Subgroups — C₁₃₉×#36088 #48030684

Order 35584.

1656 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	#2637×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2632×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2606×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2601×C₁₃₉	C₂	1	2	yes	maximal
5	#2550×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2545×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2525×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2522×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2521×C₁₃₉	C₂	1	2	yes	maximal
10	#2520×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2372×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2356×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2346×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2276×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#399×C₁₃₉	C₂²	1	2	yes	—
32	#399×C₁₃₉	C₂²	1	2	yes	—
33	#398×C₁₃₉	C₂²	1	1	yes	characteristic
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	1	yes	characteristic
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#396×C₁₃₉	C₂²	1	2	yes	—
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#395×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	1	yes	characteristic
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#393×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	1	yes	characteristic
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	1	yes	characteristic
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#388×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	2	yes	—
82	#385×C₁₃₉	C₂²	1	2	yes	—
83	#383×C₁₃₉	C₂²	1	1	yes	characteristic
84	#383×C₁₃₉	C₂²	1	1	yes	characteristic
85	#382×C₁₃₉	C₂²	1	1	yes	characteristic
86	#382×C₁₃₉	C₂²	1	2	yes	—
87	#382×C₁₃₉	C₂²	1	2	yes	—
88	#380×C₁₃₉	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
103	#376×C₁₃₉	C₂²	1	2	yes	—
104	#376×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic
106	#376×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
113	#126×C₁₃₉	—	2	8	no	—
114	#126×C₁₃₉	—	4	4	no	—
115	#125×C₁₃₉	—	4	4	no	—
116	#124×C₁₃₉	—	2	4	no	—
117	#124×C₁₃₉	—	4	2	no	—
118	C₄×Q₈×C₁₃₉	—	2	8	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×Q₈×C₁₃₉	—	2	4	no	—
121	#117×C₁₃₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×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	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	1	yes	characteristic
178	#95×C₁₃₉	C₂³	1	1	yes	characteristic
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	1	yes	characteristic
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	1	yes	characteristic
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	1	yes	characteristic
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₁₃₉	—	2	2	no	—
206	C₂×Q₈×C₁₃₉	—	2	4	no	—
207	C₂×Q₈×C₁₃₉	—	2	2	no	—
208	C₂×Q₈×C₁₃₉	—	2	2	no	—
209	C₂×Q₈×C₁₃₉	—	2	2	no	—
210	C₂×Q₈×C₁₃₉	—	4	1	no	—
211	C₂×Q₈×C₁₃₉	—	4	1	no	—
212	C₂×Q₈×C₁₃₉	—	4	1	no	—
213	C₂×D₄×C₁₃₉	—	2	2	no	—
214	C₂×D₄×C₁₃₉	—	4	1	no	—
215	C₂×D₄×C₁₃₉	—	4	1	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	no	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	2	2	no	—
278	C₄²×C₁₃₉	—	2	4	no	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	4	2	no	—
283	C₄²×C₁₃₉	—	4	2	no	—
284	C₄²×C₁₃₉	—	4	1	no	—
285	C₄²×C₁₃₉	—	4	2	no	—
286	C₄²×C₁₃₉	—	4	2	no	—
287	C₄²×C₁₃₉	—	4	1	no	—
288	C₄²×C₁₃₉	#41	1	8	yes	—
289	C₄²×C₁₃₉	#41	1	4	yes	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
298	Q₈×C₁₃₉	—	2	8	no	—
299	Q₈×C₁₃₉	—	4	4	no	—
300	Q₈×C₁₃₉	—	8	2	no	—
301	D₄×C₁₃₉	—	8	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	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	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	4	8	no	—
345	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
351	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
352	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
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	C₂²×#41	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
362	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
364	C₂²×C₁₃₉	#585	1	1	yes	characteristic
365	C₄×C₁₃₉	—	2	4	no	—
366	C₄×C₁₃₉	—	2	2	no	—
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	2	no	—
372	C₄×C₁₃₉	—	2	4	no	—
373	C₄×C₁₃₉	—	4	1	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	1	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₂×C₁₃₉	—	8	2	no	—
384	C₂×C₁₃₉	#3444	1	1	yes	characteristic
385	C₂×C₁₃₉	#3494	1	1	yes	characteristic
386	C₂×C₁₃₉	#3495	1	2	yes	—
387	C₂×C₁₃₉	#3509	1	1	yes	characteristic
388	C₂×C₁₃₉	#3511	1	2	yes	—
389	#36088	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₁₃₉	#36088	1	1	yes	characteristic, direct product factor, Sylow
391	#2637	C₂×C₁₃₉	1	2	yes	complemented
392	#2632	C₂×C₁₃₉	1	1	yes	characteristic
393	#2606	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2601	C₂×C₁₃₉	1	2	yes	—
395	#2550	C₂×C₁₃₉	1	2	yes	complemented
396	#2545	C₂×C₁₃₉	1	1	yes	characteristic
397	#2525	C₂×C₁₃₉	1	2	yes	complemented
398	#2522	C₂×C₁₃₉	1	2	yes	complemented
399	#2521	C₂×C₁₃₉	1	2	yes	—
400	#2520	C₂×C₁₃₉	1	2	yes	complemented
401	#2519	C₂×C₁₃₉	1	2	yes	complemented
402	#2519	C₂×C₁₃₉	1	2	yes	complemented
403	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	#2396	C₂×C₁₃₉	1	2	yes	complemented
405	#2373	C₂×C₁₃₉	1	2	yes	complemented
406	#2372	C₂×C₁₃₉	1	1	yes	characteristic
407	#2356	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2346	C₂×C₁₃₉	1	2	yes	complemented
409	#2276	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
412	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
414	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
420	#400	C₂²×C₁₃₉	1	2	yes	—
421	#399	C₂²×C₁₃₉	1	2	yes	—
422	#399	C₂²×C₁₃₉	1	2	yes	—
423	#398	C₂²×C₁₃₉	1	2	yes	—
424	#398	C₂²×C₁₃₉	1	2	yes	—
425	#398	C₂²×C₁₃₉	1	2	yes	—
426	#398	C₂²×C₁₃₉	1	2	yes	—
427	#398	C₂²×C₁₃₉	1	2	yes	—
428	#398	C₂²×C₁₃₉	1	2	yes	—
429	#398	C₂²×C₁₃₉	1	1	yes	characteristic
430	#398	C₂²×C₁₃₉	1	1	yes	characteristic
431	#397	C₂²×C₁₃₉	1	2	yes	—
432	#396	C₂²×C₁₃₉	1	2	yes	—
433	#396	C₂²×C₁₃₉	1	2	yes	—
434	#396	C₂²×C₁₃₉	1	2	yes	—
435	#396	C₂²×C₁₃₉	1	2	yes	—
436	#395	C₂²×C₁₃₉	1	2	yes	—
437	#395	C₂²×C₁₃₉	1	1	yes	characteristic
438	#395	C₂²×C₁₃₉	1	1	yes	characteristic
439	#395	C₂²×C₁₃₉	1	2	yes	—
440	#394	C₂²×C₁₃₉	1	2	yes	—
441	#393	C₂²×C₁₃₉	1	2	yes	—
442	#391	C₂²×C₁₃₉	1	2	yes	—
443	#391	C₂²×C₁₃₉	1	2	yes	—
444	#391	C₂²×C₁₃₉	1	1	yes	characteristic
445	#390	C₂²×C₁₃₉	1	1	yes	characteristic
446	#389	C₂²×C₁₃₉	1	2	yes	—
447	#389	C₂²×C₁₃₉	1	2	yes	—
448	#389	C₂²×C₁₃₉	1	2	yes	—
449	#389	C₂²×C₁₃₉	1	2	yes	—
450	#389	C₂²×C₁₃₉	1	2	yes	—
451	#388	C₂²×C₁₃₉	1	2	yes	—
452	#388	C₂²×C₁₃₉	1	2	yes	—
453	#388	C₂²×C₁₃₉	1	2	yes	—
454	#388	C₂²×C₁₃₉	1	2	yes	—
455	#388	C₂²×C₁₃₉	1	2	yes	—
456	#388	C₂²×C₁₃₉	1	2	yes	—
457	#388	C₂²×C₁₃₉	1	2	yes	—
458	#388	C₂²×C₁₃₉	1	2	yes	—
459	#388	C₂²×C₁₃₉	1	2	yes	—
460	#388	C₂²×C₁₃₉	1	2	yes	—
461	#388	C₂²×C₁₃₉	1	2	yes	—
462	#388	C₂²×C₁₃₉	1	2	yes	—
463	#387	C₂²×C₁₃₉	1	2	yes	—
464	#387	C₂²×C₁₃₉	1	2	yes	—
465	#387	C₂²×C₁₃₉	1	2	yes	—
466	#387	C₂²×C₁₃₉	1	2	yes	—
467	#387	C₂²×C₁₃₉	1	2	yes	—
468	#387	C₂²×C₁₃₉	1	2	yes	—
469	#387	C₂²×C₁₃₉	1	2	yes	—
470	#387	C₂²×C₁₃₉	1	2	yes	—
471	#386	C₂²×C₁₃₉	1	2	yes	—
472	#385	C₂²×C₁₃₉	1	2	yes	—
473	#383	C₂²×C₁₃₉	1	1	yes	characteristic
474	#383	C₂²×C₁₃₉	1	1	yes	characteristic
475	#382	C₂²×C₁₃₉	1	2	yes	—
476	#382	C₂²×C₁₃₉	1	2	yes	—
477	#382	C₂²×C₁₃₉	1	1	yes	characteristic
478	#380	C₂²×C₁₃₉	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
493	#376	C₂²×C₁₃₉	1	1	yes	characteristic
494	#376	C₂²×C₁₃₉	1	2	yes	—
495	#376	C₂²×C₁₃₉	1	1	yes	characteristic
496	#376	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₄⋊Q₈	—	4	2	no	—
503	#126	—	2	8	no	—
504	#126	—	4	4	no	—
505	#125	—	4	4	no	—
506	#124	—	2	4	no	—
507	#124	—	4	2	no	—
508	C₄×Q₈	—	2	8	no	—
509	C₄×Q₈	—	2	4	no	—
510	C₄×Q₈	—	2	4	no	—
511	#117	—	2	8	no	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	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	2	yes	—
553	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
565	#95	C₂³×C₁₃₉	1	1	yes	characteristic
566	#95	C₂³×C₁₃₉	1	1	yes	characteristic
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	1	yes	characteristic
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	1	yes	characteristic
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	1	yes	characteristic
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	#95	C₂³×C₁₃₉	1	2	yes	—
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	1	yes	characteristic
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	4	1	no	—
601	C₂×Q₈	—	4	1	no	—
602	C₂×Q₈	—	4	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	4	1	no	—
605	C₂×D₄	—	4	1	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	4	2	no	—
673	C₄²	—	4	2	no	—
674	C₄²	—	4	1	no	—
675	C₄²	—	4	2	no	—
676	C₄²	—	4	2	no	—
677	C₄²	—	4	1	no	—
678	C₄²	#41×C₁₃₉	1	8	yes	—
679	C₄²	#41×C₁₃₉	1	4	yes	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
688	Q₈	—	2	8	no	—
689	Q₈	—	4	4	no	—
690	Q₈	—	8	2	no	—
691	D₄	—	8	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	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	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	4	8	no	—
735	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
736	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
737	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
738	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
739	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
740	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
741	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
742	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
751	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
752	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
754	C₂²	#585×C₁₃₉	1	1	yes	characteristic
755	C₄	—	2	4	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	4	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₂	—	8	2	no	—
774	C₂	#3444×C₁₃₉	1	1	yes	characteristic
775	C₂	#3494×C₁₃₉	1	1	yes	characteristic
776	C₂	#3495×C₁₃₉	1	2	yes	—
777	C₂	#3509×C₁₃₉	1	1	yes	characteristic
778	C₂	#3511×C₁₃₉	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. #2637×C₁₃₉	C₂	semidirect
3. #2606×C₁₃₉	C₂	semidirect
5. #2550×C₁₃₉	C₂	semidirect
7. #2525×C₁₃₉	C₂	semidirect
8. #2522×C₁₃₉	C₂	semidirect
10. #2520×C₁₃₉	C₂	semidirect
11. #2519×C₁₃₉	C₂	semidirect
12. #2519×C₁₃₉	C₂	semidirect
13. #2399×C₁₃₉	C₂	semidirect
14. #2396×C₁₃₉	C₂	semidirect
15. #2373×C₁₃₉	C₂	semidirect
17. #2356×C₁₃₉	C₂	semidirect
18. #2346×C₁₃₉	C₂	semidirect
19. #2276×C₁₃₉	C₂	semidirect
389. #36088	C₁₃₉	direct (N × H)
390. C₁₃₉	#36088	direct (N × H)
391. #2637	C₂×C₁₃₉	semidirect
393. #2606	C₂×C₁₃₉	semidirect
395. #2550	C₂×C₁₃₉	semidirect
397. #2525	C₂×C₁₃₉	semidirect
398. #2522	C₂×C₁₃₉	semidirect
400. #2520	C₂×C₁₃₉	semidirect
401. #2519	C₂×C₁₃₉	semidirect
402. #2519	C₂×C₁₃₉	semidirect
403. #2399	C₂×C₁₃₉	semidirect
404. #2396	C₂×C₁₃₉	semidirect
405. #2373	C₂×C₁₃₉	semidirect
407. #2356	C₂×C₁₃₉	semidirect
408. #2346	C₂×C₁₃₉	semidirect
409. #2276	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2637×C₁₃₉	2
#2632×C₁₃₉	2
#2606×C₁₃₉	2
#2601×C₁₃₉	2
#2550×C₁₃₉	2
#2545×C₁₃₉	2
#2525×C₁₃₉	2
#2522×C₁₃₉	2
#2521×C₁₃₉	2
#2520×C₁₃₉	2
#2519×C₁₃₉	2
#2399×C₁₃₉	2
#2396×C₁₃₉	2
#2373×C₁₃₉	2
#2372×C₁₃₉	2
#2356×C₁₃₉	2
#2346×C₁₃₉	2
#2276×C₁₃₉	2
#36088	139

Subgroups — C139×#36088 #48030684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36088 #48030684