Subgroups — C₁₃₉×#36184 #48030780

Order 35584.

2302 conjugacy classes of subgroups.

The subgroup lattice has 800 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	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2565×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2553×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2519×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2499×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2425×C₁₃₉	C₂	1	4	yes	maximal, complemented
15	#2359×C₁₃₉	C₂	1	4	yes	maximal, complemented
16	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#553×C₁₃₉	—	2	8	no	—
21	#552×C₁₃₉	—	2	8	no	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
48	#399×C₁₃₉	C₂²	1	4	yes	—
49	#398×C₁₃₉	C₂²	1	4	yes	—
50	#398×C₁₃₉	C₂²	1	4	yes	—
51	#397×C₁₃₉	C₂²	1	4	yes	—
52	#396×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#391×C₁₃₉	C₂²	1	1	yes	characteristic
55	#391×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic
57	#390×C₁₃₉	C₂²	1	1	yes	characteristic
58	#390×C₁₃₉	C₂²	1	1	yes	characteristic
59	#390×C₁₃₉	C₂²	1	1	yes	characteristic
60	#389×C₁₃₉	C₂²	1	4	yes	—
61	#389×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	#387×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#384×C₁₃₉	C₂²	1	1	yes	characteristic
73	#384×C₁₃₉	C₂²	1	1	yes	characteristic
74	#384×C₁₃₉	C₂²	1	1	yes	characteristic
75	#384×C₁₃₉	C₂²	1	1	yes	characteristic
76	#382×C₁₃₉	C₂²	1	4	yes	—
77	#382×C₁₃₉	C₂²	1	1	yes	characteristic
78	#382×C₁₃₉	C₂²	1	1	yes	characteristic
79	#382×C₁₃₉	C₂²	1	1	yes	characteristic
80	#382×C₁₃₉	C₂²	1	1	yes	characteristic
81	#382×C₁₃₉	C₂²	1	1	yes	characteristic
82	#380×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
85	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
91	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	#126×C₁₃₉	—	2	8	no	—
106	#126×C₁₃₉	—	2	8	no	—
107	#125×C₁₃₉	—	2	8	no	—
108	#125×C₁₃₉	—	2	4	no	—
109	#125×C₁₃₉	—	2	4	no	—
110	#124×C₁₃₉	—	2	4	no	—
111	#123×C₁₃₉	—	2	8	no	—
112	#123×C₁₃₉	—	2	8	no	—
113	#123×C₁₃₉	—	2	16	no	—
114	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
116	#121×C₁₃₉	—	2	8	no	—
117	#121×C₁₃₉	—	2	4	no	—
118	#121×C₁₃₉	—	2	4	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	4	no	—
123	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
124	#117×C₁₃₉	—	2	4	no	—
125	#117×C₁₃₉	—	2	4	no	—
126	#117×C₁₃₉	—	2	8	no	—
127	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
128	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	—	2	4	no	—
166	C₂×C₄²×C₁₃₉	—	2	4	no	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	4	yes	—
184	#95×C₁₃₉	C₂³	1	4	yes	—
185	#95×C₁₃₉	C₂³	1	4	yes	—
186	#95×C₁₃₉	C₂³	1	4	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	4	yes	—
190	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
191	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂×Q₈×C₁₃₉	—	2	2	no	—
194	C₂×Q₈×C₁₃₉	—	2	2	no	—
195	C₂×Q₈×C₁₃₉	—	2	2	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	8	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	2	no	—
202	C₂×D₄×C₁₃₉	—	2	2	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	8	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	4	2	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	no	—
219	C₂²×C₄×C₁₃₉	—	4	4	no	—
220	C₂²×C₄×C₁₃₉	—	4	4	no	—
221	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	2	no	—
241	C₄⋊C₄×C₁₃₉	—	2	2	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	8	no	—
256	C₄⋊C₄×C₁₃₉	—	2	8	no	—
257	C₄⋊C₄×C₁₃₉	—	4	4	no	—
258	C₄⋊C₄×C₁₃₉	—	4	4	no	—
259	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	2	4	no	—
278	C₄²×C₁₃₉	—	2	4	no	—
279	C₄²×C₁₃₉	—	2	2	no	—
280	C₄²×C₁₃₉	—	2	4	no	—
281	C₄²×C₁₃₉	—	2	2	no	—
282	C₄²×C₁₃₉	—	2	4	no	—
283	C₄²×C₁₃₉	—	2	2	no	—
284	C₄²×C₁₃₉	—	4	2	no	—
285	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
286	C₄²×C₁₃₉	#41	1	4	yes	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	1	no	—
292	C₂³×C₁₃₉	—	2	1	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	4	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	2	no	—
298	C₂³×C₁₃₉	—	2	4	no	—
299	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
300	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
301	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
302	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
303	Q₈×C₁₃₉	—	4	4	no	—
304	D₄×C₁₃₉	—	2	8	no	—
305	D₄×C₁₃₉	—	4	8	no	—
306	D₄×C₁₃₉	—	4	4	no	—
307	D₄×C₁₃₉	—	8	4	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	1	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	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	8	no	—
321	C₂×C₄×C₁₃₉	—	2	8	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	4	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	4	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	4	no	—
338	C₂×C₄×C₁₃₉	—	2	4	no	—
339	C₂×C₄×C₁₃₉	—	2	4	no	—
340	C₂×C₄×C₁₃₉	—	4	8	no	—
341	C₂×C₄×C₁₃₉	—	4	8	no	—
342	C₂×C₄×C₁₃₉	—	4	8	no	—
343	C₂×C₄×C₁₃₉	—	8	4	no	—
344	C₂×C₄×C₁₃₉	—	8	4	no	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
351	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
352	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
353	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
354	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
355	C₂²×C₁₃₉	—	2	2	no	—
356	C₂²×C₁₃₉	—	2	4	no	—
357	C₂²×C₁₃₉	—	2	2	no	—
358	C₂²×C₁₃₉	—	2	4	no	—
359	C₂²×C₁₃₉	—	2	2	no	—
360	C₂²×C₁₃₉	—	2	2	no	—
361	C₂²×C₁₃₉	—	2	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	2	no	—
366	C₂²×C₁₃₉	—	4	4	no	—
367	C₂²×C₁₃₉	—	4	2	no	—
368	C₂²×C₁₃₉	—	4	4	no	—
369	C₂²×C₁₃₉	#532	1	4	yes	—
370	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
371	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
372	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
373	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂²×C₁₃₉	#585	1	2	yes	—
375	C₄×C₁₃₉	—	2	2	no	—
376	C₄×C₁₃₉	—	2	2	no	—
377	C₄×C₁₃₉	—	2	2	no	—
378	C₄×C₁₃₉	—	2	4	no	—
379	C₄×C₁₃₉	—	2	4	no	—
380	C₄×C₁₃₉	—	2	2	no	—
381	C₄×C₁₃₉	—	2	4	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	—	4	2	no	—
385	C₄×C₁₃₉	—	4	2	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	—	4	2	no	—
390	C₄×C₁₃₉	#547	1	4	yes	—
391	C₂×C₁₃₉	—	2	4	no	—
392	C₂×C₁₃₉	—	4	2	no	—
393	C₂×C₁₃₉	—	8	2	no	—
394	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
395	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
396	C₂×C₁₃₉	#3475	1	2	yes	—
397	C₂×C₁₃₉	#3500	1	1	yes	characteristic
398	C₂×C₁₃₉	#3515	1	2	yes	—
399	#36184	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₁₃₉	#36184	1	1	yes	characteristic, direct product factor, Sylow
401	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic
402	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	#2565	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2553	C₂×C₁₃₉	1	4	yes	complemented
409	#2519	C₂×C₁₃₉	1	4	yes	complemented
410	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2499	C₂×C₁₃₉	1	1	yes	characteristic, complemented
414	#2425	C₂×C₁₃₉	1	4	yes	complemented
415	#2359	C₂×C₁₃₉	1	4	yes	complemented
416	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
419	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
420	#553	—	2	8	no	—
421	#552	—	2	8	no	—
422	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
423	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
427	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
429	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
430	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
431	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
436	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
441	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
442	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
445	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
448	#399	C₂²×C₁₃₉	1	4	yes	—
449	#398	C₂²×C₁₃₉	1	4	yes	—
450	#398	C₂²×C₁₃₉	1	4	yes	—
451	#397	C₂²×C₁₃₉	1	4	yes	—
452	#396	C₂²×C₁₃₉	1	4	yes	—
453	#394	C₂²×C₁₃₉	1	4	yes	—
454	#391	C₂²×C₁₃₉	1	1	yes	characteristic
455	#391	C₂²×C₁₃₉	1	1	yes	characteristic
456	#391	C₂²×C₁₃₉	1	1	yes	characteristic
457	#390	C₂²×C₁₃₉	1	1	yes	characteristic
458	#390	C₂²×C₁₃₉	1	1	yes	characteristic
459	#390	C₂²×C₁₃₉	1	1	yes	characteristic
460	#389	C₂²×C₁₃₉	1	4	yes	—
461	#389	C₂²×C₁₃₉	1	4	yes	—
462	#388	C₂²×C₁₃₉	1	4	yes	—
463	#388	C₂²×C₁₃₉	1	4	yes	—
464	#388	C₂²×C₁₃₉	1	4	yes	—
465	#388	C₂²×C₁₃₉	1	4	yes	—
466	#387	C₂²×C₁₃₉	1	4	yes	—
467	#387	C₂²×C₁₃₉	1	4	yes	—
468	#386	C₂²×C₁₃₉	1	4	yes	—
469	#386	C₂²×C₁₃₉	1	4	yes	—
470	#385	C₂²×C₁₃₉	1	4	yes	—
471	#385	C₂²×C₁₃₉	1	4	yes	—
472	#384	C₂²×C₁₃₉	1	1	yes	characteristic
473	#384	C₂²×C₁₃₉	1	1	yes	characteristic
474	#384	C₂²×C₁₃₉	1	1	yes	characteristic
475	#384	C₂²×C₁₃₉	1	1	yes	characteristic
476	#382	C₂²×C₁₃₉	1	1	yes	characteristic
477	#382	C₂²×C₁₃₉	1	1	yes	characteristic
478	#382	C₂²×C₁₃₉	1	1	yes	characteristic
479	#382	C₂²×C₁₃₉	1	1	yes	characteristic
480	#382	C₂²×C₁₃₉	1	4	yes	—
481	#382	C₂²×C₁₃₉	1	1	yes	characteristic
482	#380	C₂²×C₁₃₉	1	4	yes	—
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
485	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
491	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
492	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
505	#126	—	2	8	no	—
506	#126	—	2	8	no	—
507	#125	—	2	8	no	—
508	#125	—	2	4	no	—
509	#125	—	2	4	no	—
510	#124	—	2	4	no	—
511	#123	—	2	8	no	—
512	#123	—	2	8	no	—
513	#123	—	2	16	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	#121	—	2	8	no	—
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	C₄×Q₈	—	2	4	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
524	#117	—	2	4	no	—
525	#117	—	2	4	no	—
526	#117	—	2	8	no	—
527	C₂×C₄⋊C₄	—	2	4	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄²	—	2	4	no	—
566	C₂×C₄²	—	2	4	no	—
567	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
579	#95	C₂³×C₁₃₉	1	4	yes	—
580	#95	C₂³×C₁₃₉	1	4	yes	—
581	#95	C₂³×C₁₃₉	1	4	yes	—
582	#95	C₂³×C₁₃₉	1	4	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	4	yes	—
587	#95	C₂³×C₁₃₉	1	4	yes	—
588	#95	C₂³×C₁₃₉	1	4	yes	—
589	#95	C₂³×C₁₃₉	1	4	yes	—
590	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
591	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
592	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
622	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
623	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	8	no	—
656	C₄⋊C₄	—	2	8	no	—
657	C₄⋊C₄	—	4	4	no	—
658	C₄⋊C₄	—	4	4	no	—
659	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	8	no	—
670	C₂²⋊C₄	—	2	8	no	—
671	C₂²⋊C₄	—	4	4	no	—
672	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
673	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
674	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	4	2	no	—
685	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
686	C₄²	#41×C₁₃₉	1	4	yes	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	4	no	—
699	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
700	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
701	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
702	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
703	Q₈	—	4	4	no	—
704	D₄	—	2	8	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	4	no	—
707	D₄	—	8	4	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	8	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
748	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
749	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
750	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
751	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
752	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
753	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
754	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	4	no	—
769	C₂²	#532×C₁₃₉	1	4	yes	—
770	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
771	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
772	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
773	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
774	C₂²	#585×C₁₃₉	1	2	yes	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	#547×C₁₃₉	1	4	yes	—
791	C₂	—	2	4	no	—
792	C₂	—	4	2	no	—
793	C₂	—	8	2	no	—
794	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
795	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
796	C₂	#3475×C₁₃₉	1	2	yes	—
797	C₂	#3500×C₁₃₉	1	1	yes	characteristic
798	C₂	#3515×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. C₂×#552×C₁₃₉	C₂	semidirect
3. #2859×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2565×C₁₃₉	C₂	semidirect
8. #2553×C₁₃₉	C₂	semidirect
9. #2519×C₁₃₉	C₂	semidirect
10. #2502×C₁₃₉	C₂	semidirect
11. #2501×C₁₃₉	C₂	semidirect
12. #2500×C₁₃₉	C₂	semidirect
13. #2499×C₁₃₉	C₂	semidirect
14. #2425×C₁₃₉	C₂	semidirect
15. #2359×C₁₃₉	C₂	semidirect
16. C₄×#124×C₁₃₉	C₂	semidirect
17. #2285×C₁₃₉	C₂	semidirect
18. C₂×#382×C₁₃₉	C₂	semidirect
19. C₄²×D₄×C₁₃₉	C₂	semidirect
399. #36184	C₁₃₉	direct (N × H)
400. C₁₃₉	#36184	direct (N × H)
402. C₂×#552	C₂×C₁₃₉	semidirect
403. #2859	C₂×C₁₃₉	semidirect
404. #2850	C₂×C₁₃₉	semidirect
405. #2850	C₂×C₁₃₉	semidirect
406. #2566	C₂×C₁₃₉	semidirect
407. #2565	C₂×C₁₃₉	semidirect
408. #2553	C₂×C₁₃₉	semidirect
409. #2519	C₂×C₁₃₉	semidirect
410. #2502	C₂×C₁₃₉	semidirect
411. #2501	C₂×C₁₃₉	semidirect
412. #2500	C₂×C₁₃₉	semidirect
413. #2499	C₂×C₁₃₉	semidirect
414. #2425	C₂×C₁₃₉	semidirect
415. #2359	C₂×C₁₃₉	semidirect
416. C₄×#124	C₂×C₁₃₉	semidirect
417. #2285	C₂×C₁₃₉	semidirect
418. C₂×#382	C₂×C₁₃₉	semidirect
419. C₄²×D₄	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
C₂×#552×C₁₃₉	2
#2859×C₁₃₉	2
#2850×C₁₃₉	2
#2566×C₁₃₉	2
#2565×C₁₃₉	2
#2553×C₁₃₉	2
#2519×C₁₃₉	2
#2502×C₁₃₉	2
#2501×C₁₃₉	2
#2500×C₁₃₉	2
#2499×C₁₃₉	2
#2425×C₁₃₉	2
#2359×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2285×C₁₃₉	2
C₂×#382×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36184	139

Subgroups — C139×#36184 #48030780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36184 #48030780