Subgroups — C₁₃₉×#36439 #48031035

Order 35584.

2500 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2852×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2601×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2599×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2499×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2485×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2480×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2478×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2474×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2472×C₁₃₉	C₂	1	2	yes	maximal
13	#2440×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2439×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2417×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2415×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2362×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2360×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2352×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
23	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#556×C₁₃₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
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×#117×C₁₃₉	—	2	8	no	—
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
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	—
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
53	#398×C₁₃₉	C₂²	1	2	yes	complemented
54	#398×C₁₃₉	C₂²	1	2	yes	complemented
55	#397×C₁₃₉	C₂²	1	2	yes	—
56	#397×C₁₃₉	C₂²	1	2	yes	—
57	#397×C₁₃₉	C₂²	1	2	yes	—
58	#397×C₁₃₉	C₂²	1	2	yes	—
59	#396×C₁₃₉	C₂²	1	2	yes	—
60	#396×C₁₃₉	C₂²	1	2	yes	complemented
61	#395×C₁₃₉	C₂²	1	2	yes	complemented
62	#394×C₁₃₉	C₂²	1	2	yes	—
63	#394×C₁₃₉	C₂²	1	2	yes	—
64	#393×C₁₃₉	C₂²	1	2	yes	—
65	#391×C₁₃₉	C₂²	1	2	yes	complemented
66	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
68	#390×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	complemented
70	#389×C₁₃₉	C₂²	1	2	yes	complemented
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#388×C₁₃₉	C₂²	1	2	yes	complemented
81	#388×C₁₃₉	C₂²	1	2	yes	complemented
82	#388×C₁₃₉	C₂²	1	2	yes	complemented
83	#388×C₁₃₉	C₂²	1	2	yes	complemented
84	#387×C₁₃₉	C₂²	1	2	yes	complemented
85	#387×C₁₃₉	C₂²	1	2	yes	complemented
86	#387×C₁₃₉	C₂²	1	2	yes	complemented
87	#387×C₁₃₉	C₂²	1	2	yes	complemented
88	#387×C₁₃₉	C₂²	1	2	yes	complemented
89	#387×C₁₃₉	C₂²	1	2	yes	complemented
90	#387×C₁₃₉	C₂²	1	2	yes	complemented
91	#386×C₁₃₉	C₂²	1	1	yes	characteristic
92	#386×C₁₃₉	C₂²	1	1	yes	characteristic
93	#386×C₁₃₉	C₂²	1	1	yes	characteristic
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	1	yes	characteristic
97	#385×C₁₃₉	C₂²	1	1	yes	characteristic
98	#385×C₁₃₉	C₂²	1	1	yes	characteristic
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	2	yes	—
101	#385×C₁₃₉	C₂²	1	2	yes	—
102	#385×C₁₃₉	C₂²	1	2	yes	—
103	#385×C₁₃₉	C₂²	1	2	yes	—
104	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
105	#383×C₁₃₉	C₂²	1	2	yes	complemented
106	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	#380×C₁₃₉	C₂²	1	2	yes	—
108	#380×C₁₃₉	C₂²	1	1	yes	characteristic
109	#380×C₁₃₉	C₂²	1	1	yes	characteristic
110	#380×C₁₃₉	C₂²	1	1	yes	characteristic
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
113	#379×C₁₃₉	C₂²	1	1	yes	characteristic
114	#379×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	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	1	yes	characteristic
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	—
124	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃₉	—	2	4	no	—
132	C₂³×C₄×C₁₃₉	—	2	4	no	—
133	C₂³×C₄×C₁₃₉	—	2	4	no	—
134	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
144	#126×C₁₃₉	—	2	8	no	—
145	#126×C₁₃₉	—	2	8	no	—
146	#124×C₁₃₉	—	2	8	no	—
147	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
148	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
149	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
150	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
152	#120×C₁₃₉	—	2	4	no	—
153	C₄×Q₈×C₁₃₉	—	2	4	no	—
154	C₄×Q₈×C₁₃₉	—	2	8	no	—
155	C₄×D₄×C₁₃₉	—	2	4	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	4	no	—
158	#117×C₁₃₉	—	2	4	no	—
159	#117×C₁₃₉	—	2	4	no	—
160	#117×C₁₃₉	—	2	4	no	—
161	#117×C₁₃₉	—	2	4	no	—
162	#117×C₁₃₉	—	2	8	no	—
163	#117×C₁₃₉	—	2	8	no	—
164	#117×C₁₃₉	D₄	1	8	yes	complemented
165	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
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	1	yes	characteristic
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	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	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
218	C₂×C₄²×C₁₃₉	—	2	8	no	—
219	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	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	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	1	yes	characteristic
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	1	yes	characteristic
245	#95×C₁₃₉	C₂³	1	1	yes	characteristic
246	#95×C₁₃₉	C₂³	1	1	yes	characteristic
247	#95×C₁₃₉	C₂³	1	1	yes	characteristic
248	#95×C₁₃₉	C₂³	1	2	yes	—
249	#95×C₁₃₉	C₂³	1	2	yes	—
250	#95×C₁₃₉	C₂³	1	2	yes	—
251	#95×C₁₃₉	C₂³	1	2	yes	—
252	#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	1	no	—
259	C₂⁴×C₁₃₉	—	4	1	no	—
260	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂×Q₈×C₁₃₉	—	2	2	no	—
265	C₂×Q₈×C₁₃₉	—	2	4	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×D₄×C₁₃₉	—	2	2	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	—	4	1	no	—
278	C₂×D₄×C₁₃₉	—	4	1	no	—
279	C₂²×C₄×C₁₃₉	—	2	32	no	—
280	C₂²×C₄×C₁₃₉	—	2	2	no	—
281	C₂²×C₄×C₁₃₉	—	2	2	no	—
282	C₂²×C₄×C₁₃₉	—	2	2	no	—
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	2	no	—
287	C₂²×C₄×C₁₃₉	—	2	2	no	—
288	C₂²×C₄×C₁₃₉	—	2	2	no	—
289	C₂²×C₄×C₁₃₉	—	2	2	no	—
290	C₂²×C₄×C₁₃₉	—	2	2	no	—
291	C₂²×C₄×C₁₃₉	—	2	2	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	4	no	—
296	C₂²×C₄×C₁₃₉	—	2	4	no	—
297	C₂²×C₄×C₁₃₉	—	2	4	no	—
298	C₂²×C₄×C₁₃₉	—	2	4	no	—
299	C₂²×C₄×C₁₃₉	—	2	2	no	—
300	C₂²×C₄×C₁₃₉	—	2	2	no	—
301	C₂²×C₄×C₁₃₉	—	2	2	no	—
302	C₂²×C₄×C₁₃₉	—	4	2	no	—
303	C₂²×C₄×C₁₃₉	—	4	2	no	—
304	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
305	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
306	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
307	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
319	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	4	no	—
327	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
333	C₄⋊C₄×C₁₃₉	—	2	4	no	—
334	C₄⋊C₄×C₁₃₉	—	2	4	no	—
335	C₄⋊C₄×C₁₃₉	—	2	4	no	—
336	C₄⋊C₄×C₁₃₉	—	2	2	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	4	no	—
339	C₄⋊C₄×C₁₃₉	—	2	2	no	—
340	C₄⋊C₄×C₁₃₉	—	2	2	no	—
341	C₄⋊C₄×C₁₃₉	—	2	4	no	—
342	C₄⋊C₄×C₁₃₉	—	2	4	no	—
343	C₄⋊C₄×C₁₃₉	—	2	4	no	—
344	C₄⋊C₄×C₁₃₉	—	2	4	no	—
345	C₄⋊C₄×C₁₃₉	—	4	2	no	—
346	C₄⋊C₄×C₁₃₉	—	4	2	no	—
347	C₄⋊C₄×C₁₃₉	—	4	2	no	—
348	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
349	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	2	no	—
354	C₂²⋊C₄×C₁₃₉	—	2	2	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	4	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	4	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	2	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	4	1	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	1	no	—
374	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
375	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
376	C₄²×C₁₃₉	—	2	4	no	—
377	C₄²×C₁₃₉	—	2	4	no	—
378	C₄²×C₁₃₉	—	2	4	no	—
379	C₄²×C₁₃₉	—	2	4	no	—
380	C₄²×C₁₃₉	—	2	2	no	—
381	C₄²×C₁₃₉	—	2	4	no	—
382	C₄²×C₁₃₉	—	2	2	no	—
383	C₄²×C₁₃₉	—	2	2	no	—
384	C₄²×C₁₃₉	—	4	2	no	—
385	C₄²×C₁₃₉	—	4	2	no	—
386	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
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	8	no	—
392	C₂³×C₁₃₉	—	2	1	no	—
393	C₂³×C₁₃₉	—	2	1	no	—
394	C₂³×C₁₃₉	—	2	1	no	—
395	C₂³×C₁₃₉	—	2	1	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	1	no	—
398	C₂³×C₁₃₉	—	2	1	no	—
399	C₂³×C₁₃₉	—	2	1	no	—
400	C₂³×C₁₃₉	—	2	1	no	—
401	C₂³×C₁₃₉	—	2	1	no	—
402	C₂³×C₁₃₉	—	2	1	no	—
403	C₂³×C₁₃₉	—	2	1	no	—
404	C₂³×C₁₃₉	—	2	1	no	—
405	C₂³×C₁₃₉	—	2	1	no	—
406	C₂³×C₁₃₉	—	2	1	no	—
407	C₂³×C₁₃₉	—	2	1	no	—
408	C₂³×C₁₃₉	—	2	1	no	—
409	C₂³×C₁₃₉	—	2	1	no	—
410	C₂³×C₁₃₉	—	2	1	no	—
411	C₂³×C₁₃₉	—	4	4	no	—
412	C₂³×C₁₃₉	—	4	4	no	—
413	C₂³×C₁₃₉	—	4	4	no	—
414	C₂³×C₁₃₉	—	4	4	no	—
415	C₂³×C₁₃₉	—	4	4	no	—
416	C₂³×C₁₃₉	—	4	4	no	—
417	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
418	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
419	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
420	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
421	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
422	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
423	Q₈×C₁₃₉	—	4	8	no	—
424	Q₈×C₁₃₉	—	4	4	no	—
425	D₄×C₁₃₉	—	4	4	no	—
426	D₄×C₁₃₉	—	4	4	no	—
427	D₄×C₁₃₉	—	4	4	no	—
428	C₂×C₄×C₁₃₉	—	2	8	no	—
429	C₂×C₄×C₁₃₉	—	2	8	no	—
430	C₂×C₄×C₁₃₉	—	2	8	no	—
431	C₂×C₄×C₁₃₉	—	2	1	no	—
432	C₂×C₄×C₁₃₉	—	2	1	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	1	no	—
435	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
442	C₂×C₄×C₁₃₉	—	2	1	no	—
443	C₂×C₄×C₁₃₉	—	2	2	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	8	no	—
446	C₂×C₄×C₁₃₉	—	2	8	no	—
447	C₂×C₄×C₁₃₉	—	2	8	no	—
448	C₂×C₄×C₁₃₉	—	2	2	no	—
449	C₂×C₄×C₁₃₉	—	2	2	no	—
450	C₂×C₄×C₁₃₉	—	2	1	no	—
451	C₂×C₄×C₁₃₉	—	2	1	no	—
452	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
459	C₂×C₄×C₁₃₉	—	2	2	no	—
460	C₂×C₄×C₁₃₉	—	2	2	no	—
461	C₂×C₄×C₁₃₉	—	2	1	no	—
462	C₂×C₄×C₁₃₉	—	2	1	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	2	no	—
465	C₂×C₄×C₁₃₉	—	2	2	no	—
466	C₂×C₄×C₁₃₉	—	2	2	no	—
467	C₂×C₄×C₁₃₉	—	2	1	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	2	no	—
470	C₂×C₄×C₁₃₉	—	2	1	no	—
471	C₂×C₄×C₁₃₉	—	2	1	no	—
472	C₂×C₄×C₁₃₉	—	2	2	no	—
473	C₂×C₄×C₁₃₉	—	2	2	no	—
474	C₂×C₄×C₁₃₉	—	2	2	no	—
475	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
480	C₂×C₄×C₁₃₉	—	2	2	no	—
481	C₂×C₄×C₁₃₉	—	4	8	no	—
482	C₂×C₄×C₁₃₉	—	4	8	no	—
483	C₂×C₄×C₁₃₉	—	4	4	no	—
484	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
485	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
487	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
489	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
490	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
491	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
492	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
493	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
494	C₂²×C₁₃₉	—	2	2	no	—
495	C₂²×C₁₃₉	—	2	2	no	—
496	C₂²×C₁₃₉	—	2	2	no	—
497	C₂²×C₁₃₉	—	2	2	no	—
498	C₂²×C₁₃₉	—	2	2	no	—
499	C₂²×C₁₃₉	—	2	2	no	—
500	C₂²×C₁₃₉	—	2	2	no	—
501	C₂²×C₁₃₉	—	2	2	no	—
502	C₂²×C₁₃₉	—	2	2	no	—
503	C₂²×C₁₃₉	—	2	2	no	—
504	C₂²×C₁₃₉	—	2	2	no	—
505	C₂²×C₁₃₉	—	2	2	no	—
506	C₂²×C₁₃₉	—	4	16	no	—
507	C₂²×C₁₃₉	—	4	1	no	—
508	C₂²×C₁₃₉	—	4	1	no	—
509	C₂²×C₁₃₉	—	4	1	no	—
510	C₂²×C₁₃₉	—	4	1	no	—
511	C₂²×C₁₃₉	—	4	1	no	—
512	C₂²×C₁₃₉	—	4	1	no	—
513	C₂²×C₁₃₉	—	4	1	no	—
514	C₂²×C₁₃₉	—	4	1	no	—
515	C₂²×C₁₃₉	—	4	1	no	—
516	C₂²×C₁₃₉	—	4	1	no	—
517	C₂²×C₁₃₉	—	4	1	no	—
518	C₂²×C₁₃₉	—	4	1	no	—
519	C₂²×C₁₃₉	—	4	1	no	—
520	C₂²×C₁₃₉	—	4	1	no	—
521	C₂²×C₁₃₉	—	4	1	no	—
522	C₂²×C₁₃₉	#556	1	4	yes	complemented
523	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
524	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
525	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
526	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
527	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
528	C₂²×C₁₃₉	#585	1	1	yes	characteristic
529	C₂²×C₁₃₉	#585	1	1	yes	characteristic
530	C₄×C₁₃₉	—	2	2	no	—
531	C₄×C₁₃₉	—	2	2	no	—
532	C₄×C₁₃₉	—	2	2	no	—
533	C₄×C₁₃₉	—	2	4	no	—
534	C₄×C₁₃₉	—	2	2	no	—
535	C₄×C₁₃₉	—	2	2	no	—
536	C₄×C₁₃₉	—	2	4	no	—
537	C₄×C₁₃₉	—	4	1	no	—
538	C₄×C₁₃₉	—	4	2	no	—
539	C₄×C₁₃₉	—	4	2	no	—
540	C₄×C₁₃₉	—	4	2	no	—
541	C₄×C₁₃₉	—	4	1	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	2	no	—
547	C₄×C₁₃₉	—	4	1	no	—
548	C₄×C₁₃₉	#525	1	4	yes	—
549	C₂×C₁₃₉	—	2	4	no	—
550	C₂×C₁₃₉	—	4	2	no	—
551	C₂×C₁₃₉	—	4	2	no	—
552	C₂×C₁₃₉	—	8	1	no	—
553	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
554	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
555	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
556	C₂×C₁₃₉	#3475	1	1	yes	characteristic
557	C₂×C₁₃₉	#3489	1	1	yes	characteristic
558	C₂×C₁₃₉	#3493	1	1	yes	characteristic
559	C₂×C₁₃₉	#3495	1	1	yes	characteristic
560	#36439	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
561	C₁₃₉	#36439	1	1	yes	characteristic, direct product factor, Sylow
562	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
563	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
564	#2852	C₂×C₁₃₉	1	2	yes	complemented
565	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
566	#2601	C₂×C₁₃₉	1	2	yes	complemented
567	#2599	C₂×C₁₃₉	1	2	yes	complemented
568	#2499	C₂×C₁₃₉	1	1	yes	characteristic, complemented
569	#2485	C₂×C₁₃₉	1	1	yes	characteristic, complemented
570	#2480	C₂×C₁₃₉	1	2	yes	complemented
571	#2478	C₂×C₁₃₉	1	2	yes	complemented
572	#2474	C₂×C₁₃₉	1	2	yes	complemented
573	#2472	C₂×C₁₃₉	1	2	yes	—
574	#2440	C₂×C₁₃₉	1	1	yes	characteristic, complemented
575	#2439	C₂×C₁₃₉	1	1	yes	characteristic, complemented
576	#2417	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	#2415	C₂×C₁₃₉	1	1	yes	characteristic, complemented
578	#2362	C₂×C₁₃₉	1	1	yes	characteristic, complemented
579	#2360	C₂×C₁₃₉	1	1	yes	characteristic, complemented
580	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
581	#2352	C₂×C₁₃₉	1	1	yes	characteristic, complemented
582	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
583	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
584	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic
585	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
586	#556	—	2	8	no	—
587	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
588	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
589	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
590	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
592	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
593	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
594	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
596	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
598	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
599	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₂×#117	—	2	8	no	—
603	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
604	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
605	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
606	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
607	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
608	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
609	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
610	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
612	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
613	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
614	#398	C₂²×C₁₃₉	1	2	yes	complemented
615	#398	C₂²×C₁₃₉	1	2	yes	complemented
616	#397	C₂²×C₁₃₉	1	2	yes	—
617	#397	C₂²×C₁₃₉	1	2	yes	—
618	#397	C₂²×C₁₃₉	1	2	yes	—
619	#397	C₂²×C₁₃₉	1	2	yes	—
620	#396	C₂²×C₁₃₉	1	2	yes	—
621	#396	C₂²×C₁₃₉	1	2	yes	complemented
622	#395	C₂²×C₁₃₉	1	2	yes	complemented
623	#394	C₂²×C₁₃₉	1	2	yes	—
624	#394	C₂²×C₁₃₉	1	2	yes	—
625	#393	C₂²×C₁₃₉	1	2	yes	—
626	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
627	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
628	#391	C₂²×C₁₃₉	1	2	yes	complemented
629	#390	C₂²×C₁₃₉	1	2	yes	—
630	#389	C₂²×C₁₃₉	1	2	yes	complemented
631	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
632	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
633	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
634	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
635	#389	C₂²×C₁₃₉	1	2	yes	complemented
636	#388	C₂²×C₁₃₉	1	2	yes	—
637	#388	C₂²×C₁₃₉	1	2	yes	—
638	#388	C₂²×C₁₃₉	1	2	yes	—
639	#388	C₂²×C₁₃₉	1	2	yes	—
640	#388	C₂²×C₁₃₉	1	2	yes	—
641	#388	C₂²×C₁₃₉	1	2	yes	complemented
642	#388	C₂²×C₁₃₉	1	2	yes	complemented
643	#388	C₂²×C₁₃₉	1	2	yes	complemented
644	#388	C₂²×C₁₃₉	1	2	yes	complemented
645	#387	C₂²×C₁₃₉	1	2	yes	complemented
646	#387	C₂²×C₁₃₉	1	2	yes	complemented
647	#387	C₂²×C₁₃₉	1	2	yes	complemented
648	#387	C₂²×C₁₃₉	1	2	yes	complemented
649	#387	C₂²×C₁₃₉	1	2	yes	complemented
650	#387	C₂²×C₁₃₉	1	2	yes	complemented
651	#387	C₂²×C₁₃₉	1	2	yes	complemented
652	#386	C₂²×C₁₃₉	1	1	yes	characteristic
653	#386	C₂²×C₁₃₉	1	2	yes	—
654	#386	C₂²×C₁₃₉	1	2	yes	—
655	#386	C₂²×C₁₃₉	1	1	yes	characteristic
656	#386	C₂²×C₁₃₉	1	1	yes	characteristic
657	#385	C₂²×C₁₃₉	1	2	yes	—
658	#385	C₂²×C₁₃₉	1	2	yes	—
659	#385	C₂²×C₁₃₉	1	2	yes	—
660	#385	C₂²×C₁₃₉	1	2	yes	—
661	#385	C₂²×C₁₃₉	1	2	yes	—
662	#385	C₂²×C₁₃₉	1	1	yes	characteristic
663	#385	C₂²×C₁₃₉	1	1	yes	characteristic
664	#385	C₂²×C₁₃₉	1	1	yes	characteristic
665	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
666	#383	C₂²×C₁₃₉	1	2	yes	complemented
667	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
668	#380	C₂²×C₁₃₉	1	1	yes	characteristic
669	#380	C₂²×C₁₃₉	1	1	yes	characteristic
670	#380	C₂²×C₁₃₉	1	1	yes	characteristic
671	#380	C₂²×C₁₃₉	1	2	yes	—
672	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
673	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
674	#379	C₂²×C₁₃₉	1	2	yes	—
675	#379	C₂²×C₁₃₉	1	1	yes	characteristic
676	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
677	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
678	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
679	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
680	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
681	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
682	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
683	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
685	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
686	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
687	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
689	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
690	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂³×C₄	—	2	4	no	—
693	C₂³×C₄	—	2	4	no	—
694	C₂³×C₄	—	2	4	no	—
695	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
700	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
701	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₄⋊Q₈	—	2	4	no	—
705	#126	—	2	8	no	—
706	#126	—	2	8	no	—
707	#124	—	2	8	no	—
708	C₂²⋊Q₈	—	2	4	no	—
709	C₂²⋊Q₈	—	2	4	no	—
710	C₂²⋊Q₈	—	2	4	no	—
711	C₂²⋊Q₈	—	2	4	no	—
712	C₂²⋊Q₈	—	2	8	no	—
713	#120	—	2	4	no	—
714	C₄×Q₈	—	2	4	no	—
715	C₄×Q₈	—	2	8	no	—
716	C₄×D₄	—	2	4	no	—
717	C₄×D₄	—	2	4	no	—
718	C₄×D₄	—	2	4	no	—
719	#117	—	2	4	no	—
720	#117	—	2	4	no	—
721	#117	—	2	4	no	—
722	#117	—	2	4	no	—
723	#117	—	2	8	no	—
724	#117	—	2	8	no	—
725	#117	D₄×C₁₃₉	1	8	yes	complemented
726	C₂×C₄⋊C₄	—	2	4	no	—
727	C₂×C₄⋊C₄	—	2	4	no	—
728	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
771	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	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	1	yes	characteristic
779	C₂×C₄²	—	2	8	no	—
780	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
784	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
786	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
788	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
789	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
790	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
791	#95	C₂³×C₁₃₉	1	1	yes	characteristic
792	#95	C₂³×C₁₃₉	1	1	yes	characteristic
793	#95	C₂³×C₁₃₉	1	2	yes	—
794	#95	C₂³×C₁₃₉	1	2	yes	—
795	#95	C₂³×C₁₃₉	1	1	yes	characteristic
796	#95	C₂³×C₁₃₉	1	1	yes	characteristic
797	#95	C₂³×C₁₃₉	1	1	yes	characteristic
798	#95	C₂³×C₁₃₉	1	1	yes	characteristic
799	#95	C₂³×C₁₃₉	1	2	yes	—
800	#95	C₂³×C₁₃₉	1	2	yes	—
801	#95	C₂³×C₁₃₉	1	2	yes	—
802	#95	C₂³×C₁₃₉	1	2	yes	—
803	#95	C₂³×C₁₃₉	1	2	yes	—
804	#95	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
812	#95	C₂³×C₁₃₉	1	2	yes	—
813	#95	C₂³×C₁₃₉	1	2	yes	—
814	C₂⁴	—	2	2	no	—
815	C₂⁴	—	2	2	no	—
816	C₂⁴	—	2	2	no	—
817	C₂⁴	—	2	2	no	—
818	C₂⁴	—	2	2	no	—
819	C₂⁴	—	4	1	no	—
820	C₂⁴	—	4	1	no	—
821	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
822	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
823	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
824	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
825	C₂×Q₈	—	2	2	no	—
826	C₂×Q₈	—	2	4	no	—
827	C₂×Q₈	—	2	4	no	—
828	C₂×Q₈	—	2	2	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	4	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	4	1	no	—
839	C₂×D₄	—	4	1	no	—
840	C₂²×C₄	—	2	32	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	4	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	4	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
866	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
867	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
868	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	4	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
910	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	4	1	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	1	no	—
935	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
936	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
937	C₄²	—	2	4	no	—
938	C₄²	—	2	4	no	—
939	C₄²	—	2	4	no	—
940	C₄²	—	2	4	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	4	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	4	2	no	—
946	C₄²	—	4	2	no	—
947	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	8	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	4	4	no	—
973	C₂³	—	4	4	no	—
974	C₂³	—	4	4	no	—
975	C₂³	—	4	4	no	—
976	C₂³	—	4	4	no	—
977	C₂³	—	4	4	no	—
978	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
979	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
980	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
981	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
982	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
983	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
984	Q₈	—	4	8	no	—
985	Q₈	—	4	4	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	C₂×C₄	—	2	8	no	—
990	C₂×C₄	—	2	8	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	8	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	4	8	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1046	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1048	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1049	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1050	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1051	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1052	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1053	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1054	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	4	16	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	#556×C₁₃₉	1	4	yes	complemented
1084	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1085	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1086	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1087	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1088	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1089	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1090	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	4	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	4	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	#525×C₁₃₉	1	4	yes	—
1110	C₂	—	2	4	no	—
1111	C₂	—	4	2	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	8	1	no	—
1114	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1115	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1116	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
1117	C₂	#3475×C₁₃₉	1	1	yes	characteristic
1118	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1119	C₂	#3493×C₁₃₉	1	1	yes	characteristic
1120	C₂	#3495×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#120×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×#556×C₁₃₉	C₂	semidirect
2. C₂²×#117×C₁₃₉	C₂	semidirect
3. #2852×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2601×C₁₃₉	C₂	semidirect
6. #2599×C₁₃₉	C₂	semidirect
7. #2499×C₁₃₉	C₂	semidirect
8. #2485×C₁₃₉	C₂	semidirect
9. #2480×C₁₃₉	C₂	semidirect
10. #2478×C₁₃₉	C₂	semidirect
11. #2474×C₁₃₉	C₂	semidirect
13. #2440×C₁₃₉	C₂	semidirect
14. #2439×C₁₃₉	C₂	semidirect
15. #2417×C₁₃₉	C₂	semidirect
16. #2415×C₁₃₉	C₂	semidirect
17. #2362×C₁₃₉	C₂	semidirect
18. #2360×C₁₃₉	C₂	semidirect
19. #2354×C₁₃₉	C₂	semidirect
20. #2352×C₁₃₉	C₂	semidirect
21. #2347×C₁₃₉	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
26. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×#126×C₁₃₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
37. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
48. C₂×#117×C₁₃₉	C₂²	semidirect
53. #398×C₁₃₉	C₂²	semidirect
54. #398×C₁₃₉	C₂²	semidirect
60. #396×C₁₃₉	C₂²	semidirect
61. #395×C₁₃₉	C₂²	semidirect
65. #391×C₁₃₉	C₂²	semidirect
66. #391×C₁₃₉	C₂²	semidirect
67. #391×C₁₃₉	C₂²	semidirect
69. #389×C₁₃₉	C₂²	semidirect
70. #389×C₁₃₉	C₂²	semidirect
71. #389×C₁₃₉	C₂²	semidirect
72. #389×C₁₃₉	C₂²	semidirect
73. #389×C₁₃₉	C₂²	semidirect
74. #389×C₁₃₉	C₂²	semidirect
80. #388×C₁₃₉	C₂²	semidirect
81. #388×C₁₃₉	C₂²	semidirect
82. #388×C₁₃₉	C₂²	semidirect
83. #388×C₁₃₉	C₂²	semidirect
84. #387×C₁₃₉	C₂²	semidirect
85. #387×C₁₃₉	C₂²	semidirect
86. #387×C₁₃₉	C₂²	semidirect
87. #387×C₁₃₉	C₂²	semidirect
88. #387×C₁₃₉	C₂²	semidirect
89. #387×C₁₃₉	C₂²	semidirect
90. #387×C₁₃₉	C₂²	semidirect
104. #384×C₁₃₉	C₂²	semidirect
105. #383×C₁₃₉	C₂²	semidirect
106. #382×C₁₃₉	C₂²	semidirect
111. #380×C₁₃₉	C₂²	semidirect
112. #380×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
164. #117×C₁₃₉	D₄	semidirect
522. C₂²×C₁₃₉	#556	semidirect
560. #36439	C₁₃₉	direct (N × H)
561. C₁₃₉	#36439	direct (N × H)
562. C₂×#556	C₂×C₁₃₉	semidirect
563. C₂²×#117	C₂×C₁₃₉	semidirect
564. #2852	C₂×C₁₃₉	semidirect
565. #2848	C₂×C₁₃₉	semidirect
566. #2601	C₂×C₁₃₉	semidirect
567. #2599	C₂×C₁₃₉	semidirect
568. #2499	C₂×C₁₃₉	semidirect
569. #2485	C₂×C₁₃₉	semidirect
570. #2480	C₂×C₁₃₉	semidirect
571. #2478	C₂×C₁₃₉	semidirect
572. #2474	C₂×C₁₃₉	semidirect
574. #2440	C₂×C₁₃₉	semidirect
575. #2439	C₂×C₁₃₉	semidirect
576. #2417	C₂×C₁₃₉	semidirect
577. #2415	C₂×C₁₃₉	semidirect
578. #2362	C₂×C₁₃₉	semidirect
579. #2360	C₂×C₁₃₉	semidirect
580. #2354	C₂×C₁₃₉	semidirect
581. #2352	C₂×C₁₃₉	semidirect
582. #2347	C₂×C₁₃₉	semidirect
583. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
587. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
589. C₂×#126	C₂²×C₁₃₉	semidirect
595. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
597. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
598. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
609. C₂×#117	C₂²×C₁₃₉	semidirect
614. #398	C₂²×C₁₃₉	semidirect
615. #398	C₂²×C₁₃₉	semidirect
621. #396	C₂²×C₁₃₉	semidirect
622. #395	C₂²×C₁₃₉	semidirect
626. #391	C₂²×C₁₃₉	semidirect
627. #391	C₂²×C₁₃₉	semidirect
628. #391	C₂²×C₁₃₉	semidirect
630. #389	C₂²×C₁₃₉	semidirect
631. #389	C₂²×C₁₃₉	semidirect
632. #389	C₂²×C₁₃₉	semidirect
633. #389	C₂²×C₁₃₉	semidirect
634. #389	C₂²×C₁₃₉	semidirect
635. #389	C₂²×C₁₃₉	semidirect
641. #388	C₂²×C₁₃₉	semidirect
642. #388	C₂²×C₁₃₉	semidirect
643. #388	C₂²×C₁₃₉	semidirect
644. #388	C₂²×C₁₃₉	semidirect
645. #387	C₂²×C₁₃₉	semidirect
646. #387	C₂²×C₁₃₉	semidirect
647. #387	C₂²×C₁₃₉	semidirect
648. #387	C₂²×C₁₃₉	semidirect
649. #387	C₂²×C₁₃₉	semidirect
650. #387	C₂²×C₁₃₉	semidirect
651. #387	C₂²×C₁₃₉	semidirect
665. #384	C₂²×C₁₃₉	semidirect
666. #383	C₂²×C₁₃₉	semidirect
667. #382	C₂²×C₁₃₉	semidirect
672. #380	C₂²×C₁₃₉	semidirect
673. #380	C₂²×C₁₃₉	semidirect
676. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
677. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
678. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
679. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
680. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
725. #117	D₄×C₁₃₉	semidirect
1083. C₂²	#556×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₉	2
C₂²×#117×C₁₃₉	2
#2852×C₁₃₉	2
#2848×C₁₃₉	2
#2601×C₁₃₉	2
#2599×C₁₃₉	2
#2499×C₁₃₉	2
#2485×C₁₃₉	2
#2480×C₁₃₉	2
#2478×C₁₃₉	2
#2474×C₁₃₉	2
#2472×C₁₃₉	2
#2440×C₁₃₉	2
#2439×C₁₃₉	2
#2417×C₁₃₉	2
#2415×C₁₃₉	2
#2362×C₁₃₉	2
#2360×C₁₃₉	2
#2354×C₁₃₉	2
#2352×C₁₃₉	2
#2347×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36439	139

Subgroups — C139×#36439 #48031035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36439 #48031035