Subgroups — C₁₃₉×#13997 #48008593

Order 35584.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#389×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#1445×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1439×C₁₃₉	C₂	1	2	yes	maximal
10	#1437×C₁₃₉	C₂	1	2	yes	maximal
11	C₄⋊#95×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
15	C₂×C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
16	C₂×C₂²⋊Q₈×C₁₃₉	C₄	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#391×C₁₃₉	—	2	4	no	—
30	#391×C₁₃₉	—	2	4	no	—
31	#389×C₁₃₉	—	2	4	no	—
32	#380×C₁₃₉	—	2	4	no	—
33	C₄×C₄⋊C₄×C₁₃₉	—	2	4	no	—
34	C₄×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
35	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
41	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
42	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
43	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
44	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃₉	—	2	2	no	—
46	C₂²×Q₈×C₁₃₉	—	2	2	no	—
47	C₂²×Q₈×C₁₃₉	—	2	2	no	—
48	C₂²×Q₈×C₁₃₉	—	2	2	no	—
49	C₂²×Q₈×C₁₃₉	—	2	2	no	—
50	C₂²×Q₈×C₁₃₉	—	2	2	no	—
51	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
52	C₂³×C₄×C₁₃₉	—	2	2	no	—
53	C₂³×C₄×C₁₃₉	—	2	2	no	—
54	C₂³×C₄×C₁₃₉	—	2	2	no	—
55	C₂³×C₄×C₁₃₉	—	2	2	no	—
56	C₂³×C₄×C₁₃₉	—	2	2	no	—
57	C₂³×C₄×C₁₃₉	—	2	2	no	—
58	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
59	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²⋊Q₈×C₁₃₉	—	2	32	no	—
70	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₁₃₉	—	4	2	no	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	Q₈	1	4	yes	complemented
97	C₂×C₄²×C₁₃₉	—	2	2	no	—
98	C₂×C₄²×C₁₃₉	—	2	2	no	—
99	C₂×C₄²×C₁₃₉	—	2	2	no	—
100	C₂×C₄²×C₁₃₉	—	2	4	no	—
101	C₂×C₄²×C₁₃₉	—	2	2	no	—
102	C₂×C₄²×C₁₃₉	—	2	2	no	—
103	C₂×C₄²×C₁₃₉	—	2	4	no	—
104	C₂×C₄²×C₁₃₉	—	4	2	no	—
105	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
106	#95×C₁₃₉	—	2	2	no	—
107	#95×C₁₃₉	—	2	2	no	—
108	#95×C₁₃₉	—	2	4	no	—
109	#95×C₁₃₉	—	2	4	no	—
110	#95×C₁₃₉	—	2	4	no	—
111	#95×C₁₃₉	—	2	4	no	—
112	#95×C₁₃₉	—	2	4	no	—
113	#95×C₁₃₉	—	2	4	no	—
114	#95×C₁₃₉	—	2	4	no	—
115	C₂⁴×C₁₃₉	—	2	1	no	—
116	C₂⁴×C₁₃₉	—	2	1	no	—
117	C₂⁴×C₁₃₉	—	2	1	no	—
118	C₂⁴×C₁₃₉	—	2	1	no	—
119	C₂⁴×C₁₃₉	—	2	1	no	—
120	C₂⁴×C₁₃₉	—	2	1	no	—
121	C₂⁴×C₁₃₉	—	2	1	no	—
122	C₂⁴×C₁₃₉	—	2	1	no	—
123	C₂⁴×C₁₃₉	—	2	1	no	—
124	C₂⁴×C₁₃₉	—	2	1	no	—
125	C₂⁴×C₁₃₉	—	2	1	no	—
126	C₂⁴×C₁₃₉	—	2	1	no	—
127	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
128	C₂⁴×C₁₃₉	C₂×Q₈	1	2	yes	—
129	C₂⁴×C₁₃₉	#41	1	2	yes	—
130	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
131	C₂×Q₈×C₁₃₉	—	2	8	no	—
132	C₂×Q₈×C₁₃₉	—	2	8	no	—
133	C₂×Q₈×C₁₃₉	—	2	8	no	—
134	C₂×Q₈×C₁₃₉	—	4	4	no	—
135	C₂×Q₈×C₁₃₉	—	4	4	no	—
136	C₂×Q₈×C₁₃₉	—	4	4	no	—
137	C₂×Q₈×C₁₃₉	—	4	4	no	—
138	C₂²×C₄×C₁₃₉	—	2	1	no	—
139	C₂²×C₄×C₁₃₉	—	2	2	no	—
140	C₂²×C₄×C₁₃₉	—	2	1	no	—
141	C₂²×C₄×C₁₃₉	—	2	2	no	—
142	C₂²×C₄×C₁₃₉	—	2	1	no	—
143	C₂²×C₄×C₁₃₉	—	2	2	no	—
144	C₂²×C₄×C₁₃₉	—	2	2	no	—
145	C₂²×C₄×C₁₃₉	—	2	1	no	—
146	C₂²×C₄×C₁₃₉	—	2	1	no	—
147	C₂²×C₄×C₁₃₉	—	2	1	no	—
148	C₂²×C₄×C₁₃₉	—	2	1	no	—
149	C₂²×C₄×C₁₃₉	—	2	1	no	—
150	C₂²×C₄×C₁₃₉	—	2	1	no	—
151	C₂²×C₄×C₁₃₉	—	2	1	no	—
152	C₂²×C₄×C₁₃₉	—	2	2	no	—
153	C₂²×C₄×C₁₃₉	—	2	2	no	—
154	C₂²×C₄×C₁₃₉	—	2	1	no	—
155	C₂²×C₄×C₁₃₉	—	2	1	no	—
156	C₂²×C₄×C₁₃₉	—	2	2	no	—
157	C₂²×C₄×C₁₃₉	—	2	1	no	—
158	C₂²×C₄×C₁₃₉	—	2	2	no	—
159	C₂²×C₄×C₁₃₉	—	2	2	no	—
160	C₂²×C₄×C₁₃₉	—	2	1	no	—
161	C₂²×C₄×C₁₃₉	—	2	1	no	—
162	C₂²×C₄×C₁₃₉	—	2	1	no	—
163	C₂²×C₄×C₁₃₉	—	2	2	no	—
164	C₂²×C₄×C₁₃₉	—	2	1	no	—
165	C₂²×C₄×C₁₃₉	—	2	1	no	—
166	C₂²×C₄×C₁₃₉	—	2	1	no	—
167	C₂²×C₄×C₁₃₉	—	2	1	no	—
168	C₂²×C₄×C₁₃₉	—	2	2	no	—
169	C₂²×C₄×C₁₃₉	—	2	2	no	—
170	C₂²×C₄×C₁₃₉	—	2	1	no	—
171	C₂²×C₄×C₁₃₉	—	2	1	no	—
172	C₂²×C₄×C₁₃₉	—	2	2	no	—
173	C₂²×C₄×C₁₃₉	—	2	2	no	—
174	C₂²×C₄×C₁₃₉	—	2	2	no	—
175	C₂²×C₄×C₁₃₉	—	2	1	no	—
176	C₂²×C₄×C₁₃₉	—	2	1	no	—
177	C₂²×C₄×C₁₃₉	—	2	1	no	—
178	C₂²×C₄×C₁₃₉	—	2	2	no	—
179	C₂²×C₄×C₁₃₉	—	2	1	no	—
180	C₂²×C₄×C₁₃₉	—	2	1	no	—
181	C₂²×C₄×C₁₃₉	—	2	1	no	—
182	C₂²×C₄×C₁₃₉	—	2	8	no	—
183	C₂²×C₄×C₁₃₉	—	2	8	no	—
184	C₂²×C₄×C₁₃₉	—	2	8	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	2	no	—
191	C₂²×C₄×C₁₃₉	—	2	2	no	—
192	C₂²×C₄×C₁₃₉	—	4	4	no	—
193	C₂²×C₄×C₁₃₉	—	4	4	no	—
194	C₂²×C₄×C₁₃₉	—	4	4	no	—
195	C₂²×C₄×C₁₃₉	—	4	4	no	—
196	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
211	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
212	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
213	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
214	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
215	C₄⋊C₄×C₁₃₉	—	2	16	no	—
216	C₄⋊C₄×C₁₃₉	—	2	8	no	—
217	C₄⋊C₄×C₁₃₉	—	4	8	no	—
218	C₄⋊C₄×C₁₃₉	—	4	4	no	—
219	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	16	yes	complemented
220	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
221	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
222	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
223	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
224	C₄²×C₁₃₉	—	2	8	no	—
225	C₄²×C₁₃₉	—	4	8	no	—
226	C₄²×C₁₃₉	—	4	4	no	—
227	C₂³×C₁₃₉	—	2	2	no	—
228	C₂³×C₁₃₉	—	2	2	no	—
229	C₂³×C₁₃₉	—	2	2	no	—
230	C₂³×C₁₃₉	—	2	2	no	—
231	C₂³×C₁₃₉	—	2	2	no	—
232	C₂³×C₁₃₉	—	2	2	no	—
233	C₂³×C₁₃₉	—	2	2	no	—
234	C₂³×C₁₃₉	—	2	2	no	—
235	C₂³×C₁₃₉	—	2	2	no	—
236	C₂³×C₁₃₉	—	2	2	no	—
237	C₂³×C₁₃₉	—	2	2	no	—
238	C₂³×C₁₃₉	—	2	2	no	—
239	C₂³×C₁₃₉	—	2	2	no	—
240	C₂³×C₁₃₉	—	2	2	no	—
241	C₂³×C₁₃₉	—	2	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	2	no	—
244	C₂³×C₁₃₉	—	2	2	no	—
245	C₂³×C₁₃₉	—	4	1	no	—
246	C₂³×C₁₃₉	—	4	1	no	—
247	C₂³×C₁₃₉	—	4	1	no	—
248	C₂³×C₁₃₉	—	4	1	no	—
249	C₂³×C₁₃₉	—	4	1	no	—
250	C₂³×C₁₃₉	—	4	1	no	—
251	C₂³×C₁₃₉	—	4	1	no	—
252	C₂³×C₁₃₉	—	4	1	no	—
253	C₂³×C₁₃₉	—	4	1	no	—
254	C₂³×C₁₃₉	—	4	1	no	—
255	C₂³×C₁₃₉	—	4	1	no	—
256	C₂³×C₁₃₉	—	4	1	no	—
257	C₂³×C₁₃₉	—	4	1	no	—
258	C₂³×C₁₃₉	—	4	1	no	—
259	C₂³×C₁₃₉	—	4	1	no	—
260	C₂³×C₁₃₉	—	4	1	no	—
261	C₂³×C₁₃₉	C₄×Q₈	1	4	yes	—
262	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
263	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
264	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
265	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
266	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
267	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
268	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
269	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
270	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
271	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
272	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
273	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
275	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
276	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
277	Q₈×C₁₃₉	—	4	16	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	4	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	4	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	4	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	4	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	4	1	no	—
309	C₂×C₄×C₁₃₉	—	4	1	no	—
310	C₂×C₄×C₁₃₉	—	4	2	no	—
311	C₂×C₄×C₁₃₉	—	4	2	no	—
312	C₂×C₄×C₁₃₉	—	4	1	no	—
313	C₂×C₄×C₁₃₉	—	4	2	no	—
314	C₂×C₄×C₁₃₉	—	4	2	no	—
315	C₂×C₄×C₁₃₉	—	4	1	no	—
316	C₂×C₄×C₁₃₉	—	4	1	no	—
317	C₂×C₄×C₁₃₉	—	4	1	no	—
318	C₂×C₄×C₁₃₉	—	4	2	no	—
319	C₂×C₄×C₁₃₉	—	4	1	no	—
320	C₂×C₄×C₁₃₉	—	4	1	no	—
321	C₂×C₄×C₁₃₉	—	4	2	no	—
322	C₂×C₄×C₁₃₉	—	4	2	no	—
323	C₂×C₄×C₁₃₉	—	4	1	no	—
324	C₂×C₄×C₁₃₉	—	4	1	no	—
325	C₂×C₄×C₁₃₉	—	4	1	no	—
326	C₂×C₄×C₁₃₉	—	4	1	no	—
327	C₂×C₄×C₁₃₉	—	4	1	no	—
328	C₂×C₄×C₁₃₉	—	4	2	no	—
329	C₂×C₄×C₁₃₉	—	4	1	no	—
330	C₂×C₄×C₁₃₉	—	4	1	no	—
331	C₂×C₄×C₁₃₉	—	4	1	no	—
332	C₂×C₄×C₁₃₉	—	4	16	no	—
333	C₂×C₄×C₁₃₉	—	4	2	no	—
334	C₂×C₄×C₁₃₉	—	4	2	no	—
335	C₂×C₄×C₁₃₉	—	4	2	no	—
336	C₂×C₄×C₁₃₉	—	4	2	no	—
337	C₂×C₄×C₁₃₉	—	4	2	no	—
338	C₂×C₄×C₁₃₉	—	4	2	no	—
339	C₂×C₄×C₁₃₉	—	4	2	no	—
340	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	—
341	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
342	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
343	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
344	C₂×C₄×C₁₃₉	#121	1	4	yes	—
345	C₂×C₄×C₁₃₉	#121	1	4	yes	—
346	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	complemented
347	C₂×C₄×C₁₃₉	#124	1	4	yes	—
348	C₂×C₄×C₁₃₉	#127	1	4	yes	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
366	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂²×C₁₃₉	C₂×C₄×Q₈	1	1	yes	characteristic
368	C₂²×C₁₃₉	C₄×#41	1	1	yes	characteristic
369	C₂²×C₁₃₉	#519	1	1	yes	characteristic
370	C₂²×C₁₃₉	#520	1	1	yes	characteristic
371	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
372	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
373	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
374	C₂²×C₁₃₉	#525	1	1	yes	characteristic
375	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
376	C₂²×C₁₃₉	#529	1	1	yes	characteristic
377	C₂²×C₁₃₉	C₂×#127	1	1	yes	characteristic
378	C₂²×C₁₃₉	#533	1	1	yes	characteristic
379	C₂²×C₁₃₉	#536	1	1	yes	characteristic
380	C₂²×C₁₃₉	#537	1	1	yes	characteristic
381	C₂²×C₁₃₉	#541	1	1	yes	characteristic
382	C₂²×C₁₃₉	#542	1	1	yes	characteristic
383	C₂²×C₁₃₉	#546	1	1	yes	characteristic
384	C₂²×C₁₃₉	#546	1	1	yes	characteristic
385	C₂²×C₁₃₉	#546	1	1	yes	characteristic
386	C₂²×C₁₃₉	#547	1	1	yes	characteristic
387	C₂²×C₁₃₉	#547	1	1	yes	characteristic
388	C₂²×C₁₃₉	#547	1	1	yes	characteristic
389	C₂²×C₁₃₉	#548	1	1	yes	characteristic
390	C₂²×C₁₃₉	#548	1	1	yes	characteristic
391	C₂²×C₁₃₉	#548	1	1	yes	characteristic
392	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
393	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
394	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
395	C₂²×C₁₃₉	#552	1	1	yes	characteristic
396	C₂²×C₁₃₉	#552	1	1	yes	characteristic
397	C₂²×C₁₃₉	#554	1	1	yes	characteristic
398	C₂²×C₁₃₉	#556	1	1	yes	characteristic
399	C₄×C₁₃₉	—	2	8	no	—
400	C₄×C₁₃₉	—	2	4	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	4	no	—
403	C₄×C₁₃₉	—	4	2	no	—
404	C₄×C₁₃₉	—	4	2	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	4	no	—
407	C₄×C₁₃₉	—	8	2	no	—
408	C₄×C₁₃₉	#390	1	8	yes	—
409	C₂×C₁₃₉	—	4	4	no	—
410	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
411	C₂×C₁₃₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
412	C₂×C₁₃₉	#2323	1	1	yes	characteristic
413	C₂×C₁₃₉	#2339	1	1	yes	characteristic
414	C₂×C₁₃₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
415	C₂×C₁₃₉	#2360	1	1	yes	characteristic
416	C₂×C₁₃₉	#2362	1	1	yes	characteristic
417	C₂×C₁₃₉	#2415	1	1	yes	characteristic
418	C₂×C₁₃₉	#2417	1	1	yes	characteristic
419	C₂×C₁₃₉	#2427	1	1	yes	characteristic
420	C₂×C₁₃₉	#2429	1	1	yes	characteristic
421	C₂×C₁₃₉	#2489	1	1	yes	characteristic
422	C₂×C₁₃₉	#2492	1	1	yes	characteristic
423	C₂×C₁₃₉	#2540	1	1	yes	characteristic
424	C₂×C₁₃₉	#2542	1	1	yes	characteristic
425	#13997	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
426	C₁₃₉	#13997	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
428	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
430	C₂×#389	C₂×C₁₃₉	1	1	yes	characteristic, complemented
431	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
434	#1445	C₂×C₁₃₉	1	2	yes	complemented
435	#1439	C₂×C₁₃₉	1	2	yes	—
436	#1437	C₂×C₁₃₉	1	2	yes	—
437	C₄⋊#95	C₂×C₁₃₉	1	2	yes	complemented
438	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₂²⋊Q₈	—	2	4	no	—
441	C₂×C₂²⋊Q₈	—	2	4	no	—
442	C₂×C₂²⋊Q₈	C₄×C₁₃₉	1	8	yes	complemented
443	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
445	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
446	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
450	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
451	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
453	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
454	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
455	#391	—	2	4	no	—
456	#391	—	2	4	no	—
457	#389	—	2	4	no	—
458	#380	—	2	4	no	—
459	C₄×C₄⋊C₄	—	2	4	no	—
460	C₄×C₂²⋊C₄	—	2	4	no	—
461	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
463	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
464	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
466	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
467	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
469	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
471	C₂²×Q₈	—	2	2	no	—
472	C₂²×Q₈	—	2	2	no	—
473	C₂²×Q₈	—	2	2	no	—
474	C₂²×Q₈	—	2	2	no	—
475	C₂²×Q₈	—	2	2	no	—
476	C₂²×Q₈	—	2	2	no	—
477	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
478	C₂³×C₄	—	2	2	no	—
479	C₂³×C₄	—	2	2	no	—
480	C₂³×C₄	—	2	2	no	—
481	C₂³×C₄	—	2	2	no	—
482	C₂³×C₄	—	2	2	no	—
483	C₂³×C₄	—	2	2	no	—
484	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
485	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂²⋊Q₈	—	2	32	no	—
496	C₂×C₄⋊C₄	—	2	4	no	—
497	C₂×C₄⋊C₄	—	2	4	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	—	2	2	no	—
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	4	no	—
502	C₂×C₄⋊C₄	—	2	2	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	4	no	—
505	C₂×C₄⋊C₄	—	4	2	no	—
506	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
507	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
508	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
509	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
510	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
511	C₂×C₂²⋊C₄	—	2	2	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	—	2	2	no	—
515	C₂×C₂²⋊C₄	—	2	2	no	—
516	C₂×C₂²⋊C₄	—	2	2	no	—
517	C₂×C₂²⋊C₄	—	2	2	no	—
518	C₂×C₂²⋊C₄	—	2	4	no	—
519	C₂×C₂²⋊C₄	—	2	4	no	—
520	C₂×C₂²⋊C₄	—	4	2	no	—
521	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
522	C₂×C₂²⋊C₄	Q₈×C₁₃₉	1	4	yes	complemented
523	C₂×C₄²	—	2	2	no	—
524	C₂×C₄²	—	2	2	no	—
525	C₂×C₄²	—	2	2	no	—
526	C₂×C₄²	—	2	4	no	—
527	C₂×C₄²	—	2	2	no	—
528	C₂×C₄²	—	2	2	no	—
529	C₂×C₄²	—	2	4	no	—
530	C₂×C₄²	—	4	2	no	—
531	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
532	#95	—	2	2	no	—
533	#95	—	2	2	no	—
534	#95	—	2	4	no	—
535	#95	—	2	4	no	—
536	#95	—	2	4	no	—
537	#95	—	2	4	no	—
538	#95	—	2	4	no	—
539	#95	—	2	4	no	—
540	#95	—	2	4	no	—
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂⁴	—	2	1	no	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	1	no	—
546	C₂⁴	—	2	1	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	2	1	no	—
550	C₂⁴	—	2	1	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	2	1	no	—
553	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
554	C₂⁴	C₂×Q₈×C₁₃₉	1	2	yes	—
555	C₂⁴	#41×C₁₃₉	1	2	yes	—
556	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
557	C₂×Q₈	—	2	8	no	—
558	C₂×Q₈	—	2	8	no	—
559	C₂×Q₈	—	2	8	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	4	no	—
562	C₂×Q₈	—	4	4	no	—
563	C₂×Q₈	—	4	4	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	8	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	8	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
623	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
624	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
625	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
628	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
637	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
638	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
639	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
640	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
641	C₄⋊C₄	—	2	16	no	—
642	C₄⋊C₄	—	2	8	no	—
643	C₄⋊C₄	—	4	8	no	—
644	C₄⋊C₄	—	4	4	no	—
645	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	16	yes	complemented
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	16	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	4	8	no	—
650	C₄²	—	2	8	no	—
651	C₄²	—	4	8	no	—
652	C₄²	—	4	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	C₄×Q₈×C₁₃₉	1	4	yes	—
688	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
689	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
690	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
691	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
692	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
693	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
694	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
695	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
696	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
697	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
698	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
699	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
700	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
701	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
702	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
703	Q₈	—	4	16	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	16	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	—
767	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
768	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
769	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
770	C₂×C₄	#121×C₁₃₉	1	4	yes	—
771	C₂×C₄	#121×C₁₃₉	1	4	yes	—
772	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	complemented
773	C₂×C₄	#124×C₁₃₉	1	4	yes	—
774	C₂×C₄	#127×C₁₃₉	1	4	yes	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
791	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
792	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
793	C₂²	C₂×C₄×Q₈×C₁₃₉	1	1	yes	characteristic
794	C₂²	C₄×#41×C₁₃₉	1	1	yes	characteristic
795	C₂²	#519×C₁₃₉	1	1	yes	characteristic
796	C₂²	#520×C₁₃₉	1	1	yes	characteristic
797	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
798	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
799	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
800	C₂²	#525×C₁₃₉	1	1	yes	characteristic
801	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
802	C₂²	#529×C₁₃₉	1	1	yes	characteristic
803	C₂²	C₂×#127×C₁₃₉	1	1	yes	characteristic
804	C₂²	#533×C₁₃₉	1	1	yes	characteristic
805	C₂²	#536×C₁₃₉	1	1	yes	characteristic
806	C₂²	#537×C₁₃₉	1	1	yes	characteristic
807	C₂²	#541×C₁₃₉	1	1	yes	characteristic
808	C₂²	#542×C₁₃₉	1	1	yes	characteristic
809	C₂²	#546×C₁₃₉	1	1	yes	characteristic
810	C₂²	#546×C₁₃₉	1	1	yes	characteristic
811	C₂²	#546×C₁₃₉	1	1	yes	characteristic
812	C₂²	#547×C₁₃₉	1	1	yes	characteristic
813	C₂²	#547×C₁₃₉	1	1	yes	characteristic
814	C₂²	#547×C₁₃₉	1	1	yes	characteristic
815	C₂²	#548×C₁₃₉	1	1	yes	characteristic
816	C₂²	#548×C₁₃₉	1	1	yes	characteristic
817	C₂²	#548×C₁₃₉	1	1	yes	characteristic
818	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
819	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
820	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
821	C₂²	#552×C₁₃₉	1	1	yes	characteristic
822	C₂²	#552×C₁₃₉	1	1	yes	characteristic
823	C₂²	#554×C₁₃₉	1	1	yes	characteristic
824	C₂²	#556×C₁₃₉	1	1	yes	characteristic
825	C₄	—	2	8	no	—
826	C₄	—	2	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	4	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	4	no	—
833	C₄	—	8	2	no	—
834	C₄	#390×C₁₃₉	1	8	yes	—
835	C₂	—	4	4	no	—
836	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
837	C₂	C₄×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
838	C₂	#2323×C₁₃₉	1	1	yes	characteristic
839	C₂	#2339×C₁₃₉	1	1	yes	characteristic
840	C₂	Q₈×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
841	C₂	#2360×C₁₃₉	1	1	yes	characteristic
842	C₂	#2362×C₁₃₉	1	1	yes	characteristic
843	C₂	#2415×C₁₃₉	1	1	yes	characteristic
844	C₂	#2417×C₁₃₉	1	1	yes	characteristic
845	C₂	#2427×C₁₃₉	1	1	yes	characteristic
846	C₂	#2429×C₁₃₉	1	1	yes	characteristic
847	C₂	#2489×C₁₃₉	1	1	yes	characteristic
848	C₂	#2492×C₁₃₉	1	1	yes	characteristic
849	C₂	#2540×C₁₃₉	1	1	yes	characteristic
850	C₂	#2542×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#391×C₁₃₉	C₂	semidirect
3. C₂×#391×C₁₃₉	C₂	semidirect
4. C₂×#389×C₁₃₉	C₂	semidirect
6. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
8. #1445×C₁₃₉	C₂	semidirect
11. C₄⋊#95×C₁₃₉	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₁₃₉	C₄	semidirect
96. C₂×C₂²⋊C₄×C₁₃₉	Q₈	semidirect
219. C₄⋊C₄×C₁₃₉	C₂²⋊C₄	semidirect
346. C₂×C₄×C₁₃₉	C₂²⋊Q₈	semidirect
425. #13997	C₁₃₉	direct (N × H)
426. C₁₃₉	#13997	direct (N × H)
428. C₂×#391	C₂×C₁₃₉	semidirect
429. C₂×#391	C₂×C₁₃₉	semidirect
430. C₂×#389	C₂×C₁₃₉	semidirect
432. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
434. #1445	C₂×C₁₃₉	semidirect
437. C₄⋊#95	C₂×C₁₃₉	semidirect
442. C₂×C₂²⋊Q₈	C₄×C₁₃₉	semidirect
522. C₂×C₂²⋊C₄	Q₈×C₁₃₉	semidirect
645. C₄⋊C₄	C₂²⋊C₄×C₁₃₉	semidirect
772. C₂×C₄	C₂²⋊Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₂×#389×C₁₃₉	2
C₂×#380×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
#1445×C₁₃₉	2
#1439×C₁₃₉	2
#1437×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#13997	139

Subgroups — C139×#13997 #48008593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#13997 #48008593