Subgroups — C₁₃₉×#36010 #48030606

Order 35584.

2446 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2638×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2633×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2626×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2611×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2599×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2564×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2561×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2482×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2480×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2475×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2466×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2460×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2419×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2405×C₁₃₉	C₂	1	2	yes	maximal
18	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
22	#2353×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2342×C₁₃₉	C₂	1	2	yes	maximal, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#552×C₁₃₉	—	2	8	no	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	#518×C₁₃₉	—	2	8	no	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	#400×C₁₃₉	C₂²	1	2	yes	complemented
55	#399×C₁₃₉	C₂²	1	1	yes	characteristic
56	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#398×C₁₃₉	C₂²	1	2	yes	complemented
61	#397×C₁₃₉	C₂²	1	1	yes	characteristic
62	#397×C₁₃₉	C₂²	1	1	yes	characteristic
63	#397×C₁₃₉	C₂²	1	2	yes	—
64	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
65	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	#397×C₁₃₉	C₂²	1	2	yes	complemented
67	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	#397×C₁₃₉	C₂²	1	2	yes	complemented
69	#397×C₁₃₉	C₂²	1	2	yes	complemented
70	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
71	#396×C₁₃₉	C₂²	1	2	yes	—
72	#396×C₁₃₉	C₂²	1	2	yes	complemented
73	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#394×C₁₃₉	C₂²	1	2	yes	—
75	#394×C₁₃₉	C₂²	1	2	yes	—
76	#394×C₁₃₉	C₂²	1	2	yes	—
77	#394×C₁₃₉	C₂²	1	2	yes	—
78	#393×C₁₃₉	C₂²	1	1	yes	characteristic
79	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#393×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	#389×C₁₃₉	C₂²	1	2	yes	complemented
82	#389×C₁₃₉	C₂²	1	2	yes	complemented
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	complemented
91	#387×C₁₃₉	C₂²	1	2	yes	complemented
92	#387×C₁₃₉	C₂²	1	2	yes	complemented
93	#387×C₁₃₉	C₂²	1	2	yes	complemented
94	#387×C₁₃₉	C₂²	1	2	yes	complemented
95	#387×C₁₃₉	C₂²	1	2	yes	complemented
96	#386×C₁₃₉	C₂²	1	2	yes	—
97	#386×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	2	yes	complemented
101	#385×C₁₃₉	C₂²	1	2	yes	complemented
102	#385×C₁₃₉	C₂²	1	2	yes	complemented
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	#383×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	#381×C₁₃₉	C₂²	1	2	yes	complemented
108	#381×C₁₃₉	C₂²	1	2	yes	complemented
109	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
110	#380×C₁₃₉	C₂²	1	2	yes	complemented
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	#380×C₁₃₉	C₂²	1	2	yes	complemented
113	#379×C₁₃₉	C₂²	1	2	yes	—
114	#379×C₁₃₉	C₂²	1	2	yes	—
115	#379×C₁₃₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
122	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
123	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic, 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	4	no	—
130	C₂²×D₄×C₁₃₉	—	2	4	no	—
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
145	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	#126×C₁₃₉	—	2	8	no	—
147	#125×C₁₃₉	—	2	8	no	—
148	#125×C₁₃₉	—	2	4	no	—
149	#123×C₁₃₉	—	2	8	no	—
150	#123×C₁₃₉	—	2	8	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
153	C₄×Q₈×C₁₃₉	—	2	4	no	—
154	C₄×D₄×C₁₃₉	—	2	4	no	—
155	C₄×D₄×C₁₃₉	—	2	4	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	4	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	C₄×D₄×C₁₃₉	—	2	4	no	—
161	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
162	#117×C₁₃₉	—	2	4	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	#117×C₁₃₉	—	2	8	no	—
165	#117×C₁₃₉	—	2	4	no	—
166	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
188	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
189	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	1	yes	characteristic
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	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	C₂⁴×C₁₃₉	—	2	2	no	—
254	C₂⁴×C₁₃₉	—	2	2	no	—
255	C₂⁴×C₁₃₉	—	2	2	no	—
256	C₂⁴×C₁₃₉	—	2	2	no	—
257	C₂⁴×C₁₃₉	—	2	2	no	—
258	C₂⁴×C₁₃₉	—	4	2	no	—
259	C₂⁴×C₁₃₉	—	4	2	no	—
260	C₂⁴×C₁₃₉	—	4	2	no	—
261	C₂⁴×C₁₃₉	—	4	2	no	—
262	C₂⁴×C₁₃₉	#41	1	4	yes	—
263	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂×Q₈×C₁₃₉	—	2	2	no	—
269	C₂×Q₈×C₁₃₉	—	4	2	no	—
270	C₂×D₄×C₁₃₉	—	2	32	no	—
271	C₂×D₄×C₁₃₉	—	2	2	no	—
272	C₂×D₄×C₁₃₉	—	2	2	no	—
273	C₂×D₄×C₁₃₉	—	2	2	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	—	2	2	no	—
279	C₂×D₄×C₁₃₉	—	2	2	no	—
280	C₂×D₄×C₁₃₉	—	2	2	no	—
281	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
282	C₂×D₄×C₁₃₉	#41	1	4	yes	—
283	C₂²×C₄×C₁₃₉	—	2	2	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	4	no	—
287	C₂²×C₄×C₁₃₉	—	2	4	no	—
288	C₂²×C₄×C₁₃₉	—	2	4	no	—
289	C₂²×C₄×C₁₃₉	—	2	2	no	—
290	C₂²×C₄×C₁₃₉	—	2	2	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	—	4	2	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	—	4	2	no	—
299	C₂²×C₄×C₁₃₉	—	4	2	no	—
300	C₂²×C₄×C₁₃₉	—	4	2	no	—
301	C₂²×C₄×C₁₃₉	—	4	2	no	—
302	C₂²×C₄×C₁₃₉	—	4	2	no	—
303	C₂²×C₄×C₁₃₉	—	4	2	no	—
304	C₂²×C₄×C₁₃₉	—	4	2	no	—
305	C₂²×C₄×C₁₃₉	—	4	2	no	—
306	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
307	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
308	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	1	yes	characteristic
321	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₁₃₉	—	2	2	no	—
327	C₄⋊C₄×C₁₃₉	—	2	2	no	—
328	C₄⋊C₄×C₁₃₉	—	2	4	no	—
329	C₄⋊C₄×C₁₃₉	—	2	2	no	—
330	C₄⋊C₄×C₁₃₉	—	2	2	no	—
331	C₄⋊C₄×C₁₃₉	—	2	2	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	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	4	no	—
340	C₄⋊C₄×C₁₃₉	—	4	2	no	—
341	C₄⋊C₄×C₁₃₉	—	4	2	no	—
342	C₄⋊C₄×C₁₃₉	—	4	2	no	—
343	C₄⋊C₄×C₁₃₉	—	4	2	no	—
344	C₄⋊C₄×C₁₃₉	—	4	2	no	—
345	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
346	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
349	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
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	4	no	—
356	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
366	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
370	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
371	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
372	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
373	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
374	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
375	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
376	C₄²×C₁₃₉	—	2	4	no	—
377	C₄²×C₁₃₉	—	2	2	no	—
378	C₄²×C₁₃₉	—	2	2	no	—
379	C₄²×C₁₃₉	—	2	2	no	—
380	C₄²×C₁₃₉	—	2	4	no	—
381	C₄²×C₁₃₉	—	4	2	no	—
382	C₄²×C₁₃₉	—	4	2	no	—
383	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
384	C₂³×C₁₃₉	—	2	2	no	—
385	C₂³×C₁₃₉	—	2	2	no	—
386	C₂³×C₁₃₉	—	2	8	no	—
387	C₂³×C₁₃₉	—	2	1	no	—
388	C₂³×C₁₃₉	—	2	1	no	—
389	C₂³×C₁₃₉	—	2	1	no	—
390	C₂³×C₁₃₉	—	2	1	no	—
391	C₂³×C₁₃₉	—	2	1	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	1	no	—
395	C₂³×C₁₃₉	—	2	2	no	—
396	C₂³×C₁₃₉	—	2	2	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	2	2	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	2	no	—
401	C₂³×C₁₃₉	—	2	2	no	—
402	C₂³×C₁₃₉	—	2	2	no	—
403	C₂³×C₁₃₉	—	2	8	no	—
404	C₂³×C₁₃₉	—	4	8	no	—
405	C₂³×C₁₃₉	—	8	2	no	—
406	C₂³×C₁₃₉	—	8	2	no	—
407	C₂³×C₁₃₉	—	8	4	no	—
408	C₂³×C₁₃₉	—	8	2	no	—
409	C₂³×C₁₃₉	—	8	4	no	—
410	C₂³×C₁₃₉	—	8	2	no	—
411	C₂³×C₁₃₉	—	8	4	no	—
412	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
413	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
414	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
415	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
416	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
417	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
418	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
419	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
420	Q₈×C₁₃₉	—	4	4	no	—
421	D₄×C₁₃₉	—	2	8	no	—
422	D₄×C₁₃₉	—	2	8	no	—
423	D₄×C₁₃₉	—	2	8	no	—
424	D₄×C₁₃₉	—	2	8	no	—
425	C₂×C₄×C₁₃₉	—	2	8	no	—
426	C₂×C₄×C₁₃₉	—	2	1	no	—
427	C₂×C₄×C₁₃₉	—	2	1	no	—
428	C₂×C₄×C₁₃₉	—	2	1	no	—
429	C₂×C₄×C₁₃₉	—	2	1	no	—
430	C₂×C₄×C₁₃₉	—	2	2	no	—
431	C₂×C₄×C₁₃₉	—	2	2	no	—
432	C₂×C₄×C₁₃₉	—	2	2	no	—
433	C₂×C₄×C₁₃₉	—	2	2	no	—
434	C₂×C₄×C₁₃₉	—	2	2	no	—
435	C₂×C₄×C₁₃₉	—	2	1	no	—
436	C₂×C₄×C₁₃₉	—	2	1	no	—
437	C₂×C₄×C₁₃₉	—	2	1	no	—
438	C₂×C₄×C₁₃₉	—	2	1	no	—
439	C₂×C₄×C₁₃₉	—	2	2	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	2	no	—
442	C₂×C₄×C₁₃₉	—	2	2	no	—
443	C₂×C₄×C₁₃₉	—	2	2	no	—
444	C₂×C₄×C₁₃₉	—	2	2	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	2	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	2	no	—
450	C₂×C₄×C₁₃₉	—	2	2	no	—
451	C₂×C₄×C₁₃₉	—	2	2	no	—
452	C₂×C₄×C₁₃₉	—	2	2	no	—
453	C₂×C₄×C₁₃₉	—	2	2	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	2	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	2	no	—
461	C₂×C₄×C₁₃₉	—	2	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	—	4	4	no	—
467	C₂×C₄×C₁₃₉	—	4	4	no	—
468	C₂×C₄×C₁₃₉	—	4	8	no	—
469	C₂×C₄×C₁₃₉	—	8	2	no	—
470	C₂×C₄×C₁₃₉	—	8	2	no	—
471	C₂×C₄×C₁₃₉	—	8	2	no	—
472	C₂×C₄×C₁₃₉	—	8	2	no	—
473	C₂×C₄×C₁₃₉	—	8	4	no	—
474	C₂×C₄×C₁₃₉	—	8	2	no	—
475	C₂×C₄×C₁₃₉	—	8	2	no	—
476	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
482	C₂²×C₁₃₉	—	2	2	no	—
483	C₂²×C₁₃₉	—	2	4	no	—
484	C₂²×C₁₃₉	—	2	2	no	—
485	C₂²×C₁₃₉	—	2	4	no	—
486	C₂²×C₁₃₉	—	2	2	no	—
487	C₂²×C₁₃₉	—	2	2	no	—
488	C₂²×C₁₃₉	—	2	2	no	—
489	C₂²×C₁₃₉	—	2	2	no	—
490	C₂²×C₁₃₉	—	2	2	no	—
491	C₂²×C₁₃₉	—	2	4	no	—
492	C₂²×C₁₃₉	—	2	4	no	—
493	C₂²×C₁₃₉	—	2	2	no	—
494	C₂²×C₁₃₉	—	2	4	no	—
495	C₂²×C₁₃₉	—	4	1	no	—
496	C₂²×C₁₃₉	—	4	1	no	—
497	C₂²×C₁₃₉	—	4	1	no	—
498	C₂²×C₁₃₉	—	4	2	no	—
499	C₂²×C₁₃₉	—	4	2	no	—
500	C₂²×C₁₃₉	—	4	1	no	—
501	C₂²×C₁₃₉	—	4	1	no	—
502	C₂²×C₁₃₉	—	4	1	no	—
503	C₂²×C₁₃₉	—	4	2	no	—
504	C₂²×C₁₃₉	—	4	2	no	—
505	C₂²×C₁₃₉	—	4	2	no	—
506	C₂²×C₁₃₉	—	8	8	no	—
507	C₂²×C₁₃₉	—	8	8	no	—
508	C₂²×C₁₃₉	#525	1	4	yes	—
509	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
510	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
511	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
512	C₂²×C₁₃₉	#585	1	2	yes	—
513	C₂²×C₁₃₉	#585	1	2	yes	—
514	C₄×C₁₃₉	—	2	2	no	—
515	C₄×C₁₃₉	—	2	2	no	—
516	C₄×C₁₃₉	—	2	2	no	—
517	C₄×C₁₃₉	—	2	2	no	—
518	C₄×C₁₃₉	—	2	2	no	—
519	C₄×C₁₃₉	—	2	2	no	—
520	C₄×C₁₃₉	—	4	2	no	—
521	C₄×C₁₃₉	—	4	2	no	—
522	C₄×C₁₃₉	—	4	1	no	—
523	C₄×C₁₃₉	—	4	2	no	—
524	C₄×C₁₃₉	—	4	2	no	—
525	C₄×C₁₃₉	—	4	2	no	—
526	C₄×C₁₃₉	—	4	2	no	—
527	C₄×C₁₃₉	—	4	1	no	—
528	C₄×C₁₃₉	—	4	1	no	—
529	C₄×C₁₃₉	—	4	1	no	—
530	C₄×C₁₃₉	—	4	2	no	—
531	C₄×C₁₃₉	—	4	2	no	—
532	C₂×C₁₃₉	—	2	4	no	—
533	C₂×C₁₃₉	—	4	2	no	—
534	C₂×C₁₃₉	—	4	2	no	—
535	C₂×C₁₃₉	—	4	2	no	—
536	C₂×C₁₃₉	—	4	2	no	—
537	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
538	C₂×C₁₃₉	#3485	1	1	yes	characteristic
539	C₂×C₁₃₉	#3491	1	2	yes	—
540	C₂×C₁₃₉	#3500	1	1	yes	characteristic
541	C₂×C₁₃₉	#3521	1	2	yes	—
542	#36010	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
543	C₁₃₉	#36010	1	1	yes	characteristic, direct product factor, Sylow
544	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
545	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic
546	#2638	C₂×C₁₃₉	1	1	yes	characteristic, complemented
547	#2633	C₂×C₁₃₉	1	1	yes	characteristic, complemented
548	#2626	C₂×C₁₃₉	1	1	yes	characteristic, complemented
549	#2611	C₂×C₁₃₉	1	1	yes	characteristic, complemented
550	#2599	C₂×C₁₃₉	1	1	yes	characteristic, complemented
551	#2564	C₂×C₁₃₉	1	1	yes	characteristic, complemented
552	#2561	C₂×C₁₃₉	1	1	yes	characteristic, complemented
553	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
554	#2482	C₂×C₁₃₉	1	1	yes	characteristic, complemented
555	#2480	C₂×C₁₃₉	1	2	yes	complemented
556	#2475	C₂×C₁₃₉	1	2	yes	complemented
557	#2466	C₂×C₁₃₉	1	2	yes	complemented
558	#2460	C₂×C₁₃₉	1	2	yes	complemented
559	#2419	C₂×C₁₃₉	1	2	yes	complemented
560	#2405	C₂×C₁₃₉	1	2	yes	—
561	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
562	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
563	C₂×#397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
564	#2359	C₂×C₁₃₉	1	2	yes	complemented
565	#2353	C₂×C₁₃₉	1	1	yes	characteristic, complemented
566	#2342	C₂×C₁₃₉	1	2	yes	complemented
567	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
568	#552	—	2	8	no	—
569	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
570	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
571	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
572	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
573	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
575	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
576	#518	—	2	8	no	—
577	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
578	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
583	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
586	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
588	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
589	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
590	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
591	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
592	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
593	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
594	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
596	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
597	#400	C₂²×C₁₃₉	1	2	yes	complemented
598	#399	C₂²×C₁₃₉	1	1	yes	characteristic
599	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
600	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
601	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
602	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
603	#398	C₂²×C₁₃₉	1	2	yes	complemented
604	#397	C₂²×C₁₃₉	1	1	yes	characteristic
605	#397	C₂²×C₁₃₉	1	1	yes	characteristic
606	#397	C₂²×C₁₃₉	1	2	yes	—
607	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
608	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
609	#397	C₂²×C₁₃₉	1	2	yes	complemented
610	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
611	#397	C₂²×C₁₃₉	1	2	yes	complemented
612	#397	C₂²×C₁₃₉	1	2	yes	complemented
613	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
614	#396	C₂²×C₁₃₉	1	2	yes	—
615	#396	C₂²×C₁₃₉	1	2	yes	complemented
616	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
617	#394	C₂²×C₁₃₉	1	2	yes	—
618	#394	C₂²×C₁₃₉	1	2	yes	—
619	#394	C₂²×C₁₃₉	1	2	yes	—
620	#394	C₂²×C₁₃₉	1	2	yes	—
621	#393	C₂²×C₁₃₉	1	1	yes	characteristic
622	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
623	#393	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
624	#389	C₂²×C₁₃₉	1	2	yes	complemented
625	#389	C₂²×C₁₃₉	1	2	yes	complemented
626	#388	C₂²×C₁₃₉	1	2	yes	—
627	#388	C₂²×C₁₃₉	1	2	yes	—
628	#388	C₂²×C₁₃₉	1	2	yes	—
629	#388	C₂²×C₁₃₉	1	2	yes	—
630	#388	C₂²×C₁₃₉	1	2	yes	complemented
631	#388	C₂²×C₁₃₉	1	2	yes	complemented
632	#388	C₂²×C₁₃₉	1	2	yes	complemented
633	#387	C₂²×C₁₃₉	1	2	yes	complemented
634	#387	C₂²×C₁₃₉	1	2	yes	complemented
635	#387	C₂²×C₁₃₉	1	2	yes	complemented
636	#387	C₂²×C₁₃₉	1	2	yes	complemented
637	#387	C₂²×C₁₃₉	1	2	yes	complemented
638	#387	C₂²×C₁₃₉	1	2	yes	complemented
639	#386	C₂²×C₁₃₉	1	2	yes	—
640	#386	C₂²×C₁₃₉	1	2	yes	—
641	#385	C₂²×C₁₃₉	1	2	yes	—
642	#385	C₂²×C₁₃₉	1	2	yes	—
643	#385	C₂²×C₁₃₉	1	2	yes	complemented
644	#385	C₂²×C₁₃₉	1	2	yes	complemented
645	#385	C₂²×C₁₃₉	1	2	yes	complemented
646	#385	C₂²×C₁₃₉	1	2	yes	complemented
647	#385	C₂²×C₁₃₉	1	2	yes	complemented
648	#385	C₂²×C₁₃₉	1	2	yes	complemented
649	#383	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
650	#381	C₂²×C₁₃₉	1	2	yes	complemented
651	#381	C₂²×C₁₃₉	1	2	yes	complemented
652	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
653	#380	C₂²×C₁₃₉	1	2	yes	complemented
654	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
655	#380	C₂²×C₁₃₉	1	2	yes	complemented
656	#379	C₂²×C₁₃₉	1	2	yes	—
657	#379	C₂²×C₁₃₉	1	2	yes	—
658	#379	C₂²×C₁₃₉	1	2	yes	—
659	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
660	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
661	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
662	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
663	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
664	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
665	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
666	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
667	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
668	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂²×D₄	—	2	4	no	—
672	C₂²×D₄	—	2	4	no	—
673	C₂²×D₄	—	2	4	no	—
674	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
679	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
687	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
689	#126	—	2	8	no	—
690	#125	—	2	8	no	—
691	#125	—	2	4	no	—
692	#123	—	2	8	no	—
693	#123	—	2	8	no	—
694	C₂²⋊Q₈	—	2	4	no	—
695	C₂²⋊Q₈	—	2	4	no	—
696	C₄×Q₈	—	2	4	no	—
697	C₄×D₄	—	2	4	no	—
698	C₄×D₄	—	2	4	no	—
699	C₄×D₄	—	2	4	no	—
700	C₄×D₄	—	2	4	no	—
701	C₄×D₄	—	2	4	no	—
702	C₄×D₄	—	2	4	no	—
703	C₄×D₄	—	2	4	no	—
704	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
705	#117	—	2	4	no	—
706	#117	—	2	4	no	—
707	#117	—	2	8	no	—
708	#117	—	2	4	no	—
709	C₂×C₄⋊C₄	—	2	4	no	—
710	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	—	2	8	no	—
731	C₂×C₂²⋊C₄	—	2	4	no	—
732	C₂×C₂²⋊C₄	—	2	4	no	—
733	C₂×C₂²⋊C₄	—	2	4	no	—
734	C₂×C₂²⋊C₄	—	2	4	no	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	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	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
772	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
773	#95	C₂³×C₁₃₉	1	1	yes	characteristic
774	#95	C₂³×C₁₃₉	1	2	yes	—
775	#95	C₂³×C₁₃₉	1	1	yes	characteristic
776	#95	C₂³×C₁₃₉	1	2	yes	—
777	#95	C₂³×C₁₃₉	1	2	yes	—
778	#95	C₂³×C₁₃₉	1	2	yes	—
779	#95	C₂³×C₁₃₉	1	2	yes	—
780	#95	C₂³×C₁₃₉	1	1	yes	characteristic
781	#95	C₂³×C₁₃₉	1	2	yes	—
782	#95	C₂³×C₁₃₉	1	2	yes	—
783	#95	C₂³×C₁₃₉	1	2	yes	—
784	#95	C₂³×C₁₃₉	1	1	yes	characteristic
785	#95	C₂³×C₁₃₉	1	2	yes	—
786	#95	C₂³×C₁₃₉	1	2	yes	—
787	#95	C₂³×C₁₃₉	1	2	yes	—
788	#95	C₂³×C₁₃₉	1	2	yes	—
789	#95	C₂³×C₁₃₉	1	2	yes	—
790	#95	C₂³×C₁₃₉	1	2	yes	—
791	#95	C₂³×C₁₃₉	1	2	yes	—
792	#95	C₂³×C₁₃₉	1	2	yes	—
793	#95	C₂³×C₁₃₉	1	2	yes	—
794	#95	C₂³×C₁₃₉	1	2	yes	—
795	#95	C₂³×C₁₃₉	1	2	yes	—
796	C₂⁴	—	2	2	no	—
797	C₂⁴	—	2	2	no	—
798	C₂⁴	—	2	2	no	—
799	C₂⁴	—	2	2	no	—
800	C₂⁴	—	2	2	no	—
801	C₂⁴	—	4	2	no	—
802	C₂⁴	—	4	2	no	—
803	C₂⁴	—	4	2	no	—
804	C₂⁴	—	4	2	no	—
805	C₂⁴	#41×C₁₃₉	1	4	yes	—
806	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
807	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
808	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
809	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
810	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
811	C₂×Q₈	—	2	2	no	—
812	C₂×Q₈	—	4	2	no	—
813	C₂×D₄	—	2	32	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
825	C₂×D₄	#41×C₁₃₉	1	4	yes	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	2	4	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
850	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
851	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	4	no	—
879	C₄⋊C₄	—	2	4	no	—
880	C₄⋊C₄	—	2	4	no	—
881	C₄⋊C₄	—	2	4	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	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	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
918	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
919	C₄²	—	2	4	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	4	no	—
924	C₄²	—	4	2	no	—
925	C₄²	—	4	2	no	—
926	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	8	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	8	no	—
947	C₂³	—	4	8	no	—
948	C₂³	—	8	2	no	—
949	C₂³	—	8	2	no	—
950	C₂³	—	8	4	no	—
951	C₂³	—	8	2	no	—
952	C₂³	—	8	4	no	—
953	C₂³	—	8	2	no	—
954	C₂³	—	8	4	no	—
955	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
956	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
957	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
958	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
959	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
960	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
961	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
962	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
963	Q₈	—	4	4	no	—
964	D₄	—	2	8	no	—
965	D₄	—	2	8	no	—
966	D₄	—	2	8	no	—
967	D₄	—	2	8	no	—
968	C₂×C₄	—	2	8	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	4	4	no	—
1011	C₂×C₄	—	4	8	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	4	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1021	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1022	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1024	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	4	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	4	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	2	4	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	4	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	8	8	no	—
1050	C₂²	—	8	8	no	—
1051	C₂²	#525×C₁₃₉	1	4	yes	—
1052	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1053	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1054	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1055	C₂²	#585×C₁₃₉	1	2	yes	—
1056	C₂²	#585×C₁₃₉	1	2	yes	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	2	no	—
1075	C₂	—	2	4	no	—
1076	C₂	—	4	2	no	—
1077	C₂	—	4	2	no	—
1078	C₂	—	4	2	no	—
1079	C₂	—	4	2	no	—
1080	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1081	C₂	#3485×C₁₃₉	1	1	yes	characteristic
1082	C₂	#3491×C₁₃₉	1	2	yes	—
1083	C₂	#3500×C₁₃₉	1	1	yes	characteristic
1084	C₂	#3521×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
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×#552×C₁₃₉	C₂	semidirect
3. #2638×C₁₃₉	C₂	semidirect
4. #2633×C₁₃₉	C₂	semidirect
5. #2626×C₁₃₉	C₂	semidirect
6. #2611×C₁₃₉	C₂	semidirect
7. #2599×C₁₃₉	C₂	semidirect
8. #2564×C₁₃₉	C₂	semidirect
9. #2561×C₁₃₉	C₂	semidirect
10. #2486×C₁₃₉	C₂	semidirect
11. #2482×C₁₃₉	C₂	semidirect
12. #2480×C₁₃₉	C₂	semidirect
13. #2475×C₁₃₉	C₂	semidirect
14. #2466×C₁₃₉	C₂	semidirect
15. #2460×C₁₃₉	C₂	semidirect
16. #2419×C₁₃₉	C₂	semidirect
18. #2398×C₁₃₉	C₂	semidirect
19. #2395×C₁₃₉	C₂	semidirect
20. C₂×#397×C₁₃₉	C₂	semidirect
21. #2359×C₁₃₉	C₂	semidirect
22. #2353×C₁₃₉	C₂	semidirect
23. #2342×C₁₃₉	C₂	semidirect
26. C₂×#126×C₁₃₉	C₂²	semidirect
27. C₂×#125×C₁₃₉	C₂²	semidirect
28. C₂×#125×C₁₃₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
45. C₂×#117×C₁₃₉	C₂²	semidirect
46. C₂×#117×C₁₃₉	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
53. #400×C₁₃₉	C₂²	semidirect
54. #400×C₁₃₉	C₂²	semidirect
56. #399×C₁₃₉	C₂²	semidirect
57. #399×C₁₃₉	C₂²	semidirect
58. #398×C₁₃₉	C₂²	semidirect
59. #398×C₁₃₉	C₂²	semidirect
60. #398×C₁₃₉	C₂²	semidirect
64. #397×C₁₃₉	C₂²	semidirect
65. #397×C₁₃₉	C₂²	semidirect
66. #397×C₁₃₉	C₂²	semidirect
67. #397×C₁₃₉	C₂²	semidirect
68. #397×C₁₃₉	C₂²	semidirect
69. #397×C₁₃₉	C₂²	semidirect
70. #397×C₁₃₉	C₂²	semidirect
72. #396×C₁₃₉	C₂²	semidirect
73. #395×C₁₃₉	C₂²	semidirect
79. #393×C₁₃₉	C₂²	semidirect
80. #393×C₁₃₉	C₂²	semidirect
81. #389×C₁₃₉	C₂²	semidirect
82. #389×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
93. #387×C₁₃₉	C₂²	semidirect
94. #387×C₁₃₉	C₂²	semidirect
95. #387×C₁₃₉	C₂²	semidirect
100. #385×C₁₃₉	C₂²	semidirect
101. #385×C₁₃₉	C₂²	semidirect
102. #385×C₁₃₉	C₂²	semidirect
103. #385×C₁₃₉	C₂²	semidirect
104. #385×C₁₃₉	C₂²	semidirect
105. #385×C₁₃₉	C₂²	semidirect
106. #383×C₁₃₉	C₂²	semidirect
107. #381×C₁₃₉	C₂²	semidirect
108. #381×C₁₃₉	C₂²	semidirect
109. #381×C₁₃₉	C₂²	semidirect
110. #380×C₁₃₉	C₂²	semidirect
111. #380×C₁₃₉	C₂²	semidirect
112. #380×C₁₃₉	C₂²	semidirect
116. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
117. C₄×C₂²⋊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. #376×C₁₃₉	C₂²	semidirect
123. C₂×#95×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
542. #36010	C₁₃₉	direct (N × H)
543. C₁₃₉	#36010	direct (N × H)
544. C₂×#552	C₂×C₁₃₉	semidirect
546. #2638	C₂×C₁₃₉	semidirect
547. #2633	C₂×C₁₃₉	semidirect
548. #2626	C₂×C₁₃₉	semidirect
549. #2611	C₂×C₁₃₉	semidirect
550. #2599	C₂×C₁₃₉	semidirect
551. #2564	C₂×C₁₃₉	semidirect
552. #2561	C₂×C₁₃₉	semidirect
553. #2486	C₂×C₁₃₉	semidirect
554. #2482	C₂×C₁₃₉	semidirect
555. #2480	C₂×C₁₃₉	semidirect
556. #2475	C₂×C₁₃₉	semidirect
557. #2466	C₂×C₁₃₉	semidirect
558. #2460	C₂×C₁₃₉	semidirect
559. #2419	C₂×C₁₃₉	semidirect
561. #2398	C₂×C₁₃₉	semidirect
562. #2395	C₂×C₁₃₉	semidirect
563. C₂×#397	C₂×C₁₃₉	semidirect
564. #2359	C₂×C₁₃₉	semidirect
565. #2353	C₂×C₁₃₉	semidirect
566. #2342	C₂×C₁₃₉	semidirect
569. C₂×#126	C₂²×C₁₃₉	semidirect
570. C₂×#125	C₂²×C₁₃₉	semidirect
571. C₂×#125	C₂²×C₁₃₉	semidirect
574. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
575. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
577. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
588. C₂×#117	C₂²×C₁₃₉	semidirect
589. C₂×#117	C₂²×C₁₃₉	semidirect
590. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
596. #400	C₂²×C₁₃₉	semidirect
597. #400	C₂²×C₁₃₉	semidirect
599. #399	C₂²×C₁₃₉	semidirect
600. #399	C₂²×C₁₃₉	semidirect
601. #398	C₂²×C₁₃₉	semidirect
602. #398	C₂²×C₁₃₉	semidirect
603. #398	C₂²×C₁₃₉	semidirect
607. #397	C₂²×C₁₃₉	semidirect
608. #397	C₂²×C₁₃₉	semidirect
609. #397	C₂²×C₁₃₉	semidirect
610. #397	C₂²×C₁₃₉	semidirect
611. #397	C₂²×C₁₃₉	semidirect
612. #397	C₂²×C₁₃₉	semidirect
613. #397	C₂²×C₁₃₉	semidirect
615. #396	C₂²×C₁₃₉	semidirect
616. #395	C₂²×C₁₃₉	semidirect
622. #393	C₂²×C₁₃₉	semidirect
623. #393	C₂²×C₁₃₉	semidirect
624. #389	C₂²×C₁₃₉	semidirect
625. #389	C₂²×C₁₃₉	semidirect
630. #388	C₂²×C₁₃₉	semidirect
631. #388	C₂²×C₁₃₉	semidirect
632. #388	C₂²×C₁₃₉	semidirect
633. #387	C₂²×C₁₃₉	semidirect
634. #387	C₂²×C₁₃₉	semidirect
635. #387	C₂²×C₁₃₉	semidirect
636. #387	C₂²×C₁₃₉	semidirect
637. #387	C₂²×C₁₃₉	semidirect
638. #387	C₂²×C₁₃₉	semidirect
643. #385	C₂²×C₁₃₉	semidirect
644. #385	C₂²×C₁₃₉	semidirect
645. #385	C₂²×C₁₃₉	semidirect
646. #385	C₂²×C₁₃₉	semidirect
647. #385	C₂²×C₁₃₉	semidirect
648. #385	C₂²×C₁₃₉	semidirect
649. #383	C₂²×C₁₃₉	semidirect
650. #381	C₂²×C₁₃₉	semidirect
651. #381	C₂²×C₁₃₉	semidirect
652. #381	C₂²×C₁₃₉	semidirect
653. #380	C₂²×C₁₃₉	semidirect
654. #380	C₂²×C₁₃₉	semidirect
655. #380	C₂²×C₁₃₉	semidirect
659. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
660. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
661. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
662. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
663. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
664. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
665. #376	C₂²×C₁₃₉	semidirect
666. C₂×#95	C₂²×C₁₃₉	semidirect
667. C₂×#95	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2638×C₁₃₉	2
#2633×C₁₃₉	2
#2626×C₁₃₉	2
#2611×C₁₃₉	2
#2599×C₁₃₉	2
#2564×C₁₃₉	2
#2561×C₁₃₉	2
#2486×C₁₃₉	2
#2482×C₁₃₉	2
#2480×C₁₃₉	2
#2475×C₁₃₉	2
#2466×C₁₃₉	2
#2460×C₁₃₉	2
#2419×C₁₃₉	2
#2405×C₁₃₉	2
#2398×C₁₃₉	2
#2395×C₁₃₉	2
C₂×#397×C₁₃₉	2
#2359×C₁₃₉	2
#2353×C₁₃₉	2
#2342×C₁₃₉	2
#36010	139

Subgroups — C139×#36010 #48030606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36010 #48030606