Subgroups — C₁₃₉×#36130 #48030726

Order 35584.

2580 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2556×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2549×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2492×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2465×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2440×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2438×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2437×C₁₃₉	C₂	1	2	yes	maximal
14	#2434×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2429×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2429×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2360×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
20	#2342×C₁₃₉	C₂	1	2	yes	maximal
21	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	#533×C₁₃₉	—	2	8	no	—
27	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×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	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
55	#400×C₁₃₉	C₂²	1	2	yes	complemented
56	#399×C₁₃₉	C₂²	1	2	yes	—
57	#398×C₁₃₉	C₂²	1	2	yes	complemented
58	#398×C₁₃₉	C₂²	1	2	yes	complemented
59	#398×C₁₃₉	C₂²	1	2	yes	complemented
60	#398×C₁₃₉	C₂²	1	2	yes	complemented
61	#396×C₁₃₉	C₂²	1	2	yes	—
62	#396×C₁₃₉	C₂²	1	2	yes	—
63	#395×C₁₃₉	C₂²	1	2	yes	complemented
64	#395×C₁₃₉	C₂²	1	2	yes	complemented
65	#395×C₁₃₉	C₂²	1	2	yes	complemented
66	#393×C₁₃₉	C₂²	1	2	yes	—
67	#391×C₁₃₉	C₂²	1	2	yes	complemented
68	#391×C₁₃₉	C₂²	1	2	yes	complemented
69	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
71	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
72	#391×C₁₃₉	C₂²	1	2	yes	complemented
73	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
74	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#389×C₁₃₉	C₂²	1	2	yes	complemented
76	#389×C₁₃₉	C₂²	1	2	yes	complemented
77	#389×C₁₃₉	C₂²	1	2	yes	complemented
78	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	#389×C₁₃₉	C₂²	1	2	yes	complemented
82	#389×C₁₃₉	C₂²	1	2	yes	complemented
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
87	#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	#387×C₁₃₉	C₂²	1	2	yes	complemented
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	2	yes	—
101	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
102	#381×C₁₃₉	C₂²	1	2	yes	—
103	#380×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	1	yes	characteristic
105	#380×C₁₃₉	C₂²	1	1	yes	characteristic
106	#380×C₁₃₉	C₂²	1	1	yes	characteristic
107	#380×C₁₃₉	C₂²	1	2	yes	—
108	#380×C₁₃₉	C₂²	1	2	yes	—
109	#379×C₁₃₉	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃₉	—	2	4	no	—
127	C₂²×Q₈×C₁₃₉	—	2	4	no	—
128	C₂²×Q₈×C₁₃₉	—	4	2	no	—
129	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
132	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
133	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	—	2	4	no	—
135	C₂³×C₄×C₁₃₉	—	2	4	no	—
136	C₂³×C₄×C₁₃₉	—	4	2	no	—
137	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₉	C₂³	1	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	1	yes	characteristic
144	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
150	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
151	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
152	#125×C₁₃₉	—	2	8	no	—
153	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
154	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
155	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
156	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
157	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
158	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
159	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
160	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
161	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
162	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
163	C₂²⋊Q₈×C₁₃₉	D₄	1	8	yes	—
164	C₄×Q₈×C₁₃₉	—	2	4	no	—
165	C₄×Q₈×C₁₃₉	—	2	4	no	—
166	C₄×Q₈×C₁₃₉	—	2	8	no	—
167	C₄×Q₈×C₁₃₉	—	4	2	no	—
168	#117×C₁₃₉	—	2	8	no	—
169	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
198	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₂²⋊C₄×C₁₃₉	Q₈	1	8	yes	complemented
200	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃₉	—	2	4	no	—
219	C₂×C₄²×C₁₃₉	—	4	2	no	—
220	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₉	C₂³	1	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	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	1	yes	characteristic
233	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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	—	2	2	no	—
258	C₂⁴×C₁₃₉	—	2	2	no	—
259	C₂⁴×C₁₃₉	—	2	2	no	—
260	C₂⁴×C₁₃₉	—	2	2	no	—
261	C₂⁴×C₁₃₉	—	4	1	no	—
262	C₂⁴×C₁₃₉	—	4	1	no	—
263	C₂⁴×C₁₃₉	C₂×Q₈	1	4	yes	—
264	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂×Q₈×C₁₃₉	—	2	4	no	—
268	C₂×Q₈×C₁₃₉	—	2	2	no	—
269	C₂×Q₈×C₁₃₉	—	2	4	no	—
270	C₂×Q₈×C₁₃₉	—	2	2	no	—
271	C₂×Q₈×C₁₃₉	—	2	2	no	—
272	C₂×Q₈×C₁₃₉	—	2	4	no	—
273	C₂×Q₈×C₁₃₉	—	2	2	no	—
274	C₂×Q₈×C₁₃₉	—	2	4	no	—
275	C₂×Q₈×C₁₃₉	—	2	2	no	—
276	C₂×Q₈×C₁₃₉	—	2	2	no	—
277	C₂×Q₈×C₁₃₉	—	2	2	no	—
278	C₂×Q₈×C₁₃₉	—	2	2	no	—
279	C₂×Q₈×C₁₃₉	—	4	2	no	—
280	C₂×Q₈×C₁₃₉	—	4	2	no	—
281	C₂×Q₈×C₁₃₉	—	4	16	no	—
282	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
283	C₂²×C₄×C₁₃₉	—	2	2	no	—
284	C₂²×C₄×C₁₃₉	—	2	2	no	—
285	C₂²×C₄×C₁₃₉	—	2	2	no	—
286	C₂²×C₄×C₁₃₉	—	2	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	4	no	—
292	C₂²×C₄×C₁₃₉	—	2	2	no	—
293	C₂²×C₄×C₁₃₉	—	2	4	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	2	no	—
298	C₂²×C₄×C₁₃₉	—	2	2	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	2	no	—
304	C₂²×C₄×C₁₃₉	—	2	2	no	—
305	C₂²×C₄×C₁₃₉	—	2	2	no	—
306	C₂²×C₄×C₁₃₉	—	4	1	no	—
307	C₂²×C₄×C₁₃₉	—	4	1	no	—
308	C₂²×C₄×C₁₃₉	—	4	1	no	—
309	C₂²×C₄×C₁₃₉	—	4	1	no	—
310	C₂²×C₄×C₁₃₉	—	4	1	no	—
311	C₂²×C₄×C₁₃₉	—	4	1	no	—
312	C₂²×C₄×C₁₃₉	—	4	2	no	—
313	C₂²×C₄×C₁₃₉	—	4	1	no	—
314	C₂²×C₄×C₁₃₉	—	4	2	no	—
315	C₂²×C₄×C₁₃₉	—	4	16	no	—
316	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
317	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
318	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
319	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
320	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	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	—	2	4	no	—
346	C₄⋊C₄×C₁₃₉	—	2	4	no	—
347	C₄⋊C₄×C₁₃₉	—	2	4	no	—
348	C₄⋊C₄×C₁₃₉	—	2	4	no	—
349	C₄⋊C₄×C₁₃₉	—	2	4	no	—
350	C₄⋊C₄×C₁₃₉	—	2	4	no	—
351	C₄⋊C₄×C₁₃₉	—	2	2	no	—
352	C₄⋊C₄×C₁₃₉	—	2	4	no	—
353	C₄⋊C₄×C₁₃₉	—	2	2	no	—
354	C₄⋊C₄×C₁₃₉	—	2	4	no	—
355	C₄⋊C₄×C₁₃₉	—	2	4	no	—
356	C₄⋊C₄×C₁₃₉	—	2	4	no	—
357	C₄⋊C₄×C₁₃₉	—	2	2	no	—
358	C₄⋊C₄×C₁₃₉	—	4	2	no	—
359	C₄⋊C₄×C₁₃₉	—	4	2	no	—
360	C₄⋊C₄×C₁₃₉	—	4	2	no	—
361	C₄⋊C₄×C₁₃₉	—	4	2	no	—
362	C₄⋊C₄×C₁₃₉	—	4	2	no	—
363	C₄⋊C₄×C₁₃₉	—	4	2	no	—
364	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
365	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
366	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
367	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
368	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
370	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
372	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
373	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
374	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
378	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
379	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
380	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
381	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
382	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
383	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
384	C₄²×C₁₃₉	—	2	2	no	—
385	C₄²×C₁₃₉	—	2	2	no	—
386	C₄²×C₁₃₉	—	2	2	no	—
387	C₄²×C₁₃₉	—	2	2	no	—
388	C₄²×C₁₃₉	—	2	4	no	—
389	C₄²×C₁₃₉	—	2	4	no	—
390	C₄²×C₁₃₉	—	2	2	no	—
391	C₄²×C₁₃₉	—	2	2	no	—
392	C₄²×C₁₃₉	—	4	1	no	—
393	C₄²×C₁₃₉	—	4	1	no	—
394	C₄²×C₁₃₉	—	4	2	no	—
395	C₄²×C₁₃₉	—	4	2	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	8	no	—
405	C₂³×C₁₃₉	—	2	8	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	—	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	C₂²×Q₈	1	2	yes	—
419	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
420	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
421	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
422	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
423	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
424	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
425	Q₈×C₁₃₉	—	2	8	no	—
426	Q₈×C₁₃₉	—	4	8	no	—
427	Q₈×C₁₃₉	—	4	8	no	—
428	Q₈×C₁₃₉	—	4	4	no	—
429	Q₈×C₁₃₉	—	4	4	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	2	no	—
438	C₂×C₄×C₁₃₉	—	2	1	no	—
439	C₂×C₄×C₁₃₉	—	2	1	no	—
440	C₂×C₄×C₁₃₉	—	2	1	no	—
441	C₂×C₄×C₁₃₉	—	2	1	no	—
442	C₂×C₄×C₁₃₉	—	2	2	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	1	no	—
446	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
451	C₂×C₄×C₁₃₉	—	2	8	no	—
452	C₂×C₄×C₁₃₉	—	2	8	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	2	no	—
456	C₂×C₄×C₁₃₉	—	2	2	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	2	no	—
465	C₂×C₄×C₁₃₉	—	2	2	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	2	2	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
478	C₂×C₄×C₁₃₉	—	2	1	no	—
479	C₂×C₄×C₁₃₉	—	2	2	no	—
480	C₂×C₄×C₁₃₉	—	4	4	no	—
481	C₂×C₄×C₁₃₉	—	4	4	no	—
482	C₂×C₄×C₁₃₉	—	4	8	no	—
483	C₂×C₄×C₁₃₉	—	4	4	no	—
484	C₂×C₄×C₁₃₉	—	4	4	no	—
485	C₂×C₄×C₁₃₉	—	4	4	no	—
486	C₂×C₄×C₁₃₉	—	4	4	no	—
487	C₂×C₄×C₁₃₉	—	4	8	no	—
488	C₂×C₄×C₁₃₉	—	4	4	no	—
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	4	yes	—
492	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
494	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
495	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
496	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
497	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
498	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
499	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
500	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
501	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
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	—	2	2	no	—
509	C₂²×C₁₃₉	—	2	2	no	—
510	C₂²×C₁₃₉	—	2	2	no	—
511	C₂²×C₁₃₉	—	2	2	no	—
512	C₂²×C₁₃₉	—	2	2	no	—
513	C₂²×C₁₃₉	—	2	2	no	—
514	C₂²×C₁₃₉	—	2	2	no	—
515	C₂²×C₁₃₉	—	2	2	no	—
516	C₂²×C₁₃₉	—	2	2	no	—
517	C₂²×C₁₃₉	—	4	16	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	#533	1	4	yes	complemented
523	C₂²×C₁₃₉	D₄×Q₈	1	4	yes	—
524	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
525	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
526	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
527	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
528	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₂²×C₁₃₉	#585	1	1	yes	characteristic
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	—	2	2	no	—
538	C₄×C₁₃₉	—	2	2	no	—
539	C₄×C₁₃₉	—	2	2	no	—
540	C₄×C₁₃₉	—	2	2	no	—
541	C₄×C₁₃₉	—	4	1	no	—
542	C₄×C₁₃₉	—	4	2	no	—
543	C₄×C₁₃₉	—	4	2	no	—
544	C₄×C₁₃₉	—	4	1	no	—
545	C₄×C₁₃₉	—	4	2	no	—
546	C₄×C₁₃₉	—	4	2	no	—
547	C₄×C₁₃₉	—	4	2	no	—
548	C₄×C₁₃₉	—	4	2	no	—
549	C₄×C₁₃₉	—	4	1	no	—
550	C₄×C₁₃₉	#546	1	4	yes	—
551	C₂×C₁₃₉	—	2	4	no	—
552	C₂×C₁₃₉	—	2	4	no	—
553	C₂×C₁₃₉	—	4	2	no	—
554	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
555	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
556	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
557	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
558	C₂×C₁₃₉	#3495	1	1	yes	characteristic
559	C₂×C₁₃₉	#3501	1	1	yes	characteristic
560	C₂×C₁₃₉	#3520	1	1	yes	characteristic
561	#36130	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
562	C₁₃₉	#36130	1	1	yes	characteristic, direct product factor, Sylow
563	C₂×#533	C₂×C₁₃₉	1	1	yes	characteristic, complemented
564	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
565	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
566	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
567	#2848	C₂×C₁₃₉	1	1	yes	characteristic
568	#2556	C₂×C₁₃₉	1	2	yes	complemented
569	#2549	C₂×C₁₃₉	1	2	yes	complemented
570	#2492	C₂×C₁₃₉	1	1	yes	characteristic, complemented
571	#2473	C₂×C₁₃₉	1	2	yes	complemented
572	#2465	C₂×C₁₃₉	1	2	yes	complemented
573	#2440	C₂×C₁₃₉	1	1	yes	characteristic, complemented
574	#2438	C₂×C₁₃₉	1	2	yes	complemented
575	#2437	C₂×C₁₃₉	1	2	yes	—
576	#2434	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	#2429	C₂×C₁₃₉	1	1	yes	characteristic, complemented
578	#2429	C₂×C₁₃₉	1	1	yes	characteristic, complemented
579	#2423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
580	#2360	C₂×C₁₃₉	1	1	yes	characteristic, complemented
581	#2360	C₂×C₁₃₉	1	2	yes	complemented
582	#2342	C₂×C₁₃₉	1	2	yes	—
583	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
584	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
585	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
586	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
588	#533	—	2	8	no	—
589	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
590	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
591	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
592	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
593	C₂×C₂²⋊Q₈	—	2	8	no	—
594	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
597	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
599	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
600	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
604	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
606	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
607	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
608	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
609	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
610	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
612	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
613	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
614	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
615	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
617	#400	C₂²×C₁₃₉	1	2	yes	complemented
618	#399	C₂²×C₁₃₉	1	2	yes	—
619	#398	C₂²×C₁₃₉	1	2	yes	complemented
620	#398	C₂²×C₁₃₉	1	2	yes	complemented
621	#398	C₂²×C₁₃₉	1	2	yes	complemented
622	#398	C₂²×C₁₃₉	1	2	yes	complemented
623	#396	C₂²×C₁₃₉	1	2	yes	—
624	#396	C₂²×C₁₃₉	1	2	yes	—
625	#395	C₂²×C₁₃₉	1	2	yes	complemented
626	#395	C₂²×C₁₃₉	1	2	yes	complemented
627	#395	C₂²×C₁₃₉	1	2	yes	complemented
628	#393	C₂²×C₁₃₉	1	2	yes	—
629	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
630	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
631	#391	C₂²×C₁₃₉	1	2	yes	complemented
632	#391	C₂²×C₁₃₉	1	2	yes	complemented
633	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
634	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
635	#391	C₂²×C₁₃₉	1	2	yes	complemented
636	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
637	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
638	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
639	#389	C₂²×C₁₃₉	1	2	yes	complemented
640	#389	C₂²×C₁₃₉	1	2	yes	complemented
641	#389	C₂²×C₁₃₉	1	2	yes	complemented
642	#389	C₂²×C₁₃₉	1	2	yes	complemented
643	#389	C₂²×C₁₃₉	1	2	yes	complemented
644	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
645	#388	C₂²×C₁₃₉	1	2	yes	—
646	#388	C₂²×C₁₃₉	1	2	yes	—
647	#388	C₂²×C₁₃₉	1	2	yes	—
648	#388	C₂²×C₁₃₉	1	2	yes	—
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	#387	C₂²×C₁₃₉	1	2	yes	complemented
653	#387	C₂²×C₁₃₉	1	2	yes	complemented
654	#385	C₂²×C₁₃₉	1	2	yes	—
655	#385	C₂²×C₁₃₉	1	2	yes	—
656	#385	C₂²×C₁₃₉	1	2	yes	—
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	2	yes	—
663	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
664	#381	C₂²×C₁₃₉	1	2	yes	—
665	#380	C₂²×C₁₃₉	1	1	yes	characteristic
666	#380	C₂²×C₁₃₉	1	1	yes	characteristic
667	#380	C₂²×C₁₃₉	1	1	yes	characteristic
668	#380	C₂²×C₁₃₉	1	2	yes	—
669	#380	C₂²×C₁₃₉	1	2	yes	—
670	#380	C₂²×C₁₃₉	1	2	yes	—
671	#379	C₂²×C₁₃₉	1	2	yes	—
672	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
673	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
674	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
675	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
676	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
677	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
678	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
679	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
680	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
681	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
682	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
683	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
685	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
686	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
687	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂²×Q₈	—	2	4	no	—
689	C₂²×Q₈	—	2	4	no	—
690	C₂²×Q₈	—	4	2	no	—
691	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
693	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
694	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
695	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
696	C₂³×C₄	—	2	4	no	—
697	C₂³×C₄	—	2	4	no	—
698	C₂³×C₄	—	4	2	no	—
699	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
701	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
702	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
706	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
708	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
709	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
711	C₄⋊Q₈	—	2	4	no	—
712	C₄⋊Q₈	—	2	4	no	—
713	C₄⋊Q₈	—	4	2	no	—
714	#125	—	2	8	no	—
715	C₂²⋊Q₈	—	2	4	no	—
716	C₂²⋊Q₈	—	2	4	no	—
717	C₂²⋊Q₈	—	2	4	no	—
718	C₂²⋊Q₈	—	2	4	no	—
719	C₂²⋊Q₈	—	2	8	no	—
720	C₂²⋊Q₈	—	2	4	no	—
721	C₂²⋊Q₈	—	2	8	no	—
722	C₂²⋊Q₈	—	2	8	no	—
723	C₂²⋊Q₈	—	2	8	no	—
724	C₂²⋊Q₈	—	4	2	no	—
725	C₂²⋊Q₈	D₄×C₁₃₉	1	8	yes	—
726	C₄×Q₈	—	2	4	no	—
727	C₄×Q₈	—	2	4	no	—
728	C₄×Q₈	—	2	8	no	—
729	C₄×Q₈	—	4	2	no	—
730	#117	—	2	8	no	—
731	C₂×C₄⋊C₄	—	2	8	no	—
732	C₂×C₄⋊C₄	—	2	4	no	—
733	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	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	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	—	2	8	no	—
760	C₂×C₂²⋊C₄	—	2	4	no	—
761	C₂×C₂²⋊C₄	Q₈×C₁₃₉	1	8	yes	complemented
762	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₄²	—	2	4	no	—
781	C₂×C₄²	—	4	2	no	—
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	1	yes	characteristic
788	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
789	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
790	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
791	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
792	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
794	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
800	#95	C₂³×C₁₃₉	1	1	yes	characteristic
801	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	#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	C₂⁴	—	2	2	no	—
820	C₂⁴	—	2	2	no	—
821	C₂⁴	—	2	2	no	—
822	C₂⁴	—	2	2	no	—
823	C₂⁴	—	4	1	no	—
824	C₂⁴	—	4	1	no	—
825	C₂⁴	C₂×Q₈×C₁₃₉	1	4	yes	—
826	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
827	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
828	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
829	C₂×Q₈	—	2	4	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	4	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	4	no	—
835	C₂×Q₈	—	2	2	no	—
836	C₂×Q₈	—	2	4	no	—
837	C₂×Q₈	—	2	2	no	—
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	4	2	no	—
842	C₂×Q₈	—	4	2	no	—
843	C₂×Q₈	—	4	16	no	—
844	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
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	4	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	4	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	2	no	—
863	C₂²×C₄	—	2	2	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	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	1	no	—
871	C₂²×C₄	—	4	1	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	1	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	16	no	—
878	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
879	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
880	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
881	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
882	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	2	yes	—
890	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	2	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	4	no	—
909	C₄⋊C₄	—	2	4	no	—
910	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	4	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	4	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
927	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
928	C₂²⋊C₄	—	2	4	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	—	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	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
941	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
942	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
943	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
944	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
945	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	4	no	—
951	C₄²	—	2	4	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	4	1	no	—
955	C₄²	—	4	1	no	—
956	C₄²	—	4	2	no	—
957	C₄²	—	4	2	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	8	no	—
967	C₂³	—	2	8	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	—	4	4	no	—
975	C₂³	—	4	4	no	—
976	C₂³	—	4	4	no	—
977	C₂³	—	4	4	no	—
978	C₂³	—	4	4	no	—
979	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
980	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
981	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
982	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
983	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
984	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
985	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
986	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
987	Q₈	—	2	8	no	—
988	Q₈	—	4	8	no	—
989	Q₈	—	4	8	no	—
990	Q₈	—	4	4	no	—
991	Q₈	—	4	4	no	—
992	C₂×C₄	—	2	8	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	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	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	8	no	—
1014	C₂×C₄	—	2	8	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	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	2	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	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	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	—	4	4	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	8	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	4	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1053	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1054	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1055	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
1056	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
1057	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
1058	C₂×C₄	C₂²×Q₈×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	C₂×#41×C₁₃₉	1	2	yes	—
1063	C₂×C₄	H(5,𝔽₂)×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	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	4	16	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	#533×C₁₃₉	1	4	yes	complemented
1085	C₂²	D₄×Q₈×C₁₃₉	1	4	yes	—
1086	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1087	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
1088	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1089	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1090	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1091	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1092	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1093	C₄	—	2	2	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	4	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	4	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	#546×C₁₃₉	1	4	yes	—
1113	C₂	—	2	4	no	—
1114	C₂	—	2	4	no	—
1115	C₂	—	4	2	no	—
1116	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
1117	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
1118	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
1119	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
1120	C₂	#3495×C₁₃₉	1	1	yes	characteristic
1121	C₂	#3501×C₁₃₉	1	1	yes	characteristic
1122	C₂	#3520×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂³
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×#533×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2855×C₁₃₉	C₂	semidirect
6. #2556×C₁₃₉	C₂	semidirect
7. #2549×C₁₃₉	C₂	semidirect
8. #2492×C₁₃₉	C₂	semidirect
9. #2473×C₁₃₉	C₂	semidirect
10. #2465×C₁₃₉	C₂	semidirect
11. #2440×C₁₃₉	C₂	semidirect
12. #2438×C₁₃₉	C₂	semidirect
14. #2434×C₁₃₉	C₂	semidirect
15. #2429×C₁₃₉	C₂	semidirect
16. #2429×C₁₃₉	C₂	semidirect
17. #2423×C₁₃₉	C₂	semidirect
18. #2360×C₁₃₉	C₂	semidirect
19. #2360×C₁₃₉	C₂	semidirect
21. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
27. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×#125×C₁₃₉	C₂²	semidirect
43. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
44. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
46. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
55. #400×C₁₃₉	C₂²	semidirect
57. #398×C₁₃₉	C₂²	semidirect
58. #398×C₁₃₉	C₂²	semidirect
59. #398×C₁₃₉	C₂²	semidirect
60. #398×C₁₃₉	C₂²	semidirect
63. #395×C₁₃₉	C₂²	semidirect
64. #395×C₁₃₉	C₂²	semidirect
65. #395×C₁₃₉	C₂²	semidirect
67. #391×C₁₃₉	C₂²	semidirect
68. #391×C₁₃₉	C₂²	semidirect
69. #391×C₁₃₉	C₂²	semidirect
70. #391×C₁₃₉	C₂²	semidirect
71. #391×C₁₃₉	C₂²	semidirect
72. #391×C₁₃₉	C₂²	semidirect
73. #391×C₁₃₉	C₂²	semidirect
74. #391×C₁₃₉	C₂²	semidirect
75. #389×C₁₃₉	C₂²	semidirect
76. #389×C₁₃₉	C₂²	semidirect
77. #389×C₁₃₉	C₂²	semidirect
78. #389×C₁₃₉	C₂²	semidirect
79. #389×C₁₃₉	C₂²	semidirect
80. #389×C₁₃₉	C₂²	semidirect
81. #389×C₁₃₉	C₂²	semidirect
82. #389×C₁₃₉	C₂²	semidirect
87. #387×C₁₃₉	C₂²	semidirect
88. #387×C₁₃₉	C₂²	semidirect
89. #387×C₁₃₉	C₂²	semidirect
90. #387×C₁₃₉	C₂²	semidirect
91. #387×C₁₃₉	C₂²	semidirect
101. #384×C₁₃₉	C₂²	semidirect
110. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
111. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
199. C₂×C₂²⋊C₄×C₁₃₉	Q₈	semidirect
317. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
318. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
381. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
382. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
522. C₂²×C₁₃₉	#533	semidirect
561. #36130	C₁₃₉	direct (N × H)
562. C₁₃₉	#36130	direct (N × H)
563. C₂×#533	C₂×C₁₃₉	semidirect
565. #2857	C₂×C₁₃₉	semidirect
566. #2855	C₂×C₁₃₉	semidirect
568. #2556	C₂×C₁₃₉	semidirect
569. #2549	C₂×C₁₃₉	semidirect
570. #2492	C₂×C₁₃₉	semidirect
571. #2473	C₂×C₁₃₉	semidirect
572. #2465	C₂×C₁₃₉	semidirect
573. #2440	C₂×C₁₃₉	semidirect
574. #2438	C₂×C₁₃₉	semidirect
576. #2434	C₂×C₁₃₉	semidirect
577. #2429	C₂×C₁₃₉	semidirect
578. #2429	C₂×C₁₃₉	semidirect
579. #2423	C₂×C₁₃₉	semidirect
580. #2360	C₂×C₁₃₉	semidirect
581. #2360	C₂×C₁₃₉	semidirect
583. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
584. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
589. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
590. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
591. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
592. C₂×#125	C₂²×C₁₃₉	semidirect
605. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
606. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
607. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
608. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
617. #400	C₂²×C₁₃₉	semidirect
619. #398	C₂²×C₁₃₉	semidirect
620. #398	C₂²×C₁₃₉	semidirect
621. #398	C₂²×C₁₃₉	semidirect
622. #398	C₂²×C₁₃₉	semidirect
625. #395	C₂²×C₁₃₉	semidirect
626. #395	C₂²×C₁₃₉	semidirect
627. #395	C₂²×C₁₃₉	semidirect
629. #391	C₂²×C₁₃₉	semidirect
630. #391	C₂²×C₁₃₉	semidirect
631. #391	C₂²×C₁₃₉	semidirect
632. #391	C₂²×C₁₃₉	semidirect
633. #391	C₂²×C₁₃₉	semidirect
634. #391	C₂²×C₁₃₉	semidirect
635. #391	C₂²×C₁₃₉	semidirect
636. #391	C₂²×C₁₃₉	semidirect
637. #389	C₂²×C₁₃₉	semidirect
638. #389	C₂²×C₁₃₉	semidirect
639. #389	C₂²×C₁₃₉	semidirect
640. #389	C₂²×C₁₃₉	semidirect
641. #389	C₂²×C₁₃₉	semidirect
642. #389	C₂²×C₁₃₉	semidirect
643. #389	C₂²×C₁₃₉	semidirect
644. #389	C₂²×C₁₃₉	semidirect
649. #387	C₂²×C₁₃₉	semidirect
650. #387	C₂²×C₁₃₉	semidirect
651. #387	C₂²×C₁₃₉	semidirect
652. #387	C₂²×C₁₃₉	semidirect
653. #387	C₂²×C₁₃₉	semidirect
663. #384	C₂²×C₁₃₉	semidirect
672. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
673. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
761. C₂×C₂²⋊C₄	Q₈×C₁₃₉	semidirect
879. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
880. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
943. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect
944. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect
1084. C₂²	#533×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₉	2
C₂²×C₂²⋊Q₈×C₁₃₉	2
#2857×C₁₃₉	2
#2855×C₁₃₉	2
#2848×C₁₃₉	2
#2556×C₁₃₉	2
#2549×C₁₃₉	2
#2492×C₁₃₉	2
#2473×C₁₃₉	2
#2465×C₁₃₉	2
#2440×C₁₃₉	2
#2438×C₁₃₉	2
#2437×C₁₃₉	2
#2434×C₁₃₉	2
#2429×C₁₃₉	2
#2423×C₁₃₉	2
#2360×C₁₃₉	2
#2342×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
#36130	139

Subgroups — C139×#36130 #48030726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36130 #48030726