Subgroups — C₁₃₉×#35623 #48030219

Order 35584.

2342 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2568×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2545×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2481×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2477×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2459×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2457×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2328×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2327×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	#542×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	2	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	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
34	#520×C₁₃₉	—	2	8	no	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	#400×C₁₃₉	C₂²	1	4	yes	—
48	#400×C₁₃₉	C₂²	1	4	yes	—
49	#397×C₁₃₉	C₂²	1	4	yes	—
50	#396×C₁₃₉	C₂²	1	4	yes	—
51	#394×C₁₃₉	C₂²	1	4	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#393×C₁₃₉	C₂²	1	4	yes	—
54	#392×C₁₃₉	C₂²	1	4	yes	—
55	#391×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
59	#391×C₁₃₉	C₂²	1	4	yes	—
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	4	yes	—
72	#387×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#386×C₁₃₉	C₂²	1	4	yes	—
75	#386×C₁₃₉	C₂²	1	4	yes	—
76	#386×C₁₃₉	C₂²	1	4	yes	—
77	#386×C₁₃₉	C₂²	1	4	yes	—
78	#385×C₁₃₉	C₂²	1	4	yes	—
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	#382×C₁₃₉	C₂²	1	1	yes	characteristic
83	#381×C₁₃₉	C₂²	1	4	yes	—
84	#380×C₁₃₉	C₂²	1	4	yes	—
85	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
91	#376×C₁₃₉	C₂²	1	1	yes	characteristic
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₃₉	—	2	4	no	—
94	C₂×#41×C₁₃₉	—	2	4	no	—
95	C₂×#41×C₁₃₉	—	2	4	no	—
96	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
111	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
112	#127×C₁₃₉	—	2	4	no	—
113	#126×C₁₃₉	—	2	8	no	—
114	#124×C₁₃₉	—	2	4	no	—
115	#124×C₁₃₉	—	2	4	no	—
116	#124×C₁₃₉	—	2	8	no	—
117	#124×C₁₃₉	—	2	4	no	—
118	#123×C₁₃₉	—	2	8	no	—
119	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
120	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
121	#121×C₁₃₉	—	2	4	no	—
122	C₄×Q₈×C₁₃₉	—	2	4	no	—
123	C₄×Q₈×C₁₃₉	—	2	4	no	—
124	C₄×Q₈×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	—	2	8	no	—
126	C₄×D₄×C₁₃₉	—	2	8	no	—
127	C₄×D₄×C₁₃₉	—	2	4	no	—
128	C₄×D₄×C₁₃₉	—	2	4	no	—
129	C₄×D₄×C₁₃₉	—	2	4	no	—
130	#117×C₁₃₉	—	2	8	no	—
131	#117×C₁₃₉	D₄	1	8	yes	complemented
132	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
177	#95×C₁₃₉	C₂³	1	4	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	2	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	4	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
194	#41×C₁₃₉	—	2	32	no	—
195	C₂×Q₈×C₁₃₉	—	2	2	no	—
196	C₂×Q₈×C₁₃₉	—	2	2	no	—
197	C₂×Q₈×C₁₃₉	—	2	4	no	—
198	C₂×Q₈×C₁₃₉	—	2	2	no	—
199	C₂×Q₈×C₁₃₉	—	2	2	no	—
200	C₂×Q₈×C₁₃₉	—	2	2	no	—
201	C₂×Q₈×C₁₃₉	—	4	4	no	—
202	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
203	C₂×D₄×C₁₃₉	—	2	4	no	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	8	no	—
207	C₂×D₄×C₁₃₉	—	2	2	no	—
208	C₂×D₄×C₁₃₉	—	2	2	no	—
209	C₂×D₄×C₁₃₉	—	2	4	no	—
210	C₂×D₄×C₁₃₉	—	2	2	no	—
211	C₂×D₄×C₁₃₉	—	2	2	no	—
212	C₂×D₄×C₁₃₉	—	2	2	no	—
213	C₂×D₄×C₁₃₉	—	4	4	no	—
214	C₂×D₄×C₁₃₉	—	4	4	no	—
215	C₂×D₄×C₁₃₉	—	4	4	no	—
216	C₂×D₄×C₁₃₉	#41	1	4	yes	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	2	no	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	4	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	4	4	no	—
227	C₂²×C₄×C₁₃₉	—	4	4	no	—
228	C₂²×C₄×C₁₃₉	—	4	4	no	—
229	C₂²×C₄×C₁₃₉	—	4	4	no	—
230	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	2	2	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	8	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	8	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	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
278	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	4	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	2	2	no	—
283	C₄²×C₁₃₉	—	2	2	no	—
284	C₄²×C₁₃₉	—	2	2	no	—
285	C₄²×C₁₃₉	—	2	2	no	—
286	C₄²×C₁₃₉	—	4	2	no	—
287	C₄²×C₁₃₉	—	4	2	no	—
288	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
289	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
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	4	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	4	no	—
298	C₂³×C₁₃₉	—	2	2	no	—
299	C₂³×C₁₃₉	—	2	2	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	4	no	—
302	C₂³×C₁₃₉	—	2	4	no	—
303	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
304	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
305	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
306	Q₈×C₁₃₉	—	2	8	no	—
307	Q₈×C₁₃₉	—	4	4	no	—
308	Q₈×C₁₃₉	—	8	4	no	—
309	D₄×C₁₃₉	—	2	16	no	—
310	D₄×C₁₃₉	—	2	8	no	—
311	D₄×C₁₃₉	—	4	4	no	—
312	D₄×C₁₃₉	—	8	4	no	—
313	D₄×C₁₃₉	—	8	8	no	—
314	C₂×C₄×C₁₃₉	—	2	16	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	4	no	—
342	C₂×C₄×C₁₃₉	—	2	4	no	—
343	C₂×C₄×C₁₃₉	—	2	4	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	4	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	8	4	no	—
348	C₂×C₄×C₁₃₉	—	8	4	no	—
349	C₂×C₄×C₁₃₉	—	8	4	no	—
350	C₂×C₄×C₁₃₉	—	8	4	no	—
351	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
358	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
360	C₂²×C₁₃₉	—	2	2	no	—
361	C₂²×C₁₃₉	—	2	4	no	—
362	C₂²×C₁₃₉	—	2	2	no	—
363	C₂²×C₁₃₉	—	2	2	no	—
364	C₂²×C₁₃₉	—	2	8	no	—
365	C₂²×C₁₃₉	—	4	2	no	—
366	C₂²×C₁₃₉	—	4	2	no	—
367	C₂²×C₁₃₉	—	4	2	no	—
368	C₂²×C₁₃₉	—	4	4	no	—
369	C₂²×C₁₃₉	—	4	2	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	4	4	no	—
374	C₂²×C₁₃₉	—	4	4	no	—
375	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
376	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
378	C₂²×C₁₃₉	#585	1	2	yes	—
379	C₂²×C₁₃₉	#585	1	2	yes	—
380	C₄×C₁₃₉	—	2	2	no	—
381	C₄×C₁₃₉	—	2	4	no	—
382	C₄×C₁₃₉	—	2	2	no	—
383	C₄×C₁₃₉	—	2	2	no	—
384	C₄×C₁₃₉	—	2	2	no	—
385	C₄×C₁₃₉	—	2	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	—	4	2	no	—
391	C₄×C₁₃₉	—	4	2	no	—
392	C₄×C₁₃₉	—	4	2	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₄×C₁₃₉	#525	1	4	yes	—
396	C₂×C₁₃₉	—	4	2	no	—
397	C₂×C₁₃₉	—	4	4	no	—
398	C₂×C₁₃₉	—	8	2	no	—
399	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
400	C₂×C₁₃₉	#3500	1	1	yes	characteristic
401	C₂×C₁₃₉	#3500	1	1	yes	characteristic
402	C₂×C₁₃₉	#3521	1	2	yes	—
403	C₂×C₁₃₉	#3524	1	2	yes	—
404	#35623	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₁₃₉	#35623	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×#542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	#2545	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	#2544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	#2504	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
414	#2481	C₂×C₁₃₉	1	4	yes	complemented
415	#2477	C₂×C₁₃₉	1	4	yes	complemented
416	#2459	C₂×C₁₃₉	1	4	yes	complemented
417	#2457	C₂×C₁₃₉	1	4	yes	complemented
418	#2432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
419	#2431	C₂×C₁₃₉	1	1	yes	characteristic
420	#2328	C₂×C₁₃₉	1	1	yes	characteristic, complemented
421	#2327	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
423	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
424	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
426	#542	—	2	8	no	—
427	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
431	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
432	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
436	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
438	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
439	#520	—	2	8	no	—
440	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
441	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
448	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
451	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
452	#400	C₂²×C₁₃₉	1	4	yes	—
453	#400	C₂²×C₁₃₉	1	4	yes	—
454	#397	C₂²×C₁₃₉	1	4	yes	—
455	#396	C₂²×C₁₃₉	1	4	yes	—
456	#394	C₂²×C₁₃₉	1	4	yes	—
457	#394	C₂²×C₁₃₉	1	4	yes	—
458	#393	C₂²×C₁₃₉	1	4	yes	—
459	#392	C₂²×C₁₃₉	1	4	yes	—
460	#391	C₂²×C₁₃₉	1	1	yes	characteristic
461	#391	C₂²×C₁₃₉	1	1	yes	characteristic
462	#391	C₂²×C₁₃₉	1	4	yes	—
463	#391	C₂²×C₁₃₉	1	1	yes	characteristic
464	#391	C₂²×C₁₃₉	1	1	yes	characteristic
465	#390	C₂²×C₁₃₉	1	1	yes	characteristic
466	#390	C₂²×C₁₃₉	1	1	yes	characteristic
467	#390	C₂²×C₁₃₉	1	1	yes	characteristic
468	#390	C₂²×C₁₃₉	1	1	yes	characteristic
469	#388	C₂²×C₁₃₉	1	2	yes	—
470	#388	C₂²×C₁₃₉	1	4	yes	—
471	#388	C₂²×C₁₃₉	1	2	yes	—
472	#388	C₂²×C₁₃₉	1	4	yes	—
473	#388	C₂²×C₁₃₉	1	4	yes	—
474	#387	C₂²×C₁₃₉	1	4	yes	—
475	#387	C₂²×C₁₃₉	1	4	yes	—
476	#387	C₂²×C₁₃₉	1	2	yes	—
477	#387	C₂²×C₁₃₉	1	2	yes	—
478	#386	C₂²×C₁₃₉	1	4	yes	—
479	#386	C₂²×C₁₃₉	1	4	yes	—
480	#386	C₂²×C₁₃₉	1	4	yes	—
481	#386	C₂²×C₁₃₉	1	4	yes	—
482	#386	C₂²×C₁₃₉	1	4	yes	—
483	#385	C₂²×C₁₃₉	1	4	yes	—
484	#382	C₂²×C₁₃₉	1	1	yes	characteristic
485	#382	C₂²×C₁₃₉	1	1	yes	characteristic
486	#382	C₂²×C₁₃₉	1	1	yes	characteristic
487	#382	C₂²×C₁₃₉	1	1	yes	characteristic
488	#381	C₂²×C₁₃₉	1	4	yes	—
489	#380	C₂²×C₁₃₉	1	4	yes	—
490	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
491	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
494	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
496	#376	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₂×#41	—	2	4	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	2	4	no	—
501	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
504	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₄⋊Q₈	—	2	4	no	—
516	C₄⋊Q₈	—	2	4	no	—
517	#127	—	2	4	no	—
518	#126	—	2	8	no	—
519	#124	—	2	4	no	—
520	#124	—	2	4	no	—
521	#124	—	2	8	no	—
522	#124	—	2	4	no	—
523	#123	—	2	8	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	8	no	—
526	#121	—	2	4	no	—
527	C₄×Q₈	—	2	4	no	—
528	C₄×Q₈	—	2	4	no	—
529	C₄×Q₈	—	2	4	no	—
530	C₄×D₄	—	2	8	no	—
531	C₄×D₄	—	2	8	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	4	no	—
535	#117	—	2	8	no	—
536	#117	D₄×C₁₃₉	1	8	yes	complemented
537	C₂×C₄⋊C₄	—	2	4	no	—
538	C₂×C₄⋊C₄	—	2	8	no	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
577	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	4	yes	—
585	#95	C₂³×C₁₃₉	1	4	yes	—
586	#95	C₂³×C₁₃₉	1	4	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	4	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	4	yes	—
593	#95	C₂³×C₁₃₉	1	4	yes	—
594	#95	C₂³×C₁₃₉	1	4	yes	—
595	#95	C₂³×C₁₃₉	1	4	yes	—
596	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
599	#41	—	2	32	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	4	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	4	4	no	—
607	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	#41×C₁₃₉	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	4	4	no	—
632	C₂²×C₄	—	4	4	no	—
633	C₂²×C₄	—	4	4	no	—
634	C₂²×C₄	—	4	4	no	—
635	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
666	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	8	no	—
676	C₂²⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	—	4	4	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
683	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
694	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	4	no	—
708	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
709	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
710	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
711	Q₈	—	2	8	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	8	4	no	—
714	D₄	—	2	16	no	—
715	D₄	—	2	8	no	—
716	D₄	—	4	4	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	8	no	—
719	C₂×C₄	—	2	16	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	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	8	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	—	8	4	no	—
754	C₂×C₄	—	8	4	no	—
755	C₂×C₄	—	8	4	no	—
756	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
758	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
762	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
763	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
764	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	8	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	4	4	no	—
780	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
781	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
782	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
783	C₂²	#585×C₁₃₉	1	2	yes	—
784	C₂²	#585×C₁₃₉	1	2	yes	—
785	C₄	—	2	2	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	#525×C₁₃₉	1	4	yes	—
801	C₂	—	4	2	no	—
802	C₂	—	4	4	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
805	C₂	#3500×C₁₃₉	1	1	yes	characteristic
806	C₂	#3500×C₁₃₉	1	1	yes	characteristic
807	C₂	#3521×C₁₃₉	1	2	yes	—
808	C₂	#3524×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2431×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#542×C₁₃₉	C₂	semidirect
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2568×C₁₃₉	C₂	semidirect
4. #2563×C₁₃₉	C₂	semidirect
5. #2545×C₁₃₉	C₂	semidirect
6. #2544×C₁₃₉	C₂	semidirect
7. #2504×C₁₃₉	C₂	semidirect
8. #2503×C₁₃₉	C₂	semidirect
9. #2481×C₁₃₉	C₂	semidirect
10. #2477×C₁₃₉	C₂	semidirect
11. #2459×C₁₃₉	C₂	semidirect
12. #2457×C₁₃₉	C₂	semidirect
13. #2432×C₁₃₉	C₂	semidirect
15. #2328×C₁₃₉	C₂	semidirect
16. #2327×C₁₃₉	C₂	semidirect
17. C₄×#124×C₁₃₉	C₂	semidirect
18. C₄×#124×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
131. #117×C₁₃₉	D₄	semidirect
404. #35623	C₁₃₉	direct (N × H)
405. C₁₃₉	#35623	direct (N × H)
406. C₂×#542	C₂×C₁₃₉	semidirect
407. C₂×#520	C₂×C₁₃₉	semidirect
408. #2568	C₂×C₁₃₉	semidirect
409. #2563	C₂×C₁₃₉	semidirect
410. #2545	C₂×C₁₃₉	semidirect
411. #2544	C₂×C₁₃₉	semidirect
412. #2504	C₂×C₁₃₉	semidirect
413. #2503	C₂×C₁₃₉	semidirect
414. #2481	C₂×C₁₃₉	semidirect
415. #2477	C₂×C₁₃₉	semidirect
416. #2459	C₂×C₁₃₉	semidirect
417. #2457	C₂×C₁₃₉	semidirect
418. #2432	C₂×C₁₃₉	semidirect
420. #2328	C₂×C₁₃₉	semidirect
421. #2327	C₂×C₁₃₉	semidirect
422. C₄×#124	C₂×C₁₃₉	semidirect
423. C₄×#124	C₂×C₁₃₉	semidirect
424. #2298	C₂×C₁₃₉	semidirect
536. #117	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×#542×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2568×C₁₃₉	2
#2563×C₁₃₉	2
#2545×C₁₃₉	2
#2544×C₁₃₉	2
#2504×C₁₃₉	2
#2503×C₁₃₉	2
#2481×C₁₃₉	2
#2477×C₁₃₉	2
#2459×C₁₃₉	2
#2457×C₁₃₉	2
#2432×C₁₃₉	2
#2431×C₁₃₉	2
#2328×C₁₃₉	2
#2327×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2298×C₁₃₉	2
#35623	139

Subgroups — C139×#35623 #48030219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35623 #48030219