Subgroups — C₁₃₉×#36156 #48030752

Order 35584.

2844 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2562×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2536×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2485×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2480×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2468×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2460×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2419×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2417×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2415×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2405×C₁₃₉	C₂	1	2	yes	maximal
18	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2352×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2342×C₁₃₉	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#2280×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	#552×C₁₃₉	—	2	8	no	—
28	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
50	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
58	#400×C₁₃₉	C₂²	1	2	yes	complemented
59	#398×C₁₃₉	C₂²	1	2	yes	complemented
60	#398×C₁₃₉	C₂²	1	2	yes	complemented
61	#398×C₁₃₉	C₂²	1	2	yes	complemented
62	#397×C₁₃₉	C₂²	1	2	yes	complemented
63	#397×C₁₃₉	C₂²	1	2	yes	complemented
64	#397×C₁₃₉	C₂²	1	2	yes	complemented
65	#396×C₁₃₉	C₂²	1	2	yes	complemented
66	#394×C₁₃₉	C₂²	1	2	yes	—
67	#394×C₁₃₉	C₂²	1	2	yes	—
68	#394×C₁₃₉	C₂²	1	2	yes	—
69	#394×C₁₃₉	C₂²	1	2	yes	—
70	#391×C₁₃₉	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
75	#388×C₁₃₉	C₂²	1	2	yes	complemented
76	#388×C₁₃₉	C₂²	1	2	yes	complemented
77	#388×C₁₃₉	C₂²	1	2	yes	complemented
78	#388×C₁₃₉	C₂²	1	2	yes	complemented
79	#388×C₁₃₉	C₂²	1	2	yes	complemented
80	#388×C₁₃₉	C₂²	1	2	yes	complemented
81	#388×C₁₃₉	C₂²	1	2	yes	complemented
82	#387×C₁₃₉	C₂²	1	2	yes	complemented
83	#387×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	#386×C₁₃₉	C₂²	1	2	yes	—
88	#386×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	complemented
95	#385×C₁₃₉	C₂²	1	2	yes	complemented
96	#385×C₁₃₉	C₂²	1	2	yes	complemented
97	#385×C₁₃₉	C₂²	1	2	yes	complemented
98	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
99	#381×C₁₃₉	C₂²	1	2	yes	complemented
100	#381×C₁₃₉	C₂²	1	2	yes	complemented
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	1	yes	characteristic
103	#380×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	1	yes	characteristic
105	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
106	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	#380×C₁₃₉	C₂²	1	2	yes	complemented
108	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
109	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
110	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
114	#380×C₁₃₉	C₂²	1	2	yes	complemented
115	#379×C₁₃₉	C₂²	1	2	yes	—
116	#379×C₁₃₉	C₂²	1	2	yes	—
117	#379×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
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	complemented
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃₉	—	2	4	no	—
129	C₂²×D₄×C₁₃₉	—	2	4	no	—
130	C₂²×D₄×C₁₃₉	—	2	4	no	—
131	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₉	—	2	4	no	—
136	C₂³×C₄×C₁₃₉	—	2	4	no	—
137	C₂³×C₄×C₁₃₉	—	2	4	no	—
138	C₂³×C₄×C₁₃₉	—	2	4	no	—
139	C₂³×C₄×C₁₃₉	—	4	2	no	—
140	C₂³×C₄×C₁₃₉	—	4	2	no	—
141	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
156	#126×C₁₃₉	—	2	8	no	—
157	#125×C₁₃₉	—	2	8	no	—
158	#125×C₁₃₉	—	2	4	no	—
159	#123×C₁₃₉	—	2	8	no	—
160	#123×C₁₃₉	—	2	8	no	—
161	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
162	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
163	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
164	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
165	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
166	C₄×Q₈×C₁₃₉	—	2	4	no	—
167	C₄×D₄×C₁₃₉	—	2	4	no	—
168	C₄×D₄×C₁₃₉	—	2	4	no	—
169	C₄×D₄×C₁₃₉	—	2	4	no	—
170	C₄×D₄×C₁₃₉	—	2	4	no	—
171	C₄×D₄×C₁₃₉	—	2	4	no	—
172	C₄×D₄×C₁₃₉	—	2	4	no	—
173	C₄×D₄×C₁₃₉	—	2	4	no	—
174	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
175	#117×C₁₃₉	—	2	4	no	—
176	#117×C₁₃₉	—	2	8	no	—
177	#117×C₁₃₉	—	4	2	no	—
178	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
180	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
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×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	1	yes	characteristic
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
201	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
206	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
207	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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×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	2	yes	—
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃₉	—	2	4	no	—
235	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
239	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
241	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
242	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
243	#95×C₁₃₉	C₂³	1	2	yes	—
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	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	#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	#95×C₁₃₉	C₂³	1	2	yes	—
258	#95×C₁₃₉	C₂³	1	2	yes	—
259	#95×C₁₃₉	C₂³	1	2	yes	—
260	#95×C₁₃₉	C₂³	1	2	yes	—
261	#95×C₁₃₉	C₂³	1	2	yes	—
262	C₂⁴×C₁₃₉	—	2	2	no	—
263	C₂⁴×C₁₃₉	—	2	2	no	—
264	C₂⁴×C₁₃₉	—	2	2	no	—
265	C₂⁴×C₁₃₉	—	2	2	no	—
266	C₂⁴×C₁₃₉	—	2	2	no	—
267	C₂⁴×C₁₃₉	—	2	2	no	—
268	C₂⁴×C₁₃₉	—	2	2	no	—
269	C₂⁴×C₁₃₉	—	2	2	no	—
270	C₂⁴×C₁₃₉	—	2	2	no	—
271	C₂⁴×C₁₃₉	—	4	1	no	—
272	C₂⁴×C₁₃₉	—	4	1	no	—
273	C₂⁴×C₁₃₉	—	4	1	no	—
274	C₂⁴×C₁₃₉	—	4	1	no	—
275	C₂⁴×C₁₃₉	#41	1	4	yes	—
276	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
281	C₂×Q₈×C₁₃₉	—	2	2	no	—
282	C₂×Q₈×C₁₃₉	—	2	2	no	—
283	C₂×Q₈×C₁₃₉	—	2	2	no	—
284	C₂×D₄×C₁₃₉	—	2	32	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	—	2	2	no	—
289	C₂×D₄×C₁₃₉	—	2	2	no	—
290	C₂×D₄×C₁₃₉	—	2	2	no	—
291	C₂×D₄×C₁₃₉	—	2	2	no	—
292	C₂×D₄×C₁₃₉	—	2	2	no	—
293	C₂×D₄×C₁₃₉	—	2	2	no	—
294	C₂×D₄×C₁₃₉	—	2	2	no	—
295	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
296	C₂×D₄×C₁₃₉	#41	1	4	yes	—
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	—	2	4	no	—
307	C₂²×C₄×C₁₃₉	—	2	2	no	—
308	C₂²×C₄×C₁₃₉	—	2	2	no	—
309	C₂²×C₄×C₁₃₉	—	2	4	no	—
310	C₂²×C₄×C₁₃₉	—	2	4	no	—
311	C₂²×C₄×C₁₃₉	—	2	2	no	—
312	C₂²×C₄×C₁₃₉	—	2	2	no	—
313	C₂²×C₄×C₁₃₉	—	2	2	no	—
314	C₂²×C₄×C₁₃₉	—	2	4	no	—
315	C₂²×C₄×C₁₃₉	—	2	2	no	—
316	C₂²×C₄×C₁₃₉	—	2	2	no	—
317	C₂²×C₄×C₁₃₉	—	2	2	no	—
318	C₂²×C₄×C₁₃₉	—	2	2	no	—
319	C₂²×C₄×C₁₃₉	—	2	2	no	—
320	C₂²×C₄×C₁₃₉	—	2	2	no	—
321	C₂²×C₄×C₁₃₉	—	2	2	no	—
322	C₂²×C₄×C₁₃₉	—	2	2	no	—
323	C₂²×C₄×C₁₃₉	—	2	2	no	—
324	C₂²×C₄×C₁₃₉	—	2	2	no	—
325	C₂²×C₄×C₁₃₉	—	2	2	no	—
326	C₂²×C₄×C₁₃₉	—	2	2	no	—
327	C₂²×C₄×C₁₃₉	—	2	2	no	—
328	C₂²×C₄×C₁₃₉	—	2	2	no	—
329	C₂²×C₄×C₁₃₉	—	2	2	no	—
330	C₂²×C₄×C₁₃₉	—	4	1	no	—
331	C₂²×C₄×C₁₃₉	—	4	1	no	—
332	C₂²×C₄×C₁₃₉	—	4	1	no	—
333	C₂²×C₄×C₁₃₉	—	4	1	no	—
334	C₂²×C₄×C₁₃₉	—	4	1	no	—
335	C₂²×C₄×C₁₃₉	—	4	1	no	—
336	C₂²×C₄×C₁₃₉	—	4	1	no	—
337	C₂²×C₄×C₁₃₉	—	4	16	no	—
338	C₂²×C₄×C₁₃₉	—	4	16	no	—
339	C₂²×C₄×C₁₃₉	—	4	2	no	—
340	C₂²×C₄×C₁₃₉	—	4	2	no	—
341	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
342	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
343	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
344	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₁₃₉	—	2	2	no	—
363	C₄⋊C₄×C₁₃₉	—	2	2	no	—
364	C₄⋊C₄×C₁₃₉	—	2	2	no	—
365	C₄⋊C₄×C₁₃₉	—	2	2	no	—
366	C₄⋊C₄×C₁₃₉	—	2	2	no	—
367	C₄⋊C₄×C₁₃₉	—	2	4	no	—
368	C₄⋊C₄×C₁₃₉	—	2	2	no	—
369	C₄⋊C₄×C₁₃₉	—	2	4	no	—
370	C₄⋊C₄×C₁₃₉	—	2	4	no	—
371	C₄⋊C₄×C₁₃₉	—	2	4	no	—
372	C₄⋊C₄×C₁₃₉	—	2	4	no	—
373	C₄⋊C₄×C₁₃₉	—	2	4	no	—
374	C₄⋊C₄×C₁₃₉	—	2	2	no	—
375	C₄⋊C₄×C₁₃₉	—	2	4	no	—
376	C₄⋊C₄×C₁₃₉	—	2	4	no	—
377	C₄⋊C₄×C₁₃₉	—	2	4	no	—
378	C₄⋊C₄×C₁₃₉	—	2	2	no	—
379	C₄⋊C₄×C₁₃₉	—	2	2	no	—
380	C₄⋊C₄×C₁₃₉	—	2	2	no	—
381	C₄⋊C₄×C₁₃₉	—	4	2	no	—
382	C₄⋊C₄×C₁₃₉	—	4	2	no	—
383	C₄⋊C₄×C₁₃₉	—	4	2	no	—
384	C₄⋊C₄×C₁₃₉	—	4	2	no	—
385	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
386	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
387	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
388	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
389	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
390	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
391	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
392	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
393	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
394	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
395	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
396	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
397	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
398	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
399	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
400	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
401	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
402	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
403	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
404	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
405	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
406	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
407	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
408	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
409	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
410	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
411	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
412	C₄²×C₁₃₉	—	2	2	no	—
413	C₄²×C₁₃₉	—	2	2	no	—
414	C₄²×C₁₃₉	—	2	2	no	—
415	C₄²×C₁₃₉	—	2	4	no	—
416	C₄²×C₁₃₉	—	2	4	no	—
417	C₄²×C₁₃₉	—	4	2	no	—
418	C₄²×C₁₃₉	—	4	2	no	—
419	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
420	C₂³×C₁₃₉	—	2	1	no	—
421	C₂³×C₁₃₉	—	2	1	no	—
422	C₂³×C₁₃₉	—	2	1	no	—
423	C₂³×C₁₃₉	—	2	1	no	—
424	C₂³×C₁₃₉	—	2	1	no	—
425	C₂³×C₁₃₉	—	2	1	no	—
426	C₂³×C₁₃₉	—	2	1	no	—
427	C₂³×C₁₃₉	—	2	1	no	—
428	C₂³×C₁₃₉	—	2	8	no	—
429	C₂³×C₁₃₉	—	2	8	no	—
430	C₂³×C₁₃₉	—	2	8	no	—
431	C₂³×C₁₃₉	—	2	1	no	—
432	C₂³×C₁₃₉	—	2	1	no	—
433	C₂³×C₁₃₉	—	2	1	no	—
434	C₂³×C₁₃₉	—	2	1	no	—
435	C₂³×C₁₃₉	—	2	1	no	—
436	C₂³×C₁₃₉	—	2	1	no	—
437	C₂³×C₁₃₉	—	2	1	no	—
438	C₂³×C₁₃₉	—	2	1	no	—
439	C₂³×C₁₃₉	—	2	1	no	—
440	C₂³×C₁₃₉	—	2	1	no	—
441	C₂³×C₁₃₉	—	2	1	no	—
442	C₂³×C₁₃₉	—	2	1	no	—
443	C₂³×C₁₃₉	—	2	1	no	—
444	C₂³×C₁₃₉	—	2	1	no	—
445	C₂³×C₁₃₉	—	2	1	no	—
446	C₂³×C₁₃₉	—	2	1	no	—
447	C₂³×C₁₃₉	—	2	1	no	—
448	C₂³×C₁₃₉	—	2	1	no	—
449	C₂³×C₁₃₉	—	4	4	no	—
450	C₂³×C₁₃₉	—	4	4	no	—
451	C₂³×C₁₃₉	—	4	4	no	—
452	C₂³×C₁₃₉	—	4	4	no	—
453	C₂³×C₁₃₉	—	4	4	no	—
454	C₂³×C₁₃₉	—	4	4	no	—
455	C₂³×C₁₃₉	—	4	4	no	—
456	C₂³×C₁₃₉	—	4	4	no	—
457	C₂³×C₁₃₉	—	4	4	no	—
458	C₂³×C₁₃₉	—	4	4	no	—
459	C₂³×C₁₃₉	—	4	4	no	—
460	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
461	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
462	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
463	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
464	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
465	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
466	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
467	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
468	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
469	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
470	Q₈×C₁₃₉	—	4	4	no	—
471	D₄×C₁₃₉	—	2	8	no	—
472	D₄×C₁₃₉	—	2	8	no	—
473	D₄×C₁₃₉	—	2	8	no	—
474	D₄×C₁₃₉	—	2	8	no	—
475	C₂×C₄×C₁₃₉	—	2	8	no	—
476	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
481	C₂×C₄×C₁₃₉	—	2	1	no	—
482	C₂×C₄×C₁₃₉	—	2	1	no	—
483	C₂×C₄×C₁₃₉	—	2	1	no	—
484	C₂×C₄×C₁₃₉	—	2	1	no	—
485	C₂×C₄×C₁₃₉	—	2	1	no	—
486	C₂×C₄×C₁₃₉	—	2	1	no	—
487	C₂×C₄×C₁₃₉	—	2	1	no	—
488	C₂×C₄×C₁₃₉	—	2	8	no	—
489	C₂×C₄×C₁₃₉	—	2	8	no	—
490	C₂×C₄×C₁₃₉	—	2	8	no	—
491	C₂×C₄×C₁₃₉	—	2	1	no	—
492	C₂×C₄×C₁₃₉	—	2	2	no	—
493	C₂×C₄×C₁₃₉	—	2	2	no	—
494	C₂×C₄×C₁₃₉	—	2	2	no	—
495	C₂×C₄×C₁₃₉	—	2	1	no	—
496	C₂×C₄×C₁₃₉	—	2	1	no	—
497	C₂×C₄×C₁₃₉	—	2	2	no	—
498	C₂×C₄×C₁₃₉	—	2	2	no	—
499	C₂×C₄×C₁₃₉	—	2	2	no	—
500	C₂×C₄×C₁₃₉	—	2	2	no	—
501	C₂×C₄×C₁₃₉	—	2	2	no	—
502	C₂×C₄×C₁₃₉	—	2	2	no	—
503	C₂×C₄×C₁₃₉	—	2	2	no	—
504	C₂×C₄×C₁₃₉	—	2	2	no	—
505	C₂×C₄×C₁₃₉	—	2	2	no	—
506	C₂×C₄×C₁₃₉	—	2	2	no	—
507	C₂×C₄×C₁₃₉	—	2	2	no	—
508	C₂×C₄×C₁₃₉	—	2	1	no	—
509	C₂×C₄×C₁₃₉	—	2	1	no	—
510	C₂×C₄×C₁₃₉	—	2	2	no	—
511	C₂×C₄×C₁₃₉	—	2	2	no	—
512	C₂×C₄×C₁₃₉	—	2	2	no	—
513	C₂×C₄×C₁₃₉	—	2	2	no	—
514	C₂×C₄×C₁₃₉	—	2	1	no	—
515	C₂×C₄×C₁₃₉	—	2	1	no	—
516	C₂×C₄×C₁₃₉	—	2	2	no	—
517	C₂×C₄×C₁₃₉	—	2	2	no	—
518	C₂×C₄×C₁₃₉	—	2	1	no	—
519	C₂×C₄×C₁₃₉	—	2	2	no	—
520	C₂×C₄×C₁₃₉	—	2	2	no	—
521	C₂×C₄×C₁₃₉	—	2	2	no	—
522	C₂×C₄×C₁₃₉	—	2	2	no	—
523	C₂×C₄×C₁₃₉	—	2	1	no	—
524	C₂×C₄×C₁₃₉	—	4	4	no	—
525	C₂×C₄×C₁₃₉	—	4	4	no	—
526	C₂×C₄×C₁₃₉	—	4	4	no	—
527	C₂×C₄×C₁₃₉	—	4	4	no	—
528	C₂×C₄×C₁₃₉	—	4	4	no	—
529	C₂×C₄×C₁₃₉	—	4	4	no	—
530	C₂×C₄×C₁₃₉	—	4	4	no	—
531	C₂×C₄×C₁₃₉	—	4	8	no	—
532	C₂×C₄×C₁₃₉	—	4	4	no	—
533	C₂×C₄×C₁₃₉	—	4	4	no	—
534	C₂×C₄×C₁₃₉	—	8	4	no	—
535	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
541	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
542	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
543	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
544	C₂²×C₁₃₉	—	2	2	no	—
545	C₂²×C₁₃₉	—	2	2	no	—
546	C₂²×C₁₃₉	—	2	2	no	—
547	C₂²×C₁₃₉	—	2	2	no	—
548	C₂²×C₁₃₉	—	2	2	no	—
549	C₂²×C₁₃₉	—	2	2	no	—
550	C₂²×C₁₃₉	—	2	2	no	—
551	C₂²×C₁₃₉	—	2	2	no	—
552	C₂²×C₁₃₉	—	2	2	no	—
553	C₂²×C₁₃₉	—	2	2	no	—
554	C₂²×C₁₃₉	—	2	2	no	—
555	C₂²×C₁₃₉	—	2	2	no	—
556	C₂²×C₁₃₉	—	2	2	no	—
557	C₂²×C₁₃₉	—	2	2	no	—
558	C₂²×C₁₃₉	—	2	2	no	—
559	C₂²×C₁₃₉	—	2	2	no	—
560	C₂²×C₁₃₉	—	2	2	no	—
561	C₂²×C₁₃₉	—	2	2	no	—
562	C₂²×C₁₃₉	—	2	2	no	—
563	C₂²×C₁₃₉	—	2	2	no	—
564	C₂²×C₁₃₉	—	2	2	no	—
565	C₂²×C₁₃₉	—	4	16	no	—
566	C₂²×C₁₃₉	—	4	16	no	—
567	C₂²×C₁₃₉	—	4	1	no	—
568	C₂²×C₁₃₉	—	4	1	no	—
569	C₂²×C₁₃₉	—	4	1	no	—
570	C₂²×C₁₃₉	—	4	1	no	—
571	C₂²×C₁₃₉	—	4	1	no	—
572	C₂²×C₁₃₉	—	4	1	no	—
573	C₂²×C₁₃₉	—	4	1	no	—
574	C₂²×C₁₃₉	—	4	1	no	—
575	C₂²×C₁₃₉	—	4	1	no	—
576	C₂²×C₁₃₉	—	4	1	no	—
577	C₂²×C₁₃₉	—	4	1	no	—
578	C₂²×C₁₃₉	—	4	1	no	—
579	C₂²×C₁₃₉	#525	1	4	yes	—
580	C₂²×C₁₃₉	#552	1	4	yes	complemented
581	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
582	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
583	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
584	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
585	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
587	C₂²×C₁₃₉	#585	1	1	yes	characteristic
588	C₄×C₁₃₉	—	2	2	no	—
589	C₄×C₁₃₉	—	2	2	no	—
590	C₄×C₁₃₉	—	2	2	no	—
591	C₄×C₁₃₉	—	2	2	no	—
592	C₄×C₁₃₉	—	2	2	no	—
593	C₄×C₁₃₉	—	2	2	no	—
594	C₄×C₁₃₉	—	4	2	no	—
595	C₄×C₁₃₉	—	4	2	no	—
596	C₄×C₁₃₉	—	4	1	no	—
597	C₄×C₁₃₉	—	4	1	no	—
598	C₄×C₁₃₉	—	4	2	no	—
599	C₄×C₁₃₉	—	4	2	no	—
600	C₄×C₁₃₉	—	4	2	no	—
601	C₄×C₁₃₉	—	4	1	no	—
602	C₄×C₁₃₉	—	4	2	no	—
603	C₄×C₁₃₉	—	4	2	no	—
604	C₄×C₁₃₉	—	4	2	no	—
605	C₄×C₁₃₉	#546	1	4	yes	—
606	C₂×C₁₃₉	—	2	4	no	—
607	C₂×C₁₃₉	—	2	4	no	—
608	C₂×C₁₃₉	—	4	2	no	—
609	C₂×C₁₃₉	—	4	2	no	—
610	C₂×C₁₃₉	—	4	2	no	—
611	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
612	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
613	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
614	C₂×C₁₃₉	#3475	1	1	yes	characteristic
615	C₂×C₁₃₉	#3489	1	1	yes	characteristic
616	C₂×C₁₃₉	#3505	1	1	yes	characteristic
617	C₂×C₁₃₉	#3520	1	1	yes	characteristic
618	#36156	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
619	C₁₃₉	#36156	1	1	yes	characteristic, direct product factor, Sylow
620	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
621	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic
622	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
623	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
624	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
625	#2562	C₂×C₁₃₉	1	1	yes	characteristic, complemented
626	#2536	C₂×C₁₃₉	1	1	yes	characteristic, complemented
627	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
628	#2485	C₂×C₁₃₉	1	1	yes	characteristic, complemented
629	#2480	C₂×C₁₃₉	1	2	yes	complemented
630	#2473	C₂×C₁₃₉	1	2	yes	complemented
631	#2468	C₂×C₁₃₉	1	2	yes	complemented
632	#2460	C₂×C₁₃₉	1	2	yes	complemented
633	#2419	C₂×C₁₃₉	1	2	yes	complemented
634	#2417	C₂×C₁₃₉	1	1	yes	characteristic, complemented
635	#2415	C₂×C₁₃₉	1	1	yes	characteristic, complemented
636	#2405	C₂×C₁₃₉	1	2	yes	—
637	#2359	C₂×C₁₃₉	1	2	yes	complemented
638	#2352	C₂×C₁₃₉	1	1	yes	characteristic, complemented
639	#2342	C₂×C₁₃₉	1	2	yes	complemented
640	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
641	#2280	C₂×C₁₃₉	1	1	yes	characteristic, complemented
642	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic, complemented
643	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
644	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
645	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
646	#552	—	2	8	no	—
647	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
648	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
649	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
650	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
651	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
652	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
653	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
654	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
655	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
656	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
657	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
658	C₂×C₄×D₄	—	2	8	no	—
659	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
660	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
661	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
662	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
663	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
664	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
665	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
666	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
667	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
668	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
669	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
670	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
671	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
672	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
673	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
674	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
675	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
676	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
677	#400	C₂²×C₁₃₉	1	2	yes	complemented
678	#398	C₂²×C₁₃₉	1	2	yes	complemented
679	#398	C₂²×C₁₃₉	1	2	yes	complemented
680	#398	C₂²×C₁₃₉	1	2	yes	complemented
681	#397	C₂²×C₁₃₉	1	2	yes	complemented
682	#397	C₂²×C₁₃₉	1	2	yes	complemented
683	#397	C₂²×C₁₃₉	1	2	yes	complemented
684	#396	C₂²×C₁₃₉	1	2	yes	complemented
685	#394	C₂²×C₁₃₉	1	2	yes	—
686	#394	C₂²×C₁₃₉	1	2	yes	—
687	#394	C₂²×C₁₃₉	1	2	yes	—
688	#394	C₂²×C₁₃₉	1	2	yes	—
689	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
690	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
691	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
692	#389	C₂²×C₁₃₉	1	2	yes	complemented
693	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
694	#388	C₂²×C₁₃₉	1	2	yes	complemented
695	#388	C₂²×C₁₃₉	1	2	yes	complemented
696	#388	C₂²×C₁₃₉	1	2	yes	complemented
697	#388	C₂²×C₁₃₉	1	2	yes	complemented
698	#388	C₂²×C₁₃₉	1	2	yes	complemented
699	#388	C₂²×C₁₃₉	1	2	yes	complemented
700	#388	C₂²×C₁₃₉	1	2	yes	complemented
701	#387	C₂²×C₁₃₉	1	2	yes	complemented
702	#387	C₂²×C₁₃₉	1	2	yes	complemented
703	#387	C₂²×C₁₃₉	1	2	yes	complemented
704	#387	C₂²×C₁₃₉	1	2	yes	complemented
705	#387	C₂²×C₁₃₉	1	2	yes	complemented
706	#386	C₂²×C₁₃₉	1	2	yes	—
707	#386	C₂²×C₁₃₉	1	2	yes	—
708	#385	C₂²×C₁₃₉	1	2	yes	—
709	#385	C₂²×C₁₃₉	1	2	yes	—
710	#385	C₂²×C₁₃₉	1	2	yes	—
711	#385	C₂²×C₁₃₉	1	2	yes	—
712	#385	C₂²×C₁₃₉	1	2	yes	—
713	#385	C₂²×C₁₃₉	1	2	yes	complemented
714	#385	C₂²×C₁₃₉	1	2	yes	complemented
715	#385	C₂²×C₁₃₉	1	2	yes	complemented
716	#385	C₂²×C₁₃₉	1	2	yes	complemented
717	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
718	#381	C₂²×C₁₃₉	1	2	yes	complemented
719	#381	C₂²×C₁₃₉	1	2	yes	complemented
720	#380	C₂²×C₁₃₉	1	1	yes	characteristic
721	#380	C₂²×C₁₃₉	1	1	yes	characteristic
722	#380	C₂²×C₁₃₉	1	2	yes	—
723	#380	C₂²×C₁₃₉	1	1	yes	characteristic
724	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
725	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
726	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
727	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
728	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
729	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
730	#380	C₂²×C₁₃₉	1	2	yes	complemented
731	#380	C₂²×C₁₃₉	1	2	yes	complemented
732	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
733	#380	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
734	#379	C₂²×C₁₃₉	1	2	yes	—
735	#379	C₂²×C₁₃₉	1	2	yes	—
736	#379	C₂²×C₁₃₉	1	2	yes	—
737	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
738	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
739	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
740	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
741	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
742	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
743	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
744	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
745	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
746	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
747	C₂²×D₄	—	2	4	no	—
748	C₂²×D₄	—	2	4	no	—
749	C₂²×D₄	—	2	4	no	—
750	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
751	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
753	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
754	C₂³×C₄	—	2	4	no	—
755	C₂³×C₄	—	2	4	no	—
756	C₂³×C₄	—	2	4	no	—
757	C₂³×C₄	—	2	4	no	—
758	C₂³×C₄	—	4	2	no	—
759	C₂³×C₄	—	4	2	no	—
760	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
761	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
763	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
764	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
765	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
766	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
767	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
768	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
769	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
770	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
771	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
772	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
773	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
774	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
775	#126	—	2	8	no	—
776	#125	—	2	8	no	—
777	#125	—	2	4	no	—
778	#123	—	2	8	no	—
779	#123	—	2	8	no	—
780	C₂²⋊Q₈	—	2	4	no	—
781	C₂²⋊Q₈	—	2	4	no	—
782	C₂²⋊Q₈	—	2	4	no	—
783	C₂²⋊Q₈	—	4	2	no	—
784	C₂²⋊Q₈	—	4	2	no	—
785	C₄×Q₈	—	2	4	no	—
786	C₄×D₄	—	2	4	no	—
787	C₄×D₄	—	2	4	no	—
788	C₄×D₄	—	2	4	no	—
789	C₄×D₄	—	2	4	no	—
790	C₄×D₄	—	2	4	no	—
791	C₄×D₄	—	2	4	no	—
792	C₄×D₄	—	2	4	no	—
793	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
794	#117	—	2	4	no	—
795	#117	—	2	8	no	—
796	#117	—	4	2	no	—
797	C₂×C₄⋊C₄	—	2	4	no	—
798	C₂×C₄⋊C₄	—	2	4	no	—
799	C₂×C₄⋊C₄	—	4	2	no	—
800	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
803	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
804	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
807	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
808	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
809	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
812	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
813	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
815	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
817	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
818	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
821	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	—	2	8	no	—
825	C₂×C₂²⋊C₄	—	2	4	no	—
826	C₂×C₂²⋊C₄	—	2	4	no	—
827	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
835	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
837	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
838	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
843	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
844	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
847	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
848	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
849	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
850	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
851	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
852	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
853	C₂×C₄²	—	2	4	no	—
854	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
855	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
856	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
857	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
858	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
859	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
860	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
861	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
862	#95	C₂³×C₁₃₉	1	2	yes	—
863	#95	C₂³×C₁₃₉	1	2	yes	—
864	#95	C₂³×C₁₃₉	1	2	yes	—
865	#95	C₂³×C₁₃₉	1	2	yes	—
866	#95	C₂³×C₁₃₉	1	2	yes	—
867	#95	C₂³×C₁₃₉	1	2	yes	—
868	#95	C₂³×C₁₃₉	1	2	yes	—
869	#95	C₂³×C₁₃₉	1	2	yes	—
870	#95	C₂³×C₁₃₉	1	2	yes	—
871	#95	C₂³×C₁₃₉	1	2	yes	—
872	#95	C₂³×C₁₃₉	1	2	yes	—
873	#95	C₂³×C₁₃₉	1	2	yes	—
874	#95	C₂³×C₁₃₉	1	2	yes	—
875	#95	C₂³×C₁₃₉	1	2	yes	—
876	#95	C₂³×C₁₃₉	1	2	yes	—
877	#95	C₂³×C₁₃₉	1	2	yes	—
878	#95	C₂³×C₁₃₉	1	2	yes	—
879	#95	C₂³×C₁₃₉	1	2	yes	—
880	#95	C₂³×C₁₃₉	1	2	yes	—
881	C₂⁴	—	2	2	no	—
882	C₂⁴	—	2	2	no	—
883	C₂⁴	—	2	2	no	—
884	C₂⁴	—	2	2	no	—
885	C₂⁴	—	2	2	no	—
886	C₂⁴	—	2	2	no	—
887	C₂⁴	—	2	2	no	—
888	C₂⁴	—	2	2	no	—
889	C₂⁴	—	2	2	no	—
890	C₂⁴	—	4	1	no	—
891	C₂⁴	—	4	1	no	—
892	C₂⁴	—	4	1	no	—
893	C₂⁴	—	4	1	no	—
894	C₂⁴	#41×C₁₃₉	1	4	yes	—
895	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
896	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
897	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
898	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
899	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×D₄	—	2	32	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
915	C₂×D₄	#41×C₁₃₉	1	4	yes	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	4	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	4	no	—
929	C₂²×C₄	—	2	4	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	4	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	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	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	4	1	no	—
950	C₂²×C₄	—	4	1	no	—
951	C₂²×C₄	—	4	1	no	—
952	C₂²×C₄	—	4	1	no	—
953	C₂²×C₄	—	4	1	no	—
954	C₂²×C₄	—	4	1	no	—
955	C₂²×C₄	—	4	1	no	—
956	C₂²×C₄	—	4	16	no	—
957	C₂²×C₄	—	4	16	no	—
958	C₂²×C₄	—	4	2	no	—
959	C₂²×C₄	—	4	2	no	—
960	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
961	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
962	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
963	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
967	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
970	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
971	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
972	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
973	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
974	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	4	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	4	no	—
989	C₄⋊C₄	—	2	4	no	—
990	C₄⋊C₄	—	2	4	no	—
991	C₄⋊C₄	—	2	4	no	—
992	C₄⋊C₄	—	2	4	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	4	no	—
995	C₄⋊C₄	—	2	4	no	—
996	C₄⋊C₄	—	2	4	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	4	2	no	—
1001	C₄⋊C₄	—	4	2	no	—
1002	C₄⋊C₄	—	4	2	no	—
1003	C₄⋊C₄	—	4	2	no	—
1004	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	4	no	—
1008	C₂²⋊C₄	—	2	4	no	—
1009	C₂²⋊C₄	—	2	4	no	—
1010	C₂²⋊C₄	—	2	4	no	—
1011	C₂²⋊C₄	—	2	4	no	—
1012	C₂²⋊C₄	—	2	4	no	—
1013	C₂²⋊C₄	—	2	4	no	—
1014	C₂²⋊C₄	—	2	4	no	—
1015	C₂²⋊C₄	—	2	4	no	—
1016	C₂²⋊C₄	—	2	4	no	—
1017	C₂²⋊C₄	—	2	4	no	—
1018	C₂²⋊C₄	—	2	4	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	4	2	no	—
1024	C₂²⋊C₄	—	4	2	no	—
1025	C₂²⋊C₄	—	4	2	no	—
1026	C₂²⋊C₄	—	4	2	no	—
1027	C₂²⋊C₄	—	4	2	no	—
1028	C₂²⋊C₄	—	4	2	no	—
1029	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	4	no	—
1035	C₄²	—	2	4	no	—
1036	C₄²	—	4	2	no	—
1037	C₄²	—	4	2	no	—
1038	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	8	no	—
1048	C₂³	—	2	8	no	—
1049	C₂³	—	2	8	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	4	4	no	—
1069	C₂³	—	4	4	no	—
1070	C₂³	—	4	4	no	—
1071	C₂³	—	4	4	no	—
1072	C₂³	—	4	4	no	—
1073	C₂³	—	4	4	no	—
1074	C₂³	—	4	4	no	—
1075	C₂³	—	4	4	no	—
1076	C₂³	—	4	4	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	4	4	no	—
1079	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1080	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
1081	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1082	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1083	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1084	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1085	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1086	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
1087	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
1088	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
1089	Q₈	—	4	4	no	—
1090	D₄	—	2	8	no	—
1091	D₄	—	2	8	no	—
1092	D₄	—	2	8	no	—
1093	D₄	—	2	8	no	—
1094	C₂×C₄	—	2	8	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	8	no	—
1108	C₂×C₄	—	2	8	no	—
1109	C₂×C₄	—	2	8	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	4	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	4	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	8	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	8	4	no	—
1154	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1155	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1156	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1157	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1158	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1159	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1160	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1161	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1162	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	16	no	—
1185	C₂²	—	4	16	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	#525×C₁₃₉	1	4	yes	—
1199	C₂²	#552×C₁₃₉	1	4	yes	complemented
1200	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1201	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1202	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1203	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1204	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1205	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
1206	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	2	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	2	no	—
1224	C₄	#546×C₁₃₉	1	4	yes	—
1225	C₂	—	2	4	no	—
1226	C₂	—	2	4	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
1231	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
1232	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
1233	C₂	#3475×C₁₃₉	1	1	yes	characteristic
1234	C₂	#3489×C₁₃₉	1	1	yes	characteristic
1235	C₂	#3505×C₁₃₉	1	1	yes	characteristic
1236	C₂	#3520×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#552×C₁₃₉	C₂	semidirect
3. #2851×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2848×C₁₃₉	C₂	semidirect
6. #2562×C₁₃₉	C₂	semidirect
7. #2536×C₁₃₉	C₂	semidirect
8. #2486×C₁₃₉	C₂	semidirect
9. #2485×C₁₃₉	C₂	semidirect
10. #2480×C₁₃₉	C₂	semidirect
11. #2473×C₁₃₉	C₂	semidirect
12. #2468×C₁₃₉	C₂	semidirect
13. #2460×C₁₃₉	C₂	semidirect
14. #2419×C₁₃₉	C₂	semidirect
15. #2417×C₁₃₉	C₂	semidirect
16. #2415×C₁₃₉	C₂	semidirect
18. #2359×C₁₃₉	C₂	semidirect
19. #2352×C₁₃₉	C₂	semidirect
20. #2342×C₁₃₉	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
22. #2280×C₁₃₉	C₂	semidirect
23. C₂×#380×C₁₃₉	C₂	semidirect
28. C₂×#126×C₁₃₉	C₂²	semidirect
29. C₂×#125×C₁₃₉	C₂²	semidirect
30. C₂×#125×C₁₃₉	C₂²	semidirect
34. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
38. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
48. C₂×#117×C₁₃₉	C₂²	semidirect
49. C₂×#117×C₁₃₉	C₂²	semidirect
50. C₂×#117×C₁₃₉	C₂²	semidirect
52. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
53. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
58. #400×C₁₃₉	C₂²	semidirect
59. #398×C₁₃₉	C₂²	semidirect
60. #398×C₁₃₉	C₂²	semidirect
61. #398×C₁₃₉	C₂²	semidirect
62. #397×C₁₃₉	C₂²	semidirect
63. #397×C₁₃₉	C₂²	semidirect
64. #397×C₁₃₉	C₂²	semidirect
65. #396×C₁₃₉	C₂²	semidirect
70. #391×C₁₃₉	C₂²	semidirect
71. #389×C₁₃₉	C₂²	semidirect
72. #389×C₁₃₉	C₂²	semidirect
73. #389×C₁₃₉	C₂²	semidirect
74. #389×C₁₃₉	C₂²	semidirect
75. #388×C₁₃₉	C₂²	semidirect
76. #388×C₁₃₉	C₂²	semidirect
77. #388×C₁₃₉	C₂²	semidirect
78. #388×C₁₃₉	C₂²	semidirect
79. #388×C₁₃₉	C₂²	semidirect
80. #388×C₁₃₉	C₂²	semidirect
81. #388×C₁₃₉	C₂²	semidirect
82. #387×C₁₃₉	C₂²	semidirect
83. #387×C₁₃₉	C₂²	semidirect
84. #387×C₁₃₉	C₂²	semidirect
85. #387×C₁₃₉	C₂²	semidirect
86. #387×C₁₃₉	C₂²	semidirect
94. #385×C₁₃₉	C₂²	semidirect
95. #385×C₁₃₉	C₂²	semidirect
96. #385×C₁₃₉	C₂²	semidirect
97. #385×C₁₃₉	C₂²	semidirect
98. #382×C₁₃₉	C₂²	semidirect
99. #381×C₁₃₉	C₂²	semidirect
100. #381×C₁₃₉	C₂²	semidirect
105. #380×C₁₃₉	C₂²	semidirect
106. #380×C₁₃₉	C₂²	semidirect
107. #380×C₁₃₉	C₂²	semidirect
108. #380×C₁₃₉	C₂²	semidirect
109. #380×C₁₃₉	C₂²	semidirect
110. #380×C₁₃₉	C₂²	semidirect
111. #380×C₁₃₉	C₂²	semidirect
112. #380×C₁₃₉	C₂²	semidirect
113. #380×C₁₃₉	C₂²	semidirect
114. #380×C₁₃₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
580. C₂²×C₁₃₉	#552	semidirect
618. #36156	C₁₃₉	direct (N × H)
619. C₁₃₉	#36156	direct (N × H)
620. C₂×#552	C₂×C₁₃₉	semidirect
622. #2851	C₂×C₁₃₉	semidirect
623. #2848	C₂×C₁₃₉	semidirect
624. #2848	C₂×C₁₃₉	semidirect
625. #2562	C₂×C₁₃₉	semidirect
626. #2536	C₂×C₁₃₉	semidirect
627. #2486	C₂×C₁₃₉	semidirect
628. #2485	C₂×C₁₃₉	semidirect
629. #2480	C₂×C₁₃₉	semidirect
630. #2473	C₂×C₁₃₉	semidirect
631. #2468	C₂×C₁₃₉	semidirect
632. #2460	C₂×C₁₃₉	semidirect
633. #2419	C₂×C₁₃₉	semidirect
634. #2417	C₂×C₁₃₉	semidirect
635. #2415	C₂×C₁₃₉	semidirect
637. #2359	C₂×C₁₃₉	semidirect
638. #2352	C₂×C₁₃₉	semidirect
639. #2342	C₂×C₁₃₉	semidirect
640. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
641. #2280	C₂×C₁₃₉	semidirect
642. C₂×#380	C₂×C₁₃₉	semidirect
647. C₂×#126	C₂²×C₁₃₉	semidirect
648. C₂×#125	C₂²×C₁₃₉	semidirect
649. C₂×#125	C₂²×C₁₃₉	semidirect
653. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
654. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
655. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
656. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
657. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
667. C₂×#117	C₂²×C₁₃₉	semidirect
668. C₂×#117	C₂²×C₁₃₉	semidirect
669. C₂×#117	C₂²×C₁₃₉	semidirect
671. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
672. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
677. #400	C₂²×C₁₃₉	semidirect
678. #398	C₂²×C₁₃₉	semidirect
679. #398	C₂²×C₁₃₉	semidirect
680. #398	C₂²×C₁₃₉	semidirect
681. #397	C₂²×C₁₃₉	semidirect
682. #397	C₂²×C₁₃₉	semidirect
683. #397	C₂²×C₁₃₉	semidirect
684. #396	C₂²×C₁₃₉	semidirect
689. #391	C₂²×C₁₃₉	semidirect
690. #389	C₂²×C₁₃₉	semidirect
691. #389	C₂²×C₁₃₉	semidirect
692. #389	C₂²×C₁₃₉	semidirect
693. #389	C₂²×C₁₃₉	semidirect
694. #388	C₂²×C₁₃₉	semidirect
695. #388	C₂²×C₁₃₉	semidirect
696. #388	C₂²×C₁₃₉	semidirect
697. #388	C₂²×C₁₃₉	semidirect
698. #388	C₂²×C₁₃₉	semidirect
699. #388	C₂²×C₁₃₉	semidirect
700. #388	C₂²×C₁₃₉	semidirect
701. #387	C₂²×C₁₃₉	semidirect
702. #387	C₂²×C₁₃₉	semidirect
703. #387	C₂²×C₁₃₉	semidirect
704. #387	C₂²×C₁₃₉	semidirect
705. #387	C₂²×C₁₃₉	semidirect
713. #385	C₂²×C₁₃₉	semidirect
714. #385	C₂²×C₁₃₉	semidirect
715. #385	C₂²×C₁₃₉	semidirect
716. #385	C₂²×C₁₃₉	semidirect
717. #382	C₂²×C₁₃₉	semidirect
718. #381	C₂²×C₁₃₉	semidirect
719. #381	C₂²×C₁₃₉	semidirect
724. #380	C₂²×C₁₃₉	semidirect
725. #380	C₂²×C₁₃₉	semidirect
726. #380	C₂²×C₁₃₉	semidirect
727. #380	C₂²×C₁₃₉	semidirect
728. #380	C₂²×C₁₃₉	semidirect
729. #380	C₂²×C₁₃₉	semidirect
730. #380	C₂²×C₁₃₉	semidirect
731. #380	C₂²×C₁₃₉	semidirect
732. #380	C₂²×C₁₃₉	semidirect
733. #380	C₂²×C₁₃₉	semidirect
737. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
738. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
741. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
742. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
743. C₂×#95	C₂²×C₁₃₉	semidirect
1199. C₂²	#552×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2851×C₁₃₉	2
#2848×C₁₃₉	2
#2562×C₁₃₉	2
#2536×C₁₃₉	2
#2486×C₁₃₉	2
#2485×C₁₃₉	2
#2480×C₁₃₉	2
#2473×C₁₃₉	2
#2468×C₁₃₉	2
#2460×C₁₃₉	2
#2419×C₁₃₉	2
#2417×C₁₃₉	2
#2415×C₁₃₉	2
#2405×C₁₃₉	2
#2359×C₁₃₉	2
#2352×C₁₃₉	2
#2342×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#2280×C₁₃₉	2
C₂×#380×C₁₃₉	2
#36156	139

Subgroups — C139×#36156 #48030752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36156 #48030752