Subgroups — C₁₃₉×#36582 #48031178

Order 35584.

2416 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2591×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2579×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2469×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2458×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2453×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	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2345×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	#553×C₁₃₉	—	2	8	no	—
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃₉	—	2	8	no	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	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	1	yes	characteristic
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
42	#400×C₁₃₉	C₂²	1	4	yes	—
43	#398×C₁₃₉	C₂²	1	4	yes	—
44	#396×C₁₃₉	C₂²	1	4	yes	—
45	#395×C₁₃₉	C₂²	1	2	yes	—
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#393×C₁₃₉	C₂²	1	2	yes	—
48	#393×C₁₃₉	C₂²	1	4	yes	—
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#390×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	4	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	4	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#388×C₁₃₉	C₂²	1	2	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#388×C₁₃₉	C₂²	1	4	yes	—
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#387×C₁₃₉	C₂²	1	4	yes	—
64	#387×C₁₃₉	C₂²	1	2	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#387×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	1	yes	characteristic
68	#386×C₁₃₉	C₂²	1	2	yes	—
69	#386×C₁₃₉	C₂²	1	2	yes	—
70	#386×C₁₃₉	C₂²	1	2	yes	—
71	#386×C₁₃₉	C₂²	1	2	yes	—
72	#385×C₁₃₉	C₂²	1	1	yes	characteristic
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	—
75	#381×C₁₃₉	C₂²	1	1	yes	characteristic
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊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×D₄×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	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	#126×C₁₃₉	—	2	8	no	—
101	#125×C₁₃₉	—	2	4	no	—
102	#124×C₁₃₉	—	2	8	no	—
103	#123×C₁₃₉	—	2	8	no	—
104	#123×C₁₃₉	—	2	4	no	—
105	#123×C₁₃₉	—	2	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
107	#121×C₁₃₉	—	2	8	no	—
108	#121×C₁₃₉	—	2	4	no	—
109	#121×C₁₃₉	—	2	4	no	—
110	C₄×Q₈×C₁₃₉	—	2	8	no	—
111	C₄×Q₈×C₁₃₉	—	2	8	no	—
112	C₄×Q₈×C₁₃₉	—	2	16	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	#117×C₁₃₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
118	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃₉	—	2	8	no	—
151	C₂×C₄²×C₁₃₉	—	2	4	no	—
152	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	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	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₁₃₉	—	2	32	no	—
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	8	no	—
180	C₂×Q₈×C₁₃₉	—	2	4	no	—
181	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
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	—	2	2	no	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	4	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	2	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	8	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	2	no	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	4	no	—
201	C₂²×C₄×C₁₃₉	—	4	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	2	no	—
203	C₂²×C₄×C₁₃₉	—	4	4	no	—
204	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
206	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₁₃₉	—	2	8	no	—
222	C₄⋊C₄×C₁₃₉	—	2	8	no	—
223	C₄⋊C₄×C₁₃₉	—	2	2	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	8	no	—
229	C₄⋊C₄×C₁₃₉	—	2	8	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	4	4	no	—
232	C₄⋊C₄×C₁₃₉	—	4	2	no	—
233	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
234	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
235	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
236	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
252	C₄²×C₁₃₉	—	2	8	no	—
253	C₄²×C₁₃₉	—	2	8	no	—
254	C₄²×C₁₃₉	—	2	4	no	—
255	C₄²×C₁₃₉	—	2	4	no	—
256	C₄²×C₁₃₉	—	2	4	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	2	4	no	—
259	C₄²×C₁₃₉	—	4	4	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	2	no	—
262	C₂³×C₁₃₉	—	2	1	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	4	no	—
266	C₂³×C₁₃₉	—	2	1	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	1	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
273	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
274	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
275	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
276	Q₈×C₁₃₉	—	2	16	no	—
277	Q₈×C₁₃₉	—	2	16	no	—
278	D₄×C₁₃₉	—	4	8	no	—
279	D₄×C₁₃₉	—	4	4	no	—
280	D₄×C₁₃₉	—	4	4	no	—
281	D₄×C₁₃₉	—	8	4	no	—
282	C₂×C₄×C₁₃₉	—	2	16	no	—
283	C₂×C₄×C₁₃₉	—	2	8	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	4	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	4	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	2	8	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	1	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	4	no	—
301	C₂×C₄×C₁₃₉	—	2	4	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	4	8	no	—
315	C₂×C₄×C₁₃₉	—	4	4	no	—
316	C₂×C₄×C₁₃₉	—	4	4	no	—
317	C₂×C₄×C₁₃₉	—	8	4	no	—
318	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
323	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
324	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
325	C₂²×C₁₃₉	—	2	2	no	—
326	C₂²×C₁₃₉	—	2	4	no	—
327	C₂²×C₁₃₉	—	2	2	no	—
328	C₂²×C₁₃₉	—	2	4	no	—
329	C₂²×C₁₃₉	—	4	1	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	1	no	—
332	C₂²×C₁₃₉	—	4	2	no	—
333	C₂²×C₁₃₉	—	4	2	no	—
334	C₂²×C₁₃₉	—	4	4	no	—
335	C₂²×C₁₃₉	—	4	2	no	—
336	C₂²×C₁₃₉	—	4	1	no	—
337	C₂²×C₁₃₉	—	4	2	no	—
338	C₂²×C₁₃₉	—	4	4	no	—
339	C₂²×C₁₃₉	#548	1	4	yes	—
340	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
341	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
342	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₁₃₉	#585	1	2	yes	—
345	C₄×C₁₃₉	—	2	2	no	—
346	C₄×C₁₃₉	—	2	8	no	—
347	C₄×C₁₃₉	—	2	4	no	—
348	C₄×C₁₃₉	—	2	4	no	—
349	C₄×C₁₃₉	—	2	4	no	—
350	C₄×C₁₃₉	—	4	1	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	—	4	1	no	—
353	C₄×C₁₃₉	—	4	2	no	—
354	C₄×C₁₃₉	—	4	4	no	—
355	C₄×C₁₃₉	—	4	2	no	—
356	C₄×C₁₃₉	—	4	1	no	—
357	C₄×C₁₃₉	—	4	2	no	—
358	C₄×C₁₃₉	#525	1	4	yes	—
359	C₂×C₁₃₉	—	2	4	no	—
360	C₂×C₁₃₉	—	8	1	no	—
361	C₂×C₁₃₉	—	8	2	no	—
362	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
363	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
364	C₂×C₁₃₉	#3480	1	2	yes	—
365	C₂×C₁₃₉	#3485	1	1	yes	characteristic
366	C₂×C₁₃₉	#3516	1	2	yes	—
367	#36582	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₁₃₉	#36582	1	1	yes	characteristic, direct product factor, Sylow
369	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic
370	C₂²×C₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	#2854	C₂×C₁₃₉	1	2	yes	complemented
372	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	#2591	C₂×C₁₃₉	1	2	yes	complemented
374	#2579	C₂×C₁₃₉	1	2	yes	complemented
375	#2469	C₂×C₁₃₉	1	4	yes	complemented
376	#2458	C₂×C₁₃₉	1	4	yes	complemented
377	#2453	C₂×C₁₃₉	1	2	yes	complemented
378	#2436	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	#2426	C₂×C₁₃₉	1	2	yes	complemented
380	#2409	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	#2367	C₂×C₁₃₉	1	2	yes	complemented
382	#2362	C₂×C₁₃₉	1	2	yes	complemented
383	#2345	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	C₄×#123	C₂×C₁₃₉	1	2	yes	complemented
385	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
387	#553	—	2	8	no	—
388	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
389	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
391	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
392	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
393	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
395	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
398	C₂×C₄×Q₈	—	2	8	no	—
399	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
400	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
401	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
402	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
407	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
409	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
410	#400	C₂²×C₁₃₉	1	4	yes	—
411	#398	C₂²×C₁₃₉	1	4	yes	—
412	#396	C₂²×C₁₃₉	1	4	yes	—
413	#395	C₂²×C₁₃₉	1	2	yes	—
414	#394	C₂²×C₁₃₉	1	4	yes	—
415	#393	C₂²×C₁₃₉	1	2	yes	—
416	#393	C₂²×C₁₃₉	1	4	yes	—
417	#391	C₂²×C₁₃₉	1	2	yes	—
418	#391	C₂²×C₁₃₉	1	2	yes	—
419	#390	C₂²×C₁₃₉	1	2	yes	—
420	#390	C₂²×C₁₃₉	1	4	yes	—
421	#389	C₂²×C₁₃₉	1	2	yes	—
422	#389	C₂²×C₁₃₉	1	4	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	#388	C₂²×C₁₃₉	1	2	yes	—
431	#387	C₂²×C₁₃₉	1	4	yes	—
432	#387	C₂²×C₁₃₉	1	4	yes	—
433	#387	C₂²×C₁₃₉	1	4	yes	—
434	#387	C₂²×C₁₃₉	1	2	yes	—
435	#386	C₂²×C₁₃₉	1	2	yes	—
436	#386	C₂²×C₁₃₉	1	2	yes	—
437	#386	C₂²×C₁₃₉	1	1	yes	characteristic
438	#386	C₂²×C₁₃₉	1	2	yes	—
439	#386	C₂²×C₁₃₉	1	2	yes	—
440	#385	C₂²×C₁₃₉	1	1	yes	characteristic
441	#385	C₂²×C₁₃₉	1	4	yes	—
442	#385	C₂²×C₁₃₉	1	2	yes	—
443	#381	C₂²×C₁₃₉	1	1	yes	characteristic
444	#380	C₂²×C₁₃₉	1	2	yes	—
445	#380	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
453	C₂²×Q₈	—	2	8	no	—
454	C₂²×Q₈	—	2	4	no	—
455	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
456	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
457	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
461	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
462	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
468	#126	—	2	8	no	—
469	#125	—	2	4	no	—
470	#124	—	2	8	no	—
471	#123	—	2	8	no	—
472	#123	—	2	4	no	—
473	#123	—	2	8	no	—
474	C₂²⋊Q₈	—	2	8	no	—
475	#121	—	2	8	no	—
476	#121	—	2	4	no	—
477	#121	—	2	4	no	—
478	C₄×Q₈	—	2	8	no	—
479	C₄×Q₈	—	2	8	no	—
480	C₄×Q₈	—	2	16	no	—
481	C₄×D₄	—	2	8	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	4	no	—
484	#117	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	8	no	—
486	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₄²	—	2	8	no	—
519	C₂×C₄²	—	2	4	no	—
520	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
528	#95	C₂³×C₁₃₉	1	2	yes	—
529	#95	C₂³×C₁₃₉	1	2	yes	—
530	#95	C₂³×C₁₃₉	1	4	yes	—
531	#95	C₂³×C₁₃₉	1	2	yes	—
532	#95	C₂³×C₁₃₉	1	2	yes	—
533	#95	C₂³×C₁₃₉	1	4	yes	—
534	#95	C₂³×C₁₃₉	1	4	yes	—
535	#95	C₂³×C₁₃₉	1	2	yes	—
536	#95	C₂³×C₁₃₉	1	4	yes	—
537	#95	C₂³×C₁₃₉	1	2	yes	—
538	#95	C₂³×C₁₃₉	1	4	yes	—
539	#95	C₂³×C₁₃₉	1	4	yes	—
540	#95	C₂³×C₁₃₉	1	4	yes	—
541	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
542	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
543	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
544	C₂×Q₈	—	2	32	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	8	no	—
548	C₂×Q₈	—	2	4	no	—
549	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	8	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
573	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
574	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
589	C₄⋊C₄	—	2	8	no	—
590	C₄⋊C₄	—	2	8	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
602	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
603	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	8	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₄²	—	2	8	no	—
621	C₄²	—	2	8	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	4	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	4	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
641	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
642	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
643	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
644	Q₈	—	2	16	no	—
645	Q₈	—	2	16	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	D₄	—	8	4	no	—
650	C₂×C₄	—	2	16	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	8	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
689	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
690	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
691	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
692	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	4	no	—
707	C₂²	#548×C₁₃₉	1	4	yes	—
708	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
709	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
710	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
711	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
712	C₂²	#585×C₁₃₉	1	2	yes	—
713	C₄	—	2	2	no	—
714	C₄	—	2	8	no	—
715	C₄	—	2	4	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	4	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	4	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	#525×C₁₃₉	1	4	yes	—
727	C₂	—	2	4	no	—
728	C₂	—	8	1	no	—
729	C₂	—	8	2	no	—
730	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
731	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
732	C₂	#3480×C₁₃₉	1	2	yes	—
733	C₂	#3485×C₁₃₉	1	1	yes	characteristic
734	C₂	#3516×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
2. C₂²×C₄×Q₈×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2591×C₁₃₉	C₂	semidirect
6. #2579×C₁₃₉	C₂	semidirect
7. #2469×C₁₃₉	C₂	semidirect
8. #2458×C₁₃₉	C₂	semidirect
9. #2453×C₁₃₉	C₂	semidirect
10. #2436×C₁₃₉	C₂	semidirect
11. #2426×C₁₃₉	C₂	semidirect
12. #2409×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2362×C₁₃₉	C₂	semidirect
15. #2345×C₁₃₉	C₂	semidirect
16. C₄×#123×C₁₃₉	C₂	semidirect
17. C₄×#123×C₁₃₉	C₂	semidirect
367. #36582	C₁₃₉	direct (N × H)
368. C₁₃₉	#36582	direct (N × H)
370. C₂²×C₄×Q₈	C₂×C₁₃₉	semidirect
371. #2854	C₂×C₁₃₉	semidirect
372. #2854	C₂×C₁₃₉	semidirect
373. #2591	C₂×C₁₃₉	semidirect
374. #2579	C₂×C₁₃₉	semidirect
375. #2469	C₂×C₁₃₉	semidirect
376. #2458	C₂×C₁₃₉	semidirect
377. #2453	C₂×C₁₃₉	semidirect
378. #2436	C₂×C₁₃₉	semidirect
379. #2426	C₂×C₁₃₉	semidirect
380. #2409	C₂×C₁₃₉	semidirect
381. #2367	C₂×C₁₃₉	semidirect
382. #2362	C₂×C₁₃₉	semidirect
383. #2345	C₂×C₁₃₉	semidirect
384. C₄×#123	C₂×C₁₃₉	semidirect
385. C₄×#123	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×#553×C₁₃₉	2
C₂²×C₄×Q₈×C₁₃₉	2
#2854×C₁₃₉	2
#2591×C₁₃₉	2
#2579×C₁₃₉	2
#2469×C₁₃₉	2
#2458×C₁₃₉	2
#2453×C₁₃₉	2
#2436×C₁₃₉	2
#2426×C₁₃₉	2
#2409×C₁₃₉	2
#2367×C₁₃₉	2
#2362×C₁₃₉	2
#2345×C₁₃₉	2
C₄×#123×C₁₃₉	2
#36582	139

Subgroups — C139×#36582 #48031178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36582 #48031178