Subgroups — C₁₃₉×#35856 #48030452

Order 35584.

2186 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2663×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2642×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2564×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2559×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2496×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#556×C₁₃₉	—	2	8	no	—
19	#553×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	#400×C₁₃₉	C₂²	1	4	yes	—
42	#400×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	2	yes	—
44	#400×C₁₃₉	C₂²	1	2	yes	—
45	#399×C₁₃₉	C₂²	1	2	yes	—
46	#399×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	1	yes	characteristic
49	#397×C₁₃₉	C₂²	1	4	yes	—
50	#397×C₁₃₉	C₂²	1	1	yes	characteristic
51	#397×C₁₃₉	C₂²	1	4	yes	—
52	#395×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#393×C₁₃₉	C₂²	1	1	yes	characteristic
57	#393×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	4	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	—
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#387×C₁₃₉	C₂²	1	4	yes	—
68	#387×C₁₃₉	C₂²	1	4	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	—
70	#386×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#384×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	4	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	#376×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
85	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
97	#126×C₁₃₉	—	2	8	no	—
98	#126×C₁₃₉	—	2	16	no	—
99	#125×C₁₃₉	—	2	4	no	—
100	#124×C₁₃₉	—	2	8	no	—
101	#123×C₁₃₉	—	2	8	no	—
102	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
105	#121×C₁₃₉	—	2	4	no	—
106	#121×C₁₃₉	—	2	4	no	—
107	#121×C₁₃₉	—	2	8	no	—
108	C₄×Q₈×C₁₃₉	—	2	8	no	—
109	C₄×Q₈×C₁₃₉	—	2	4	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
114	#117×C₁₃₉	—	2	8	no	—
115	#117×C₁₃₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	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	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	1	yes	characteristic
162	#95×C₁₃₉	C₂³	1	1	yes	characteristic
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂×Q₈×C₁₃₉	—	2	2	no	—
175	C₂×Q₈×C₁₃₉	—	2	4	no	—
176	C₂×Q₈×C₁₃₉	—	2	4	no	—
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	4	2	no	—
179	C₂×D₄×C₁₃₉	—	2	4	no	—
180	C₂×D₄×C₁₃₉	—	2	2	no	—
181	C₂×D₄×C₁₃₉	—	2	4	no	—
182	C₂×D₄×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	2	no	—
184	C₂×D₄×C₁₃₉	—	2	4	no	—
185	C₂×D₄×C₁₃₉	—	4	1	no	—
186	C₂×D₄×C₁₃₉	—	4	2	no	—
187	C₂×D₄×C₁₃₉	—	4	4	no	—
188	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	2	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	8	no	—
195	C₂²×C₄×C₁₃₉	—	4	4	no	—
196	C₂²×C₄×C₁₃₉	—	4	4	no	—
197	C₂²×C₄×C₁₃₉	—	4	4	no	—
198	C₂²×C₄×C₁₃₉	—	4	4	no	—
199	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₄×C₁₃₉	—	2	2	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	—	2	2	no	—
217	C₄⋊C₄×C₁₃₉	—	2	2	no	—
218	C₄⋊C₄×C₁₃₉	—	2	4	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	8	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	8	no	—
226	C₄⋊C₄×C₁₃₉	—	2	8	no	—
227	C₄⋊C₄×C₁₃₉	—	4	4	no	—
228	C₄⋊C₄×C₁₃₉	—	4	4	no	—
229	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
230	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
231	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
235	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
244	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
245	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
246	C₄²×C₁₃₉	—	2	4	no	—
247	C₄²×C₁₃₉	—	2	8	no	—
248	C₄²×C₁₃₉	—	2	4	no	—
249	C₄²×C₁₃₉	—	2	4	no	—
250	C₄²×C₁₃₉	—	4	2	no	—
251	C₄²×C₁₃₉	—	4	4	no	—
252	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
253	C₂³×C₁₃₉	—	2	1	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	4	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	—	2	4	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	1	no	—
261	C₂³×C₁₃₉	—	2	1	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	1	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
267	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
268	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
269	Q₈×C₁₃₉	—	4	4	no	—
270	Q₈×C₁₃₉	—	4	8	no	—
271	D₄×C₁₃₉	—	2	8	no	—
272	D₄×C₁₃₉	—	4	4	no	—
273	D₄×C₁₃₉	—	4	8	no	—
274	D₄×C₁₃₉	—	8	4	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	1	no	—
277	C₂×C₄×C₁₃₉	—	2	4	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	1	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	2	4	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	4	8	no	—
306	C₂×C₄×C₁₃₉	—	4	4	no	—
307	C₂×C₄×C₁₃₉	—	4	4	no	—
308	C₂×C₄×C₁₃₉	—	8	4	no	—
309	C₂×C₄×C₁₃₉	—	8	8	no	—
310	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
315	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
316	C₂²×C₁₃₉	—	2	4	no	—
317	C₂²×C₁₃₉	—	2	4	no	—
318	C₂²×C₁₃₉	—	2	2	no	—
319	C₂²×C₁₃₉	—	2	4	no	—
320	C₂²×C₁₃₉	—	2	4	no	—
321	C₂²×C₁₃₉	—	4	1	no	—
322	C₂²×C₁₃₉	—	4	1	no	—
323	C₂²×C₁₃₉	—	4	4	no	—
324	C₂²×C₁₃₉	—	4	4	no	—
325	C₂²×C₁₃₉	—	4	2	no	—
326	C₂²×C₁₃₉	—	4	1	no	—
327	C₂²×C₁₃₉	—	4	1	no	—
328	C₂²×C₁₃₉	—	4	1	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
332	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
333	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
334	C₂²×C₁₃₉	#585	1	2	yes	—
335	C₂²×C₁₃₉	#585	1	1	yes	characteristic
336	C₄×C₁₃₉	—	2	2	no	—
337	C₄×C₁₃₉	—	2	4	no	—
338	C₄×C₁₃₉	—	2	2	no	—
339	C₄×C₁₃₉	—	2	8	no	—
340	C₄×C₁₃₉	—	4	1	no	—
341	C₄×C₁₃₉	—	4	1	no	—
342	C₄×C₁₃₉	—	4	4	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	2	no	—
347	C₄×C₁₃₉	—	4	2	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	#532	1	4	yes	—
350	C₂×C₁₃₉	—	4	4	no	—
351	C₂×C₁₃₉	—	4	2	no	—
352	C₂×C₁₃₉	—	8	1	no	—
353	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
354	C₂×C₁₃₉	#3485	1	1	yes	characteristic
355	C₂×C₁₃₉	#3489	1	1	yes	characteristic
356	C₂×C₁₃₉	#3516	1	2	yes	—
357	C₂×C₁₃₉	#3521	1	2	yes	—
358	#35856	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
359	C₁₃₉	#35856	1	1	yes	characteristic, direct product factor, Sylow
360	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
361	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic
362	#2663	C₂×C₁₃₉	1	2	yes	complemented
363	#2642	C₂×C₁₃₉	1	1	yes	characteristic, complemented
364	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
365	#2564	C₂×C₁₃₉	1	2	yes	complemented
366	#2559	C₂×C₁₃₉	1	4	yes	complemented
367	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#2498	C₂×C₁₃₉	1	2	yes	complemented
369	#2496	C₂×C₁₃₉	1	4	yes	complemented
370	#2427	C₂×C₁₃₉	1	2	yes	complemented
371	#2427	C₂×C₁₃₉	1	2	yes	complemented
372	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	#2395	C₂×C₁₃₉	1	2	yes	complemented
374	#2362	C₂×C₁₃₉	1	2	yes	complemented
375	#2360	C₂×C₁₃₉	1	2	yes	complemented
376	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	#556	—	2	8	no	—
378	#553	—	2	8	no	—
379	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
381	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
382	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
384	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
385	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
388	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
389	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
391	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
393	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
394	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
398	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
399	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
400	#400	C₂²×C₁₃₉	1	2	yes	—
401	#400	C₂²×C₁₃₉	1	2	yes	—
402	#400	C₂²×C₁₃₉	1	4	yes	—
403	#400	C₂²×C₁₃₉	1	2	yes	—
404	#399	C₂²×C₁₃₉	1	2	yes	—
405	#399	C₂²×C₁₃₉	1	2	yes	—
406	#398	C₂²×C₁₃₉	1	2	yes	—
407	#397	C₂²×C₁₃₉	1	1	yes	characteristic
408	#397	C₂²×C₁₃₉	1	4	yes	—
409	#397	C₂²×C₁₃₉	1	1	yes	characteristic
410	#397	C₂²×C₁₃₉	1	4	yes	—
411	#395	C₂²×C₁₃₉	1	2	yes	—
412	#394	C₂²×C₁₃₉	1	4	yes	—
413	#394	C₂²×C₁₃₉	1	2	yes	—
414	#394	C₂²×C₁₃₉	1	4	yes	—
415	#393	C₂²×C₁₃₉	1	1	yes	characteristic
416	#393	C₂²×C₁₃₉	1	1	yes	characteristic
417	#391	C₂²×C₁₃₉	1	2	yes	—
418	#391	C₂²×C₁₃₉	1	2	yes	—
419	#390	C₂²×C₁₃₉	1	2	yes	—
420	#389	C₂²×C₁₃₉	1	2	yes	—
421	#389	C₂²×C₁₃₉	1	2	yes	—
422	#389	C₂²×C₁₃₉	1	4	yes	—
423	#389	C₂²×C₁₃₉	1	4	yes	—
424	#388	C₂²×C₁₃₉	1	4	yes	—
425	#388	C₂²×C₁₃₉	1	4	yes	—
426	#387	C₂²×C₁₃₉	1	4	yes	—
427	#387	C₂²×C₁₃₉	1	4	yes	—
428	#386	C₂²×C₁₃₉	1	4	yes	—
429	#386	C₂²×C₁₃₉	1	4	yes	—
430	#385	C₂²×C₁₃₉	1	4	yes	—
431	#384	C₂²×C₁₃₉	1	2	yes	—
432	#380	C₂²×C₁₃₉	1	4	yes	—
433	#380	C₂²×C₁₃₉	1	4	yes	—
434	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
441	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
442	#376	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
444	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
445	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
450	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
454	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
455	C₄⋊Q₈	—	2	4	no	—
456	#126	—	2	8	no	—
457	#126	—	2	16	no	—
458	#125	—	2	4	no	—
459	#124	—	2	8	no	—
460	#123	—	2	8	no	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₂²⋊Q₈	—	2	8	no	—
463	C₂²⋊Q₈	—	2	8	no	—
464	#121	—	2	4	no	—
465	#121	—	2	4	no	—
466	#121	—	2	8	no	—
467	C₄×Q₈	—	2	8	no	—
468	C₄×Q₈	—	2	4	no	—
469	C₄×D₄	—	2	8	no	—
470	C₄×D₄	—	2	8	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
473	#117	—	2	8	no	—
474	#117	—	2	4	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
515	#95	C₂³×C₁₃₉	1	1	yes	characteristic
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	#95	C₂³×C₁₃₉	1	2	yes	—
518	#95	C₂³×C₁₃₉	1	1	yes	characteristic
519	#95	C₂³×C₁₃₉	1	2	yes	—
520	#95	C₂³×C₁₃₉	1	2	yes	—
521	#95	C₂³×C₁₃₉	1	2	yes	—
522	#95	C₂³×C₁₃₉	1	2	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	2	yes	—
525	#95	C₂³×C₁₃₉	1	4	yes	—
526	#95	C₂³×C₁₃₉	1	4	yes	—
527	#95	C₂³×C₁₃₉	1	4	yes	—
528	#95	C₂³×C₁₃₉	1	4	yes	—
529	#95	C₂³×C₁₃₉	1	4	yes	—
530	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
531	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
532	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	2	4	no	—
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	8	no	—
554	C₂²×C₄	—	4	4	no	—
555	C₂²×C₄	—	4	4	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
559	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	8	no	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	—	4	4	no	—
587	C₄⋊C₄	—	4	4	no	—
588	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
589	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	8	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	8	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	4	2	no	—
610	C₄²	—	4	4	no	—
611	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	2	no	—
625	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
626	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
627	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
628	Q₈	—	4	4	no	—
629	Q₈	—	4	8	no	—
630	D₄	—	2	8	no	—
631	D₄	—	4	4	no	—
632	D₄	—	4	8	no	—
633	D₄	—	8	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	4	8	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	8	4	no	—
668	C₂×C₄	—	8	8	no	—
669	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
673	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
674	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
691	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
692	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
693	C₂²	#585×C₁₃₉	1	2	yes	—
694	C₂²	#585×C₁₃₉	1	1	yes	characteristic
695	C₄	—	2	2	no	—
696	C₄	—	2	4	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	8	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	4	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	#532×C₁₃₉	1	4	yes	—
709	C₂	—	4	4	no	—
710	C₂	—	4	2	no	—
711	C₂	—	8	1	no	—
712	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
713	C₂	#3485×C₁₃₉	1	1	yes	characteristic
714	C₂	#3489×C₁₃₉	1	1	yes	characteristic
715	C₂	#3516×C₁₃₉	1	2	yes	—
716	C₂	#3521×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#553×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×#556×C₁₃₉	C₂	semidirect
3. #2663×C₁₃₉	C₂	semidirect
4. #2642×C₁₃₉	C₂	semidirect
5. #2584×C₁₃₉	C₂	semidirect
6. #2564×C₁₃₉	C₂	semidirect
7. #2559×C₁₃₉	C₂	semidirect
8. #2542×C₁₃₉	C₂	semidirect
9. #2498×C₁₃₉	C₂	semidirect
10. #2496×C₁₃₉	C₂	semidirect
11. #2427×C₁₃₉	C₂	semidirect
12. #2427×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. #2362×C₁₃₉	C₂	semidirect
16. #2360×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
358. #35856	C₁₃₉	direct (N × H)
359. C₁₃₉	#35856	direct (N × H)
360. C₂×#556	C₂×C₁₃₉	semidirect
362. #2663	C₂×C₁₃₉	semidirect
363. #2642	C₂×C₁₃₉	semidirect
364. #2584	C₂×C₁₃₉	semidirect
365. #2564	C₂×C₁₃₉	semidirect
366. #2559	C₂×C₁₃₉	semidirect
367. #2542	C₂×C₁₃₉	semidirect
368. #2498	C₂×C₁₃₉	semidirect
369. #2496	C₂×C₁₃₉	semidirect
370. #2427	C₂×C₁₃₉	semidirect
371. #2427	C₂×C₁₃₉	semidirect
372. #2398	C₂×C₁₃₉	semidirect
373. #2395	C₂×C₁₃₉	semidirect
374. #2362	C₂×C₁₃₉	semidirect
375. #2360	C₂×C₁₃₉	semidirect
376. #2275	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₉	2
C₂×#553×C₁₃₉	2
#2663×C₁₃₉	2
#2642×C₁₃₉	2
#2584×C₁₃₉	2
#2564×C₁₃₉	2
#2559×C₁₃₉	2
#2542×C₁₃₉	2
#2498×C₁₃₉	2
#2496×C₁₃₉	2
#2427×C₁₃₉	2
#2398×C₁₃₉	2
#2395×C₁₃₉	2
#2362×C₁₃₉	2
#2360×C₁₃₉	2
#2275×C₁₃₉	2
#35856	139

Subgroups — C139×#35856 #48030452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35856 #48030452