Subgroups — C₁₃₉×#36062 #48030658

Order 35584.

2374 conjugacy classes of subgroups.

The subgroup lattice has 776 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, complemented
2	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2661×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2562×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2555×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2543×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2537×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2535×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2521×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2354×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#555×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	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	#400×C₁₃₉	C₂²	1	2	yes	—
44	#399×C₁₃₉	C₂²	1	2	yes	—
45	#399×C₁₃₉	C₂²	1	1	yes	characteristic
46	#399×C₁₃₉	C₂²	1	1	yes	characteristic
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	4	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#395×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	4	yes	—
57	#392×C₁₃₉	C₂²	1	1	yes	characteristic
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	1	yes	characteristic
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	—
66	#387×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	—
70	#384×C₁₃₉	C₂²	1	2	yes	—
71	#382×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	4	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	2	yes	—
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊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	4	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×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
101	#126×C₁₃₉	—	2	8	no	—
102	#125×C₁₃₉	—	2	4	no	—
103	#124×C₁₃₉	—	2	16	no	—
104	#124×C₁₃₉	—	4	4	no	—
105	#123×C₁₃₉	—	2	8	no	—
106	#121×C₁₃₉	—	2	4	no	—
107	#121×C₁₃₉	—	2	4	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#121×C₁₃₉	—	2	8	no	—
111	#121×C₁₃₉	—	4	8	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	2	4	no	—
114	C₄×D₄×C₁₃₉	—	2	4	no	—
115	C₄×D₄×C₁₃₉	—	2	8	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
119	#117×C₁₃₉	—	2	8	no	—
120	#117×C₁₃₉	—	2	4	no	—
121	#117×C₁₃₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×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	2	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	1	yes	characteristic
171	#95×C₁₃₉	C₂³	1	4	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	2	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	4	2	no	—
179	C₂×Q₈×C₁₃₉	—	4	2	no	—
180	C₂×D₄×C₁₃₉	—	2	4	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	—	2	8	no	—
186	C₂×D₄×C₁₃₉	—	2	2	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	4	2	no	—
192	C₂×D₄×C₁₃₉	—	4	2	no	—
193	C₂×D₄×C₁₃₉	—	4	2	no	—
194	C₂×D₄×C₁₃₉	—	4	2	no	—
195	C₂×D₄×C₁₃₉	—	4	1	no	—
196	C₂×D₄×C₁₃₉	—	4	2	no	—
197	C₂×D₄×C₁₃₉	—	4	4	no	—
198	C₂×D₄×C₁₃₉	—	4	4	no	—
199	C₂×D₄×C₁₃₉	—	4	4	no	—
200	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₁₃₉	—	2	2	no	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	4	no	—
205	C₂²×C₄×C₁₃₉	—	2	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	8	no	—
210	C₂²×C₄×C₁₃₉	—	4	4	no	—
211	C₂²×C₄×C₁₃₉	—	4	4	no	—
212	C₂²×C₄×C₁₃₉	—	4	4	no	—
213	C₂²×C₄×C₁₃₉	—	4	4	no	—
214	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₁₃₉	—	2	2	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	2	no	—
231	C₄⋊C₄×C₁₃₉	—	2	2	no	—
232	C₄⋊C₄×C₁₃₉	—	2	4	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	4	4	no	—
241	C₄⋊C₄×C₁₃₉	—	4	4	no	—
242	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
260	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
261	C₄²×C₁₃₉	—	2	8	no	—
262	C₄²×C₁₃₉	—	2	4	no	—
263	C₄²×C₁₃₉	—	4	4	no	—
264	C₄²×C₁₃₉	—	4	2	no	—
265	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
266	C₄²×C₁₃₉	#41	1	8	yes	—
267	C₂³×C₁₃₉	—	2	1	no	—
268	C₂³×C₁₃₉	—	2	4	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	4	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	1	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	1	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
288	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
289	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
290	Q₈×C₁₃₉	—	8	4	no	—
291	D₄×C₁₃₉	—	2	8	no	—
292	D₄×C₁₃₉	—	4	4	no	—
293	D₄×C₁₃₉	—	4	8	no	—
294	D₄×C₁₃₉	—	4	4	no	—
295	D₄×C₁₃₉	—	4	8	no	—
296	D₄×C₁₃₉	—	4	8	no	—
297	D₄×C₁₃₉	—	8	4	no	—
298	D₄×C₁₃₉	—	8	8	no	—
299	C₂×C₄×C₁₃₉	—	2	1	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	4	no	—
303	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	4	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	2	4	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	4	8	no	—
326	C₂×C₄×C₁₃₉	—	4	4	no	—
327	C₂×C₄×C₁₃₉	—	4	4	no	—
328	C₂×C₄×C₁₃₉	—	4	8	no	—
329	C₂×C₄×C₁₃₉	—	8	4	no	—
330	C₂×C₄×C₁₃₉	—	8	8	no	—
331	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
336	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
337	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
338	C₂²×C₁₃₉	—	2	4	no	—
339	C₂²×C₁₃₉	—	2	4	no	—
340	C₂²×C₁₃₉	—	2	2	no	—
341	C₂²×C₁₃₉	—	2	4	no	—
342	C₂²×C₁₃₉	—	2	4	no	—
343	C₂²×C₁₃₉	—	4	1	no	—
344	C₂²×C₁₃₉	—	4	1	no	—
345	C₂²×C₁₃₉	—	4	4	no	—
346	C₂²×C₁₃₉	—	4	2	no	—
347	C₂²×C₁₃₉	—	4	4	no	—
348	C₂²×C₁₃₉	—	4	2	no	—
349	C₂²×C₁₃₉	—	4	1	no	—
350	C₂²×C₁₃₉	—	4	2	no	—
351	C₂²×C₁₃₉	—	4	1	no	—
352	C₂²×C₁₃₉	—	4	1	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
362	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²×C₁₃₉	#585	1	2	yes	—
364	C₂²×C₁₃₉	#585	1	1	yes	characteristic
365	C₄×C₁₃₉	—	2	2	no	—
366	C₄×C₁₃₉	—	2	4	no	—
367	C₄×C₁₃₉	—	2	2	no	—
368	C₄×C₁₃₉	—	2	4	no	—
369	C₄×C₁₃₉	—	2	4	no	—
370	C₄×C₁₃₉	—	4	2	no	—
371	C₄×C₁₃₉	—	4	1	no	—
372	C₄×C₁₃₉	—	4	1	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₄×C₁₃₉	—	4	4	no	—
376	C₄×C₁₃₉	—	4	4	no	—
377	C₄×C₁₃₉	#532	1	4	yes	—
378	C₂×C₁₃₉	—	4	4	no	—
379	C₂×C₁₃₉	—	4	2	no	—
380	C₂×C₁₃₉	—	8	2	no	—
381	C₂×C₁₃₉	—	8	1	no	—
382	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
383	C₂×C₁₃₉	#3485	1	1	yes	characteristic
384	C₂×C₁₃₉	#3488	1	1	yes	characteristic
385	C₂×C₁₃₉	#3493	1	2	yes	—
386	C₂×C₁₃₉	#3494	1	2	yes	—
387	#36062	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₁₃₉	#36062	1	1	yes	characteristic, direct product factor, Sylow
389	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
390	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	#2661	C₂×C₁₃₉	1	2	yes	complemented
392	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2562	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2555	C₂×C₁₃₉	1	4	yes	complemented
395	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	#2543	C₂×C₁₃₉	1	2	yes	complemented
397	#2537	C₂×C₁₃₉	1	2	yes	complemented
398	#2535	C₂×C₁₃₉	1	2	yes	complemented
399	#2521	C₂×C₁₃₉	1	4	yes	complemented
400	#2498	C₂×C₁₃₉	1	2	yes	complemented
401	#2397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2395	C₂×C₁₃₉	1	2	yes	complemented
403	#2354	C₂×C₁₃₉	1	2	yes	complemented
404	#2352	C₂×C₁₃₉	1	2	yes	complemented
405	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#555	—	2	8	no	—
407	#553	—	2	8	no	—
408	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
409	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
410	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
412	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
414	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
415	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
418	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
420	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
426	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
428	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
430	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	#400	C₂²×C₁₃₉	1	2	yes	—
432	#399	C₂²×C₁₃₉	1	1	yes	characteristic
433	#399	C₂²×C₁₃₉	1	1	yes	characteristic
434	#399	C₂²×C₁₃₉	1	2	yes	—
435	#398	C₂²×C₁₃₉	1	2	yes	—
436	#398	C₂²×C₁₃₉	1	2	yes	—
437	#397	C₂²×C₁₃₉	1	4	yes	—
438	#397	C₂²×C₁₃₉	1	2	yes	—
439	#397	C₂²×C₁₃₉	1	2	yes	—
440	#395	C₂²×C₁₃₉	1	4	yes	—
441	#394	C₂²×C₁₃₉	1	2	yes	—
442	#394	C₂²×C₁₃₉	1	4	yes	—
443	#394	C₂²×C₁₃₉	1	4	yes	—
444	#392	C₂²×C₁₃₉	1	1	yes	characteristic
445	#392	C₂²×C₁₃₉	1	1	yes	characteristic
446	#392	C₂²×C₁₃₉	1	2	yes	—
447	#392	C₂²×C₁₃₉	1	4	yes	—
448	#391	C₂²×C₁₃₉	1	2	yes	—
449	#390	C₂²×C₁₃₉	1	4	yes	—
450	#388	C₂²×C₁₃₉	1	4	yes	—
451	#388	C₂²×C₁₃₉	1	4	yes	—
452	#388	C₂²×C₁₃₉	1	4	yes	—
453	#388	C₂²×C₁₃₉	1	4	yes	—
454	#387	C₂²×C₁₃₉	1	4	yes	—
455	#386	C₂²×C₁₃₉	1	4	yes	—
456	#386	C₂²×C₁₃₉	1	4	yes	—
457	#386	C₂²×C₁₃₉	1	4	yes	—
458	#384	C₂²×C₁₃₉	1	2	yes	—
459	#382	C₂²×C₁₃₉	1	2	yes	—
460	#380	C₂²×C₁₃₉	1	2	yes	—
461	#380	C₂²×C₁₃₉	1	2	yes	—
462	#380	C₂²×C₁₃₉	1	2	yes	—
463	#380	C₂²×C₁₃₉	1	2	yes	—
464	#380	C₂²×C₁₃₉	1	4	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
471	#376	C₂²×C₁₃₉	1	1	yes	characteristic
472	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
473	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
474	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₄⋊Q₈	—	2	4	no	—
489	#126	—	2	8	no	—
490	#125	—	2	4	no	—
491	#124	—	2	16	no	—
492	#124	—	4	4	no	—
493	#123	—	2	8	no	—
494	#121	—	2	4	no	—
495	#121	—	2	4	no	—
496	#121	—	2	8	no	—
497	#121	—	2	8	no	—
498	#121	—	2	8	no	—
499	#121	—	4	8	no	—
500	C₄×D₄	—	2	8	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	2	4	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
507	#117	—	2	8	no	—
508	#117	—	2	4	no	—
509	#117	—	2	8	no	—
510	C₂×C₄⋊C₄	—	2	4	no	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	#95	C₂³×C₁₃₉	1	1	yes	characteristic
551	#95	C₂³×C₁₃₉	1	4	yes	—
552	#95	C₂³×C₁₃₉	1	2	yes	—
553	#95	C₂³×C₁₃₉	1	2	yes	—
554	#95	C₂³×C₁₃₉	1	1	yes	characteristic
555	#95	C₂³×C₁₃₉	1	4	yes	—
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	#95	C₂³×C₁₃₉	1	4	yes	—
559	#95	C₂³×C₁₃₉	1	4	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
562	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
563	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	4	2	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	8	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	—	4	4	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
589	C₂²×C₄	—	2	2	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	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	8	no	—
598	C₂²×C₄	—	4	4	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	4	4	no	—
629	C₄⋊C₄	—	4	4	no	—
630	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₂²⋊C₄	—	4	4	no	—
648	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
649	C₄²	—	2	8	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	4	4	no	—
652	C₄²	—	4	2	no	—
653	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
654	C₄²	#41×C₁₃₉	1	8	yes	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
676	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
677	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
678	Q₈	—	8	4	no	—
679	D₄	—	2	8	no	—
680	D₄	—	4	4	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	8	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	8	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	8	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	8	no	—
719	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
720	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
723	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
724	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
725	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
750	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
751	C₂²	#585×C₁₃₉	1	2	yes	—
752	C₂²	#585×C₁₃₉	1	1	yes	characteristic
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	4	no	—
765	C₄	#532×C₁₃₉	1	4	yes	—
766	C₂	—	4	4	no	—
767	C₂	—	4	2	no	—
768	C₂	—	8	2	no	—
769	C₂	—	8	1	no	—
770	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
771	C₂	#3485×C₁₃₉	1	1	yes	characteristic
772	C₂	#3488×C₁₃₉	1	1	yes	characteristic
773	C₂	#3493×C₁₃₉	1	2	yes	—
774	C₂	#3494×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#555×C₁₃₉	C₂	semidirect
2. C₂×#553×C₁₃₉	C₂	semidirect
3. #2661×C₁₃₉	C₂	semidirect
4. #2660×C₁₃₉	C₂	semidirect
5. #2562×C₁₃₉	C₂	semidirect
6. #2555×C₁₃₉	C₂	semidirect
7. #2547×C₁₃₉	C₂	semidirect
8. #2543×C₁₃₉	C₂	semidirect
9. #2537×C₁₃₉	C₂	semidirect
10. #2535×C₁₃₉	C₂	semidirect
11. #2521×C₁₃₉	C₂	semidirect
12. #2498×C₁₃₉	C₂	semidirect
13. #2397×C₁₃₉	C₂	semidirect
14. #2395×C₁₃₉	C₂	semidirect
15. #2354×C₁₃₉	C₂	semidirect
16. #2352×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
118. C₄×D₄×C₁₃₉	D₄	semidirect
387. #36062	C₁₃₉	direct (N × H)
388. C₁₃₉	#36062	direct (N × H)
389. C₂×#555	C₂×C₁₃₉	semidirect
390. C₂×#553	C₂×C₁₃₉	semidirect
391. #2661	C₂×C₁₃₉	semidirect
392. #2660	C₂×C₁₃₉	semidirect
393. #2562	C₂×C₁₃₉	semidirect
394. #2555	C₂×C₁₃₉	semidirect
395. #2547	C₂×C₁₃₉	semidirect
396. #2543	C₂×C₁₃₉	semidirect
397. #2537	C₂×C₁₃₉	semidirect
398. #2535	C₂×C₁₃₉	semidirect
399. #2521	C₂×C₁₃₉	semidirect
400. #2498	C₂×C₁₃₉	semidirect
401. #2397	C₂×C₁₃₉	semidirect
402. #2395	C₂×C₁₃₉	semidirect
403. #2354	C₂×C₁₃₉	semidirect
404. #2352	C₂×C₁₃₉	semidirect
405. #2275	C₂×C₁₃₉	semidirect
506. C₄×D₄	D₄×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×#553×C₁₃₉	2
#2661×C₁₃₉	2
#2660×C₁₃₉	2
#2562×C₁₃₉	2
#2555×C₁₃₉	2
#2547×C₁₃₉	2
#2543×C₁₃₉	2
#2537×C₁₃₉	2
#2535×C₁₃₉	2
#2521×C₁₃₉	2
#2498×C₁₃₉	2
#2397×C₁₃₉	2
#2395×C₁₃₉	2
#2354×C₁₃₉	2
#2352×C₁₃₉	2
#2275×C₁₃₉	2
#36062	139

Subgroups — C139×#36062 #48030658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36062 #48030658