Subgroups — C₁₃₉×#37236 #48031832

Order 35584.

1730 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2795×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2794×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2793×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2792×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2791×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2790×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2721×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2720×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2718×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2680×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2627×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2618×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2481×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2473×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2443×C₁₃₉	C₂	1	2	yes	maximal
18	#2322×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	1	yes	characteristic
35	#400×C₁₃₉	C₂²	1	1	yes	characteristic
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#399×C₁₃₉	C₂²	1	2	yes	—
39	#399×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	1	yes	characteristic
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	1	yes	characteristic
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#396×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#396×C₁₃₉	C₂²	1	2	yes	—
55	#395×C₁₃₉	C₂²	1	1	yes	characteristic
56	#395×C₁₃₉	C₂²	1	2	yes	—
57	#395×C₁₃₉	C₂²	1	1	yes	characteristic
58	#394×C₁₃₉	C₂²	1	1	yes	characteristic
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#394×C₁₃₉	C₂²	1	1	yes	characteristic
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×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	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#386×C₁₃₉	C₂²	1	2	yes	—
86	#386×C₁₃₉	C₂²	1	2	yes	—
87	#386×C₁₃₉	C₂²	1	2	yes	—
88	#386×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#384×C₁₃₉	C₂²	1	1	yes	characteristic
98	#384×C₁₃₉	C₂²	1	2	yes	—
99	#384×C₁₃₉	C₂²	1	1	yes	characteristic
100	#384×C₁₃₉	C₂²	1	2	yes	—
101	#384×C₁₃₉	C₂²	1	1	yes	characteristic
102	#384×C₁₃₉	C₂²	1	1	yes	characteristic
103	#381×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	1	yes	characteristic
105	#380×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	#126×C₁₃₉	—	4	4	no	—
117	#125×C₁₃₉	—	4	4	no	—
118	#123×C₁₃₉	—	2	8	no	—
119	#123×C₁₃₉	—	4	4	no	—
120	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
121	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
122	#121×C₁₃₉	—	4	2	no	—
123	C₄×D₄×C₁₃₉	—	4	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
125	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
126	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
127	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
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	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	—	2	4	no	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	1	yes	characteristic
197	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂×Q₈×C₁₃₉	—	4	1	no	—
210	C₂×Q₈×C₁₃₉	—	4	2	no	—
211	C₂×D₄×C₁₃₉	—	2	4	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	4	1	no	—
215	C₂×D₄×C₁₃₉	—	4	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	2	no	—
218	C₂²×C₄×C₁₃₉	—	2	2	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	—	4	2	no	—
227	C₂²×C₄×C₁₃₉	—	4	2	no	—
228	C₂²×C₄×C₁₃₉	—	4	2	no	—
229	C₂²×C₄×C₁₃₉	—	4	2	no	—
230	C₂²×C₄×C₁₃₉	—	4	2	no	—
231	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	1	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	1	no	—
264	C₄⋊C₄×C₁₃₉	—	4	1	no	—
265	C₄⋊C₄×C₁₃₉	—	4	2	no	—
266	C₄⋊C₄×C₁₃₉	—	4	2	no	—
267	C₄⋊C₄×C₁₃₉	—	4	1	no	—
268	C₄⋊C₄×C₁₃₉	—	4	1	no	—
269	C₄⋊C₄×C₁₃₉	—	4	1	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	1	no	—
272	C₄⋊C₄×C₁₃₉	—	4	1	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	2	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	—	4	2	no	—
279	C₄⋊C₄×C₁₃₉	—	4	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
295	C₄²×C₁₃₉	—	2	2	no	—
296	C₄²×C₁₃₉	—	2	4	no	—
297	C₄²×C₁₃₉	—	2	2	no	—
298	C₄²×C₁₃₉	—	4	2	no	—
299	C₄²×C₁₃₉	—	4	2	no	—
300	C₄²×C₁₃₉	—	4	2	no	—
301	C₂³×C₁₃₉	—	2	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
311	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
312	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
313	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
314	Q₈×C₁₃₉	—	8	2	no	—
315	D₄×C₁₃₉	—	4	8	no	—
316	D₄×C₁₃₉	—	8	2	no	—
317	C₂×C₄×C₁₃₉	—	2	16	no	—
318	C₂×C₄×C₁₃₉	—	2	8	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	1	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	2	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	1	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	8	4	no	—
363	C₂×C₄×C₁₃₉	—	8	2	no	—
364	C₂×C₄×C₁₃₉	—	8	2	no	—
365	C₂×C₄×C₁₃₉	—	8	4	no	—
366	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
368	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
369	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
370	C₂²×C₁₃₉	—	2	4	no	—
371	C₂²×C₁₃₉	—	2	2	no	—
372	C₂²×C₁₃₉	—	2	2	no	—
373	C₂²×C₁₃₉	—	2	4	no	—
374	C₂²×C₁₃₉	—	4	2	no	—
375	C₂²×C₁₃₉	—	4	2	no	—
376	C₂²×C₁₃₉	—	4	2	no	—
377	C₂²×C₁₃₉	—	4	2	no	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	2	no	—
380	C₂²×C₁₃₉	—	4	2	no	—
381	C₂²×C₁₃₉	#539	1	4	yes	—
382	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
383	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
385	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
386	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
387	C₄×C₁₃₉	—	2	2	no	—
388	C₄×C₁₃₉	—	2	2	no	—
389	C₄×C₁₃₉	—	2	4	no	—
390	C₄×C₁₃₉	—	2	4	no	—
391	C₄×C₁₃₉	—	4	2	no	—
392	C₄×C₁₃₉	—	4	2	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₄×C₁₃₉	—	4	1	no	—
396	C₄×C₁₃₉	—	4	1	no	—
397	C₄×C₁₃₉	—	4	2	no	—
398	C₄×C₁₃₉	—	4	1	no	—
399	C₄×C₁₃₉	—	4	2	no	—
400	C₄×C₁₃₉	—	4	1	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	2	no	—
403	C₄×C₁₃₉	—	4	2	no	—
404	C₂×C₁₃₉	—	2	4	no	—
405	C₂×C₁₃₉	—	8	2	no	—
406	C₂×C₁₃₉	C₂×#539	1	1	yes	characteristic
407	C₂×C₁₃₉	#3492	1	2	yes	—
408	C₂×C₁₃₉	#3543	1	1	yes	characteristic
409	C₂×C₁₃₉	#3544	1	1	yes	characteristic
410	C₂×C₁₃₉	#3552	1	2	yes	—
411	#37236	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₁₃₉	#37236	1	1	yes	characteristic, direct product factor, Sylow
413	#2853	C₂×C₁₃₉	1	2	yes	complemented
414	#2795	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	#2794	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2793	C₂×C₁₃₉	1	2	yes	complemented
417	#2792	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	#2791	C₂×C₁₃₉	1	2	yes	complemented
419	#2790	C₂×C₁₃₉	1	2	yes	complemented
420	#2721	C₂×C₁₃₉	1	2	yes	complemented
421	#2720	C₂×C₁₃₉	1	2	yes	complemented
422	#2718	C₂×C₁₃₉	1	2	yes	complemented
423	#2680	C₂×C₁₃₉	1	1	yes	characteristic, complemented
424	#2627	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	#2618	C₂×C₁₃₉	1	1	yes	characteristic
426	#2481	C₂×C₁₃₉	1	2	yes	complemented
427	#2473	C₂×C₁₃₉	1	2	yes	complemented
428	#2449	C₂×C₁₃₉	1	2	yes	complemented
429	#2443	C₂×C₁₃₉	1	2	yes	—
430	#2322	C₂×C₁₃₉	1	2	yes	complemented
431	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
434	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
435	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
436	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
438	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
440	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
441	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
444	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
445	#400	C₂²×C₁₃₉	1	1	yes	characteristic
446	#400	C₂²×C₁₃₉	1	1	yes	characteristic
447	#400	C₂²×C₁₃₉	1	2	yes	—
448	#400	C₂²×C₁₃₉	1	2	yes	—
449	#400	C₂²×C₁₃₉	1	2	yes	—
450	#399	C₂²×C₁₃₉	1	2	yes	—
451	#399	C₂²×C₁₃₉	1	2	yes	—
452	#398	C₂²×C₁₃₉	1	1	yes	characteristic
453	#398	C₂²×C₁₃₉	1	1	yes	characteristic
454	#398	C₂²×C₁₃₉	1	2	yes	—
455	#398	C₂²×C₁₃₉	1	2	yes	—
456	#398	C₂²×C₁₃₉	1	2	yes	—
457	#398	C₂²×C₁₃₉	1	2	yes	—
458	#398	C₂²×C₁₃₉	1	2	yes	—
459	#398	C₂²×C₁₃₉	1	2	yes	—
460	#398	C₂²×C₁₃₉	1	2	yes	—
461	#397	C₂²×C₁₃₉	1	2	yes	—
462	#397	C₂²×C₁₃₉	1	2	yes	—
463	#396	C₂²×C₁₃₉	1	2	yes	—
464	#396	C₂²×C₁₃₉	1	2	yes	—
465	#396	C₂²×C₁₃₉	1	2	yes	—
466	#396	C₂²×C₁₃₉	1	2	yes	—
467	#395	C₂²×C₁₃₉	1	1	yes	characteristic
468	#395	C₂²×C₁₃₉	1	1	yes	characteristic
469	#395	C₂²×C₁₃₉	1	2	yes	—
470	#394	C₂²×C₁₃₉	1	1	yes	characteristic
471	#394	C₂²×C₁₃₉	1	1	yes	characteristic
472	#394	C₂²×C₁₃₉	1	2	yes	—
473	#389	C₂²×C₁₃₉	1	2	yes	—
474	#389	C₂²×C₁₃₉	1	2	yes	—
475	#389	C₂²×C₁₃₉	1	2	yes	—
476	#389	C₂²×C₁₃₉	1	2	yes	—
477	#388	C₂²×C₁₃₉	1	2	yes	—
478	#388	C₂²×C₁₃₉	1	2	yes	—
479	#388	C₂²×C₁₃₉	1	2	yes	—
480	#388	C₂²×C₁₃₉	1	2	yes	—
481	#388	C₂²×C₁₃₉	1	2	yes	—
482	#388	C₂²×C₁₃₉	1	2	yes	—
483	#388	C₂²×C₁₃₉	1	2	yes	—
484	#388	C₂²×C₁₃₉	1	2	yes	—
485	#387	C₂²×C₁₃₉	1	2	yes	—
486	#387	C₂²×C₁₃₉	1	2	yes	—
487	#387	C₂²×C₁₃₉	1	2	yes	—
488	#387	C₂²×C₁₃₉	1	2	yes	—
489	#387	C₂²×C₁₃₉	1	2	yes	—
490	#387	C₂²×C₁₃₉	1	2	yes	—
491	#387	C₂²×C₁₃₉	1	2	yes	—
492	#387	C₂²×C₁₃₉	1	2	yes	—
493	#387	C₂²×C₁₃₉	1	2	yes	—
494	#387	C₂²×C₁₃₉	1	2	yes	—
495	#387	C₂²×C₁₃₉	1	2	yes	—
496	#387	C₂²×C₁₃₉	1	2	yes	—
497	#386	C₂²×C₁₃₉	1	2	yes	—
498	#386	C₂²×C₁₃₉	1	2	yes	—
499	#386	C₂²×C₁₃₉	1	2	yes	—
500	#386	C₂²×C₁₃₉	1	2	yes	—
501	#385	C₂²×C₁₃₉	1	2	yes	—
502	#385	C₂²×C₁₃₉	1	2	yes	—
503	#385	C₂²×C₁₃₉	1	2	yes	—
504	#385	C₂²×C₁₃₉	1	2	yes	—
505	#385	C₂²×C₁₃₉	1	2	yes	—
506	#385	C₂²×C₁₃₉	1	2	yes	—
507	#385	C₂²×C₁₃₉	1	2	yes	—
508	#385	C₂²×C₁₃₉	1	2	yes	—
509	#384	C₂²×C₁₃₉	1	1	yes	characteristic
510	#384	C₂²×C₁₃₉	1	2	yes	—
511	#384	C₂²×C₁₃₉	1	2	yes	—
512	#384	C₂²×C₁₃₉	1	1	yes	characteristic
513	#384	C₂²×C₁₃₉	1	1	yes	characteristic
514	#384	C₂²×C₁₃₉	1	1	yes	characteristic
515	#381	C₂²×C₁₃₉	1	2	yes	—
516	#380	C₂²×C₁₃₉	1	1	yes	characteristic
517	#380	C₂²×C₁₃₉	1	1	yes	characteristic
518	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
519	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
528	#126	—	4	4	no	—
529	#125	—	4	4	no	—
530	#123	—	2	8	no	—
531	#123	—	4	4	no	—
532	C₂²⋊Q₈	—	4	2	no	—
533	C₂²⋊Q₈	—	4	4	no	—
534	#121	—	4	2	no	—
535	C₄×D₄	—	4	4	no	—
536	C₂×C₄⋊C₄	—	4	4	no	—
537	C₂×C₄⋊C₄	—	4	4	no	—
538	C₂×C₄⋊C₄	—	4	2	no	—
539	C₂×C₄⋊C₄	—	4	2	no	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄²	—	2	4	no	—
587	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	1	yes	characteristic
596	#95	C₂³×C₁₃₉	1	1	yes	characteristic
597	#95	C₂³×C₁₃₉	1	1	yes	characteristic
598	#95	C₂³×C₁₃₉	1	1	yes	characteristic
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	2	yes	—
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	2	yes	—
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
621	C₂×Q₈	—	4	1	no	—
622	C₂×Q₈	—	4	2	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	4	1	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	1	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	1	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	1	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	1	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	4	2	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
723	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
724	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
725	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
726	Q₈	—	8	2	no	—
727	D₄	—	4	8	no	—
728	D₄	—	8	2	no	—
729	C₂×C₄	—	2	16	no	—
730	C₂×C₄	—	2	8	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	8	4	no	—
775	C₂×C₄	—	8	2	no	—
776	C₂×C₄	—	8	2	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
779	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
780	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
781	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	#539×C₁₃₉	1	4	yes	—
794	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
795	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
796	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
797	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
798	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	4	no	—
802	C₄	—	2	4	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₂	—	2	4	no	—
817	C₂	—	8	2	no	—
818	C₂	C₂×#539×C₁₃₉	1	1	yes	characteristic
819	C₂	#3492×C₁₃₉	1	2	yes	—
820	C₂	#3543×C₁₃₉	1	1	yes	characteristic
821	C₂	#3544×C₁₃₉	1	1	yes	characteristic
822	C₂	#3552×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×C₁₃₉	C₂²
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. #2853×C₁₃₉	C₂	semidirect
2. #2795×C₁₃₉	C₂	semidirect
3. #2794×C₁₃₉	C₂	semidirect
4. #2793×C₁₃₉	C₂	semidirect
5. #2792×C₁₃₉	C₂	semidirect
6. #2791×C₁₃₉	C₂	semidirect
7. #2790×C₁₃₉	C₂	semidirect
8. #2721×C₁₃₉	C₂	semidirect
9. #2720×C₁₃₉	C₂	semidirect
10. #2718×C₁₃₉	C₂	semidirect
11. #2680×C₁₃₉	C₂	semidirect
12. #2627×C₁₃₉	C₂	semidirect
14. #2481×C₁₃₉	C₂	semidirect
15. #2473×C₁₃₉	C₂	semidirect
16. #2449×C₁₃₉	C₂	semidirect
18. #2322×C₁₃₉	C₂	semidirect
19. C₂×#384×C₁₃₉	C₂	semidirect
411. #37236	C₁₃₉	direct (N × H)
412. C₁₃₉	#37236	direct (N × H)
413. #2853	C₂×C₁₃₉	semidirect
414. #2795	C₂×C₁₃₉	semidirect
415. #2794	C₂×C₁₃₉	semidirect
416. #2793	C₂×C₁₃₉	semidirect
417. #2792	C₂×C₁₃₉	semidirect
418. #2791	C₂×C₁₃₉	semidirect
419. #2790	C₂×C₁₃₉	semidirect
420. #2721	C₂×C₁₃₉	semidirect
421. #2720	C₂×C₁₃₉	semidirect
422. #2718	C₂×C₁₃₉	semidirect
423. #2680	C₂×C₁₃₉	semidirect
424. #2627	C₂×C₁₃₉	semidirect
426. #2481	C₂×C₁₃₉	semidirect
427. #2473	C₂×C₁₃₉	semidirect
428. #2449	C₂×C₁₃₉	semidirect
430. #2322	C₂×C₁₃₉	semidirect
431. C₂×#384	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2853×C₁₃₉	2
#2795×C₁₃₉	2
#2794×C₁₃₉	2
#2793×C₁₃₉	2
#2792×C₁₃₉	2
#2791×C₁₃₉	2
#2790×C₁₃₉	2
#2721×C₁₃₉	2
#2720×C₁₃₉	2
#2718×C₁₃₉	2
#2680×C₁₃₉	2
#2627×C₁₃₉	2
#2618×C₁₃₉	2
#2481×C₁₃₉	2
#2473×C₁₃₉	2
#2449×C₁₃₉	2
#2443×C₁₃₉	2
#2322×C₁₃₉	2
C₂×#384×C₁₃₉	2
#37236	139

Subgroups — C139×#37236 #48031832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37236 #48031832