Subgroups — C₁₃₉×#34986 #48029582

Order 35584.

2902 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×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	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2626×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2617×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2613×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2466×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2459×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2456×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2455×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2322×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2312×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#538×C₁₃₉	—	2	8	no	—
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
21	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
39	#399×C₁₃₉	C₂²	1	2	yes	complemented
40	#397×C₁₃₉	C₂²	1	2	yes	complemented
41	#396×C₁₃₉	C₂²	1	4	yes	complemented
42	#394×C₁₃₉	C₂²	1	4	yes	—
43	#394×C₁₃₉	C₂²	1	4	yes	—
44	#394×C₁₃₉	C₂²	1	4	yes	complemented
45	#393×C₁₃₉	C₂²	1	2	yes	complemented
46	#392×C₁₃₉	C₂²	1	4	yes	—
47	#392×C₁₃₉	C₂²	1	4	yes	—
48	#392×C₁₃₉	C₂²	1	2	yes	complemented
49	#391×C₁₃₉	C₂²	1	2	yes	complemented
50	#390×C₁₃₉	C₂²	1	2	yes	complemented
51	#389×C₁₃₉	C₂²	1	4	yes	complemented
52	#389×C₁₃₉	C₂²	1	2	yes	complemented
53	#389×C₁₃₉	C₂²	1	2	yes	complemented
54	#388×C₁₃₉	C₂²	1	4	yes	complemented
55	#388×C₁₃₉	C₂²	1	4	yes	complemented
56	#388×C₁₃₉	C₂²	1	4	yes	complemented
57	#388×C₁₃₉	C₂²	1	4	yes	complemented
58	#387×C₁₃₉	C₂²	1	4	yes	complemented
59	#387×C₁₃₉	C₂²	1	4	yes	complemented
60	#386×C₁₃₉	C₂²	1	2	yes	—
61	#386×C₁₃₉	C₂²	1	2	yes	—
62	#386×C₁₃₉	C₂²	1	4	yes	complemented
63	#386×C₁₃₉	C₂²	1	4	yes	complemented
64	#385×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	2	yes	—
66	#385×C₁₃₉	C₂²	1	4	yes	complemented
67	#385×C₁₃₉	C₂²	1	4	yes	complemented
68	#385×C₁₃₉	C₂²	1	4	yes	complemented
69	#381×C₁₃₉	C₂²	1	2	yes	—
70	#381×C₁₃₉	C₂²	1	4	yes	complemented
71	#380×C₁₃₉	C₂²	1	1	yes	characteristic
72	#380×C₁₃₉	C₂²	1	1	yes	characteristic
73	#379×C₁₃₉	C₂²	1	2	yes	—
74	#379×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
77	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₉	—	2	4	no	—
81	C₂²×D₄×C₁₃₉	—	2	4	no	—
82	C₂²×D₄×C₁₃₉	—	2	4	no	—
83	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	—	2	4	no	—
90	C₂³×C₄×C₁₃₉	—	2	4	no	—
91	C₂³×C₄×C₁₃₉	—	4	4	no	—
92	C₂³×C₄×C₁₃₉	—	4	4	no	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	#126×C₁₃₉	—	2	8	no	—
102	#124×C₁₃₉	—	2	8	no	—
103	#123×C₁₃₉	—	2	8	no	—
104	#123×C₁₃₉	—	2	8	no	—
105	#123×C₁₃₉	—	4	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
107	#121×C₁₃₉	—	2	4	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#120×C₁₃₉	—	2	8	no	—
110	#120×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	16	no	—
113	C₄×D₄×C₁₃₉	—	2	16	no	—
114	C₄×D₄×C₁₃₉	—	4	8	no	—
115	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
127	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	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	2	yes	—
147	C₂×C₄²×C₁₃₉	—	2	4	no	—
148	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	2	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	C₂⁴×C₁₃₉	—	2	2	no	—
162	C₂⁴×C₁₃₉	—	2	2	no	—
163	C₂⁴×C₁₃₉	—	2	2	no	—
164	C₂⁴×C₁₃₉	—	2	2	no	—
165	C₂⁴×C₁₃₉	—	4	2	no	—
166	C₂⁴×C₁₃₉	—	4	2	no	—
167	C₂⁴×C₁₃₉	—	4	2	no	—
168	C₂⁴×C₁₃₉	—	4	2	no	—
169	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
170	C₂⁴×C₁₃₉	#41	1	4	yes	—
171	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂×Q₈×C₁₃₉	—	2	2	no	—
176	C₂×Q₈×C₁₃₉	—	4	2	no	—
177	C₂×D₄×C₁₃₉	—	2	32	no	—
178	C₂×D₄×C₁₃₉	—	2	8	no	—
179	C₂×D₄×C₁₃₉	—	2	8	no	—
180	C₂×D₄×C₁₃₉	—	2	4	no	—
181	C₂×D₄×C₁₃₉	—	2	8	no	—
182	C₂×D₄×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	4	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	2	no	—
187	C₂×D₄×C₁₃₉	—	2	8	no	—
188	C₂×D₄×C₁₃₉	—	4	4	no	—
189	C₂×D₄×C₁₃₉	—	4	4	no	—
190	C₂×D₄×C₁₃₉	—	4	4	no	—
191	C₂×D₄×C₁₃₉	—	4	2	no	—
192	C₂×D₄×C₁₃₉	—	4	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	2	no	—
198	C₂²×C₄×C₁₃₉	—	2	8	no	—
199	C₂²×C₄×C₁₃₉	—	2	8	no	—
200	C₂²×C₄×C₁₃₉	—	2	8	no	—
201	C₂²×C₄×C₁₃₉	—	2	8	no	—
202	C₂²×C₄×C₁₃₉	—	2	4	no	—
203	C₂²×C₄×C₁₃₉	—	4	2	no	—
204	C₂²×C₄×C₁₃₉	—	4	4	no	—
205	C₂²×C₄×C₁₃₉	—	4	4	no	—
206	C₂²×C₄×C₁₃₉	—	4	2	no	—
207	C₂²×C₄×C₁₃₉	—	4	2	no	—
208	C₂²×C₄×C₁₃₉	—	4	4	no	—
209	C₂²×C₄×C₁₃₉	—	4	16	no	—
210	C₂²×C₄×C₁₃₉	—	4	16	no	—
211	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₄⋊C₄×C₁₃₉	—	2	8	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	2	no	—
229	C₄⋊C₄×C₁₃₉	—	2	2	no	—
230	C₄⋊C₄×C₁₃₉	—	2	8	no	—
231	C₄⋊C₄×C₁₃₉	—	2	8	no	—
232	C₄⋊C₄×C₁₃₉	—	4	2	no	—
233	C₄⋊C₄×C₁₃₉	—	4	2	no	—
234	C₄⋊C₄×C₁₃₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
252	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
253	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
254	C₄²×C₁₃₉	—	2	4	no	—
255	C₄²×C₁₃₉	—	2	4	no	—
256	C₄²×C₁₃₉	—	2	4	no	—
257	C₄²×C₁₃₉	—	4	4	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	8	no	—
261	C₂³×C₁₃₉	—	2	8	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	4	no	—
267	C₂³×C₁₃₉	—	2	4	no	—
268	C₂³×C₁₃₉	—	2	4	no	—
269	C₂³×C₁₃₉	—	2	4	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	4	no	—
274	C₂³×C₁₃₉	—	2	4	no	—
275	C₂³×C₁₃₉	—	4	4	no	—
276	C₂³×C₁₃₉	—	4	4	no	—
277	C₂³×C₁₃₉	—	4	8	no	—
278	C₂³×C₁₃₉	—	4	4	no	—
279	C₂³×C₁₃₉	—	4	8	no	—
280	C₂³×C₁₃₉	—	4	4	no	—
281	C₂³×C₁₃₉	—	4	8	no	—
282	C₂³×C₁₃₉	—	4	8	no	—
283	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
284	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
285	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
286	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
287	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
288	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
289	Q₈×C₁₃₉	—	8	2	no	—
290	D₄×C₁₃₉	—	2	32	no	—
291	D₄×C₁₃₉	—	4	16	no	—
292	D₄×C₁₃₉	—	4	8	no	—
293	D₄×C₁₃₉	—	8	2	no	—
294	D₄×C₁₃₉	—	8	4	no	—
295	D₄×C₁₃₉	—	8	4	no	—
296	C₂×C₄×C₁₃₉	—	2	8	no	—
297	C₂×C₄×C₁₃₉	—	2	8	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	4	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	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	4	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	4	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	2	4	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	4	4	no	—
321	C₂×C₄×C₁₃₉	—	4	4	no	—
322	C₂×C₄×C₁₃₉	—	4	16	no	—
323	C₂×C₄×C₁₃₉	—	4	16	no	—
324	C₂×C₄×C₁₃₉	—	4	4	no	—
325	C₂×C₄×C₁₃₉	—	8	4	no	—
326	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
329	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
330	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
331	C₂²×C₁₃₉	—	2	4	no	—
332	C₂²×C₁₃₉	—	2	2	no	—
333	C₂²×C₁₃₉	—	2	2	no	—
334	C₂²×C₁₃₉	—	2	4	no	—
335	C₂²×C₁₃₉	—	2	4	no	—
336	C₂²×C₁₃₉	—	2	4	no	—
337	C₂²×C₁₃₉	—	2	8	no	—
338	C₂²×C₁₃₉	—	2	4	no	—
339	C₂²×C₁₃₉	—	2	4	no	—
340	C₂²×C₁₃₉	—	4	16	no	—
341	C₂²×C₁₃₉	—	4	16	no	—
342	C₂²×C₁₃₉	—	4	4	no	—
343	C₂²×C₁₃₉	—	4	2	no	—
344	C₂²×C₁₃₉	—	4	2	no	—
345	C₂²×C₁₃₉	—	4	4	no	—
346	C₂²×C₁₃₉	—	4	4	no	—
347	C₂²×C₁₃₉	—	4	2	no	—
348	C₂²×C₁₃₉	—	4	4	no	—
349	C₂²×C₁₃₉	—	4	2	no	—
350	C₂²×C₁₃₉	—	4	2	no	—
351	C₂²×C₁₃₉	—	4	4	no	—
352	C₂²×C₁₃₉	#525	1	4	yes	—
353	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
356	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
357	C₂²×C₁₃₉	#585	1	2	yes	—
358	C₄×C₁₃₉	—	2	4	no	—
359	C₄×C₁₃₉	—	2	4	no	—
360	C₄×C₁₃₉	—	2	4	no	—
361	C₄×C₁₃₉	—	2	2	no	—
362	C₄×C₁₃₉	—	2	2	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	—	4	4	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	2	no	—
367	C₄×C₁₃₉	—	4	2	no	—
368	C₄×C₁₃₉	—	4	4	no	—
369	C₂×C₁₃₉	—	2	4	no	—
370	C₂×C₁₃₉	—	4	4	no	—
371	C₂×C₁₃₉	—	4	4	no	—
372	C₂×C₁₃₉	—	8	2	no	—
373	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
374	C₂×C₁₃₉	#3459	1	2	yes	—
375	C₂×C₁₃₉	#3484	1	1	yes	characteristic
376	C₂×C₁₃₉	#3485	1	1	yes	characteristic
377	C₂×C₁₃₉	#3506	1	2	yes	—
378	#34986	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₁₃₉	#34986	1	1	yes	characteristic, direct product factor, Sylow
380	C₂×#538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
383	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	#2849	C₂×C₁₃₉	1	2	yes	complemented
385	#2626	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	#2617	C₂×C₁₃₉	1	1	yes	characteristic, complemented
387	#2613	C₂×C₁₃₉	1	2	yes	complemented
388	#2466	C₂×C₁₃₉	1	4	yes	complemented
389	#2459	C₂×C₁₃₉	1	4	yes	complemented
390	#2456	C₂×C₁₃₉	1	4	yes	complemented
391	#2455	C₂×C₁₃₉	1	4	yes	complemented
392	#2322	C₂×C₁₃₉	1	2	yes	complemented
393	#2312	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	C₄×#120	C₂×C₁₃₉	1	2	yes	complemented
395	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
398	#538	—	2	8	no	—
399	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
400	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
401	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
402	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
403	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
404	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
407	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
408	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
409	C₂×C₄×D₄	—	2	8	no	—
410	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
412	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
413	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
414	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
418	#399	C₂²×C₁₃₉	1	2	yes	complemented
419	#397	C₂²×C₁₃₉	1	2	yes	complemented
420	#396	C₂²×C₁₃₉	1	4	yes	complemented
421	#394	C₂²×C₁₃₉	1	4	yes	—
422	#394	C₂²×C₁₃₉	1	4	yes	—
423	#394	C₂²×C₁₃₉	1	4	yes	complemented
424	#393	C₂²×C₁₃₉	1	2	yes	complemented
425	#392	C₂²×C₁₃₉	1	4	yes	—
426	#392	C₂²×C₁₃₉	1	4	yes	—
427	#392	C₂²×C₁₃₉	1	2	yes	complemented
428	#391	C₂²×C₁₃₉	1	2	yes	complemented
429	#390	C₂²×C₁₃₉	1	2	yes	complemented
430	#389	C₂²×C₁₃₉	1	4	yes	complemented
431	#389	C₂²×C₁₃₉	1	2	yes	complemented
432	#389	C₂²×C₁₃₉	1	2	yes	complemented
433	#388	C₂²×C₁₃₉	1	4	yes	complemented
434	#388	C₂²×C₁₃₉	1	4	yes	complemented
435	#388	C₂²×C₁₃₉	1	4	yes	complemented
436	#388	C₂²×C₁₃₉	1	4	yes	complemented
437	#387	C₂²×C₁₃₉	1	4	yes	complemented
438	#387	C₂²×C₁₃₉	1	4	yes	complemented
439	#386	C₂²×C₁₃₉	1	2	yes	—
440	#386	C₂²×C₁₃₉	1	2	yes	—
441	#386	C₂²×C₁₃₉	1	4	yes	complemented
442	#386	C₂²×C₁₃₉	1	4	yes	complemented
443	#385	C₂²×C₁₃₉	1	2	yes	—
444	#385	C₂²×C₁₃₉	1	2	yes	—
445	#385	C₂²×C₁₃₉	1	4	yes	complemented
446	#385	C₂²×C₁₃₉	1	4	yes	complemented
447	#385	C₂²×C₁₃₉	1	4	yes	complemented
448	#381	C₂²×C₁₃₉	1	2	yes	—
449	#381	C₂²×C₁₃₉	1	4	yes	complemented
450	#380	C₂²×C₁₃₉	1	1	yes	characteristic
451	#380	C₂²×C₁₃₉	1	1	yes	characteristic
452	#379	C₂²×C₁₃₉	1	2	yes	—
453	#379	C₂²×C₁₃₉	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
456	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂²×D₄	—	2	4	no	—
460	C₂²×D₄	—	2	4	no	—
461	C₂²×D₄	—	2	4	no	—
462	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
463	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
464	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
465	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂³×C₄	—	2	4	no	—
469	C₂³×C₄	—	2	4	no	—
470	C₂³×C₄	—	4	4	no	—
471	C₂³×C₄	—	4	4	no	—
472	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
474	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
475	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
480	#126	—	2	8	no	—
481	#124	—	2	8	no	—
482	#123	—	2	8	no	—
483	#123	—	2	8	no	—
484	#123	—	4	8	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	#121	—	2	4	no	—
487	#121	—	2	8	no	—
488	#120	—	2	8	no	—
489	#120	—	2	8	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	16	no	—
492	C₄×D₄	—	2	16	no	—
493	C₄×D₄	—	4	8	no	—
494	C₂×C₄⋊C₄	—	2	4	no	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	—	2	4	no	—
506	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄²	—	2	4	no	—
527	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
531	#95	C₂³×C₁₃₉	1	4	yes	—
532	#95	C₂³×C₁₃₉	1	4	yes	—
533	#95	C₂³×C₁₃₉	1	4	yes	—
534	#95	C₂³×C₁₃₉	1	2	yes	—
535	#95	C₂³×C₁₃₉	1	2	yes	—
536	#95	C₂³×C₁₃₉	1	4	yes	—
537	#95	C₂³×C₁₃₉	1	4	yes	—
538	#95	C₂³×C₁₃₉	1	4	yes	—
539	#95	C₂³×C₁₃₉	1	4	yes	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	2	2	no	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	4	2	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	—	4	2	no	—
547	C₂⁴	—	4	2	no	—
548	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
549	C₂⁴	#41×C₁₃₉	1	4	yes	—
550	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
551	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
552	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
553	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	4	2	no	—
556	C₂×D₄	—	2	32	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	2	8	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	8	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	16	no	—
589	C₂²×C₄	—	4	16	no	—
590	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
591	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
592	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	—	4	4	no	—
631	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
632	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	4	4	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	8	no	—
640	C₂³	—	2	8	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	4	no	—
658	C₂³	—	4	8	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	8	no	—
661	C₂³	—	4	8	no	—
662	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
663	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
664	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
665	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
666	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
667	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
668	Q₈	—	8	2	no	—
669	D₄	—	2	32	no	—
670	D₄	—	4	16	no	—
671	D₄	—	4	8	no	—
672	D₄	—	8	2	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	8	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	16	no	—
702	C₂×C₄	—	4	16	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
708	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
709	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	8	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	4	16	no	—
720	C₂²	—	4	16	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	#525×C₁₃₉	1	4	yes	—
732	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
733	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
734	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
735	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
736	C₂²	#585×C₁₃₉	1	2	yes	—
737	C₄	—	2	4	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	4	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	4	no	—
748	C₂	—	2	4	no	—
749	C₂	—	4	4	no	—
750	C₂	—	4	4	no	—
751	C₂	—	8	2	no	—
752	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
753	C₂	#3459×C₁₃₉	1	2	yes	—
754	C₂	#3484×C₁₃₉	1	1	yes	characteristic
755	C₂	#3485×C₁₃₉	1	1	yes	characteristic
756	C₂	#3506×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#538×C₁₃₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2849×C₁₃₉	C₂	semidirect
6. #2626×C₁₃₉	C₂	semidirect
7. #2617×C₁₃₉	C₂	semidirect
8. #2613×C₁₃₉	C₂	semidirect
9. #2466×C₁₃₉	C₂	semidirect
10. #2459×C₁₃₉	C₂	semidirect
11. #2456×C₁₃₉	C₂	semidirect
12. #2455×C₁₃₉	C₂	semidirect
13. #2322×C₁₃₉	C₂	semidirect
14. #2312×C₁₃₉	C₂	semidirect
15. C₄×#120×C₁₃₉	C₂	semidirect
20. C₂×#126×C₁₃₉	C₂²	semidirect
21. C₂×#124×C₁₃₉	C₂²	semidirect
23. C₂×#123×C₁₃₉	C₂²	semidirect
24. C₂×#123×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. #399×C₁₃₉	C₂²	semidirect
40. #397×C₁₃₉	C₂²	semidirect
41. #396×C₁₃₉	C₂²	semidirect
44. #394×C₁₃₉	C₂²	semidirect
45. #393×C₁₃₉	C₂²	semidirect
48. #392×C₁₃₉	C₂²	semidirect
49. #391×C₁₃₉	C₂²	semidirect
50. #390×C₁₃₉	C₂²	semidirect
51. #389×C₁₃₉	C₂²	semidirect
52. #389×C₁₃₉	C₂²	semidirect
53. #389×C₁₃₉	C₂²	semidirect
54. #388×C₁₃₉	C₂²	semidirect
55. #388×C₁₃₉	C₂²	semidirect
56. #388×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #387×C₁₃₉	C₂²	semidirect
59. #387×C₁₃₉	C₂²	semidirect
62. #386×C₁₃₉	C₂²	semidirect
63. #386×C₁₃₉	C₂²	semidirect
66. #385×C₁₃₉	C₂²	semidirect
67. #385×C₁₃₉	C₂²	semidirect
68. #385×C₁₃₉	C₂²	semidirect
70. #381×C₁₃₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
127. C₂×C₂²⋊C₄×C₁₃₉	D₄	semidirect
378. #34986	C₁₃₉	direct (N × H)
379. C₁₃₉	#34986	direct (N × H)
380. C₂×#538	C₂×C₁₃₉	semidirect
381. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
382. #2855	C₂×C₁₃₉	semidirect
383. #2854	C₂×C₁₃₉	semidirect
384. #2849	C₂×C₁₃₉	semidirect
385. #2626	C₂×C₁₃₉	semidirect
386. #2617	C₂×C₁₃₉	semidirect
387. #2613	C₂×C₁₃₉	semidirect
388. #2466	C₂×C₁₃₉	semidirect
389. #2459	C₂×C₁₃₉	semidirect
390. #2456	C₂×C₁₃₉	semidirect
391. #2455	C₂×C₁₃₉	semidirect
392. #2322	C₂×C₁₃₉	semidirect
393. #2312	C₂×C₁₃₉	semidirect
394. C₄×#120	C₂×C₁₃₉	semidirect
399. C₂×#126	C₂²×C₁₃₉	semidirect
400. C₂×#124	C₂²×C₁₃₉	semidirect
402. C₂×#123	C₂²×C₁₃₉	semidirect
403. C₂×#123	C₂²×C₁₃₉	semidirect
406. C₂×#121	C₂²×C₁₃₉	semidirect
413. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
418. #399	C₂²×C₁₃₉	semidirect
419. #397	C₂²×C₁₃₉	semidirect
420. #396	C₂²×C₁₃₉	semidirect
423. #394	C₂²×C₁₃₉	semidirect
424. #393	C₂²×C₁₃₉	semidirect
427. #392	C₂²×C₁₃₉	semidirect
428. #391	C₂²×C₁₃₉	semidirect
429. #390	C₂²×C₁₃₉	semidirect
430. #389	C₂²×C₁₃₉	semidirect
431. #389	C₂²×C₁₃₉	semidirect
432. #389	C₂²×C₁₃₉	semidirect
433. #388	C₂²×C₁₃₉	semidirect
434. #388	C₂²×C₁₃₉	semidirect
435. #388	C₂²×C₁₃₉	semidirect
436. #388	C₂²×C₁₃₉	semidirect
437. #387	C₂²×C₁₃₉	semidirect
438. #387	C₂²×C₁₃₉	semidirect
441. #386	C₂²×C₁₃₉	semidirect
442. #386	C₂²×C₁₃₉	semidirect
445. #385	C₂²×C₁₃₉	semidirect
446. #385	C₂²×C₁₃₉	semidirect
447. #385	C₂²×C₁₃₉	semidirect
449. #381	C₂²×C₁₃₉	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
506. C₂×C₂²⋊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×#538×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2855×C₁₃₉	2
#2854×C₁₃₉	2
#2849×C₁₃₉	2
#2626×C₁₃₉	2
#2617×C₁₃₉	2
#2613×C₁₃₉	2
#2466×C₁₃₉	2
#2459×C₁₃₉	2
#2456×C₁₃₉	2
#2455×C₁₃₉	2
#2322×C₁₃₉	2
#2312×C₁₃₉	2
C₄×#120×C₁₃₉	2
#34986	139

Subgroups — C139×#34986 #48029582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#34986 #48029582