Subgroups — C₁₃₉×#36528 #48031124

Order 35584.

2966 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2848×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2534×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2463×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2460×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2452×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2345×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#120×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
20	#554×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	#397×C₁₃₉	C₂²	1	4	yes	complemented
45	#396×C₁₃₉	C₂²	1	4	yes	complemented
46	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#393×C₁₃₉	C₂²	1	4	yes	complemented
50	#392×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	2	yes	complemented
56	#388×C₁₃₉	C₂²	1	4	yes	complemented
57	#388×C₁₃₉	C₂²	1	2	yes	complemented
58	#388×C₁₃₉	C₂²	1	4	yes	complemented
59	#388×C₁₃₉	C₂²	1	4	yes	complemented
60	#387×C₁₃₉	C₂²	1	2	yes	complemented
61	#387×C₁₃₉	C₂²	1	4	yes	complemented
62	#387×C₁₃₉	C₂²	1	4	yes	complemented
63	#386×C₁₃₉	C₂²	1	1	yes	characteristic
64	#386×C₁₃₉	C₂²	1	4	yes	complemented
65	#386×C₁₃₉	C₂²	1	4	yes	complemented
66	#385×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	1	yes	characteristic
68	#385×C₁₃₉	C₂²	1	4	yes	complemented
69	#385×C₁₃₉	C₂²	1	4	yes	complemented
70	#385×C₁₃₉	C₂²	1	4	yes	complemented
71	#381×C₁₃₉	C₂²	1	2	yes	—
72	#381×C₁₃₉	C₂²	1	1	yes	characteristic
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	1	yes	characteristic
75	#380×C₁₃₉	C₂²	1	4	yes	complemented
76	#379×C₁₃₉	C₂²	1	2	yes	—
77	#379×C₁₃₉	C₂²	1	2	yes	—
78	#379×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	—	2	8	no	—
89	C₂²×D₄×C₁₃₉	—	2	4	no	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	—	2	8	no	—
95	C₂³×C₄×C₁₃₉	—	4	8	no	—
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
105	#125×C₁₃₉	—	2	8	no	—
106	#124×C₁₃₉	—	2	8	no	—
107	#123×C₁₃₉	—	2	4	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
111	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
112	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
113	#121×C₁₃₉	—	2	8	no	—
114	#120×C₁₃₉	—	2	8	no	—
115	C₄×Q₈×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	4	no	—
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	—	2	16	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	4	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃₉	—	2	4	no	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	C₂⁴×C₁₃₉	—	2	4	no	—
177	C₂⁴×C₁₃₉	—	2	8	no	—
178	C₂⁴×C₁₃₉	—	2	4	no	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	—	4	4	no	—
181	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
182	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₂×Q₈×C₁₃₉	—	2	2	no	—
185	C₂×Q₈×C₁₃₉	—	2	4	no	—
186	C₂×Q₈×C₁₃₉	—	2	4	no	—
187	C₂×Q₈×C₁₃₉	—	4	4	no	—
188	C₂×D₄×C₁₃₉	—	2	32	no	—
189	C₂×D₄×C₁₃₉	—	2	2	no	—
190	C₂×D₄×C₁₃₉	—	2	8	no	—
191	C₂×D₄×C₁₃₉	—	2	2	no	—
192	C₂×D₄×C₁₃₉	—	2	8	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	4	4	no	—
198	C₂×D₄×C₁₃₉	#41	1	4	yes	—
199	C₂×D₄×C₁₃₉	#41	1	8	yes	—
200	C₂²×C₄×C₁₃₉	—	2	2	no	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	2	4	no	—
203	C₂²×C₄×C₁₃₉	—	2	2	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	8	no	—
208	C₂²×C₄×C₁₃₉	—	2	8	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	8	no	—
211	C₂²×C₄×C₁₃₉	—	2	8	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	4	4	no	—
214	C₂²×C₄×C₁₃₉	—	4	4	no	—
215	C₂²×C₄×C₁₃₉	—	4	4	no	—
216	C₂²×C₄×C₁₃₉	—	4	4	no	—
217	C₂²×C₄×C₁₃₉	—	4	32	no	—
218	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	8	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	4	4	no	—
246	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
248	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₄²×C₁₃₉	—	2	4	no	—
268	C₄²×C₁₃₉	—	2	4	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	2	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	4	4	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	16	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	4	no	—
278	C₂³×C₁₃₉	—	2	4	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	4	no	—
283	C₂³×C₁₃₉	—	2	4	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	4	16	no	—
287	C₂³×C₁₃₉	—	4	16	no	—
288	C₂³×C₁₃₉	—	4	8	no	—
289	C₂³×C₁₃₉	—	4	8	no	—
290	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
291	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
292	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
293	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
294	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
295	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
296	Q₈×C₁₃₉	—	4	4	no	—
297	Q₈×C₁₃₉	—	8	4	no	—
298	D₄×C₁₃₉	—	2	16	no	—
299	D₄×C₁₃₉	—	2	8	no	—
300	D₄×C₁₃₉	—	2	16	no	—
301	D₄×C₁₃₉	—	4	16	no	—
302	C₂×C₄×C₁₃₉	—	2	8	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	8	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	4	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	4	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	4	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	4	8	no	—
332	C₂×C₄×C₁₃₉	—	4	16	no	—
333	C₂×C₄×C₁₃₉	—	4	16	no	—
334	C₂×C₄×C₁₃₉	—	4	4	no	—
335	C₂×C₄×C₁₃₉	—	4	4	no	—
336	C₂×C₄×C₁₃₉	—	8	4	no	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
342	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
343	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
344	C₂²×C₁₃₉	—	2	2	no	—
345	C₂²×C₁₃₉	—	2	4	no	—
346	C₂²×C₁₃₉	—	2	2	no	—
347	C₂²×C₁₃₉	—	2	4	no	—
348	C₂²×C₁₃₉	—	2	8	no	—
349	C₂²×C₁₃₉	—	2	2	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	8	no	—
352	C₂²×C₁₃₉	—	2	8	no	—
353	C₂²×C₁₃₉	—	4	32	no	—
354	C₂²×C₁₃₉	—	4	1	no	—
355	C₂²×C₁₃₉	—	4	4	no	—
356	C₂²×C₁₃₉	—	4	4	no	—
357	C₂²×C₁₃₉	—	4	4	no	—
358	C₂²×C₁₃₉	—	4	1	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	—	4	4	no	—
361	C₂²×C₁₃₉	#548	1	4	yes	—
362	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
364	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
366	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₄×C₁₃₉	—	2	2	no	—
368	C₄×C₁₃₉	—	2	2	no	—
369	C₄×C₁₃₉	—	2	4	no	—
370	C₄×C₁₃₉	—	2	4	no	—
371	C₄×C₁₃₉	—	2	4	no	—
372	C₄×C₁₃₉	—	4	1	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	4	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	1	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	#525	1	4	yes	—
381	C₂×C₁₃₉	—	2	4	no	—
382	C₂×C₁₃₉	—	4	2	no	—
383	C₂×C₁₃₉	—	4	8	no	—
384	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
385	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
386	C₂×C₁₃₉	#3481	1	2	yes	—
387	C₂×C₁₃₉	#3484	1	1	yes	characteristic
388	C₂×C₁₃₉	#3520	1	2	yes	—
389	#36528	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₁₃₉	#36528	1	1	yes	characteristic, direct product factor, Sylow
391	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2848	C₂×C₁₃₉	1	2	yes	complemented
395	#2561	C₂×C₁₃₉	1	2	yes	complemented
396	#2534	C₂×C₁₃₉	1	2	yes	complemented
397	#2463	C₂×C₁₃₉	1	4	yes	complemented
398	#2460	C₂×C₁₃₉	1	4	yes	complemented
399	#2452	C₂×C₁₃₉	1	2	yes	complemented
400	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
401	#2427	C₂×C₁₃₉	1	2	yes	complemented
402	#2408	C₂×C₁₃₉	1	1	yes	characteristic
403	#2367	C₂×C₁₃₉	1	2	yes	complemented
404	#2361	C₂×C₁₃₉	1	2	yes	complemented
405	#2345	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	C₄×#120	C₂×C₁₃₉	1	2	yes	complemented
408	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
409	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
410	#554	—	2	8	no	—
411	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
412	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
413	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
414	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
418	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
419	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
420	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
421	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
422	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
423	C₂×C₄×D₄	—	2	8	no	—
424	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
427	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
430	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
433	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
434	#397	C₂²×C₁₃₉	1	4	yes	complemented
435	#396	C₂²×C₁₃₉	1	4	yes	complemented
436	#394	C₂²×C₁₃₉	1	2	yes	—
437	#394	C₂²×C₁₃₉	1	4	yes	—
438	#394	C₂²×C₁₃₉	1	4	yes	complemented
439	#393	C₂²×C₁₃₉	1	4	yes	complemented
440	#392	C₂²×C₁₃₉	1	2	yes	—
441	#391	C₂²×C₁₃₉	1	2	yes	complemented
442	#390	C₂²×C₁₃₉	1	2	yes	—
443	#390	C₂²×C₁₃₉	1	2	yes	—
444	#389	C₂²×C₁₃₉	1	2	yes	complemented
445	#389	C₂²×C₁₃₉	1	2	yes	complemented
446	#388	C₂²×C₁₃₉	1	4	yes	complemented
447	#388	C₂²×C₁₃₉	1	4	yes	complemented
448	#388	C₂²×C₁₃₉	1	4	yes	complemented
449	#388	C₂²×C₁₃₉	1	2	yes	complemented
450	#387	C₂²×C₁₃₉	1	4	yes	complemented
451	#387	C₂²×C₁₃₉	1	4	yes	complemented
452	#387	C₂²×C₁₃₉	1	2	yes	complemented
453	#386	C₂²×C₁₃₉	1	1	yes	characteristic
454	#386	C₂²×C₁₃₉	1	4	yes	complemented
455	#386	C₂²×C₁₃₉	1	4	yes	complemented
456	#385	C₂²×C₁₃₉	1	1	yes	characteristic
457	#385	C₂²×C₁₃₉	1	2	yes	—
458	#385	C₂²×C₁₃₉	1	4	yes	complemented
459	#385	C₂²×C₁₃₉	1	4	yes	complemented
460	#385	C₂²×C₁₃₉	1	4	yes	complemented
461	#381	C₂²×C₁₃₉	1	1	yes	characteristic
462	#381	C₂²×C₁₃₉	1	2	yes	—
463	#380	C₂²×C₁₃₉	1	2	yes	—
464	#380	C₂²×C₁₃₉	1	1	yes	characteristic
465	#380	C₂²×C₁₃₉	1	4	yes	complemented
466	#379	C₂²×C₁₃₉	1	2	yes	—
467	#379	C₂²×C₁₃₉	1	2	yes	—
468	#379	C₂²×C₁₃₉	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
470	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
471	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
473	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
474	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
475	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
476	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
478	C₂²×D₄	—	2	8	no	—
479	C₂²×D₄	—	2	4	no	—
480	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂³×C₄	—	2	8	no	—
485	C₂³×C₄	—	4	8	no	—
486	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₄⋊Q₈	—	2	4	no	—
495	#125	—	2	8	no	—
496	#124	—	2	8	no	—
497	#123	—	2	4	no	—
498	C₂²⋊Q₈	—	2	8	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	8	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	4	8	no	—
503	#121	—	2	8	no	—
504	#120	—	2	8	no	—
505	C₄×Q₈	—	2	4	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	16	no	—
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	4	8	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	8	no	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂×C₄²	—	2	4	no	—
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
555	#95	C₂³×C₁₃₉	1	4	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	2	yes	—
559	#95	C₂³×C₁₃₉	1	4	yes	—
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	2	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	2	8	no	—
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	2	4	no	—
570	C₂⁴	—	4	4	no	—
571	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
572	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
573	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	4	4	no	—
578	C₂×D₄	—	2	32	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	#41×C₁₃₉	1	4	yes	—
589	C₂×D₄	#41×C₁₃₉	1	8	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	8	no	—
598	C₂²×C₄	—	2	8	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	8	no	—
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	32	no	—
608	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
609	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	4	4	no	—
636	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
637	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
638	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	—	4	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	4	4	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	16	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	4	16	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	4	8	no	—
679	C₂³	—	4	8	no	—
680	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
681	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
682	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
683	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
684	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
685	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	8	4	no	—
688	D₄	—	2	16	no	—
689	D₄	—	2	8	no	—
690	D₄	—	2	16	no	—
691	D₄	—	4	16	no	—
692	C₂×C₄	—	2	8	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	16	no	—
723	C₂×C₄	—	4	16	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
732	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
733	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	8	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	4	32	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	4	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	2	no	—
751	C₂²	#548×C₁₃₉	1	4	yes	—
752	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
754	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
755	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
756	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	4	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	2	no	—
770	C₄	#525×C₁₃₉	1	4	yes	—
771	C₂	—	2	4	no	—
772	C₂	—	4	8	no	—
773	C₂	—	4	2	no	—
774	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
775	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
776	C₂	#3481×C₁₃₉	1	2	yes	—
777	C₂	#3484×C₁₃₉	1	1	yes	characteristic
778	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2408×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₁₃₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2561×C₁₃₉	C₂	semidirect
6. #2534×C₁₃₉	C₂	semidirect
7. #2463×C₁₃₉	C₂	semidirect
8. #2460×C₁₃₉	C₂	semidirect
9. #2452×C₁₃₉	C₂	semidirect
10. #2435×C₁₃₉	C₂	semidirect
11. #2427×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2361×C₁₃₉	C₂	semidirect
15. #2345×C₁₃₉	C₂	semidirect
16. C₄×#123×C₁₃₉	C₂	semidirect
17. C₄×#120×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×#125×C₁₃₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
41. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
44. #397×C₁₃₉	C₂²	semidirect
45. #396×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
49. #393×C₁₃₉	C₂²	semidirect
51. #391×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
56. #388×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #388×C₁₃₉	C₂²	semidirect
59. #388×C₁₃₉	C₂²	semidirect
60. #387×C₁₃₉	C₂²	semidirect
61. #387×C₁₃₉	C₂²	semidirect
62. #387×C₁₃₉	C₂²	semidirect
64. #386×C₁₃₉	C₂²	semidirect
65. #386×C₁₃₉	C₂²	semidirect
68. #385×C₁₃₉	C₂²	semidirect
69. #385×C₁₃₉	C₂²	semidirect
70. #385×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
123. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
389. #36528	C₁₃₉	direct (N × H)
390. C₁₃₉	#36528	direct (N × H)
391. C₂×#554	C₂×C₁₃₉	semidirect
392. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
393. #2855	C₂×C₁₃₉	semidirect
394. #2848	C₂×C₁₃₉	semidirect
395. #2561	C₂×C₁₃₉	semidirect
396. #2534	C₂×C₁₃₉	semidirect
397. #2463	C₂×C₁₃₉	semidirect
398. #2460	C₂×C₁₃₉	semidirect
399. #2452	C₂×C₁₃₉	semidirect
400. #2435	C₂×C₁₃₉	semidirect
401. #2427	C₂×C₁₃₉	semidirect
403. #2367	C₂×C₁₃₉	semidirect
404. #2361	C₂×C₁₃₉	semidirect
405. #2345	C₂×C₁₃₉	semidirect
406. C₄×#123	C₂×C₁₃₉	semidirect
407. C₄×#120	C₂×C₁₃₉	semidirect
411. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
412. C₂×#125	C₂²×C₁₃₉	semidirect
417. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
418. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
419. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
422. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
429. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
431. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
434. #397	C₂²×C₁₃₉	semidirect
435. #396	C₂²×C₁₃₉	semidirect
438. #394	C₂²×C₁₃₉	semidirect
439. #393	C₂²×C₁₃₉	semidirect
441. #391	C₂²×C₁₃₉	semidirect
444. #389	C₂²×C₁₃₉	semidirect
445. #389	C₂²×C₁₃₉	semidirect
446. #388	C₂²×C₁₃₉	semidirect
447. #388	C₂²×C₁₃₉	semidirect
448. #388	C₂²×C₁₃₉	semidirect
449. #388	C₂²×C₁₃₉	semidirect
450. #387	C₂²×C₁₃₉	semidirect
451. #387	C₂²×C₁₃₉	semidirect
452. #387	C₂²×C₁₃₉	semidirect
454. #386	C₂²×C₁₃₉	semidirect
455. #386	C₂²×C₁₃₉	semidirect
458. #385	C₂²×C₁₃₉	semidirect
459. #385	C₂²×C₁₃₉	semidirect
460. #385	C₂²×C₁₃₉	semidirect
465. #380	C₂²×C₁₃₉	semidirect
469. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
470. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
473. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
474. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
513. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2855×C₁₃₉	2
#2848×C₁₃₉	2
#2561×C₁₃₉	2
#2534×C₁₃₉	2
#2463×C₁₃₉	2
#2460×C₁₃₉	2
#2452×C₁₃₉	2
#2435×C₁₃₉	2
#2427×C₁₃₉	2
#2408×C₁₃₉	2
#2367×C₁₃₉	2
#2361×C₁₃₉	2
#2345×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36528	139

Subgroups — C139×#36528 #48031124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36528 #48031124