Subgroups — C₁₃₉×#36077 #48030673

Order 35584.

2286 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2632×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2624×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2599×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2592×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2476×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2474×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2436×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2409×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	#555×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	#519×C₁₃₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
39	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
40	#400×C₁₃₉	C₂²	1	1	yes	characteristic
41	#399×C₁₃₉	C₂²	1	2	yes	—
42	#399×C₁₃₉	C₂²	1	1	yes	characteristic
43	#398×C₁₃₉	C₂²	1	1	yes	characteristic
44	#398×C₁₃₉	C₂²	1	4	yes	—
45	#397×C₁₃₉	C₂²	1	1	yes	characteristic
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	4	yes	—
49	#395×C₁₃₉	C₂²	1	2	yes	—
50	#395×C₁₃₉	C₂²	1	4	yes	—
51	#394×C₁₃₉	C₂²	1	4	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#393×C₁₃₉	C₂²	1	2	yes	—
55	#393×C₁₃₉	C₂²	1	2	yes	—
56	#393×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	4	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	4	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	—
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#388×C₁₃₉	C₂²	1	4	yes	—
70	#387×C₁₃₉	C₂²	1	4	yes	—
71	#387×C₁₃₉	C₂²	1	4	yes	—
72	#386×C₁₃₉	C₂²	1	2	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	2	yes	—
76	#383×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
85	C₂²×Q₈×C₁₃₉	—	2	8	no	—
86	C₂²×Q₈×C₁₃₉	—	2	4	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
99	#124×C₁₃₉	—	2	8	no	—
100	#124×C₁₃₉	—	2	8	no	—
101	#124×C₁₃₉	—	2	8	no	—
102	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
103	#121×C₁₃₉	—	2	4	no	—
104	#121×C₁₃₉	—	2	4	no	—
105	#121×C₁₃₉	—	2	8	no	—
106	C₄×Q₈×C₁₃₉	—	2	8	no	—
107	C₄×Q₈×C₁₃₉	—	2	8	no	—
108	C₄×Q₈×C₁₃₉	—	2	8	no	—
109	C₄×Q₈×C₁₃₉	—	2	8	no	—
110	C₄×D₄×C₁₃₉	—	2	4	no	—
111	C₄×D₄×C₁₃₉	—	2	4	no	—
112	#117×C₁₃₉	—	2	4	no	—
113	#117×C₁₃₉	—	2	4	no	—
114	#117×C₁₃₉	—	2	16	no	—
115	#117×C₁₃₉	—	2	8	no	—
116	#117×C₁₃₉	D₄	1	8	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	4	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	1	yes	characteristic
169	#95×C₁₃₉	C₂³	1	4	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	32	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	—	2	8	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	4	4	no	—
181	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
182	C₂×D₄×C₁₃₉	—	2	2	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	2	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	4	1	no	—
189	C₂×D₄×C₁₃₉	—	4	4	no	—
190	C₂×D₄×C₁₃₉	—	4	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	8	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	4	2	no	—
199	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₄×C₁₃₉	—	2	2	no	—
215	C₄⋊C₄×C₁₃₉	—	2	8	no	—
216	C₄⋊C₄×C₁₃₉	—	2	8	no	—
217	C₄⋊C₄×C₁₃₉	—	2	2	no	—
218	C₄⋊C₄×C₁₃₉	—	2	2	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	8	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	4	4	no	—
225	C₄⋊C₄×C₁₃₉	—	4	2	no	—
226	C₄⋊C₄×C₁₃₉	—	4	4	no	—
227	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
228	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
229	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
239	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
240	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
241	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	4	4	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	8	no	—
249	C₄²×C₁₃₉	—	2	4	no	—
250	C₄²×C₁₃₉	—	2	2	no	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₄²×C₁₃₉	—	4	4	no	—
253	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	1	no	—
256	C₂³×C₁₃₉	—	2	1	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	—	2	1	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	4	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	1	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	4	no	—
268	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
269	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
270	Q₈×C₁₃₉	—	2	16	no	—
271	Q₈×C₁₃₉	—	2	16	no	—
272	Q₈×C₁₃₉	—	8	4	no	—
273	D₄×C₁₃₉	—	4	4	no	—
274	D₄×C₁₃₉	—	4	4	no	—
275	D₄×C₁₃₉	—	8	4	no	—
276	D₄×C₁₃₉	—	8	4	no	—
277	C₂×C₄×C₁₃₉	—	2	16	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	1	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	4	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	8	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	1	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	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	4	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	2	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	4	8	no	—
309	C₂×C₄×C₁₃₉	—	4	4	no	—
310	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	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	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
317	C₂²×C₁₃₉	—	2	2	no	—
318	C₂²×C₁₃₉	—	2	2	no	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	4	2	no	—
321	C₂²×C₁₃₉	—	4	2	no	—
322	C₂²×C₁₃₉	—	4	1	no	—
323	C₂²×C₁₃₉	—	4	2	no	—
324	C₂²×C₁₃₉	—	4	2	no	—
325	C₂²×C₁₃₉	—	4	1	no	—
326	C₂²×C₁₃₉	—	4	1	no	—
327	C₂²×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	4	2	no	—
329	C₂²×C₁₃₉	—	4	4	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	4	no	—
332	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
333	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
334	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂²×C₁₃₉	#585	1	1	yes	characteristic
336	C₂²×C₁₃₉	#585	1	2	yes	—
337	C₄×C₁₃₉	—	2	2	no	—
338	C₄×C₁₃₉	—	2	8	no	—
339	C₄×C₁₃₉	—	2	2	no	—
340	C₄×C₁₃₉	—	2	4	no	—
341	C₄×C₁₃₉	—	2	4	no	—
342	C₄×C₁₃₉	—	4	1	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	1	no	—
347	C₄×C₁₃₉	—	4	2	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	4	no	—
350	C₄×C₁₃₉	#525	1	4	yes	—
351	C₂×C₁₃₉	—	4	2	no	—
352	C₂×C₁₃₉	—	8	1	no	—
353	C₂×C₁₃₉	—	8	2	no	—
354	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
355	C₂×C₁₃₉	#3489	1	1	yes	characteristic
356	C₂×C₁₃₉	#3500	1	1	yes	characteristic
357	C₂×C₁₃₉	#3518	1	2	yes	—
358	C₂×C₁₃₉	#3524	1	2	yes	—
359	#36077	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₁₃₉	#36077	1	1	yes	characteristic, direct product factor, Sylow
361	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic
362	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
363	#2632	C₂×C₁₃₉	1	2	yes	complemented
364	#2624	C₂×C₁₃₉	1	1	yes	characteristic, complemented
365	#2599	C₂×C₁₃₉	1	2	yes	complemented
366	#2592	C₂×C₁₃₉	1	2	yes	complemented
367	#2476	C₂×C₁₃₉	1	4	yes	complemented
368	#2474	C₂×C₁₃₉	1	4	yes	complemented
369	#2451	C₂×C₁₃₉	1	2	yes	complemented
370	#2436	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	#2426	C₂×C₁₃₉	1	2	yes	complemented
372	#2409	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	#2396	C₂×C₁₃₉	1	2	yes	complemented
374	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	#2367	C₂×C₁₃₉	1	2	yes	complemented
376	#2362	C₂×C₁₃₉	1	2	yes	complemented
377	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
378	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
379	#555	—	2	8	no	—
380	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
382	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
383	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
384	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
385	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
386	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
387	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
388	#519	—	2	8	no	—
389	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
390	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
391	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
392	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
393	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
398	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
399	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
400	#400	C₂²×C₁₃₉	1	1	yes	characteristic
401	#399	C₂²×C₁₃₉	1	2	yes	—
402	#399	C₂²×C₁₃₉	1	1	yes	characteristic
403	#398	C₂²×C₁₃₉	1	1	yes	characteristic
404	#398	C₂²×C₁₃₉	1	4	yes	—
405	#397	C₂²×C₁₃₉	1	1	yes	characteristic
406	#397	C₂²×C₁₃₉	1	2	yes	—
407	#397	C₂²×C₁₃₉	1	2	yes	—
408	#396	C₂²×C₁₃₉	1	4	yes	—
409	#395	C₂²×C₁₃₉	1	2	yes	—
410	#395	C₂²×C₁₃₉	1	4	yes	—
411	#394	C₂²×C₁₃₉	1	4	yes	—
412	#394	C₂²×C₁₃₉	1	4	yes	—
413	#394	C₂²×C₁₃₉	1	2	yes	—
414	#393	C₂²×C₁₃₉	1	2	yes	—
415	#393	C₂²×C₁₃₉	1	2	yes	—
416	#393	C₂²×C₁₃₉	1	2	yes	—
417	#391	C₂²×C₁₃₉	1	4	yes	—
418	#391	C₂²×C₁₃₉	1	2	yes	—
419	#391	C₂²×C₁₃₉	1	2	yes	—
420	#390	C₂²×C₁₃₉	1	4	yes	—
421	#390	C₂²×C₁₃₉	1	2	yes	—
422	#389	C₂²×C₁₃₉	1	2	yes	—
423	#389	C₂²×C₁₃₉	1	2	yes	—
424	#388	C₂²×C₁₃₉	1	4	yes	—
425	#388	C₂²×C₁₃₉	1	4	yes	—
426	#388	C₂²×C₁₃₉	1	4	yes	—
427	#388	C₂²×C₁₃₉	1	4	yes	—
428	#388	C₂²×C₁₃₉	1	4	yes	—
429	#388	C₂²×C₁₃₉	1	4	yes	—
430	#387	C₂²×C₁₃₉	1	4	yes	—
431	#387	C₂²×C₁₃₉	1	4	yes	—
432	#386	C₂²×C₁₃₉	1	2	yes	—
433	#386	C₂²×C₁₃₉	1	4	yes	—
434	#385	C₂²×C₁₃₉	1	4	yes	—
435	#385	C₂²×C₁₃₉	1	2	yes	—
436	#383	C₂²×C₁₃₉	1	2	yes	—
437	#380	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
441	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
445	C₂²×Q₈	—	2	8	no	—
446	C₂²×Q₈	—	2	4	no	—
447	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
448	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
449	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
450	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
455	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
457	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
458	C₄⋊Q₈	—	2	4	no	—
459	#124	—	2	8	no	—
460	#124	—	2	8	no	—
461	#124	—	2	8	no	—
462	C₂²⋊Q₈	—	2	8	no	—
463	#121	—	2	4	no	—
464	#121	—	2	4	no	—
465	#121	—	2	8	no	—
466	C₄×Q₈	—	2	8	no	—
467	C₄×Q₈	—	2	8	no	—
468	C₄×Q₈	—	2	8	no	—
469	C₄×Q₈	—	2	8	no	—
470	C₄×D₄	—	2	4	no	—
471	C₄×D₄	—	2	4	no	—
472	#117	—	2	4	no	—
473	#117	—	2	4	no	—
474	#117	—	2	16	no	—
475	#117	—	2	8	no	—
476	#117	D₄×C₁₃₉	1	8	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	2	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	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₄²	C₂³×C₁₃₉	1	2	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	1	yes	characteristic
521	#95	C₂³×C₁₃₉	1	4	yes	—
522	#95	C₂³×C₁₃₉	1	2	yes	—
523	#95	C₂³×C₁₃₉	1	2	yes	—
524	#95	C₂³×C₁₃₉	1	4	yes	—
525	#95	C₂³×C₁₃₉	1	4	yes	—
526	#95	C₂³×C₁₃₉	1	2	yes	—
527	#95	C₂³×C₁₃₉	1	4	yes	—
528	#95	C₂³×C₁₃₉	1	4	yes	—
529	#95	C₂³×C₁₃₉	1	4	yes	—
530	#95	C₂³×C₁₃₉	1	4	yes	—
531	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
532	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
533	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
534	C₂×Q₈	—	2	32	no	—
535	C₂×Q₈	—	2	4	no	—
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	2	4	no	—
538	C₂×Q₈	—	2	8	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	4	1	no	—
549	C₂×D₄	—	4	4	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	8	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	8	no	—
576	C₄⋊C₄	—	2	8	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	4	4	no	—
587	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
588	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	8	no	—
608	C₄²	—	2	8	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	4	4	no	—
613	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
629	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
630	Q₈	—	2	16	no	—
631	Q₈	—	2	16	no	—
632	Q₈	—	8	4	no	—
633	D₄	—	4	4	no	—
634	D₄	—	4	4	no	—
635	D₄	—	8	4	no	—
636	D₄	—	8	4	no	—
637	C₂×C₄	—	2	16	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	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	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
672	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
674	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
675	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
676	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	4	no	—
692	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
693	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
694	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
695	C₂²	#585×C₁₃₉	1	1	yes	characteristic
696	C₂²	#585×C₁₃₉	1	2	yes	—
697	C₄	—	2	2	no	—
698	C₄	—	2	8	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	4	no	—
701	C₄	—	2	4	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	4	no	—
710	C₄	#525×C₁₃₉	1	4	yes	—
711	C₂	—	4	2	no	—
712	C₂	—	8	1	no	—
713	C₂	—	8	2	no	—
714	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
715	C₂	#3489×C₁₃₉	1	1	yes	characteristic
716	C₂	#3500×C₁₃₉	1	1	yes	characteristic
717	C₂	#3518×C₁₃₉	1	2	yes	—
718	C₂	#3524×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#555×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
2. C₂×#519×C₁₃₉	C₂	semidirect
3. #2632×C₁₃₉	C₂	semidirect
4. #2624×C₁₃₉	C₂	semidirect
5. #2599×C₁₃₉	C₂	semidirect
6. #2592×C₁₃₉	C₂	semidirect
7. #2476×C₁₃₉	C₂	semidirect
8. #2474×C₁₃₉	C₂	semidirect
9. #2451×C₁₃₉	C₂	semidirect
10. #2436×C₁₃₉	C₂	semidirect
11. #2426×C₁₃₉	C₂	semidirect
12. #2409×C₁₃₉	C₂	semidirect
13. #2396×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. #2367×C₁₃₉	C₂	semidirect
16. #2362×C₁₃₉	C₂	semidirect
17. #2347×C₁₃₉	C₂	semidirect
359. #36077	C₁₃₉	direct (N × H)
360. C₁₃₉	#36077	direct (N × H)
362. C₂×#519	C₂×C₁₃₉	semidirect
363. #2632	C₂×C₁₃₉	semidirect
364. #2624	C₂×C₁₃₉	semidirect
365. #2599	C₂×C₁₃₉	semidirect
366. #2592	C₂×C₁₃₉	semidirect
367. #2476	C₂×C₁₃₉	semidirect
368. #2474	C₂×C₁₃₉	semidirect
369. #2451	C₂×C₁₃₉	semidirect
370. #2436	C₂×C₁₃₉	semidirect
371. #2426	C₂×C₁₃₉	semidirect
372. #2409	C₂×C₁₃₉	semidirect
373. #2396	C₂×C₁₃₉	semidirect
374. #2395	C₂×C₁₃₉	semidirect
375. #2367	C₂×C₁₃₉	semidirect
376. #2362	C₂×C₁₃₉	semidirect
377. #2347	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×#555×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2632×C₁₃₉	2
#2624×C₁₃₉	2
#2599×C₁₃₉	2
#2592×C₁₃₉	2
#2476×C₁₃₉	2
#2474×C₁₃₉	2
#2451×C₁₃₉	2
#2436×C₁₃₉	2
#2426×C₁₃₉	2
#2409×C₁₃₉	2
#2396×C₁₃₉	2
#2395×C₁₃₉	2
#2367×C₁₃₉	2
#2362×C₁₃₉	2
#2347×C₁₃₉	2
#36077	139

Subgroups — C139×#36077 #48030673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36077 #48030673