Subgroups — C₁₃₉×#35611 #48030207

Order 35584.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2480×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2472×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2466×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2459×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2447×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2439×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2427×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2420×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2415×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2411×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
19	#2324×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2323×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2293×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2293×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#542×C₁₃₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
39	#518×C₁₃₉	—	2	8	no	—
40	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
52	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
54	#397×C₁₃₉	C₂²	1	2	yes	—
55	#397×C₁₃₉	C₂²	1	2	yes	complemented
56	#397×C₁₃₉	C₂²	1	2	yes	complemented
57	#397×C₁₃₉	C₂²	1	2	yes	complemented
58	#397×C₁₃₉	C₂²	1	2	yes	complemented
59	#396×C₁₃₉	C₂²	1	2	yes	—
60	#396×C₁₃₉	C₂²	1	2	yes	complemented
61	#394×C₁₃₉	C₂²	1	2	yes	—
62	#394×C₁₃₉	C₂²	1	2	yes	—
63	#394×C₁₃₉	C₂²	1	2	yes	—
64	#394×C₁₃₉	C₂²	1	2	yes	—
65	#394×C₁₃₉	C₂²	1	2	yes	complemented
66	#394×C₁₃₉	C₂²	1	2	yes	complemented
67	#393×C₁₃₉	C₂²	1	2	yes	—
68	#393×C₁₃₉	C₂²	1	2	yes	complemented
69	#392×C₁₃₉	C₂²	1	2	yes	—
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
71	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
72	#391×C₁₃₉	C₂²	1	2	yes	complemented
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
77	#390×C₁₃₉	C₂²	1	1	yes	characteristic
78	#390×C₁₃₉	C₂²	1	1	yes	characteristic
79	#390×C₁₃₉	C₂²	1	2	yes	complemented
80	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
82	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
83	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
84	#389×C₁₃₉	C₂²	1	2	yes	complemented
85	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
87	#389×C₁₃₉	C₂²	1	2	yes	complemented
88	#388×C₁₃₉	C₂²	1	1	yes	characteristic
89	#388×C₁₃₉	C₂²	1	1	yes	characteristic
90	#388×C₁₃₉	C₂²	1	2	yes	—
91	#388×C₁₃₉	C₂²	1	2	yes	—
92	#388×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
93	#388×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
94	#388×C₁₃₉	C₂²	1	2	yes	complemented
95	#388×C₁₃₉	C₂²	1	2	yes	complemented
96	#388×C₁₃₉	C₂²	1	2	yes	complemented
97	#388×C₁₃₉	C₂²	1	2	yes	complemented
98	#388×C₁₃₉	C₂²	1	2	yes	complemented
99	#388×C₁₃₉	C₂²	1	2	yes	complemented
100	#387×C₁₃₉	C₂²	1	2	yes	complemented
101	#387×C₁₃₉	C₂²	1	2	yes	complemented
102	#386×C₁₃₉	C₂²	1	2	yes	complemented
103	#386×C₁₃₉	C₂²	1	2	yes	complemented
104	#386×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	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
109	#381×C₁₃₉	C₂²	1	2	yes	complemented
110	#381×C₁₃₉	C₂²	1	2	yes	complemented
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
113	#380×C₁₃₉	C₂²	1	2	yes	complemented
114	#379×C₁₃₉	C₂²	1	2	yes	—
115	#379×C₁₃₉	C₂²	1	2	yes	—
116	#379×C₁₃₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
124	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
144	#126×C₁₃₉	—	2	8	no	—
145	#124×C₁₃₉	—	2	4	no	—
146	#124×C₁₃₉	—	2	4	no	—
147	#124×C₁₃₉	—	2	8	no	—
148	#123×C₁₃₉	—	2	8	no	—
149	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
152	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
153	#121×C₁₃₉	—	2	4	no	—
154	#121×C₁₃₉	—	2	4	no	—
155	#120×C₁₃₉	—	4	4	no	—
156	C₄×Q₈×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	4	no	—
158	C₄×D₄×C₁₃₉	—	2	8	no	—
159	C₄×D₄×C₁₃₉	—	2	4	no	—
160	C₄×D₄×C₁₃₉	—	2	4	no	—
161	C₄×D₄×C₁₃₉	—	2	8	no	—
162	C₄×D₄×C₁₃₉	—	2	4	no	—
163	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
164	#117×C₁₃₉	—	2	4	no	—
165	#117×C₁₃₉	—	2	4	no	—
166	#117×C₁₃₉	—	2	4	no	—
167	#117×C₁₃₉	—	4	4	no	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	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	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
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	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	2	yes	—
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
235	#95×C₁₃₉	C₂³	1	2	yes	—
236	#95×C₁₃₉	C₂³	1	2	yes	—
237	#95×C₁₃₉	C₂³	1	2	yes	—
238	#95×C₁₃₉	C₂³	1	2	yes	—
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	1	yes	characteristic
242	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
249	#95×C₁₃₉	C₂³	1	1	yes	characteristic
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	1	yes	characteristic
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	C₂⁴×C₁₃₉	—	2	4	no	—
255	C₂⁴×C₁₃₉	—	2	4	no	—
256	C₂⁴×C₁₃₉	—	2	4	no	—
257	C₂⁴×C₁₃₉	—	4	2	no	—
258	C₂⁴×C₁₃₉	—	4	2	no	—
259	C₂⁴×C₁₃₉	—	4	2	no	—
260	C₂⁴×C₁₃₉	—	4	2	no	—
261	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂×Q₈×C₁₃₉	—	2	2	no	—
266	C₂×Q₈×C₁₃₉	—	2	4	no	—
267	C₂×Q₈×C₁₃₉	—	2	2	no	—
268	C₂×Q₈×C₁₃₉	—	2	2	no	—
269	C₂×Q₈×C₁₃₉	—	4	2	no	—
270	C₂×Q₈×C₁₃₉	—	4	2	no	—
271	C₂×D₄×C₁₃₉	—	2	32	no	—
272	C₂×D₄×C₁₃₉	—	2	4	no	—
273	C₂×D₄×C₁₃₉	—	2	4	no	—
274	C₂×D₄×C₁₃₉	—	2	2	no	—
275	C₂×D₄×C₁₃₉	—	2	4	no	—
276	C₂×D₄×C₁₃₉	—	2	4	no	—
277	C₂×D₄×C₁₃₉	—	2	2	no	—
278	C₂×D₄×C₁₃₉	—	2	4	no	—
279	C₂×D₄×C₁₃₉	—	2	2	no	—
280	C₂×D₄×C₁₃₉	—	2	2	no	—
281	C₂×D₄×C₁₃₉	—	2	2	no	—
282	C₂×D₄×C₁₃₉	—	2	2	no	—
283	C₂×D₄×C₁₃₉	—	4	1	no	—
284	C₂×D₄×C₁₃₉	—	4	2	no	—
285	C₂×D₄×C₁₃₉	—	4	2	no	—
286	C₂×D₄×C₁₃₉	—	4	2	no	—
287	C₂×D₄×C₁₃₉	—	4	2	no	—
288	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
289	C₂×D₄×C₁₃₉	#41	1	4	yes	—
290	C₂²×C₄×C₁₃₉	—	2	2	no	—
291	C₂²×C₄×C₁₃₉	—	2	2	no	—
292	C₂²×C₄×C₁₃₉	—	2	4	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	2	2	no	—
295	C₂²×C₄×C₁₃₉	—	2	2	no	—
296	C₂²×C₄×C₁₃₉	—	2	4	no	—
297	C₂²×C₄×C₁₃₉	—	2	4	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	8	yes	—
307	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
315	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₁₃₉	—	2	2	no	—
328	C₄⋊C₄×C₁₃₉	—	2	2	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	2	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	2	no	—
339	C₄⋊C₄×C₁₃₉	—	2	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	no	—
342	C₄⋊C₄×C₁₃₉	—	4	1	no	—
343	C₄⋊C₄×C₁₃₉	—	4	2	no	—
344	C₄⋊C₄×C₁₃₉	—	4	2	no	—
345	C₄⋊C₄×C₁₃₉	—	4	2	no	—
346	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
347	C₂²⋊C₄×C₁₃₉	—	2	4	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	2	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	2	no	—
357	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
367	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
369	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
370	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
371	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
372	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
373	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
374	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
378	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
379	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
380	C₄²×C₁₃₉	—	2	4	no	—
381	C₄²×C₁₃₉	—	2	2	no	—
382	C₄²×C₁₃₉	—	2	2	no	—
383	C₄²×C₁₃₉	—	2	4	no	—
384	C₄²×C₁₃₉	—	2	2	no	—
385	C₄²×C₁₃₉	—	2	2	no	—
386	C₄²×C₁₃₉	—	2	2	no	—
387	C₄²×C₁₃₉	—	4	1	no	—
388	C₄²×C₁₃₉	—	4	1	no	—
389	C₄²×C₁₃₉	—	4	1	no	—
390	C₄²×C₁₃₉	—	4	2	no	—
391	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
392	C₂³×C₁₃₉	—	2	16	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	2	no	—
395	C₂³×C₁₃₉	—	2	1	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	1	no	—
402	C₂³×C₁₃₉	—	2	2	no	—
403	C₂³×C₁₃₉	—	2	2	no	—
404	C₂³×C₁₃₉	—	2	2	no	—
405	C₂³×C₁₃₉	—	2	2	no	—
406	C₂³×C₁₃₉	—	2	1	no	—
407	C₂³×C₁₃₉	—	2	1	no	—
408	C₂³×C₁₃₉	—	2	2	no	—
409	C₂³×C₁₃₉	—	2	2	no	—
410	C₂³×C₁₃₉	—	2	1	no	—
411	C₂³×C₁₃₉	—	2	1	no	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	2	1	no	—
414	C₂³×C₁₃₉	—	2	1	no	—
415	C₂³×C₁₃₉	—	2	1	no	—
416	C₂³×C₁₃₉	—	2	1	no	—
417	C₂³×C₁₃₉	—	2	1	no	—
418	C₂³×C₁₃₉	—	8	4	no	—
419	C₂³×C₁₃₉	—	8	4	no	—
420	C₂³×C₁₃₉	—	8	4	no	—
421	C₂³×C₁₃₉	—	8	4	no	—
422	C₂³×C₁₃₉	—	8	4	no	—
423	C₂³×C₁₃₉	—	8	4	no	—
424	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
425	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
426	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
427	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
428	Q₈×C₁₃₉	—	4	4	no	—
429	Q₈×C₁₃₉	—	8	4	no	—
430	D₄×C₁₃₉	—	2	16	no	—
431	D₄×C₁₃₉	—	2	8	no	—
432	D₄×C₁₃₉	—	2	8	no	—
433	D₄×C₁₃₉	—	4	4	no	—
434	D₄×C₁₃₉	—	8	4	no	—
435	D₄×C₁₃₉	—	8	4	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	1	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	1	no	—
442	C₂×C₄×C₁₃₉	—	2	1	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	8	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	2	no	—
451	C₂×C₄×C₁₃₉	—	2	1	no	—
452	C₂×C₄×C₁₃₉	—	2	1	no	—
453	C₂×C₄×C₁₃₉	—	2	2	no	—
454	C₂×C₄×C₁₃₉	—	2	1	no	—
455	C₂×C₄×C₁₃₉	—	2	1	no	—
456	C₂×C₄×C₁₃₉	—	2	1	no	—
457	C₂×C₄×C₁₃₉	—	2	1	no	—
458	C₂×C₄×C₁₃₉	—	2	1	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	2	no	—
461	C₂×C₄×C₁₃₉	—	2	1	no	—
462	C₂×C₄×C₁₃₉	—	2	2	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	1	no	—
465	C₂×C₄×C₁₃₉	—	2	2	no	—
466	C₂×C₄×C₁₃₉	—	2	2	no	—
467	C₂×C₄×C₁₃₉	—	2	2	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	1	no	—
470	C₂×C₄×C₁₃₉	—	2	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	1	no	—
477	C₂×C₄×C₁₃₉	—	2	1	no	—
478	C₂×C₄×C₁₃₉	—	2	2	no	—
479	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
484	C₂×C₄×C₁₃₉	—	2	1	no	—
485	C₂×C₄×C₁₃₉	—	2	2	no	—
486	C₂×C₄×C₁₃₉	—	4	8	no	—
487	C₂×C₄×C₁₃₉	—	4	4	no	—
488	C₂×C₄×C₁₃₉	—	8	4	no	—
489	C₂×C₄×C₁₃₉	—	8	4	no	—
490	C₂×C₄×C₁₃₉	—	8	4	no	—
491	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
493	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
496	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
497	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
498	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₁₃₉	—	2	2	no	—
500	C₂²×C₁₃₉	—	2	4	no	—
501	C₂²×C₁₃₉	—	2	4	no	—
502	C₂²×C₁₃₉	—	2	2	no	—
503	C₂²×C₁₃₉	—	2	4	no	—
504	C₂²×C₁₃₉	—	2	4	no	—
505	C₂²×C₁₃₉	—	2	2	no	—
506	C₂²×C₁₃₉	—	2	4	no	—
507	C₂²×C₁₃₉	—	2	4	no	—
508	C₂²×C₁₃₉	—	4	2	no	—
509	C₂²×C₁₃₉	—	4	2	no	—
510	C₂²×C₁₃₉	—	4	2	no	—
511	C₂²×C₁₃₉	—	4	1	no	—
512	C₂²×C₁₃₉	—	4	2	no	—
513	C₂²×C₁₃₉	—	4	1	no	—
514	C₂²×C₁₃₉	—	4	2	no	—
515	C₂²×C₁₃₉	—	4	2	no	—
516	C₂²×C₁₃₉	—	4	2	no	—
517	C₂²×C₁₃₉	—	4	1	no	—
518	C₂²×C₁₃₉	—	4	2	no	—
519	C₂²×C₁₃₉	—	4	1	no	—
520	C₂²×C₁₃₉	—	4	1	no	—
521	C₂²×C₁₃₉	—	4	1	no	—
522	C₂²×C₁₃₉	—	4	1	no	—
523	C₂²×C₁₃₉	—	4	1	no	—
524	C₂²×C₁₃₉	—	4	1	no	—
525	C₂²×C₁₃₉	—	4	1	no	—
526	C₂²×C₁₃₉	—	4	1	no	—
527	C₂²×C₁₃₉	—	8	16	no	—
528	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
529	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
530	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
531	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂²×C₁₃₉	#585	1	1	yes	characteristic
533	C₂²×C₁₃₉	#585	1	1	yes	characteristic
534	C₂²×C₁₃₉	#585	1	1	yes	characteristic
535	C₄×C₁₃₉	—	2	2	no	—
536	C₄×C₁₃₉	—	2	2	no	—
537	C₄×C₁₃₉	—	2	2	no	—
538	C₄×C₁₃₉	—	2	4	no	—
539	C₄×C₁₃₉	—	2	2	no	—
540	C₄×C₁₃₉	—	4	1	no	—
541	C₄×C₁₃₉	—	4	2	no	—
542	C₄×C₁₃₉	—	4	2	no	—
543	C₄×C₁₃₉	—	4	1	no	—
544	C₄×C₁₃₉	—	4	2	no	—
545	C₄×C₁₃₉	—	4	1	no	—
546	C₄×C₁₃₉	—	4	1	no	—
547	C₄×C₁₃₉	—	4	2	no	—
548	C₄×C₁₃₉	—	4	1	no	—
549	C₄×C₁₃₉	—	4	1	no	—
550	C₄×C₁₃₉	—	4	1	no	—
551	C₄×C₁₃₉	—	4	2	no	—
552	C₄×C₁₃₉	—	4	1	no	—
553	C₄×C₁₃₉	#525	1	4	yes	—
554	C₂×C₁₃₉	—	4	4	no	—
555	C₂×C₁₃₉	—	4	4	no	—
556	C₂×C₁₃₉	—	4	2	no	—
557	C₂×C₁₃₉	—	8	1	no	—
558	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
559	C₂×C₁₃₉	#3494	1	1	yes	characteristic
560	C₂×C₁₃₉	#3496	1	1	yes	characteristic
561	C₂×C₁₃₉	#3500	1	1	yes	characteristic
562	C₂×C₁₃₉	#3510	1	1	yes	characteristic
563	C₂×C₁₃₉	#3514	1	1	yes	characteristic
564	C₂×C₁₃₉	#3521	1	1	yes	characteristic
565	#35611	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
566	C₁₃₉	#35611	1	1	yes	characteristic, direct product factor, Sylow
567	C₂×#542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
568	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
569	#2602	C₂×C₁₃₉	1	2	yes	complemented
570	#2561	C₂×C₁₃₉	1	2	yes	complemented
571	#2480	C₂×C₁₃₉	1	2	yes	complemented
572	#2472	C₂×C₁₃₉	1	2	yes	complemented
573	#2466	C₂×C₁₃₉	1	2	yes	complemented
574	#2459	C₂×C₁₃₉	1	2	yes	complemented
575	#2452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
576	#2447	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	#2439	C₂×C₁₃₉	1	1	yes	characteristic, complemented
578	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
579	#2427	C₂×C₁₃₉	1	1	yes	characteristic, complemented
580	#2420	C₂×C₁₃₉	1	1	yes	characteristic, complemented
581	#2415	C₂×C₁₃₉	1	1	yes	characteristic, complemented
582	#2415	C₂×C₁₃₉	1	2	yes	complemented
583	#2411	C₂×C₁₃₉	1	2	yes	complemented
584	#2408	C₂×C₁₃₉	1	1	yes	characteristic
585	#2324	C₂×C₁₃₉	1	1	yes	characteristic, complemented
586	#2323	C₂×C₁₃₉	1	1	yes	characteristic, complemented
587	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
588	#2293	C₂×C₁₃₉	1	1	yes	characteristic, complemented
589	#2293	C₂×C₁₃₉	1	1	yes	characteristic, complemented
590	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
591	#542	—	2	8	no	—
592	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
593	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
594	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
597	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
598	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
599	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
600	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
601	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
602	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
603	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
604	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
605	#518	—	2	8	no	—
606	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
607	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
608	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
609	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
612	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
615	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
616	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
617	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
618	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
619	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
620	#397	C₂²×C₁₃₉	1	2	yes	—
621	#397	C₂²×C₁₃₉	1	2	yes	complemented
622	#397	C₂²×C₁₃₉	1	2	yes	complemented
623	#397	C₂²×C₁₃₉	1	2	yes	complemented
624	#397	C₂²×C₁₃₉	1	2	yes	complemented
625	#396	C₂²×C₁₃₉	1	2	yes	—
626	#396	C₂²×C₁₃₉	1	2	yes	complemented
627	#394	C₂²×C₁₃₉	1	2	yes	—
628	#394	C₂²×C₁₃₉	1	2	yes	—
629	#394	C₂²×C₁₃₉	1	2	yes	—
630	#394	C₂²×C₁₃₉	1	2	yes	—
631	#394	C₂²×C₁₃₉	1	2	yes	complemented
632	#394	C₂²×C₁₃₉	1	2	yes	complemented
633	#393	C₂²×C₁₃₉	1	2	yes	—
634	#393	C₂²×C₁₃₉	1	2	yes	complemented
635	#392	C₂²×C₁₃₉	1	2	yes	—
636	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
637	#391	C₂²×C₁₃₉	1	2	yes	complemented
638	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
639	#390	C₂²×C₁₃₉	1	1	yes	characteristic
640	#390	C₂²×C₁₃₉	1	1	yes	characteristic
641	#390	C₂²×C₁₃₉	1	1	yes	characteristic
642	#390	C₂²×C₁₃₉	1	1	yes	characteristic
643	#390	C₂²×C₁₃₉	1	1	yes	characteristic
644	#390	C₂²×C₁₃₉	1	1	yes	characteristic
645	#390	C₂²×C₁₃₉	1	2	yes	complemented
646	#389	C₂²×C₁₃₉	1	2	yes	complemented
647	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
648	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
649	#389	C₂²×C₁₃₉	1	2	yes	complemented
650	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
651	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
652	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
653	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
654	#388	C₂²×C₁₃₉	1	1	yes	characteristic
655	#388	C₂²×C₁₃₉	1	2	yes	—
656	#388	C₂²×C₁₃₉	1	2	yes	—
657	#388	C₂²×C₁₃₉	1	1	yes	characteristic
658	#388	C₂²×C₁₃₉	1	2	yes	complemented
659	#388	C₂²×C₁₃₉	1	2	yes	complemented
660	#388	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
661	#388	C₂²×C₁₃₉	1	2	yes	complemented
662	#388	C₂²×C₁₃₉	1	2	yes	complemented
663	#388	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
664	#388	C₂²×C₁₃₉	1	2	yes	complemented
665	#388	C₂²×C₁₃₉	1	2	yes	complemented
666	#387	C₂²×C₁₃₉	1	2	yes	complemented
667	#387	C₂²×C₁₃₉	1	2	yes	complemented
668	#386	C₂²×C₁₃₉	1	2	yes	complemented
669	#386	C₂²×C₁₃₉	1	2	yes	complemented
670	#386	C₂²×C₁₃₉	1	2	yes	complemented
671	#385	C₂²×C₁₃₉	1	2	yes	complemented
672	#385	C₂²×C₁₃₉	1	2	yes	complemented
673	#385	C₂²×C₁₃₉	1	2	yes	complemented
674	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
675	#381	C₂²×C₁₃₉	1	2	yes	complemented
676	#381	C₂²×C₁₃₉	1	2	yes	complemented
677	#380	C₂²×C₁₃₉	1	1	yes	characteristic
678	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
679	#380	C₂²×C₁₃₉	1	2	yes	complemented
680	#379	C₂²×C₁₃₉	1	2	yes	—
681	#379	C₂²×C₁₃₉	1	2	yes	—
682	#379	C₂²×C₁₃₉	1	2	yes	—
683	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
684	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
685	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
686	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
687	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
688	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
689	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
690	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
691	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
692	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
693	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
694	C₂²×D₄	—	2	4	no	—
695	C₂²×D₄	—	2	4	no	—
696	C₂²×D₄	—	2	4	no	—
697	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
698	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
701	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
702	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
703	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
706	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
707	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
708	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
709	C₄⋊Q₈	—	2	4	no	—
710	#126	—	2	8	no	—
711	#124	—	2	4	no	—
712	#124	—	2	4	no	—
713	#124	—	2	8	no	—
714	#123	—	2	8	no	—
715	C₂²⋊Q₈	—	2	8	no	—
716	C₂²⋊Q₈	—	2	4	no	—
717	C₂²⋊Q₈	—	2	4	no	—
718	C₂²⋊Q₈	—	4	4	no	—
719	#121	—	2	4	no	—
720	#121	—	2	4	no	—
721	#120	—	4	4	no	—
722	C₄×Q₈	—	2	4	no	—
723	C₄×D₄	—	2	4	no	—
724	C₄×D₄	—	2	8	no	—
725	C₄×D₄	—	2	4	no	—
726	C₄×D₄	—	2	4	no	—
727	C₄×D₄	—	2	8	no	—
728	C₄×D₄	—	2	4	no	—
729	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
730	#117	—	2	4	no	—
731	#117	—	2	4	no	—
732	#117	—	2	4	no	—
733	#117	—	4	4	no	—
734	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
754	C₂×C₂²⋊C₄	—	2	8	no	—
755	C₂×C₂²⋊C₄	—	2	8	no	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	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	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
789	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
790	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
791	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
795	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
797	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
801	#95	C₂³×C₁₃₉	1	1	yes	characteristic
802	#95	C₂³×C₁₃₉	1	1	yes	characteristic
803	#95	C₂³×C₁₃₉	1	1	yes	characteristic
804	#95	C₂³×C₁₃₉	1	1	yes	characteristic
805	#95	C₂³×C₁₃₉	1	2	yes	—
806	#95	C₂³×C₁₃₉	1	2	yes	—
807	#95	C₂³×C₁₃₉	1	2	yes	—
808	#95	C₂³×C₁₃₉	1	2	yes	—
809	#95	C₂³×C₁₃₉	1	2	yes	—
810	#95	C₂³×C₁₃₉	1	2	yes	—
811	#95	C₂³×C₁₃₉	1	1	yes	characteristic
812	#95	C₂³×C₁₃₉	1	1	yes	characteristic
813	#95	C₂³×C₁₃₉	1	2	yes	—
814	#95	C₂³×C₁₃₉	1	2	yes	—
815	#95	C₂³×C₁₃₉	1	2	yes	—
816	#95	C₂³×C₁₃₉	1	2	yes	—
817	#95	C₂³×C₁₃₉	1	2	yes	—
818	#95	C₂³×C₁₃₉	1	2	yes	—
819	#95	C₂³×C₁₃₉	1	2	yes	—
820	C₂⁴	—	2	4	no	—
821	C₂⁴	—	2	4	no	—
822	C₂⁴	—	2	4	no	—
823	C₂⁴	—	4	2	no	—
824	C₂⁴	—	4	2	no	—
825	C₂⁴	—	4	2	no	—
826	C₂⁴	—	4	2	no	—
827	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
828	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
829	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
830	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	4	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×D₄	—	2	32	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	4	1	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
855	C₂×D₄	#41×C₁₃₉	1	4	yes	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
873	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
874	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	4	1	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	1	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	1	no	—
937	C₂²⋊C₄	—	4	1	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	1	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
946	C₄²	—	2	4	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	4	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	4	1	no	—
954	C₄²	—	4	1	no	—
955	C₄²	—	4	1	no	—
956	C₄²	—	4	2	no	—
957	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
958	C₂³	—	2	16	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	8	4	no	—
985	C₂³	—	8	4	no	—
986	C₂³	—	8	4	no	—
987	C₂³	—	8	4	no	—
988	C₂³	—	8	4	no	—
989	C₂³	—	8	4	no	—
990	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
991	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
992	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
993	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
994	Q₈	—	4	4	no	—
995	Q₈	—	8	4	no	—
996	D₄	—	2	16	no	—
997	D₄	—	2	8	no	—
998	D₄	—	2	8	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	8	4	no	—
1001	D₄	—	8	4	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	8	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	4	8	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	8	4	no	—
1055	C₂×C₄	—	8	4	no	—
1056	C₂×C₄	—	8	4	no	—
1057	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1059	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1061	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1062	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1063	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1064	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	2	4	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	16	no	—
1094	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1095	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1096	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1097	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1098	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1099	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1100	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	4	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	#525×C₁₃₉	1	4	yes	—
1120	C₂	—	4	2	no	—
1121	C₂	—	4	4	no	—
1122	C₂	—	4	4	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1125	C₂	#3494×C₁₃₉	1	1	yes	characteristic
1126	C₂	#3496×C₁₃₉	1	1	yes	characteristic
1127	C₂	#3500×C₁₃₉	1	1	yes	characteristic
1128	C₂	#3510×C₁₃₉	1	1	yes	characteristic
1129	C₂	#3514×C₁₃₉	1	1	yes	characteristic
1130	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2408×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#542×C₁₃₉	C₂	semidirect
2. C₂×#518×C₁₃₉	C₂	semidirect
3. #2602×C₁₃₉	C₂	semidirect
4. #2561×C₁₃₉	C₂	semidirect
5. #2480×C₁₃₉	C₂	semidirect
6. #2472×C₁₃₉	C₂	semidirect
7. #2466×C₁₃₉	C₂	semidirect
8. #2459×C₁₃₉	C₂	semidirect
9. #2452×C₁₃₉	C₂	semidirect
10. #2447×C₁₃₉	C₂	semidirect
11. #2439×C₁₃₉	C₂	semidirect
12. #2435×C₁₃₉	C₂	semidirect
13. #2427×C₁₃₉	C₂	semidirect
14. #2420×C₁₃₉	C₂	semidirect
15. #2415×C₁₃₉	C₂	semidirect
16. #2415×C₁₃₉	C₂	semidirect
17. #2411×C₁₃₉	C₂	semidirect
19. #2324×C₁₃₉	C₂	semidirect
20. #2323×C₁₃₉	C₂	semidirect
21. C₄×#124×C₁₃₉	C₂	semidirect
22. #2293×C₁₃₉	C₂	semidirect
23. #2293×C₁₃₉	C₂	semidirect
26. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×#126×C₁₃₉	C₂²	semidirect
30. C₂×#124×C₁₃₉	C₂²	semidirect
31. C₂×#123×C₁₃₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
40. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
50. C₂×#117×C₁₃₉	C₂²	semidirect
51. C₂×#117×C₁₃₉	C₂²	semidirect
55. #397×C₁₃₉	C₂²	semidirect
56. #397×C₁₃₉	C₂²	semidirect
57. #397×C₁₃₉	C₂²	semidirect
58. #397×C₁₃₉	C₂²	semidirect
60. #396×C₁₃₉	C₂²	semidirect
65. #394×C₁₃₉	C₂²	semidirect
66. #394×C₁₃₉	C₂²	semidirect
68. #393×C₁₃₉	C₂²	semidirect
70. #391×C₁₃₉	C₂²	semidirect
71. #391×C₁₃₉	C₂²	semidirect
72. #391×C₁₃₉	C₂²	semidirect
79. #390×C₁₃₉	C₂²	semidirect
80. #389×C₁₃₉	C₂²	semidirect
81. #389×C₁₃₉	C₂²	semidirect
82. #389×C₁₃₉	C₂²	semidirect
83. #389×C₁₃₉	C₂²	semidirect
84. #389×C₁₃₉	C₂²	semidirect
85. #389×C₁₃₉	C₂²	semidirect
86. #389×C₁₃₉	C₂²	semidirect
87. #389×C₁₃₉	C₂²	semidirect
92. #388×C₁₃₉	C₂²	semidirect
93. #388×C₁₃₉	C₂²	semidirect
94. #388×C₁₃₉	C₂²	semidirect
95. #388×C₁₃₉	C₂²	semidirect
96. #388×C₁₃₉	C₂²	semidirect
97. #388×C₁₃₉	C₂²	semidirect
98. #388×C₁₃₉	C₂²	semidirect
99. #388×C₁₃₉	C₂²	semidirect
100. #387×C₁₃₉	C₂²	semidirect
101. #387×C₁₃₉	C₂²	semidirect
102. #386×C₁₃₉	C₂²	semidirect
103. #386×C₁₃₉	C₂²	semidirect
104. #386×C₁₃₉	C₂²	semidirect
105. #385×C₁₃₉	C₂²	semidirect
106. #385×C₁₃₉	C₂²	semidirect
107. #385×C₁₃₉	C₂²	semidirect
108. #382×C₁₃₉	C₂²	semidirect
109. #381×C₁₃₉	C₂²	semidirect
110. #381×C₁₃₉	C₂²	semidirect
112. #380×C₁₃₉	C₂²	semidirect
113. #380×C₁₃₉	C₂²	semidirect
117. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
124. C₄³×C₁₃₉	C₂²	semidirect
163. C₄×D₄×C₁₃₉	D₄	semidirect
565. #35611	C₁₃₉	direct (N × H)
566. C₁₃₉	#35611	direct (N × H)
567. C₂×#542	C₂×C₁₃₉	semidirect
568. C₂×#518	C₂×C₁₃₉	semidirect
569. #2602	C₂×C₁₃₉	semidirect
570. #2561	C₂×C₁₃₉	semidirect
571. #2480	C₂×C₁₃₉	semidirect
572. #2472	C₂×C₁₃₉	semidirect
573. #2466	C₂×C₁₃₉	semidirect
574. #2459	C₂×C₁₃₉	semidirect
575. #2452	C₂×C₁₃₉	semidirect
576. #2447	C₂×C₁₃₉	semidirect
577. #2439	C₂×C₁₃₉	semidirect
578. #2435	C₂×C₁₃₉	semidirect
579. #2427	C₂×C₁₃₉	semidirect
580. #2420	C₂×C₁₃₉	semidirect
581. #2415	C₂×C₁₃₉	semidirect
582. #2415	C₂×C₁₃₉	semidirect
583. #2411	C₂×C₁₃₉	semidirect
585. #2324	C₂×C₁₃₉	semidirect
586. #2323	C₂×C₁₃₉	semidirect
587. C₄×#124	C₂×C₁₃₉	semidirect
588. #2293	C₂×C₁₃₉	semidirect
589. #2293	C₂×C₁₃₉	semidirect
592. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
593. C₂×#126	C₂²×C₁₃₉	semidirect
596. C₂×#124	C₂²×C₁₃₉	semidirect
597. C₂×#123	C₂²×C₁₃₉	semidirect
599. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
600. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
601. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
606. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
616. C₂×#117	C₂²×C₁₃₉	semidirect
617. C₂×#117	C₂²×C₁₃₉	semidirect
621. #397	C₂²×C₁₃₉	semidirect
622. #397	C₂²×C₁₃₉	semidirect
623. #397	C₂²×C₁₃₉	semidirect
624. #397	C₂²×C₁₃₉	semidirect
626. #396	C₂²×C₁₃₉	semidirect
631. #394	C₂²×C₁₃₉	semidirect
632. #394	C₂²×C₁₃₉	semidirect
634. #393	C₂²×C₁₃₉	semidirect
636. #391	C₂²×C₁₃₉	semidirect
637. #391	C₂²×C₁₃₉	semidirect
638. #391	C₂²×C₁₃₉	semidirect
645. #390	C₂²×C₁₃₉	semidirect
646. #389	C₂²×C₁₃₉	semidirect
647. #389	C₂²×C₁₃₉	semidirect
648. #389	C₂²×C₁₃₉	semidirect
649. #389	C₂²×C₁₃₉	semidirect
650. #389	C₂²×C₁₃₉	semidirect
651. #389	C₂²×C₁₃₉	semidirect
652. #389	C₂²×C₁₃₉	semidirect
653. #389	C₂²×C₁₃₉	semidirect
658. #388	C₂²×C₁₃₉	semidirect
659. #388	C₂²×C₁₃₉	semidirect
660. #388	C₂²×C₁₃₉	semidirect
661. #388	C₂²×C₁₃₉	semidirect
662. #388	C₂²×C₁₃₉	semidirect
663. #388	C₂²×C₁₃₉	semidirect
664. #388	C₂²×C₁₃₉	semidirect
665. #388	C₂²×C₁₃₉	semidirect
666. #387	C₂²×C₁₃₉	semidirect
667. #387	C₂²×C₁₃₉	semidirect
668. #386	C₂²×C₁₃₉	semidirect
669. #386	C₂²×C₁₃₉	semidirect
670. #386	C₂²×C₁₃₉	semidirect
671. #385	C₂²×C₁₃₉	semidirect
672. #385	C₂²×C₁₃₉	semidirect
673. #385	C₂²×C₁₃₉	semidirect
674. #382	C₂²×C₁₃₉	semidirect
675. #381	C₂²×C₁₃₉	semidirect
676. #381	C₂²×C₁₃₉	semidirect
678. #380	C₂²×C₁₃₉	semidirect
679. #380	C₂²×C₁₃₉	semidirect
683. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
684. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
686. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
687. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
688. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
690. C₄³	C₂²×C₁₃₉	semidirect
729. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2602×C₁₃₉	2
#2561×C₁₃₉	2
#2480×C₁₃₉	2
#2472×C₁₃₉	2
#2466×C₁₃₉	2
#2459×C₁₃₉	2
#2452×C₁₃₉	2
#2447×C₁₃₉	2
#2439×C₁₃₉	2
#2435×C₁₃₉	2
#2427×C₁₃₉	2
#2420×C₁₃₉	2
#2415×C₁₃₉	2
#2411×C₁₃₉	2
#2408×C₁₃₉	2
#2324×C₁₃₉	2
#2323×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2293×C₁₃₉	2
#35611	139

Subgroups — C139×#35611 #48030207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35611 #48030207