Subgroups — C₁₃₉×#35697 #48030293

Order 35584.

2526 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2663×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2620×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2558×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2556×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2551×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2492×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2491×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2461×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2452×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2432×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2415×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2414×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2392×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2388×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2367×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2361×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2360×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
25	#554×C₁₃₉	—	2	8	no	—
26	#547×C₁₃₉	—	2	8	no	—
27	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
41	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×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×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
57	#400×C₁₃₉	C₂²	1	2	yes	—
58	#399×C₁₃₉	C₂²	1	2	yes	—
59	#398×C₁₃₉	C₂²	1	1	yes	characteristic
60	#397×C₁₃₉	C₂²	1	2	yes	—
61	#397×C₁₃₉	C₂²	1	1	yes	characteristic
62	#396×C₁₃₉	C₂²	1	2	yes	—
63	#396×C₁₃₉	C₂²	1	1	yes	characteristic
64	#396×C₁₃₉	C₂²	1	2	yes	—
65	#396×C₁₃₉	C₂²	1	1	yes	characteristic
66	#395×C₁₃₉	C₂²	1	2	yes	—
67	#395×C₁₃₉	C₂²	1	2	yes	—
68	#394×C₁₃₉	C₂²	1	2	yes	—
69	#394×C₁₃₉	C₂²	1	1	yes	characteristic
70	#394×C₁₃₉	C₂²	1	2	yes	—
71	#394×C₁₃₉	C₂²	1	2	yes	—
72	#394×C₁₃₉	C₂²	1	2	yes	—
73	#394×C₁₃₉	C₂²	1	1	yes	characteristic
74	#394×C₁₃₉	C₂²	1	1	yes	characteristic
75	#394×C₁₃₉	C₂²	1	2	yes	—
76	#393×C₁₃₉	C₂²	1	2	yes	—
77	#393×C₁₃₉	C₂²	1	2	yes	—
78	#392×C₁₃₉	C₂²	1	2	yes	—
79	#392×C₁₃₉	C₂²	1	2	yes	—
80	#392×C₁₃₉	C₂²	1	1	yes	characteristic
81	#391×C₁₃₉	C₂²	1	2	yes	—
82	#391×C₁₃₉	C₂²	1	1	yes	characteristic
83	#391×C₁₃₉	C₂²	1	1	yes	characteristic
84	#390×C₁₃₉	C₂²	1	2	yes	—
85	#390×C₁₃₉	C₂²	1	2	yes	—
86	#390×C₁₃₉	C₂²	1	1	yes	characteristic
87	#390×C₁₃₉	C₂²	1	1	yes	characteristic
88	#390×C₁₃₉	C₂²	1	2	yes	—
89	#389×C₁₃₉	C₂²	1	2	yes	—
90	#389×C₁₃₉	C₂²	1	1	yes	characteristic
91	#389×C₁₃₉	C₂²	1	1	yes	characteristic
92	#389×C₁₃₉	C₂²	1	2	yes	—
93	#389×C₁₃₉	C₂²	1	2	yes	—
94	#389×C₁₃₉	C₂²	1	2	yes	—
95	#388×C₁₃₉	C₂²	1	2	yes	—
96	#388×C₁₃₉	C₂²	1	2	yes	—
97	#388×C₁₃₉	C₂²	1	2	yes	—
98	#388×C₁₃₉	C₂²	1	2	yes	—
99	#388×C₁₃₉	C₂²	1	2	yes	—
100	#388×C₁₃₉	C₂²	1	2	yes	—
101	#388×C₁₃₉	C₂²	1	2	yes	—
102	#387×C₁₃₉	C₂²	1	2	yes	—
103	#386×C₁₃₉	C₂²	1	2	yes	—
104	#385×C₁₃₉	C₂²	1	2	yes	—
105	#385×C₁₃₉	C₂²	1	2	yes	—
106	#385×C₁₃₉	C₂²	1	2	yes	—
107	#385×C₁₃₉	C₂²	1	2	yes	—
108	#385×C₁₃₉	C₂²	1	2	yes	—
109	#384×C₁₃₉	C₂²	1	1	yes	characteristic
110	#380×C₁₃₉	C₂²	1	1	yes	characteristic
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
125	C₂×#41×C₁₃₉	—	2	8	no	—
126	C₂×#41×C₁₃₉	—	4	4	no	—
127	C₂×#41×C₁₃₉	—	4	4	no	—
128	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
130	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	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	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
146	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
147	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
148	#125×C₁₃₉	—	2	8	no	—
149	#124×C₁₃₉	—	2	4	no	—
150	#124×C₁₃₉	—	4	4	no	—
151	#123×C₁₃₉	—	2	8	no	—
152	#123×C₁₃₉	—	2	8	no	—
153	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
154	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
155	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
156	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
157	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
158	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
159	#121×C₁₃₉	—	2	4	no	—
160	#121×C₁₃₉	—	2	4	no	—
161	#121×C₁₃₉	—	2	4	no	—
162	C₄×Q₈×C₁₃₉	—	2	4	no	—
163	C₄×D₄×C₁₃₉	—	2	4	no	—
164	C₄×D₄×C₁₃₉	—	2	8	no	—
165	C₄×D₄×C₁₃₉	—	2	4	no	—
166	C₄×D₄×C₁₃₉	—	2	4	no	—
167	C₄×D₄×C₁₃₉	—	2	4	no	—
168	C₄×D₄×C₁₃₉	—	4	4	no	—
169	C₄×D₄×C₁₃₉	—	4	4	no	—
170	#117×C₁₃₉	—	2	4	no	—
171	#117×C₁₃₉	—	2	4	no	—
172	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
173	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
174	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×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	2	yes	—
233	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
235	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
236	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
237	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
239	#95×C₁₃₉	C₂³	1	1	yes	characteristic
240	#95×C₁₃₉	C₂³	1	1	yes	characteristic
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	1	yes	characteristic
245	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
251	#95×C₁₃₉	C₂³	1	1	yes	characteristic
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	2	yes	—
255	#95×C₁₃₉	C₂³	1	2	yes	—
256	#95×C₁₃₉	C₂³	1	2	yes	—
257	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
258	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	#41×C₁₃₉	—	4	32	no	—
262	C₂×Q₈×C₁₃₉	—	2	2	no	—
263	C₂×Q₈×C₁₃₉	—	2	4	no	—
264	C₂×Q₈×C₁₃₉	—	2	4	no	—
265	C₂×Q₈×C₁₃₉	—	2	2	no	—
266	C₂×Q₈×C₁₃₉	—	2	2	no	—
267	C₂×Q₈×C₁₃₉	—	2	4	no	—
268	C₂×Q₈×C₁₃₉	—	4	2	no	—
269	C₂×Q₈×C₁₃₉	—	4	2	no	—
270	C₂×Q₈×C₁₃₉	—	4	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	—	2	4	no	—
278	C₂×D₄×C₁₃₉	—	2	4	no	—
279	C₂×D₄×C₁₃₉	—	2	4	no	—
280	C₂×D₄×C₁₃₉	—	2	2	no	—
281	C₂×D₄×C₁₃₉	—	2	4	no	—
282	C₂×D₄×C₁₃₉	—	2	2	no	—
283	C₂×D₄×C₁₃₉	—	2	4	no	—
284	C₂×D₄×C₁₃₉	—	2	2	no	—
285	C₂×D₄×C₁₃₉	—	2	2	no	—
286	C₂×D₄×C₁₃₉	—	2	2	no	—
287	C₂×D₄×C₁₃₉	—	2	2	no	—
288	C₂×D₄×C₁₃₉	—	4	2	no	—
289	C₂×D₄×C₁₃₉	—	4	2	no	—
290	C₂×D₄×C₁₃₉	—	4	2	no	—
291	C₂×D₄×C₁₃₉	—	4	2	no	—
292	C₂²×C₄×C₁₃₉	—	2	2	no	—
293	C₂²×C₄×C₁₃₉	—	2	2	no	—
294	C₂²×C₄×C₁₃₉	—	2	4	no	—
295	C₂²×C₄×C₁₃₉	—	2	2	no	—
296	C₂²×C₄×C₁₃₉	—	2	2	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	—	2	2	no	—
303	C₂²×C₄×C₁₃₉	—	2	4	no	—
304	C₂²×C₄×C₁₃₉	—	2	4	no	—
305	C₂²×C₄×C₁₃₉	—	4	2	no	—
306	C₂²×C₄×C₁₃₉	—	4	2	no	—
307	C₂²×C₄×C₁₃₉	—	4	2	no	—
308	C₂²×C₄×C₁₃₉	—	4	2	no	—
309	C₂²×C₄×C₁₃₉	—	4	2	no	—
310	C₂²×C₄×C₁₃₉	—	4	2	no	—
311	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
312	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
313	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	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	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	4	no	—
342	C₄⋊C₄×C₁₃₉	—	2	4	no	—
343	C₄⋊C₄×C₁₃₉	—	2	2	no	—
344	C₄⋊C₄×C₁₃₉	—	2	2	no	—
345	C₄⋊C₄×C₁₃₉	—	2	2	no	—
346	C₄⋊C₄×C₁₃₉	—	2	2	no	—
347	C₄⋊C₄×C₁₃₉	—	2	4	no	—
348	C₄⋊C₄×C₁₃₉	—	2	4	no	—
349	C₄⋊C₄×C₁₃₉	—	2	2	no	—
350	C₄⋊C₄×C₁₃₉	—	2	2	no	—
351	C₄⋊C₄×C₁₃₉	—	4	2	no	—
352	C₄⋊C₄×C₁₃₉	—	4	2	no	—
353	C₄⋊C₄×C₁₃₉	—	4	2	no	—
354	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
355	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
356	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
357	C₄⋊C₄×C₁₃₉	#41	1	4	yes	complemented
358	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
367	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
370	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
373	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
374	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
376	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
377	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
378	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
379	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
380	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
381	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
382	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
383	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
384	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
385	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
386	C₄²×C₁₃₉	—	2	2	no	—
387	C₄²×C₁₃₉	—	2	4	no	—
388	C₄²×C₁₃₉	—	2	2	no	—
389	C₄²×C₁₃₉	—	2	4	no	—
390	C₄²×C₁₃₉	—	2	2	no	—
391	C₄²×C₁₃₉	—	4	2	no	—
392	C₄²×C₁₃₉	—	4	2	no	—
393	C₄²×C₁₃₉	—	4	2	no	—
394	C₄²×C₁₃₉	—	4	2	no	—
395	C₄²×C₁₃₉	#41	1	4	yes	complemented
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	—	2	1	no	—
412	C₂³×C₁₃₉	—	2	1	no	—
413	C₂³×C₁₃₉	—	2	1	no	—
414	C₂³×C₁₃₉	—	2	2	no	—
415	C₂³×C₁₃₉	—	2	2	no	—
416	C₂³×C₁₃₉	—	2	2	no	—
417	C₂³×C₁₃₉	—	2	2	no	—
418	C₂³×C₁₃₉	—	2	2	no	—
419	C₂³×C₁₃₉	—	2	2	no	—
420	C₂³×C₁₃₉	—	2	2	no	—
421	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
422	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
423	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
424	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
425	Q₈×C₁₃₉	—	4	8	no	—
426	Q₈×C₁₃₉	—	4	4	no	—
427	Q₈×C₁₃₉	—	8	4	no	—
428	D₄×C₁₃₉	—	2	8	no	—
429	D₄×C₁₃₉	—	2	8	no	—
430	D₄×C₁₃₉	—	2	8	no	—
431	D₄×C₁₃₉	—	4	8	no	—
432	D₄×C₁₃₉	—	4	8	no	—
433	D₄×C₁₃₉	—	4	8	no	—
434	D₄×C₁₃₉	—	4	4	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	1	no	—
440	C₂×C₄×C₁₃₉	—	2	2	no	—
441	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	1	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	2	no	—
451	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	2	1	no	—
460	C₂×C₄×C₁₃₉	—	2	1	no	—
461	C₂×C₄×C₁₃₉	—	2	2	no	—
462	C₂×C₄×C₁₃₉	—	2	1	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	1	no	—
465	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
470	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
477	C₂×C₄×C₁₃₉	—	2	1	no	—
478	C₂×C₄×C₁₃₉	—	2	1	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	—	4	8	no	—
483	C₂×C₄×C₁₃₉	—	4	8	no	—
484	C₂×C₄×C₁₃₉	—	4	8	no	—
485	C₂×C₄×C₁₃₉	—	4	4	no	—
486	C₂×C₄×C₁₃₉	—	4	4	no	—
487	C₂×C₄×C₁₃₉	—	8	4	no	—
488	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
489	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
491	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
493	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
494	C₂×C₄×C₁₃₉	C₂×#41	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	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
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	—	2	2	no	—
507	C₂²×C₁₃₉	—	2	2	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	2	no	—
521	C₂²×C₁₃₉	—	4	2	no	—
522	C₂²×C₁₃₉	—	4	2	no	—
523	C₂²×C₁₃₉	—	4	2	no	—
524	C₂²×C₁₃₉	—	4	2	no	—
525	C₂²×C₁₃₉	—	4	2	no	—
526	C₂²×C₁₃₉	—	4	2	no	—
527	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
528	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
529	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
530	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₄×C₁₃₉	—	2	2	no	—
535	C₄×C₁₃₉	—	2	4	no	—
536	C₄×C₁₃₉	—	2	2	no	—
537	C₄×C₁₃₉	—	2	4	no	—
538	C₄×C₁₃₉	—	2	2	no	—
539	C₄×C₁₃₉	—	2	2	no	—
540	C₄×C₁₃₉	—	2	2	no	—
541	C₄×C₁₃₉	—	2	4	no	—
542	C₄×C₁₃₉	—	4	1	no	—
543	C₄×C₁₃₉	—	4	1	no	—
544	C₄×C₁₃₉	—	4	2	no	—
545	C₄×C₁₃₉	—	4	2	no	—
546	C₄×C₁₃₉	—	4	2	no	—
547	C₄×C₁₃₉	—	4	1	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	#532	1	4	yes	—
553	C₂×C₁₃₉	—	4	2	no	—
554	C₂×C₁₃₉	—	4	2	no	—
555	C₂×C₁₃₉	—	4	2	no	—
556	C₂×C₁₃₉	—	8	2	no	—
557	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
558	C₂×C₁₃₉	#3484	1	1	yes	characteristic
559	C₂×C₁₃₉	#3486	1	1	yes	characteristic
560	C₂×C₁₃₉	#3492	1	1	yes	characteristic
561	C₂×C₁₃₉	#3511	1	1	yes	characteristic
562	C₂×C₁₃₉	#3520	1	1	yes	characteristic
563	C₂×C₁₃₉	#3522	1	1	yes	characteristic
564	#35697	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
565	C₁₃₉	#35697	1	1	yes	characteristic, direct product factor, Sylow
566	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
567	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
568	#2663	C₂×C₁₃₉	1	2	yes	complemented
569	#2620	C₂×C₁₃₉	1	1	yes	characteristic, complemented
570	#2602	C₂×C₁₃₉	1	2	yes	complemented
571	#2558	C₂×C₁₃₉	1	2	yes	complemented
572	#2556	C₂×C₁₃₉	1	2	yes	complemented
573	#2551	C₂×C₁₃₉	1	1	yes	characteristic, complemented
574	#2540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
575	#2492	C₂×C₁₃₉	1	1	yes	characteristic, complemented
576	#2491	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	#2461	C₂×C₁₃₉	1	2	yes	complemented
578	#2452	C₂×C₁₃₉	1	2	yes	complemented
579	#2432	C₂×C₁₃₉	1	2	yes	complemented
580	#2415	C₂×C₁₃₉	1	1	yes	characteristic, complemented
581	#2414	C₂×C₁₃₉	1	1	yes	characteristic, complemented
582	#2392	C₂×C₁₃₉	1	1	yes	characteristic, complemented
583	#2388	C₂×C₁₃₉	1	2	yes	complemented
584	#2367	C₂×C₁₃₉	1	1	yes	characteristic, complemented
585	#2361	C₂×C₁₃₉	1	1	yes	characteristic, complemented
586	#2360	C₂×C₁₃₉	1	1	yes	characteristic, complemented
587	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
588	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
589	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
590	#554	—	2	8	no	—
591	#547	—	2	8	no	—
592	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
595	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
596	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
597	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
598	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
599	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
600	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
605	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
606	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
607	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
608	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
609	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
611	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
616	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
617	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
618	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
619	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
621	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
622	#400	C₂²×C₁₃₉	1	2	yes	—
623	#399	C₂²×C₁₃₉	1	2	yes	—
624	#398	C₂²×C₁₃₉	1	1	yes	characteristic
625	#397	C₂²×C₁₃₉	1	2	yes	—
626	#397	C₂²×C₁₃₉	1	1	yes	characteristic
627	#396	C₂²×C₁₃₉	1	2	yes	—
628	#396	C₂²×C₁₃₉	1	2	yes	—
629	#396	C₂²×C₁₃₉	1	1	yes	characteristic
630	#396	C₂²×C₁₃₉	1	1	yes	characteristic
631	#395	C₂²×C₁₃₉	1	2	yes	—
632	#395	C₂²×C₁₃₉	1	2	yes	—
633	#394	C₂²×C₁₃₉	1	1	yes	characteristic
634	#394	C₂²×C₁₃₉	1	2	yes	—
635	#394	C₂²×C₁₃₉	1	2	yes	—
636	#394	C₂²×C₁₃₉	1	2	yes	—
637	#394	C₂²×C₁₃₉	1	2	yes	—
638	#394	C₂²×C₁₃₉	1	1	yes	characteristic
639	#394	C₂²×C₁₃₉	1	1	yes	characteristic
640	#394	C₂²×C₁₃₉	1	2	yes	—
641	#393	C₂²×C₁₃₉	1	2	yes	—
642	#393	C₂²×C₁₃₉	1	2	yes	—
643	#392	C₂²×C₁₃₉	1	2	yes	—
644	#392	C₂²×C₁₃₉	1	1	yes	characteristic
645	#392	C₂²×C₁₃₉	1	2	yes	—
646	#391	C₂²×C₁₃₉	1	1	yes	characteristic
647	#391	C₂²×C₁₃₉	1	1	yes	characteristic
648	#391	C₂²×C₁₃₉	1	2	yes	—
649	#390	C₂²×C₁₃₉	1	2	yes	—
650	#390	C₂²×C₁₃₉	1	1	yes	characteristic
651	#390	C₂²×C₁₃₉	1	1	yes	characteristic
652	#390	C₂²×C₁₃₉	1	2	yes	—
653	#390	C₂²×C₁₃₉	1	2	yes	—
654	#389	C₂²×C₁₃₉	1	2	yes	—
655	#389	C₂²×C₁₃₉	1	2	yes	—
656	#389	C₂²×C₁₃₉	1	2	yes	—
657	#389	C₂²×C₁₃₉	1	1	yes	characteristic
658	#389	C₂²×C₁₃₉	1	1	yes	characteristic
659	#389	C₂²×C₁₃₉	1	2	yes	—
660	#388	C₂²×C₁₃₉	1	2	yes	—
661	#388	C₂²×C₁₃₉	1	2	yes	—
662	#388	C₂²×C₁₃₉	1	2	yes	—
663	#388	C₂²×C₁₃₉	1	2	yes	—
664	#388	C₂²×C₁₃₉	1	2	yes	—
665	#388	C₂²×C₁₃₉	1	2	yes	—
666	#388	C₂²×C₁₃₉	1	2	yes	—
667	#387	C₂²×C₁₃₉	1	2	yes	—
668	#386	C₂²×C₁₃₉	1	2	yes	—
669	#385	C₂²×C₁₃₉	1	2	yes	—
670	#385	C₂²×C₁₃₉	1	2	yes	—
671	#385	C₂²×C₁₃₉	1	2	yes	—
672	#385	C₂²×C₁₃₉	1	2	yes	—
673	#385	C₂²×C₁₃₉	1	2	yes	—
674	#384	C₂²×C₁₃₉	1	1	yes	characteristic
675	#380	C₂²×C₁₃₉	1	1	yes	characteristic
676	#380	C₂²×C₁₃₉	1	1	yes	characteristic
677	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
678	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
679	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
680	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
681	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
682	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
683	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
685	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
686	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
687	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
689	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
690	C₂×#41	—	2	8	no	—
691	C₂×#41	—	4	4	no	—
692	C₂×#41	—	4	4	no	—
693	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
694	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
695	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
696	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
697	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
698	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
708	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
709	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
710	C₄⋊Q₈	—	2	4	no	—
711	C₄⋊Q₈	—	2	4	no	—
712	C₄⋊Q₈	—	4	4	no	—
713	#125	—	2	8	no	—
714	#124	—	2	4	no	—
715	#124	—	4	4	no	—
716	#123	—	2	8	no	—
717	#123	—	2	8	no	—
718	C₂²⋊Q₈	—	2	8	no	—
719	C₂²⋊Q₈	—	2	4	no	—
720	C₂²⋊Q₈	—	2	8	no	—
721	C₂²⋊Q₈	—	2	8	no	—
722	C₂²⋊Q₈	—	2	4	no	—
723	C₂²⋊Q₈	—	2	4	no	—
724	#121	—	2	4	no	—
725	#121	—	2	4	no	—
726	#121	—	2	4	no	—
727	C₄×Q₈	—	2	4	no	—
728	C₄×D₄	—	2	4	no	—
729	C₄×D₄	—	2	8	no	—
730	C₄×D₄	—	2	4	no	—
731	C₄×D₄	—	2	4	no	—
732	C₄×D₄	—	2	4	no	—
733	C₄×D₄	—	4	4	no	—
734	C₄×D₄	—	4	4	no	—
735	#117	—	2	4	no	—
736	#117	—	2	4	no	—
737	C₂×C₄⋊C₄	—	2	4	no	—
738	C₂×C₄⋊C₄	—	2	4	no	—
739	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
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	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
756	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
765	C₂×C₄⋊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	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
770	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	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	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
789	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
794	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
796	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
798	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
800	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
801	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
802	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
803	C₂×C₄²	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	1	yes	characteristic
810	#95	C₂³×C₁₃₉	1	2	yes	—
811	#95	C₂³×C₁₃₉	1	1	yes	characteristic
812	#95	C₂³×C₁₃₉	1	2	yes	—
813	#95	C₂³×C₁₃₉	1	1	yes	characteristic
814	#95	C₂³×C₁₃₉	1	1	yes	characteristic
815	#95	C₂³×C₁₃₉	1	2	yes	—
816	#95	C₂³×C₁₃₉	1	1	yes	characteristic
817	#95	C₂³×C₁₃₉	1	2	yes	—
818	#95	C₂³×C₁₃₉	1	2	yes	—
819	#95	C₂³×C₁₃₉	1	2	yes	—
820	#95	C₂³×C₁₃₉	1	2	yes	—
821	#95	C₂³×C₁₃₉	1	2	yes	—
822	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
823	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
824	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
825	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
826	#41	—	4	32	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	4	no	—
829	C₂×Q₈	—	2	4	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	4	no	—
833	C₂×Q₈	—	4	2	no	—
834	C₂×Q₈	—	4	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	—	4	2	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	4	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	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	4	no	—
869	C₂²×C₄	—	2	4	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
877	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
878	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	4	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	4	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
920	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
921	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
922	C₄⋊C₄	#41×C₁₃₉	1	4	yes	complemented
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	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	2	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	4	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	4	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	4	2	no	—
957	C₄²	—	4	2	no	—
958	C₄²	—	4	2	no	—
959	C₄²	—	4	2	no	—
960	C₄²	#41×C₁₃₉	1	4	yes	complemented
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	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
987	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
988	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
989	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
990	Q₈	—	4	8	no	—
991	Q₈	—	4	4	no	—
992	Q₈	—	8	4	no	—
993	D₄	—	2	8	no	—
994	D₄	—	2	8	no	—
995	D₄	—	2	8	no	—
996	D₄	—	4	8	no	—
997	D₄	—	4	8	no	—
998	D₄	—	4	8	no	—
999	D₄	—	4	4	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	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	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	8	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	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	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	8	4	no	—
1053	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1054	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1055	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1056	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1057	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
1058	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1059	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1060	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1061	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1062	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1063	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	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	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1093	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1094	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1095	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1096	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1097	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1098	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1099	C₄	—	2	2	no	—
1100	C₄	—	2	4	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	4	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	4	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	#532×C₁₃₉	1	4	yes	—
1118	C₂	—	4	2	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	4	2	no	—
1121	C₂	—	8	2	no	—
1122	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
1123	C₂	#3484×C₁₃₉	1	1	yes	characteristic
1124	C₂	#3486×C₁₃₉	1	1	yes	characteristic
1125	C₂	#3492×C₁₃₉	1	1	yes	characteristic
1126	C₂	#3511×C₁₃₉	1	1	yes	characteristic
1127	C₂	#3520×C₁₃₉	1	1	yes	characteristic
1128	C₂	#3522×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#554×C₁₃₉	C₂	semidirect
2. C₂×#547×C₁₃₉	C₂	semidirect
3. #2663×C₁₃₉	C₂	semidirect
4. #2620×C₁₃₉	C₂	semidirect
5. #2602×C₁₃₉	C₂	semidirect
6. #2558×C₁₃₉	C₂	semidirect
7. #2556×C₁₃₉	C₂	semidirect
8. #2551×C₁₃₉	C₂	semidirect
9. #2540×C₁₃₉	C₂	semidirect
10. #2492×C₁₃₉	C₂	semidirect
11. #2491×C₁₃₉	C₂	semidirect
12. #2461×C₁₃₉	C₂	semidirect
13. #2452×C₁₃₉	C₂	semidirect
14. #2432×C₁₃₉	C₂	semidirect
15. #2415×C₁₃₉	C₂	semidirect
16. #2414×C₁₃₉	C₂	semidirect
17. #2392×C₁₃₉	C₂	semidirect
18. #2388×C₁₃₉	C₂	semidirect
19. #2367×C₁₃₉	C₂	semidirect
20. #2361×C₁₃₉	C₂	semidirect
21. #2360×C₁₃₉	C₂	semidirect
22. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
23. #2274×C₁₃₉	C₂	semidirect
174. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
357. C₄⋊C₄×C₁₃₉	#41	semidirect
395. C₄²×C₁₃₉	#41	semidirect
564. #35697	C₁₃₉	direct (N × H)
565. C₁₃₉	#35697	direct (N × H)
566. C₂×#554	C₂×C₁₃₉	semidirect
567. C₂×#547	C₂×C₁₃₉	semidirect
568. #2663	C₂×C₁₃₉	semidirect
569. #2620	C₂×C₁₃₉	semidirect
570. #2602	C₂×C₁₃₉	semidirect
571. #2558	C₂×C₁₃₉	semidirect
572. #2556	C₂×C₁₃₉	semidirect
573. #2551	C₂×C₁₃₉	semidirect
574. #2540	C₂×C₁₃₉	semidirect
575. #2492	C₂×C₁₃₉	semidirect
576. #2491	C₂×C₁₃₉	semidirect
577. #2461	C₂×C₁₃₉	semidirect
578. #2452	C₂×C₁₃₉	semidirect
579. #2432	C₂×C₁₃₉	semidirect
580. #2415	C₂×C₁₃₉	semidirect
581. #2414	C₂×C₁₃₉	semidirect
582. #2392	C₂×C₁₃₉	semidirect
583. #2388	C₂×C₁₃₉	semidirect
584. #2367	C₂×C₁₃₉	semidirect
585. #2361	C₂×C₁₃₉	semidirect
586. #2360	C₂×C₁₃₉	semidirect
587. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
588. #2274	C₂×C₁₃₉	semidirect
739. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
922. C₄⋊C₄	#41×C₁₃₉	semidirect
960. C₄²	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂×#547×C₁₃₉	2
#2663×C₁₃₉	2
#2620×C₁₃₉	2
#2602×C₁₃₉	2
#2558×C₁₃₉	2
#2556×C₁₃₉	2
#2551×C₁₃₉	2
#2540×C₁₃₉	2
#2492×C₁₃₉	2
#2491×C₁₃₉	2
#2461×C₁₃₉	2
#2452×C₁₃₉	2
#2432×C₁₃₉	2
#2415×C₁₃₉	2
#2414×C₁₃₉	2
#2392×C₁₃₉	2
#2388×C₁₃₉	2
#2367×C₁₃₉	2
#2361×C₁₃₉	2
#2360×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2274×C₁₃₉	2
#35697	139

Subgroups — C139×#35697 #48030293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35697 #48030293