Subgroups — C₁₃₉×#36503 #48031099

Order 35584.

1808 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2601×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2594×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2527×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2497×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2494×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2491×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2490×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2474×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2466×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2373×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2370×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
37	#401×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#397×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	#395×C₁₃₉	C₂²	1	2	yes	—
46	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	2	yes	—
48	#393×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#390×C₁₃₉	C₂²	1	1	yes	characteristic
52	#390×C₁₃₉	C₂²	1	1	yes	characteristic
53	#390×C₁₃₉	C₂²	1	1	yes	characteristic
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	1	yes	characteristic
56	#390×C₁₃₉	C₂²	1	1	yes	characteristic
57	#389×C₁₃₉	C₂²	1	1	yes	characteristic
58	#389×C₁₃₉	C₂²	1	1	yes	characteristic
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	1	yes	characteristic
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
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	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	—
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×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	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×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	#384×C₁₃₉	C₂²	1	1	yes	characteristic
94	#382×C₁₃₉	C₂²	1	1	yes	characteristic
95	#382×C₁₃₉	C₂²	1	1	yes	characteristic
96	#381×C₁₃₉	C₂²	1	2	yes	—
97	#380×C₁₃₉	C₂²	1	1	yes	characteristic
98	#380×C₁₃₉	C₂²	1	1	yes	characteristic
99	#380×C₁₃₉	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
119	#376×C₁₃₉	C₂²	1	1	yes	characteristic
120	#376×C₁₃₉	C₂²	1	1	yes	characteristic
121	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
124	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
131	#126×C₁₃₉	—	2	8	no	—
132	#126×C₁₃₉	—	4	4	no	—
133	#125×C₁₃₉	—	2	4	no	—
134	#125×C₁₃₉	—	2	4	no	—
135	#124×C₁₃₉	—	2	8	no	—
136	#121×C₁₃₉	—	2	4	no	—
137	C₄×Q₈×C₁₃₉	—	4	4	no	—
138	C₄×D₄×C₁₃₉	—	2	4	no	—
139	C₄×D₄×C₁₃₉	—	4	4	no	—
140	#117×C₁₃₉	—	2	4	no	—
141	#117×C₁₃₉	—	2	4	no	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	—	2	4	no	—
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	1	yes	characteristic
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	2	yes	—
217	#95×C₁₃₉	C₂³	1	2	yes	—
218	#95×C₁₃₉	C₂³	1	2	yes	—
219	#95×C₁₃₉	C₂³	1	2	yes	—
220	#95×C₁₃₉	C₂³	1	1	yes	characteristic
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	1	yes	characteristic
224	#95×C₁₃₉	C₂³	1	1	yes	characteristic
225	#95×C₁₃₉	C₂³	1	1	yes	characteristic
226	#95×C₁₃₉	C₂³	1	1	yes	characteristic
227	#95×C₁₃₉	C₂³	1	1	yes	characteristic
228	#95×C₁₃₉	C₂³	1	1	yes	characteristic
229	#95×C₁₃₉	C₂³	1	2	yes	—
230	#95×C₁₃₉	C₂³	1	2	yes	—
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	#95×C₁₃₉	C₂³	1	2	yes	—
233	#95×C₁₃₉	C₂³	1	2	yes	—
234	#95×C₁₃₉	C₂³	1	2	yes	—
235	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₁₃₉	—	2	4	no	—
238	C₂×Q₈×C₁₃₉	—	2	4	no	—
239	C₂×Q₈×C₁₃₉	—	4	2	no	—
240	C₂×D₄×C₁₃₉	—	2	4	no	—
241	C₂×D₄×C₁₃₉	—	2	2	no	—
242	C₂×D₄×C₁₃₉	—	2	4	no	—
243	C₂×D₄×C₁₃₉	—	2	2	no	—
244	C₂×D₄×C₁₃₉	—	2	2	no	—
245	C₂×D₄×C₁₃₉	—	4	2	no	—
246	C₂²×C₄×C₁₃₉	—	2	2	no	—
247	C₂²×C₄×C₁₃₉	—	2	2	no	—
248	C₂²×C₄×C₁₃₉	—	2	2	no	—
249	C₂²×C₄×C₁₃₉	—	2	2	no	—
250	C₂²×C₄×C₁₃₉	—	2	2	no	—
251	C₂²×C₄×C₁₃₉	—	2	2	no	—
252	C₂²×C₄×C₁₃₉	—	2	2	no	—
253	C₂²×C₄×C₁₃₉	—	2	2	no	—
254	C₂²×C₄×C₁₃₉	—	2	4	no	—
255	C₂²×C₄×C₁₃₉	—	4	1	no	—
256	C₂²×C₄×C₁₃₉	—	4	2	no	—
257	C₂²×C₄×C₁₃₉	—	4	2	no	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	2	no	—
283	C₄⋊C₄×C₁₃₉	—	2	2	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	4	no	—
287	C₄⋊C₄×C₁₃₉	—	2	4	no	—
288	C₄⋊C₄×C₁₃₉	—	2	2	no	—
289	C₄⋊C₄×C₁₃₉	—	2	2	no	—
290	C₄⋊C₄×C₁₃₉	—	2	2	no	—
291	C₄⋊C₄×C₁₃₉	—	2	4	no	—
292	C₄⋊C₄×C₁₃₉	—	2	4	no	—
293	C₄⋊C₄×C₁₃₉	—	2	4	no	—
294	C₄⋊C₄×C₁₃₉	—	2	4	no	—
295	C₄⋊C₄×C₁₃₉	—	2	2	no	—
296	C₄⋊C₄×C₁₃₉	—	2	4	no	—
297	C₄⋊C₄×C₁₃₉	—	2	4	no	—
298	C₄⋊C₄×C₁₃₉	—	2	2	no	—
299	C₄⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	2	no	—
302	C₄⋊C₄×C₁₃₉	—	4	2	no	—
303	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
304	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
305	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
307	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
309	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
310	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
313	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
315	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
316	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
318	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
319	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
320	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
321	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
322	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
323	C₄²×C₁₃₉	—	2	2	no	—
324	C₄²×C₁₃₉	—	2	2	no	—
325	C₄²×C₁₃₉	—	2	2	no	—
326	C₄²×C₁₃₉	—	2	2	no	—
327	C₄²×C₁₃₉	—	2	2	no	—
328	C₄²×C₁₃₉	—	2	2	no	—
329	C₄²×C₁₃₉	—	2	4	no	—
330	C₄²×C₁₃₉	—	2	2	no	—
331	C₄²×C₁₃₉	—	2	2	no	—
332	C₄²×C₁₃₉	—	2	2	no	—
333	C₄²×C₁₃₉	—	2	2	no	—
334	C₄²×C₁₃₉	—	2	2	no	—
335	C₄²×C₁₃₉	—	2	2	no	—
336	C₄²×C₁₃₉	—	4	1	no	—
337	C₄²×C₁₃₉	—	4	2	no	—
338	C₄²×C₁₃₉	—	4	1	no	—
339	C₄²×C₁₃₉	—	4	2	no	—
340	C₄²×C₁₃₉	—	4	2	no	—
341	C₄²×C₁₃₉	—	4	2	no	—
342	C₄²×C₁₃₉	#41	1	4	yes	—
343	C₄²×C₁₃₉	#41	1	4	yes	—
344	C₂³×C₁₃₉	—	2	1	no	—
345	C₂³×C₁₃₉	—	2	1	no	—
346	C₂³×C₁₃₉	—	2	1	no	—
347	C₂³×C₁₃₉	—	2	1	no	—
348	C₂³×C₁₃₉	—	2	1	no	—
349	C₂³×C₁₃₉	—	2	1	no	—
350	C₂³×C₁₃₉	—	2	2	no	—
351	C₂³×C₁₃₉	—	2	2	no	—
352	C₂³×C₁₃₉	—	2	2	no	—
353	C₂³×C₁₃₉	—	2	2	no	—
354	C₂³×C₁₃₉	—	2	2	no	—
355	C₂³×C₁₃₉	—	2	2	no	—
356	C₂³×C₁₃₉	—	2	2	no	—
357	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
358	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
359	Q₈×C₁₃₉	—	4	8	no	—
360	D₄×C₁₃₉	—	4	8	no	—
361	D₄×C₁₃₉	—	4	4	no	—
362	C₂×C₄×C₁₃₉	—	2	8	no	—
363	C₂×C₄×C₁₃₉	—	2	1	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	1	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	1	no	—
369	C₂×C₄×C₁₃₉	—	2	1	no	—
370	C₂×C₄×C₁₃₉	—	2	1	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	1	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	1	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	1	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	1	no	—
384	C₂×C₄×C₁₃₉	—	2	1	no	—
385	C₂×C₄×C₁₃₉	—	2	1	no	—
386	C₂×C₄×C₁₃₉	—	2	1	no	—
387	C₂×C₄×C₁₃₉	—	2	1	no	—
388	C₂×C₄×C₁₃₉	—	2	1	no	—
389	C₂×C₄×C₁₃₉	—	2	1	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	2	no	—
394	C₂×C₄×C₁₃₉	—	2	2	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	2	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	2	1	no	—
400	C₂×C₄×C₁₃₉	—	2	1	no	—
401	C₂×C₄×C₁₃₉	—	2	2	no	—
402	C₂×C₄×C₁₃₉	—	2	2	no	—
403	C₂×C₄×C₁₃₉	—	2	2	no	—
404	C₂×C₄×C₁₃₉	—	2	2	no	—
405	C₂×C₄×C₁₃₉	—	2	1	no	—
406	C₂×C₄×C₁₃₉	—	2	1	no	—
407	C₂×C₄×C₁₃₉	—	2	2	no	—
408	C₂×C₄×C₁₃₉	—	2	1	no	—
409	C₂×C₄×C₁₃₉	—	2	1	no	—
410	C₂×C₄×C₁₃₉	—	2	2	no	—
411	C₂×C₄×C₁₃₉	—	2	1	no	—
412	C₂×C₄×C₁₃₉	—	2	2	no	—
413	C₂×C₄×C₁₃₉	—	2	2	no	—
414	C₂×C₄×C₁₃₉	—	4	4	no	—
415	C₂×C₄×C₁₃₉	—	4	4	no	—
416	C₂×C₄×C₁₃₉	—	8	4	no	—
417	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
418	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
419	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
420	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
421	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
425	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
426	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
427	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
428	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
429	C₂²×C₁₃₉	—	2	2	no	—
430	C₂²×C₁₃₉	—	2	2	no	—
431	C₂²×C₁₃₉	—	2	2	no	—
432	C₂²×C₁₃₉	—	4	1	no	—
433	C₂²×C₁₃₉	—	4	1	no	—
434	C₂²×C₁₃₉	—	4	1	no	—
435	C₂²×C₁₃₉	—	4	1	no	—
436	C₂²×C₁₃₉	—	4	2	no	—
437	C₂²×C₁₃₉	—	4	2	no	—
438	C₂²×C₁₃₉	—	4	2	no	—
439	C₂²×C₁₃₉	—	4	2	no	—
440	C₂²×C₁₃₉	—	4	2	no	—
441	C₂²×C₁₃₉	—	4	2	no	—
442	C₂²×C₁₃₉	—	4	2	no	—
443	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
447	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂²×C₁₃₉	#585	1	1	yes	characteristic
450	C₄×C₁₃₉	—	2	2	no	—
451	C₄×C₁₃₉	—	2	2	no	—
452	C₄×C₁₃₉	—	2	2	no	—
453	C₄×C₁₃₉	—	2	4	no	—
454	C₄×C₁₃₉	—	2	2	no	—
455	C₄×C₁₃₉	—	2	2	no	—
456	C₄×C₁₃₉	—	2	2	no	—
457	C₄×C₁₃₉	—	2	2	no	—
458	C₄×C₁₃₉	—	2	2	no	—
459	C₄×C₁₃₉	—	4	2	no	—
460	C₄×C₁₃₉	—	4	1	no	—
461	C₄×C₁₃₉	—	4	1	no	—
462	C₄×C₁₃₉	—	4	2	no	—
463	C₄×C₁₃₉	—	4	1	no	—
464	C₄×C₁₃₉	—	4	2	no	—
465	C₄×C₁₃₉	—	4	2	no	—
466	C₄×C₁₃₉	—	4	2	no	—
467	C₄×C₁₃₉	—	4	1	no	—
468	C₄×C₁₃₉	—	4	2	no	—
469	C₄×C₁₃₉	—	4	1	no	—
470	C₄×C₁₃₉	#556	1	4	yes	—
471	C₂×C₁₃₉	—	4	2	no	—
472	C₂×C₁₃₉	—	8	2	no	—
473	C₂×C₁₃₉	#3444	1	1	yes	characteristic
474	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
475	C₂×C₁₃₉	#3480	1	1	yes	characteristic
476	C₂×C₁₃₉	#3481	1	1	yes	characteristic
477	C₂×C₁₃₉	#3494	1	1	yes	characteristic
478	C₂×C₁₃₉	#3511	1	1	yes	characteristic
479	C₂×C₁₃₉	#3515	1	1	yes	characteristic
480	#36503	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
481	C₁₃₉	#36503	1	1	yes	characteristic, direct product factor, Sylow
482	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	#2851	C₂×C₁₃₉	1	1	yes	characteristic, complemented
485	#2601	C₂×C₁₃₉	1	2	yes	complemented
486	#2594	C₂×C₁₃₉	1	2	yes	complemented
487	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
488	#2550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
489	#2527	C₂×C₁₃₉	1	2	yes	complemented
490	#2497	C₂×C₁₃₉	1	1	yes	characteristic, complemented
491	#2494	C₂×C₁₃₉	1	1	yes	characteristic, complemented
492	#2491	C₂×C₁₃₉	1	1	yes	characteristic
493	#2490	C₂×C₁₃₉	1	1	yes	characteristic
494	#2474	C₂×C₁₃₉	1	2	yes	complemented
495	#2469	C₂×C₁₃₉	1	2	yes	complemented
496	#2466	C₂×C₁₃₉	1	2	yes	complemented
497	#2373	C₂×C₁₃₉	1	2	yes	complemented
498	#2370	C₂×C₁₃₉	1	1	yes	characteristic, complemented
499	#2367	C₂×C₁₃₉	1	2	yes	complemented
500	#2357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
501	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
502	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
503	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic
504	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
505	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
507	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
508	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
509	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
510	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
511	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
512	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
515	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
516	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
517	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
518	#401	C₂²×C₁₃₉	1	2	yes	—
519	#400	C₂²×C₁₃₉	1	2	yes	—
520	#398	C₂²×C₁₃₉	1	2	yes	—
521	#397	C₂²×C₁₃₉	1	2	yes	—
522	#397	C₂²×C₁₃₉	1	2	yes	—
523	#396	C₂²×C₁₃₉	1	2	yes	—
524	#396	C₂²×C₁₃₉	1	2	yes	—
525	#396	C₂²×C₁₃₉	1	2	yes	—
526	#395	C₂²×C₁₃₉	1	2	yes	—
527	#394	C₂²×C₁₃₉	1	2	yes	—
528	#394	C₂²×C₁₃₉	1	2	yes	—
529	#393	C₂²×C₁₃₉	1	2	yes	—
530	#391	C₂²×C₁₃₉	1	2	yes	—
531	#391	C₂²×C₁₃₉	1	2	yes	—
532	#390	C₂²×C₁₃₉	1	1	yes	characteristic
533	#390	C₂²×C₁₃₉	1	1	yes	characteristic
534	#390	C₂²×C₁₃₉	1	2	yes	—
535	#390	C₂²×C₁₃₉	1	1	yes	characteristic
536	#390	C₂²×C₁₃₉	1	1	yes	characteristic
537	#390	C₂²×C₁₃₉	1	1	yes	characteristic
538	#389	C₂²×C₁₃₉	1	1	yes	characteristic
539	#389	C₂²×C₁₃₉	1	1	yes	characteristic
540	#389	C₂²×C₁₃₉	1	2	yes	—
541	#389	C₂²×C₁₃₉	1	1	yes	characteristic
542	#389	C₂²×C₁₃₉	1	2	yes	—
543	#389	C₂²×C₁₃₉	1	1	yes	characteristic
544	#389	C₂²×C₁₃₉	1	1	yes	characteristic
545	#389	C₂²×C₁₃₉	1	1	yes	characteristic
546	#389	C₂²×C₁₃₉	1	1	yes	characteristic
547	#389	C₂²×C₁₃₉	1	2	yes	—
548	#388	C₂²×C₁₃₉	1	2	yes	—
549	#388	C₂²×C₁₃₉	1	2	yes	—
550	#388	C₂²×C₁₃₉	1	2	yes	—
551	#388	C₂²×C₁₃₉	1	2	yes	—
552	#388	C₂²×C₁₃₉	1	2	yes	—
553	#388	C₂²×C₁₃₉	1	2	yes	—
554	#388	C₂²×C₁₃₉	1	2	yes	—
555	#388	C₂²×C₁₃₉	1	2	yes	—
556	#388	C₂²×C₁₃₉	1	2	yes	—
557	#388	C₂²×C₁₃₉	1	2	yes	—
558	#388	C₂²×C₁₃₉	1	2	yes	—
559	#388	C₂²×C₁₃₉	1	2	yes	—
560	#388	C₂²×C₁₃₉	1	2	yes	—
561	#387	C₂²×C₁₃₉	1	2	yes	—
562	#387	C₂²×C₁₃₉	1	2	yes	—
563	#387	C₂²×C₁₃₉	1	2	yes	—
564	#387	C₂²×C₁₃₉	1	2	yes	—
565	#387	C₂²×C₁₃₉	1	2	yes	—
566	#387	C₂²×C₁₃₉	1	2	yes	—
567	#387	C₂²×C₁₃₉	1	2	yes	—
568	#387	C₂²×C₁₃₉	1	2	yes	—
569	#386	C₂²×C₁₃₉	1	2	yes	—
570	#385	C₂²×C₁₃₉	1	2	yes	—
571	#385	C₂²×C₁₃₉	1	2	yes	—
572	#385	C₂²×C₁₃₉	1	2	yes	—
573	#385	C₂²×C₁₃₉	1	2	yes	—
574	#384	C₂²×C₁₃₉	1	1	yes	characteristic
575	#382	C₂²×C₁₃₉	1	1	yes	characteristic
576	#382	C₂²×C₁₃₉	1	1	yes	characteristic
577	#381	C₂²×C₁₃₉	1	2	yes	—
578	#380	C₂²×C₁₃₉	1	1	yes	characteristic
579	#380	C₂²×C₁₃₉	1	1	yes	characteristic
580	#380	C₂²×C₁₃₉	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
582	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
586	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
592	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
594	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
595	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
597	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
598	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
600	#376	C₂²×C₁₃₉	1	1	yes	characteristic
601	#376	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
603	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₄⋊Q₈	—	2	4	no	—
612	#126	—	2	8	no	—
613	#126	—	4	4	no	—
614	#125	—	2	4	no	—
615	#125	—	2	4	no	—
616	#124	—	2	8	no	—
617	#121	—	2	4	no	—
618	C₄×Q₈	—	4	4	no	—
619	C₄×D₄	—	2	4	no	—
620	C₄×D₄	—	4	4	no	—
621	#117	—	2	4	no	—
622	#117	—	2	4	no	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
667	C₂×C₄²	—	2	4	no	—
668	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
673	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
682	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
683	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
684	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
687	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
689	#95	C₂³×C₁₃₉	1	1	yes	characteristic
690	#95	C₂³×C₁₃₉	1	1	yes	characteristic
691	#95	C₂³×C₁₃₉	1	1	yes	characteristic
692	#95	C₂³×C₁₃₉	1	1	yes	characteristic
693	#95	C₂³×C₁₃₉	1	1	yes	characteristic
694	#95	C₂³×C₁₃₉	1	1	yes	characteristic
695	#95	C₂³×C₁₃₉	1	1	yes	characteristic
696	#95	C₂³×C₁₃₉	1	1	yes	characteristic
697	#95	C₂³×C₁₃₉	1	2	yes	—
698	#95	C₂³×C₁₃₉	1	2	yes	—
699	#95	C₂³×C₁₃₉	1	2	yes	—
700	#95	C₂³×C₁₃₉	1	2	yes	—
701	#95	C₂³×C₁₃₉	1	2	yes	—
702	#95	C₂³×C₁₃₉	1	2	yes	—
703	#95	C₂³×C₁₃₉	1	2	yes	—
704	#95	C₂³×C₁₃₉	1	2	yes	—
705	#95	C₂³×C₁₃₉	1	2	yes	—
706	#95	C₂³×C₁₃₉	1	2	yes	—
707	#95	C₂³×C₁₃₉	1	2	yes	—
708	#95	C₂³×C₁₃₉	1	2	yes	—
709	#95	C₂³×C₁₃₉	1	2	yes	—
710	#95	C₂³×C₁₃₉	1	2	yes	—
711	#95	C₂³×C₁₃₉	1	2	yes	—
712	#95	C₂³×C₁₃₉	1	2	yes	—
713	#95	C₂³×C₁₃₉	1	2	yes	—
714	#95	C₂³×C₁₃₉	1	2	yes	—
715	#95	C₂³×C₁₃₉	1	2	yes	—
716	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
717	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	4	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	4	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	4	1	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	1	no	—
820	C₄²	—	4	2	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	#41×C₁₃₉	1	4	yes	—
824	C₄²	#41×C₁₃₉	1	4	yes	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
839	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
840	Q₈	—	4	8	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	4	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
899	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
900	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
901	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
902	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
903	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
904	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
905	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
906	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
907	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
908	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
909	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
925	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
926	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
927	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
928	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
929	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
930	C₂²	#585×C₁₃₉	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	4	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	1	no	—
951	C₄	#556×C₁₃₉	1	4	yes	—
952	C₂	—	4	2	no	—
953	C₂	—	8	2	no	—
954	C₂	#3444×C₁₃₉	1	1	yes	characteristic
955	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
956	C₂	#3480×C₁₃₉	1	1	yes	characteristic
957	C₂	#3481×C₁₃₉	1	1	yes	characteristic
958	C₂	#3494×C₁₃₉	1	1	yes	characteristic
959	C₂	#3511×C₁₃₉	1	1	yes	characteristic
960	C₂	#3515×C₁₃₉	1	1	yes	characteristic

	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. #2860×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2851×C₁₃₉	C₂	semidirect
4. #2601×C₁₃₉	C₂	semidirect
5. #2594×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2550×C₁₃₉	C₂	semidirect
8. #2527×C₁₃₉	C₂	semidirect
9. #2497×C₁₃₉	C₂	semidirect
10. #2494×C₁₃₉	C₂	semidirect
13. #2474×C₁₃₉	C₂	semidirect
14. #2469×C₁₃₉	C₂	semidirect
15. #2466×C₁₃₉	C₂	semidirect
16. #2373×C₁₃₉	C₂	semidirect
17. #2370×C₁₃₉	C₂	semidirect
18. #2367×C₁₃₉	C₂	semidirect
19. #2357×C₁₃₉	C₂	semidirect
20. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
21. C₄×#125×C₁₃₉	C₂	semidirect
23. C₄×#117×C₁₃₉	C₂	semidirect
480. #36503	C₁₃₉	direct (N × H)
481. C₁₃₉	#36503	direct (N × H)
482. #2860	C₂×C₁₃₉	semidirect
483. #2860	C₂×C₁₃₉	semidirect
484. #2851	C₂×C₁₃₉	semidirect
485. #2601	C₂×C₁₃₉	semidirect
486. #2594	C₂×C₁₃₉	semidirect
487. #2566	C₂×C₁₃₉	semidirect
488. #2550	C₂×C₁₃₉	semidirect
489. #2527	C₂×C₁₃₉	semidirect
490. #2497	C₂×C₁₃₉	semidirect
491. #2494	C₂×C₁₃₉	semidirect
494. #2474	C₂×C₁₃₉	semidirect
495. #2469	C₂×C₁₃₉	semidirect
496. #2466	C₂×C₁₃₉	semidirect
497. #2373	C₂×C₁₃₉	semidirect
498. #2370	C₂×C₁₃₉	semidirect
499. #2367	C₂×C₁₃₉	semidirect
500. #2357	C₂×C₁₃₉	semidirect
501. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
502. C₄×#125	C₂×C₁₃₉	semidirect
504. C₄×#117	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2851×C₁₃₉	2
#2601×C₁₃₉	2
#2594×C₁₃₉	2
#2566×C₁₃₉	2
#2550×C₁₃₉	2
#2527×C₁₃₉	2
#2497×C₁₃₉	2
#2494×C₁₃₉	2
#2491×C₁₃₉	2
#2490×C₁₃₉	2
#2474×C₁₃₉	2
#2469×C₁₃₉	2
#2466×C₁₃₉	2
#2373×C₁₃₉	2
#2370×C₁₃₉	2
#2367×C₁₃₉	2
#2357×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄×#125×C₁₃₉	2
C₄×#121×C₁₃₉	2
C₄×#117×C₁₃₉	2
#36503	139

Subgroups — C139×#36503 #48031099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36503 #48031099