁₃₉	—	4	4	no	—
177	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
178	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
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	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	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	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
226	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃₉	—	2	4	no	—
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	2	yes	—
233	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
237	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
239	#95×C₁₃₉	C₂³	1	1	yes	characteristic
240	#95×C₁₃₉	C₂³	1	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
250	#95×C₁₃₉	C₂³	1	1	yes	characteristic
251	#95×C₁₃₉	C₂³	1	1	yes	characteristic
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	1	yes	characteristic
255	#95×C₁₃₉	C₂³	1	1	yes	characteristic
256	#95×C₁₃₉	C₂³	1	1	yes	characteristic
257	#95×C₁₃₉	C₂³	1	2	yes	—
258	#95×C₁₃₉	C₂³	1	2	yes	—
259	C₂⁴×C₁₃₉	—	2	4	no	—
260	C₂⁴×C₁₃₉	—	2	4	no	—
261	C₂⁴×C₁₃₉	—	2	4	no	—
262	C₂⁴×C₁₃₉	—	2	4	no	—
263	C₂⁴×C₁₃₉	—	2	4	no	—
264	C₂⁴×C₁₃₉	—	4	2	no	—
265	C₂⁴×C₁₃₉	—	4	2	no	—
266	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂×Q₈×C₁₃₉	—	2	2	no	—
271	C₂×Q₈×C₁₃₉	—	2	2	no	—
272	C₂×Q₈×C₁₃₉	—	2	2	no	—
273	C₂×Q₈×C₁₃₉	—	2	2	no	—
274	C₂×Q₈×C₁₃₉	—	2	2	no	—
275	C₂×Q₈×C₁₃₉	—	4	1	no	—
276	C₂×D₄×C₁₃₉	—	2	32	no	—
277	C₂×D₄×C₁₃₉	—	2	4	no	—
278	C₂×D₄×C₁₃₉	—	2	4	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	4	no	—
284	C₂×D₄×C₁₃₉	—	2	4	no	—
285	C₂×D₄×C₁₃₉	—	2	4	no	—
286	C₂×D₄×C₁₃₉	—	2	2	no	—
287	C₂×D₄×C₁₃₉	—	2	2	no	—
288	C₂×D₄×C₁₃₉	—	2	4	no	—
289	C₂×D₄×C₁₃₉	—	2	2	no	—
290	C₂×D₄×C₁₃₉	—	2	2	no	—
291	C₂×D₄×C₁₃₉	—	2	2	no	—
292	C₂×D₄×C₁₃₉	—	2	4	no	—
293	C₂×D₄×C₁₃₉	—	2	4	no	—
294	C₂×D₄×C₁₃₉	—	2	2	no	—
295	C₂×D₄×C₁₃₉	—	2	2	no	—
296	C₂×D₄×C₁₃₉	—	4	2	no	—
297	C₂×D₄×C₁₃₉	—	4	2	no	—
298	C₂×D₄×C₁₃₉	—	4	2	no	—
299	C₂×D₄×C₁₃₉	—	4	2	no	—
300	C₂×D₄×C₁₃₉	—	4	2	no	—
301	C₂×D₄×C₁₃₉	—	4	2	no	—
302	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
303	C₂×D₄×C₁₃₉	#41	1	4	yes	—
304	C₂²×C₄×C₁₃₉	—	2	2	no	—
305	C₂²×C₄×C₁₃₉	—	2	2	no	—
306	C₂²×C₄×C₁₃₉	—	2	2	no	—
307	C₂²×C₄×C₁₃₉	—	2	2	no	—
308	C₂²×C₄×C₁₃₉	—	2	2	no	—
309	C₂²×C₄×C₁₃₉	—	2	4	no	—
310	C₂²×C₄×C₁₃₉	—	2	2	no	—
311	C₂²×C₄×C₁₃₉	—	2	4	no	—
312	C₂²×C₄×C₁₃₉	—	2	2	no	—
313	C₂²×C₄×C₁₃₉	—	2	4	no	—
314	C₂²×C₄×C₁₃₉	—	2	4	no	—
315	C₂²×C₄×C₁₃₉	—	2	4	no	—
316	C₂²×C₄×C₁₃₉	—	2	4	no	—
317	C₂²×C₄×C₁₃₉	—	2	4	no	—
318	C₂²×C₄×C₁₃₉	—	2	4	no	—
319	C₂²×C₄×C₁₃₉	—	4	2	no	—
320	C₂²×C₄×C₁₃₉	—	4	2	no	—
321	C₂²×C₄×C₁₃₉	—	4	2	no	—
322	C₂²×C₄×C₁₃₉	—	4	2	no	—
323	C₂²×C₄×C₁₃₉	—	4	2	no	—
324	C₂²×C₄×C₁₃₉	—	4	2	no	—
325	C₂²×C₄×C₁₃₉	—	4	2	no	—
326	C₂²×C₄×C₁₃₉	—	4	1	no	—
327	C₂²×C₄×C₁₃₉	—	4	2	no	—
328	C₂²×C₄×C₁₃₉	—	4	2	no	—
329	C₂²×C₄×C₁₃₉	—	4	32	no	—
330	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
331	C₂²×C₄×C₁₃₉	#41	1	4	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	1	yes	characteristic
337	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
346	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
351	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
356	C₄⋊C₄×C₁₃₉	—	2	2	no	—
357	C₄⋊C₄×C₁₃₉	—	2	2	no	—
358	C₄⋊C₄×C₁₃₉	—	2	2	no	—
359	C₄⋊C₄×C₁₃₉	—	2	2	no	—
360	C₄⋊C₄×C₁₃₉	—	2	4	no	—
361	C₄⋊C₄×C₁₃₉	—	2	2	no	—
362	C₄⋊C₄×C₁₃₉	—	2	2	no	—
363	C₄⋊C₄×C₁₃₉	—	2	2	no	—
364	C₄⋊C₄×C₁₃₉	—	2	2	no	—
365	C₄⋊C₄×C₁₃₉	—	4	1	no	—
366	C₄⋊C₄×C₁₃₉	—	4	2	no	—
367	C₄⋊C₄×C₁₃₉	—	4	2	no	—
368	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
374	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
375	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
376	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	2	2	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	4	no	—
382	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
383	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
384	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
385	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
386	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
387	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
388	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
389	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
390	C₂²⋊C₄×C₁₃₉	—	4	2	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	8	yes	—
397	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
398	C₄²×C₁₃₉	—	2	2	no	—
399	C₄²×C₁₃₉	—	2	2	no	—
400	C₄²×C₁₃₉	—	2	2	no	—
401	C₄²×C₁₃₉	—	2	4	no	—
402	C₄²×C₁₃₉	—	2	2	no	—
403	C₄²×C₁₃₉	—	2	2	no	—
404	C₄²×C₁₃₉	—	2	2	no	—
405	C₄²×C₁₃₉	—	2	2	no	—
406	C₄²×C₁₃₉	—	4	2	no	—
407	C₄²×C₁₃₉	—	4	2	no	—
408	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
409	C₂³×C₁₃₉	—	2	1	no	—
410	C₂³×C₁₃₉	—	2	1	no	—
411	C₂³×C₁₃₉	—	2	1	no	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	2	16	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	—	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	2	no	—
425	C₂³×C₁₃₉	—	2	2	no	—
426	C₂³×C₁₃₉	—	2	2	no	—
427	C₂³×C₁₃₉	—	2	2	no	—
428	C₂³×C₁₃₉	—	2	2	no	—
429	C₂³×C₁₃₉	—	2	2	no	—
430	C₂³×C₁₃₉	—	2	2	no	—
431	C₂³×C₁₃₉	—	2	2	no	—
432	C₂³×C₁₃₉	—	2	2	no	—
433	C₂³×C₁₃₉	—	4	8	no	—
434	C₂³×C₁₃₉	—	4	8	no	—
435	C₂³×C₁₃₉	—	4	8	no	—
436	C₂³×C₁₃₉	—	4	8	no	—
437	C₂³×C₁₃₉	—	4	8	no	—
438	C₂³×C₁₃₉	—	4	8	no	—
439	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
440	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
441	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
442	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
443	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
444	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
445	Q₈×C₁₃₉	—	4	4	no	—
446	Q₈×C₁₃₉	—	4	4	no	—
447	D₄×C₁₃₉	—	2	16	no	—
448	D₄×C₁₃₉	—	2	8	no	—
449	D₄×C₁₃₉	—	2	8	no	—
450	D₄×C₁₃₉	—	4	8	no	—
451	D₄×C₁₃₉	—	4	8	no	—
452	D₄×C₁₃₉	—	4	8	no	—
453	D₄×C₁₃₉	—	4	4	no	—
454	D₄×C₁₃₉	—	8	4	no	—
455	D₄×C₁₃₉	—	8	4	no	—
456	C₂×C₄×C₁₃₉	—	2	8	no	—
457	C₂×C₄×C₁₃₉	—	2	1	no	—
458	C₂×C₄×C₁₃₉	—	2	1	no	—
459	C₂×C₄×C₁₃₉	—	2	1	no	—
460	C₂×C₄×C₁₃₉	—	2	1	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	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	8	no	—
472	C₂×C₄×C₁₃₉	—	2	1	no	—
473	C₂×C₄×C₁₃₉	—	2	2	no	—
474	C₂×C₄×C₁₃₉	—	2	1	no	—
475	C₂×C₄×C₁₃₉	—	2	1	no	—
476	C₂×C₄×C₁₃₉	—	2	1	no	—
477	C₂×C₄×C₁₃₉	—	2	2	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	1	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	1	no	—
488	C₂×C₄×C₁₃₉	—	2	1	no	—
489	C₂×C₄×C₁₃₉	—	2	1	no	—
490	C₂×C₄×C₁₃₉	—	2	2	no	—
491	C₂×C₄×C₁₃₉	—	2	2	no	—
492	C₂×C₄×C₁₃₉	—	2	1	no	—
493	C₂×C₄×C₁₃₉	—	2	1	no	—
494	C₂×C₄×C₁₃₉	—	2	1	no	—
495	C₂×C₄×C₁₃₉	—	2	1	no	—
496	C₂×C₄×C₁₃₉	—	2	1	no	—
497	C₂×C₄×C₁₃₉	—	2	2	no	—
498	C₂×C₄×C₁₃₉	—	2	2	no	—
499	C₂×C₄×C₁₃₉	—	2	1	no	—
500	C₂×C₄×C₁₃₉	—	2	2	no	—
501	C₂×C₄×C₁₃₉	—	2	1	no	—
502	C₂×C₄×C₁₃₉	—	2	1	no	—
503	C₂×C₄×C₁₃₉	—	2	1	no	—
504	C₂×C₄×C₁₃₉	—	2	1	no	—
505	C₂×C₄×C₁₃₉	—	4	8	no	—
506	C₂×C₄×C₁₃₉	—	4	8	no	—
507	C₂×C₄×C₁₃₉	—	4	4	no	—
508	C₂×C₄×C₁₃₉	—	4	8	no	—
509	C₂×C₄×C₁₃₉	—	4	8	no	—
510	C₂×C₄×C₁₃₉	—	4	8	no	—
511	C₂×C₄×C₁₃₉	—	8	4	no	—
512	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
515	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
517	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
518	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
519	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
520	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
521	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
522	C₂²×C₁₃₉	—	2	2	no	—
523	C₂²×C₁₃₉	—	2	2	no	—
524	C₂²×C₁₃₉	—	2	2	no	—
525	C₂²×C₁₃₉	—	2	2	no	—
526	C₂²×C₁₃₉	—	2	2	no	—
527	C₂²×C₁₃₉	—	2	2	no	—
528	C₂²×C₁₃₉	—	2	4	no	—
529	C₂²×C₁₃₉	—	2	4	no	—
530	C₂²×C₁₃₉	—	2	4	no	—
531	C₂²×C₁₃₉	—	2	4	no	—
532	C₂²×C₁₃₉	—	2	4	no	—
533	C₂²×C₁₃₉	—	2	4	no	—
534	C₂²×C₁₃₉	—	4	32	no	—
535	C₂²×C₁₃₉	—	4	2	no	—
536	C₂²×C₁₃₉	—	4	2	no	—
537	C₂²×C₁₃₉	—	4	2	no	—
538	C₂²×C₁₃₉	—	4	2	no	—
539	C₂²×C₁₃₉	—	4	2	no	—
540	C₂²×C₁₃₉	—	4	2	no	—
541	C₂²×C₁₃₉	—	4	2	no	—
542	C₂²×C₁₃₉	—	4	2	no	—
543	C₂²×C₁₃₉	—	4	2	no	—
544	C₂²×C₁₃₉	—	4	2	no	—
545	C₂²×C₁₃₉	—	4	2	no	—
546	C₂²×C₁₃₉	—	4	2	no	—
547	C₂²×C₁₃₉	—	4	2	no	—
548	C₂²×C₁₃₉	—	4	2	no	—
549	C₂²×C₁₃₉	—	4	2	no	—
550	C₂²×C₁₃₉	#559	1	4	yes	complemented
551	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
552	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
553	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
554	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
555	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂²×C₁₃₉	#585	1	1	yes	characteristic
558	C₄×C₁₃₉	—	2	2	no	—
559	C₄×C₁₃₉	—	2	2	no	—
560	C₄×C₁₃₉	—	2	2	no	—
561	C₄×C₁₃₉	—	2	2	no	—
562	C₄×C₁₃₉	—	2	2	no	—
563	C₄×C₁₃₉	—	2	2	no	—
564	C₄×C₁₃₉	—	2	4	no	—
565	C₄×C₁₃₉	—	4	2	no	—
566	C₄×C₁₃₉	—	4	1	no	—
567	C₄×C₁₃₉	—	4	1	no	—
568	C₄×C₁₃₉	—	4	2	no	—
569	C₄×C₁₃₉	—	4	1	no	—
570	C₄×C₁₃₉	—	4	2	no	—
571	C₄×C₁₃₉	—	4	1	no	—
572	C₄×C₁₃₉	—	4	1	no	—
573	C₄×C₁₃₉	—	4	2	no	—
574	C₄×C₁₃₉	—	4	1	no	—
575	C₄×C₁₃₉	—	4	1	no	—
576	C₄×C₁₃₉	#525	1	4	yes	—
577	C₂×C₁₃₉	—	2	4	no	—
578	C₂×C₁₃₉	—	4	4	no	—
579	C₂×C₁₃₉	—	4	4	no	—
580	C₂×C₁₃₉	—	8	2	no	—
581	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
582	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
583	C₂×C₁₃₉	C₂×#559	1	1	yes	characteristic
584	C₂×C₁₃₉	#3481	1	1	yes	characteristic
585	C₂×C₁₃₉	#3484	1	1	yes	characteristic
586	C₂×C₁₃₉	#3506	1	1	yes	characteristic
587	C₂×C₁₃₉	#3513	1	1	yes	characteristic
588	#36441	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
589	C₁₃₉	#36441	1	1	yes	characteristic, direct product factor, Sylow
590	C₂×#559	C₂×C₁₃₉	1	1	yes	characteristic, complemented
591	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
592	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
593	#2849	C₂×C₁₃₉	1	2	yes	complemented
594	#2602	C₂×C₁₃₉	1	2	yes	complemented
595	#2600	C₂×C₁₃₉	1	2	yes	complemented
596	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
597	#2544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
598	#2472	C₂×C₁₃₉	1	2	yes	complemented
599	#2459	C₂×C₁₃₉	1	2	yes	complemented
600	#2455	C₂×C₁₃₉	1	2	yes	complemented
601	#2447	C₂×C₁₃₉	1	1	yes	characteristic, complemented
602	#2445	C₂×C₁₃₉	1	1	yes	characteristic, complemented
603	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
604	#2433	C₂×C₁₃₉	1	1	yes	characteristic
605	#2418	C₂×C₁₃₉	1	2	yes	complemented
606	#2367	C₂×C₁₃₉	1	1	yes	characteristic, complemented
607	#2366	C₂×C₁₃₉	1	1	yes	characteristic, complemented
608	#2361	C₂×C₁₃₉	1	1	yes	characteristic, complemented
609	#2360	C₂×C₁₃₉	1	1	yes	characteristic, complemented
610	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
611	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
612	C₄×#120	C₂×C₁₃₉	1	2	yes	complemented
613	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
615	#559	—	2	8	no	—
616	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
617	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
618	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
619	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
620	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
621	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
622	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
623	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
624	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
625	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
626	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
627	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
628	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
629	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
630	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
631	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
632	C₂×C₄×D₄	—	2	8	no	—
633	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
635	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
638	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
639	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
640	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
641	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
642	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
643	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
644	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
645	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
646	#399	C₂²×C₁₃₉	1	2	yes	complemented
647	#397	C₂²×C₁₃₉	1	2	yes	complemented
648	#397	C₂²×C₁₃₉	1	2	yes	complemented
649	#394	C₂²×C₁₃₉	1	2	yes	—
650	#394	C₂²×C₁₃₉	1	2	yes	—
651	#394	C₂²×C₁₃₉	1	2	yes	complemented
652	#394	C₂²×C₁₃₉	1	2	yes	complemented
653	#394	C₂²×C₁₃₉	1	2	yes	complemented
654	#394	C₂²×C₁₃₉	1	2	yes	complemented
655	#393	C₂²×C₁₃₉	1	2	yes	complemented
656	#392	C₂²×C₁₃₉	1	2	yes	—
657	#392	C₂²×C₁₃₉	1	2	yes	—
658	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
659	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
660	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
661	#390	C₂²×C₁₃₉	1	1	yes	characteristic
662	#390	C₂²×C₁₃₉	1	1	yes	characteristic
663	#390	C₂²×C₁₃₉	1	1	yes	characteristic
664	#390	C₂²×C₁₃₉	1	1	yes	characteristic
665	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
666	#390	C₂²×C₁₃₉	1	2	yes	complemented
667	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
668	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
669	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
670	#389	C₂²×C₁₃₉	1	2	yes	complemented
671	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
672	#388	C₂²×C₁₃₉	1	2	yes	complemented
673	#388	C₂²×C₁₃₉	1	2	yes	complemented
674	#388	C₂²×C₁₃₉	1	2	yes	complemented
675	#388	C₂²×C₁₃₉	1	2	yes	complemented
676	#388	C₂²×C₁₃₉	1	2	yes	complemented
677	#388	C₂²×C₁₃₉	1	2	yes	complemented
678	#388	C₂²×C₁₃₉	1	2	yes	complemented
679	#387	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
680	#387	C₂²×C₁₃₉	1	2	yes	complemented
681	#387	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
682	#386	C₂²×C₁₃₉	1	2	yes	—
683	#386	C₂²×C₁₃₉	1	2	yes	—
684	#386	C₂²×C₁₃₉	1	2	yes	—
685	#386	C₂²×C₁₃₉	1	2	yes	complemented
686	#386	C₂²×C₁₃₉	1	2	yes	complemented
687	#386	C₂²×C₁₃₉	1	2	yes	complemented
688	#386	C₂²×C₁₃₉	1	2	yes	complemented
689	#386	C₂²×C₁₃₉	1	2	yes	complemented
690	#385	C₂²×C₁₃₉	1	1	yes	characteristic
691	#385	C₂²×C₁₃₉	1	2	yes	—
692	#385	C₂²×C₁₃₉	1	1	yes	characteristic
693	#385	C₂²×C₁₃₉	1	2	yes	complemented
694	#385	C₂²×C₁₃₉	1	2	yes	complemented
695	#385	C₂²×C₁₃₉	1	2	yes	complemented
696	#385	C₂²×C₁₃₉	1	2	yes	complemented
697	#385	C₂²×C₁₃₉	1	2	yes	complemented
698	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
699	#381	C₂²×C₁₃₉	1	2	yes	complemented
700	#381	C₂²×C₁₃₉	1	2	yes	complemented
701	#380	C₂²×C₁₃₉	1	1	yes	characteristic
702	#379	C₂²×C₁₃₉	1	2	yes	—
703	#379	C₂²×C₁₃₉	1	2	yes	—
704	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
705	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
706	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
707	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
708	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
709	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
710	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
711	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
712	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
713	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
714	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
715	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
717	C₂²×D₄	—	2	4	no	—
718	C₂²×D₄	—	2	4	no	—
719	C₂²×D₄	—	2	4	no	—
720	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
723	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
726	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
727	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
728	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂³×C₄	—	2	8	no	—
730	C₂³×C₄	—	4	4	no	—
731	C₂³×C₄	—	4	4	no	—
732	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
733	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
735	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
736	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
737	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
741	#127	—	2	4	no	—
742	#127	—	2	4	no	—
743	#124	—	2	4	no	—
744	#124	—	2	4	no	—
745	#124	—	2	8	no	—
746	#124	—	2	4	no	—
747	#123	—	2	8	no	—
748	#123	—	2	8	no	—
749	#123	—	4	4	no	—
750	C₂²⋊Q₈	—	2	4	no	—
751	C₂²⋊Q₈	—	2	4	no	—
752	#121	—	2	4	no	—
753	#120	—	2	8	no	—
754	#120	—	4	4	no	—
755	C₄×Q₈	—	2	4	no	—
756	C₄×Q₈	—	2	4	no	—
757	C₄×D₄	—	2	4	no	—
758	C₄×D₄	—	2	8	no	—
759	C₄×D₄	—	2	8	no	—
760	C₄×D₄	—	2	4	no	—
761	C₄×D₄	—	2	4	no	—
762	C₄×D₄	—	2	8	no	—
763	C₄×D₄	—	2	4	no	—
764	C₄×D₄	—	4	4	no	—
765	C₄×D₄	—	4	4	no	—
766	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
767	C₂×C₄⋊C₄	—	2	4	no	—
768	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
774	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
778	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
782	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
784	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	—	2	8	no	—
787	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
796	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
801	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
816	C₂×C₄²	—	2	4	no	—
817	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
821	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
822	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
824	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
825	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
826	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
827	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
828	#95	C₂³×C₁₃₉	1	1	yes	characteristic
829	#95	C₂³×C₁₃₉	1	2	yes	—
830	#95	C₂³×C₁₃₉	1	2	yes	—
831	#95	C₂³×C₁₃₉	1	1	yes	characteristic
832	#95	C₂³×C₁₃₉	1	1	yes	characteristic
833	#95	C₂³×C₁₃₉	1	1	yes	characteristic
834	#95	C₂³×C₁₃₉	1	1	yes	characteristic
835	#95	C₂³×C₁₃₉	1	1	yes	characteristic
836	#95	C₂³×C₁₃₉	1	2	yes	—
837	#95	C₂³×C₁₃₉	1	2	yes	—
838	#95	C₂³×C₁₃₉	1	1	yes	characteristic
839	#95	C₂³×C₁₃₉	1	1	yes	characteristic
840	#95	C₂³×C₁₃₉	1	1	yes	characteristic
841	#95	C₂³×C₁₃₉	1	1	yes	characteristic
842	#95	C₂³×C₁₃₉	1	2	yes	—
843	#95	C₂³×C₁₃₉	1	2	yes	—
844	#95	C₂³×C₁₃₉	1	2	yes	—
845	#95	C₂³×C₁₃₉	1	2	yes	—
846	#95	C₂³×C₁₃₉	1	2	yes	—
847	#95	C₂³×C₁₃₉	1	2	yes	—
848	C₂⁴	—	2	4	no	—
849	C₂⁴	—	2	4	no	—
850	C₂⁴	—	2	4	no	—
851	C₂⁴	—	2	4	no	—
852	C₂⁴	—	2	4	no	—
853	C₂⁴	—	4	2	no	—
854	C₂⁴	—	4	2	no	—
855	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
856	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
857	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
858	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	4	1	no	—
865	C₂×D₄	—	2	32	no	—
866	C₂×D₄	—	2	4	no	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	4	no	—
872	C₂×D₄	—	2	4	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	2	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
892	C₂×D₄	#41×C₁₃₉	1	4	yes	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	4	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	2	4	no	—
905	C₂²×C₄	—	2	4	no	—
906	C₂²×C₄	—	2	4	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	—	4	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	1	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	—	4	2	no	—
918	C₂²×C₄	—	4	32	no	—
919	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
920	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
921	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
927	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
940	C₄⋊C₄	—	2	4	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	4	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	4	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	4	1	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	4	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	4	no	—
968	C₂²⋊C₄	—	2	4	no	—
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
986	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	4	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	4	2	no	—
996	C₄²	—	4	2	no	—
997	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	16	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	4	8	no	—
1023	C₂³	—	4	8	no	—
1024	C₂³	—	4	8	no	—
1025	C₂³	—	4	8	no	—
1026	C₂³	—	4	8	no	—
1027	C₂³	—	4	8	no	—
1028	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
1029	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
1030	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1031	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1032	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1033	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1034	Q₈	—	4	4	no	—
1035	Q₈	—	4	4	no	—
1036	D₄	—	2	16	no	—
1037	D₄	—	2	8	no	—
1038	D₄	—	2	8	no	—
1039	D₄	—	4	8	no	—
1040	D₄	—	4	8	no	—
1041	D₄	—	4	8	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	8	4	no	—
1044	D₄	—	8	4	no	—
1045	C₂×C₄	—	2	8	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	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	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	8	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	4	8	no	—
1095	C₂×C₄	—	4	8	no	—
1096	C₂×C₄	—	4	8	no	—
1097	C₂×C₄	—	4	8	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	8	no	—
1100	C₂×C₄	—	8	4	no	—
1101	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1104	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1105	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1106	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1107	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1108	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1109	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1110	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	4	no	—
1118	C₂²	—	2	4	no	—
1119	C₂²	—	2	4	no	—
1120	C₂²	—	2	4	no	—
1121	C₂²	—	2	4	no	—
1122	C₂²	—	2	4	no	—
1123	C₂²	—	4	32	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	#559×C₁₃₉	1	4	yes	complemented
1140	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1141	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1142	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1143	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1144	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1145	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1146	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	4	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	#525×C₁₃₉	1	4	yes	—
1166	C₂	—	2	4	no	—
1167	C₂	—	4	4	no	—
1168	C₂	—	4	4	no	—
1169	C₂	—	8	2	no	—
1170	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1171	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1172	C₂	C₂×#559×C₁₃₉	1	1	yes	characteristic
1173	C₂	#3481×C₁₃₉	1	1	yes	characteristic
1174	C₂	#3484×C₁₃₉	1	1	yes	characteristic
1175	C₂	#3506×C₁₃₉	1	1	yes	characteristic
1176	C₂	#3513×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2433×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×#559×C₁₃₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2850×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2602×C₁₃₉	C₂	semidirect
6. #2600×C₁₃₉	C₂	semidirect
7. #2580×C₁₃₉	C₂	semidirect
8. #2544×C₁₃₉	C₂	semidirect
9. #2472×C₁₃₉	C₂	semidirect
10. #2459×C₁₃₉	C₂	semidirect
11. #2455×C₁₃₉	C₂	semidirect
12. #2447×C₁₃₉	C₂	semidirect
13. #2445×C₁₃₉	C₂	semidirect
14. #2435×C₁₃₉	C₂	semidirect
16. #2418×C₁₃₉	C₂	semidirect
17. #2367×C₁₃₉	C₂	semidirect
18. #2366×C₁₃₉	C₂	semidirect
19. #2361×C₁₃₉	C₂	semidirect
20. #2360×C₁₃₉	C₂	semidirect
21. #2357×C₁₃₉	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
23. C₄×#120×C₁₃₉	C₂	semidirect
31. C₂×#124×C₁₃₉	C₂²	semidirect
32. C₂×#124×C₁₃₉	C₂²	semidirect
33. C₂×#123×C₁₃₉	C₂²	semidirect
34. C₂×#123×C₁₃₉	C₂²	semidirect
35. C₂×#123×C₁₃₉	C₂²	semidirect
41. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
42. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
51. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
52. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
53. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
57. #399×C₁₃₉	C₂²	semidirect
58. #397×C₁₃₉	C₂²	semidirect
59. #397×C₁₃₉	C₂²	semidirect
62. #394×C₁₃₉	C₂²	semidirect
63. #394×C₁₃₉	C₂²	semidirect
64. #394×C₁₃₉	C₂²	semidirect
65. #394×C₁₃₉	C₂²	semidirect
66. #393×C₁₃₉	C₂²	semidirect
69. #391×C₁₃₉	C₂²	semidirect
70. #391×C₁₃₉	C₂²	semidirect
71. #391×C₁₃₉	C₂²	semidirect
76. #390×C₁₃₉	C₂²	semidirect
77. #390×C₁₃₉	C₂²	semidirect
78. #390×C₁₃₉	C₂²	semidirect
79. #389×C₁₃₉	C₂²	semidirect
80. #389×C₁₃₉	C₂²	semidirect
81. #389×C₁₃₉	C₂²	semidirect
82. #389×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. #387×C₁₃₉	C₂²	semidirect
91. #387×C₁₃₉	C₂²	semidirect
92. #387×C₁₃₉	C₂²	semidirect
96. #386×C₁₃₉	C₂²	semidirect
97. #386×C₁₃₉	C₂²	semidirect
98. #386×C₁₃₉	C₂²	semidirect
99. #386×C₁₃₉	C₂²	semidirect
100. #386×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. #382×C₁₃₉	C₂²	semidirect
110. #381×C₁₃₉	C₂²	semidirect
111. #381×C₁₃₉	C₂²	semidirect
115. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
116. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
117. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
177. C₄×D₄×C₁₃₉	D₄	semidirect
550. C₂²×C₁₃₉	#559	semidirect
588. #36441	C₁₃₉	direct (N × H)
589. C₁₃₉	#36441	direct (N × H)
590. C₂×#559	C₂×C₁₃₉	semidirect
591. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
592. #2850	C₂×C₁₃₉	semidirect
593. #2849	C₂×C₁₃₉	semidirect
594. #2602	C₂×C₁₃₉	semidirect
595. #2600	C₂×C₁₃₉	semidirect
596. #2580	C₂×C₁₃₉	semidirect
597. #2544	C₂×C₁₃₉	semidirect
598. #2472	C₂×C₁₃₉	semidirect
599. #2459	C₂×C₁₃₉	semidirect
600. #2455	C₂×C₁₃₉	semidirect
601. #2447	C₂×C₁₃₉	semidirect
602. #2445	C₂×C₁₃₉	semidirect
603. #2435	C₂×C₁₃₉	semidirect
605. #2418	C₂×C₁₃₉	semidirect
606. #2367	C₂×C₁₃₉	semidirect
607. #2366	C₂×C₁₃₉	semidirect
608. #2361	C₂×C₁₃₉	semidirect
609. #2360	C₂×C₁₃₉	semidirect
610. #2357	C₂×C₁₃₉	semidirect
611. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
612. C₄×#120	C₂×C₁₃₉	semidirect
620. C₂×#124	C₂²×C₁₃₉	semidirect
621. C₂×#124	C₂²×C₁₃₉	semidirect
622. C₂×#123	C₂²×C₁₃₉	semidirect
623. C₂×#123	C₂²×C₁₃₉	semidirect
624. C₂×#123	C₂²×C₁₃₉	semidirect
630. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
631. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
640. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
641. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
642. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
646. #399	C₂²×C₁₃₉	semidirect
647. #397	C₂²×C₁₃₉	semidirect
648. #397	C₂²×C₁₃₉	semidirect
651. #394	C₂²×C₁₃₉	semidirect
652. #394	C₂²×C₁₃₉	semidirect
653. #394	C₂²×C₁₃₉	semidirect
654. #394	C₂²×C₁₃₉	semidirect
655. #393	C₂²×C₁₃₉	semidirect
658. #391	C₂²×C₁₃₉	semidirect
659. #391	C₂²×C₁₃₉	semidirect
660. #391	C₂²×C₁₃₉	semidirect
665. #390	C₂²×C₁₃₉	semidirect
666. #390	C₂²×C₁₃₉	semidirect
667. #390	C₂²×C₁₃₉	semidirect
668. #389	C₂²×C₁₃₉	semidirect
669. #389	C₂²×C₁₃₉	semidirect
670. #389	C₂²×C₁₃₉	semidirect
671. #389	C₂²×C₁₃₉	semidirect
672. #388	C₂²×C₁₃₉	semidirect
673. #388	C₂²×C₁₃₉	semidirect
674. #388	C₂²×C₁₃₉	semidirect
675. #388	C₂²×C₁₃₉	semidirect
676. #388	C₂²×C₁₃₉	semidirect
677. #388	C₂²×C₁₃₉	semidirect
678. #388	C₂²×C₁₃₉	semidirect
679. #387	C₂²×C₁₃₉	semidirect
680. #387	C₂²×C₁₃₉	semidirect
681. #387	C₂²×C₁₃₉	semidirect
685. #386	C₂²×C₁₃₉	semidirect
686. #386	C₂²×C₁₃₉	semidirect
687. #386	C₂²×C₁₃₉	semidirect
688. #386	C₂²×C₁₃₉	semidirect
689. #386	C₂²×C₁₃₉	semidirect
693. #385	C₂²×C₁₃₉	semidirect
694. #385	C₂²×C₁₃₉	semidirect
695. #385	C₂²×C₁₃₉	semidirect
696. #385	C₂²×C₁₃₉	semidirect
697. #385	C₂²×C₁₃₉	semidirect
698. #382	C₂²×C₁₃₉	semidirect
699. #381	C₂²×C₁₃₉	semidirect
700. #381	C₂²×C₁₃₉	semidirect
704. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
705. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
706. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
707. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
708. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
712. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
713. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
766. C₄×D₄	D₄×C₁₃₉	semidirect
1139. C₂²	#559×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2850×C₁₃₉	2
#2849×C₁₃₉	2
#2602×C₁₃₉	2
#2600×C₁₃₉	2
#2580×C₁₃₉	2
#2544×C₁₃₉	2
#2472×C₁₃₉	2
#2459×C₁₃₉	2
#2455×C₁₃₉	2
#2447×C₁₃₉	2
#2445×C₁₃₉	2
#2435×C₁₃₉	2
#2433×C₁₃₉	2
#2418×C₁₃₉	2
#2367×C₁₃₉	2
#2366×C₁₃₉	2
#2361×C₁₃₉	2
#2360×C₁₃₉	2
#2357×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36441	139

Subgroups — C139×#36441 #48031037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36441 #48031037