Subgroups — C₁₃₉×#36580 #48031176

Order 35584.

2560 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2592×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2582×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2580×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2458×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2448×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2443×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2436×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2355×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	#559×C₁₃₉	—	2	8	no	—
20	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	—	2	8	no	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	#399×C₁₃₉	C₂²	1	4	yes	—
45	#398×C₁₃₉	C₂²	1	4	yes	—
46	#397×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#393×C₁₃₉	C₂²	1	4	yes	—
49	#393×C₁₃₉	C₂²	1	4	yes	—
50	#391×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	2	yes	—
56	#390×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	—
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#387×C₁₃₉	C₂²	1	2	yes	—
69	#387×C₁₃₉	C₂²	1	4	yes	—
70	#386×C₁₃₉	C₂²	1	4	yes	—
71	#386×C₁₃₉	C₂²	1	4	yes	—
72	#386×C₁₃₉	C₂²	1	4	yes	—
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	#384×C₁₃₉	C₂²	1	1	yes	characteristic
77	#382×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₂²×Q₈×C₁₃₉	—	2	4	no	—
86	C₂²×Q₈×C₁₃₉	—	2	4	no	—
87	C₂²×Q₈×C₁₃₉	—	2	4	no	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
102	#127×C₁₃₉	—	2	4	no	—
103	#124×C₁₃₉	—	2	8	no	—
104	#124×C₁₃₉	—	2	8	no	—
105	#124×C₁₃₉	—	2	8	no	—
106	#123×C₁₃₉	—	2	16	no	—
107	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#121×C₁₃₉	—	4	4	no	—
111	C₄×Q₈×C₁₃₉	—	2	4	no	—
112	C₄×Q₈×C₁₃₉	—	2	4	no	—
113	C₄×Q₈×C₁₃₉	—	2	8	no	—
114	C₄×Q₈×C₁₃₉	—	2	8	no	—
115	C₄×Q₈×C₁₃₉	—	2	4	no	—
116	C₄×Q₈×C₁₃₉	—	2	4	no	—
117	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	—	2	8	no	—
120	C₄×D₄×C₁₃₉	—	4	8	no	—
121	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	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	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃₉	—	2	8	no	—
153	C₂×C₄²×C₁₃₉	—	2	4	no	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
177	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	C₂×Q₈×C₁₃₉	—	2	32	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	2	2	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×Q₈×C₁₃₉	—	2	4	no	—
184	C₂×Q₈×C₁₃₉	—	2	2	no	—
185	C₂×Q₈×C₁₃₉	—	2	2	no	—
186	C₂×Q₈×C₁₃₉	—	2	2	no	—
187	C₂×Q₈×C₁₃₉	—	2	2	no	—
188	C₂×Q₈×C₁₃₉	—	2	2	no	—
189	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
190	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
191	C₂×D₄×C₁₃₉	—	2	8	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	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	4	2	no	—
202	C₂×D₄×C₁₃₉	—	4	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	8	no	—
215	C₂²×C₄×C₁₃₉	—	4	2	no	—
216	C₂²×C₄×C₁₃₉	—	4	1	no	—
217	C₂²×C₄×C₁₃₉	—	4	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	4	no	—
219	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
220	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
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	4	yes	—
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	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₄⋊C₄×C₁₃₉	—	2	4	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	2	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	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	2	no	—
249	C₄⋊C₄×C₁₃₉	—	4	4	no	—
250	C₄⋊C₄×C₁₃₉	—	4	2	no	—
251	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	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	8	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₄²×C₁₃₉	—	2	4	no	—
266	C₄²×C₁₃₉	—	2	2	no	—
267	C₄²×C₁₃₉	—	2	4	no	—
268	C₄²×C₁₃₉	—	2	2	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	2	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	2	4	no	—
273	C₄²×C₁₃₉	—	4	4	no	—
274	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
275	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	1	no	—
278	C₂³×C₁₃₉	—	2	1	no	—
279	C₂³×C₁₃₉	—	2	1	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	4	no	—
282	C₂³×C₁₃₉	—	2	4	no	—
283	C₂³×C₁₃₉	—	2	4	no	—
284	C₂³×C₁₃₉	—	2	4	no	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	2	4	no	—
287	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
288	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
289	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
290	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
291	Q₈×C₁₃₉	—	2	16	no	—
292	Q₈×C₁₃₉	—	2	8	no	—
293	Q₈×C₁₃₉	—	2	8	no	—
294	Q₈×C₁₃₉	—	4	4	no	—
295	D₄×C₁₃₉	—	4	16	no	—
296	D₄×C₁₃₉	—	4	8	no	—
297	D₄×C₁₃₉	—	4	8	no	—
298	D₄×C₁₃₉	—	8	4	no	—
299	C₂×C₄×C₁₃₉	—	2	16	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	8	no	—
313	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	2	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	1	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	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	4	8	no	—
336	C₂×C₄×C₁₃₉	—	4	4	no	—
337	C₂×C₄×C₁₃₉	—	8	8	no	—
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	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
345	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
350	C₂²×C₁₃₉	—	2	2	no	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	2	2	no	—
354	C₂²×C₁₃₉	—	2	2	no	—
355	C₂²×C₁₃₉	—	2	2	no	—
356	C₂²×C₁₃₉	—	4	4	no	—
357	C₂²×C₁₃₉	—	4	4	no	—
358	C₂²×C₁₃₉	—	4	4	no	—
359	C₂²×C₁₃₉	—	4	4	no	—
360	C₂²×C₁₃₉	—	4	4	no	—
361	C₂²×C₁₃₉	—	4	4	no	—
362	C₂²×C₁₃₉	—	4	4	no	—
363	C₂²×C₁₃₉	#559	1	4	yes	complemented
364	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
365	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
366	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
367	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
368	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	C₂²×C₁₃₉	#585	1	1	yes	characteristic
371	C₄×C₁₃₉	—	2	4	no	—
372	C₄×C₁₃₉	—	2	4	no	—
373	C₄×C₁₃₉	—	2	2	no	—
374	C₄×C₁₃₉	—	2	2	no	—
375	C₄×C₁₃₉	—	2	4	no	—
376	C₄×C₁₃₉	—	2	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	4	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	1	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	#525	1	4	yes	—
385	C₄×C₁₃₉	#548	1	4	yes	—
386	C₂×C₁₃₉	—	2	4	no	—
387	C₂×C₁₃₉	—	8	4	no	—
388	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
389	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
390	C₂×C₁₃₉	C₂×#559	1	1	yes	characteristic
391	C₂×C₁₃₉	#3480	1	1	yes	characteristic
392	C₂×C₁₃₉	#3488	1	1	yes	characteristic
393	C₂×C₁₃₉	#3507	1	1	yes	characteristic
394	C₂×C₁₃₉	#3522	1	1	yes	characteristic
395	#36580	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₁₃₉	#36580	1	1	yes	characteristic, direct product factor, Sylow
397	C₂×#559	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	C₂²×C₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	#2856	C₂×C₁₃₉	1	1	yes	characteristic
400	#2850	C₂×C₁₃₉	1	2	yes	complemented
401	#2592	C₂×C₁₃₉	1	2	yes	complemented
402	#2582	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	#2580	C₂×C₁₃₉	1	2	yes	complemented
404	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2458	C₂×C₁₃₉	1	4	yes	complemented
406	#2448	C₂×C₁₃₉	1	2	yes	complemented
407	#2443	C₂×C₁₃₉	1	4	yes	complemented
408	#2436	C₂×C₁₃₉	1	2	yes	complemented
409	#2367	C₂×C₁₃₉	1	2	yes	complemented
410	#2361	C₂×C₁₃₉	1	2	yes	complemented
411	#2355	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	C₄×#121	C₂×C₁₃₉	1	2	yes	complemented
414	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
415	#559	—	2	8	no	—
416	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
418	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
420	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
423	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
425	C₂×C₄×Q₈	—	2	8	no	—
426	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
427	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
432	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
434	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
436	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
438	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
439	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
440	#399	C₂²×C₁₃₉	1	4	yes	—
441	#398	C₂²×C₁₃₉	1	4	yes	—
442	#397	C₂²×C₁₃₉	1	4	yes	—
443	#394	C₂²×C₁₃₉	1	4	yes	—
444	#393	C₂²×C₁₃₉	1	4	yes	—
445	#393	C₂²×C₁₃₉	1	4	yes	—
446	#391	C₂²×C₁₃₉	1	2	yes	—
447	#391	C₂²×C₁₃₉	1	2	yes	—
448	#391	C₂²×C₁₃₉	1	1	yes	characteristic
449	#391	C₂²×C₁₃₉	1	2	yes	—
450	#390	C₂²×C₁₃₉	1	2	yes	—
451	#390	C₂²×C₁₃₉	1	2	yes	—
452	#390	C₂²×C₁₃₉	1	2	yes	—
453	#390	C₂²×C₁₃₉	1	2	yes	—
454	#390	C₂²×C₁₃₉	1	2	yes	—
455	#390	C₂²×C₁₃₉	1	2	yes	—
456	#389	C₂²×C₁₃₉	1	1	yes	characteristic
457	#389	C₂²×C₁₃₉	1	2	yes	—
458	#389	C₂²×C₁₃₉	1	2	yes	—
459	#388	C₂²×C₁₃₉	1	4	yes	—
460	#388	C₂²×C₁₃₉	1	4	yes	—
461	#388	C₂²×C₁₃₉	1	4	yes	—
462	#388	C₂²×C₁₃₉	1	4	yes	—
463	#388	C₂²×C₁₃₉	1	4	yes	—
464	#387	C₂²×C₁₃₉	1	4	yes	—
465	#387	C₂²×C₁₃₉	1	2	yes	—
466	#386	C₂²×C₁₃₉	1	4	yes	—
467	#386	C₂²×C₁₃₉	1	4	yes	—
468	#386	C₂²×C₁₃₉	1	4	yes	—
469	#385	C₂²×C₁₃₉	1	4	yes	—
470	#385	C₂²×C₁₃₉	1	4	yes	—
471	#385	C₂²×C₁₃₉	1	2	yes	—
472	#384	C₂²×C₁₃₉	1	1	yes	characteristic
473	#382	C₂²×C₁₃₉	1	2	yes	—
474	#380	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
481	C₂²×Q₈	—	2	4	no	—
482	C₂²×Q₈	—	2	4	no	—
483	C₂²×Q₈	—	2	4	no	—
484	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
485	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
498	#127	—	2	4	no	—
499	#124	—	2	8	no	—
500	#124	—	2	8	no	—
501	#124	—	2	8	no	—
502	#123	—	2	16	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	#121	—	2	8	no	—
505	#121	—	2	8	no	—
506	#121	—	4	4	no	—
507	C₄×Q₈	—	2	4	no	—
508	C₄×Q₈	—	2	4	no	—
509	C₄×Q₈	—	2	8	no	—
510	C₄×Q₈	—	2	8	no	—
511	C₄×Q₈	—	2	4	no	—
512	C₄×Q₈	—	2	4	no	—
513	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
514	C₄×D₄	—	2	8	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	4	8	no	—
517	C₂×C₄⋊C₄	—	2	4	no	—
518	C₂×C₄⋊C₄	—	2	8	no	—
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	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	1	yes	characteristic
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	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
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	4	yes	—
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	8	no	—
549	C₂×C₄²	—	2	4	no	—
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	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
559	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
561	#95	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	4	yes	—
569	#95	C₂³×C₁₃₉	1	4	yes	—
570	#95	C₂³×C₁₃₉	1	4	yes	—
571	#95	C₂³×C₁₃₉	1	4	yes	—
572	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
573	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
574	C₂×Q₈	—	2	32	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
586	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	8	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	4	no	—
614	C₂²×C₄	—	4	4	no	—
615	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
616	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
621	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
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	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	4	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
648	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	8	no	—
655	C₂²⋊C₄	—	2	8	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	8	no	—
658	C₂²⋊C₄	—	4	4	no	—
659	C₂²⋊C₄	—	4	4	no	—
660	C₂²⋊C₄	—	4	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	2	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	4	4	no	—
670	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
671	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	4	no	—
683	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
684	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
685	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
686	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
687	Q₈	—	2	16	no	—
688	Q₈	—	2	8	no	—
689	Q₈	—	2	8	no	—
690	Q₈	—	4	4	no	—
691	D₄	—	4	16	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	8	no	—
694	D₄	—	8	4	no	—
695	C₂×C₄	—	2	16	no	—
696	C₂×C₄	—	2	1	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	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	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	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	8	8	no	—
734	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
737	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
739	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
740	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
741	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
742	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
743	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
744	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
745	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	4	4	no	—
759	C₂²	#559×C₁₃₉	1	4	yes	complemented
760	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
761	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
762	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
763	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
764	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
765	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
766	C₂²	#585×C₁₃₉	1	1	yes	characteristic
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	4	no	—
772	C₄	—	2	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	4	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	#525×C₁₃₉	1	4	yes	—
781	C₄	#548×C₁₃₉	1	4	yes	—
782	C₂	—	2	4	no	—
783	C₂	—	8	4	no	—
784	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
785	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
786	C₂	C₂×#559×C₁₃₉	1	1	yes	characteristic
787	C₂	#3480×C₁₃₉	1	1	yes	characteristic
788	C₂	#3488×C₁₃₉	1	1	yes	characteristic
789	C₂	#3507×C₁₃₉	1	1	yes	characteristic
790	C₂	#3522×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2856×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×#559×C₁₃₉	C₂	semidirect
2. C₂²×C₄×Q₈×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2592×C₁₃₉	C₂	semidirect
6. #2582×C₁₃₉	C₂	semidirect
7. #2580×C₁₃₉	C₂	semidirect
8. #2548×C₁₃₉	C₂	semidirect
9. #2458×C₁₃₉	C₂	semidirect
10. #2448×C₁₃₉	C₂	semidirect
11. #2443×C₁₃₉	C₂	semidirect
12. #2436×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2361×C₁₃₉	C₂	semidirect
15. #2355×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₄×#121×C₁₃₉	C₂	semidirect
117. C₄×Q₈×C₁₃₉	D₄	semidirect
363. C₂²×C₁₃₉	#559	semidirect
395. #36580	C₁₃₉	direct (N × H)
396. C₁₃₉	#36580	direct (N × H)
397. C₂×#559	C₂×C₁₃₉	semidirect
398. C₂²×C₄×Q₈	C₂×C₁₃₉	semidirect
400. #2850	C₂×C₁₃₉	semidirect
401. #2592	C₂×C₁₃₉	semidirect
402. #2582	C₂×C₁₃₉	semidirect
403. #2580	C₂×C₁₃₉	semidirect
404. #2548	C₂×C₁₃₉	semidirect
405. #2458	C₂×C₁₃₉	semidirect
406. #2448	C₂×C₁₃₉	semidirect
407. #2443	C₂×C₁₃₉	semidirect
408. #2436	C₂×C₁₃₉	semidirect
409. #2367	C₂×C₁₃₉	semidirect
410. #2361	C₂×C₁₃₉	semidirect
411. #2355	C₂×C₁₃₉	semidirect
412. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
413. C₄×#121	C₂×C₁₃₉	semidirect
513. C₄×Q₈	D₄×C₁₃₉	semidirect
759. C₂²	#559×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₁₃₉	2
C₂²×C₄×Q₈×C₁₃₉	2
#2856×C₁₃₉	2
#2850×C₁₃₉	2
#2592×C₁₃₉	2
#2582×C₁₃₉	2
#2580×C₁₃₉	2
#2548×C₁₃₉	2
#2458×C₁₃₉	2
#2448×C₁₃₉	2
#2443×C₁₃₉	2
#2436×C₁₃₉	2
#2367×C₁₃₉	2
#2361×C₁₃₉	2
#2355×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#121×C₁₃₉	2
#36580	139

Subgroups — C139×#36580 #48031176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36580 #48031176