Subgroups — C₁₃₉×#36024 #48030620

Order 35584.

2142 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2664×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2618×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2601×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2565×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2560×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2556×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2549×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2519×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2506×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2488×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	C₂×#398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2364×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#552×C₁₃₉	—	2	16	no	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
41	#400×C₁₃₉	C₂²	1	2	yes	—
42	#400×C₁₃₉	C₂²	1	2	yes	—
43	#399×C₁₃₉	C₂²	1	2	yes	—
44	#399×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	1	yes	characteristic
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	1	yes	characteristic
48	#398×C₁₃₉	C₂²	1	2	yes	—
49	#398×C₁₃₉	C₂²	1	1	yes	characteristic
50	#398×C₁₃₉	C₂²	1	2	yes	—
51	#398×C₁₃₉	C₂²	1	2	yes	—
52	#398×C₁₃₉	C₂²	1	2	yes	—
53	#398×C₁₃₉	C₂²	1	1	yes	characteristic
54	#398×C₁₃₉	C₂²	1	1	yes	characteristic
55	#398×C₁₃₉	C₂²	1	1	yes	characteristic
56	#397×C₁₃₉	C₂²	1	2	yes	—
57	#396×C₁₃₉	C₂²	1	2	yes	—
58	#396×C₁₃₉	C₂²	1	2	yes	—
59	#396×C₁₃₉	C₂²	1	2	yes	—
60	#396×C₁₃₉	C₂²	1	2	yes	—
61	#395×C₁₃₉	C₂²	1	2	yes	—
62	#394×C₁₃₉	C₂²	1	1	yes	characteristic
63	#394×C₁₃₉	C₂²	1	1	yes	characteristic
64	#393×C₁₃₉	C₂²	1	2	yes	—
65	#391×C₁₃₉	C₂²	1	2	yes	—
66	#391×C₁₃₉	C₂²	1	2	yes	—
67	#390×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	2	yes	—
71	#389×C₁₃₉	C₂²	1	2	yes	—
72	#389×C₁₃₉	C₂²	1	2	yes	—
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	—
75	#388×C₁₃₉	C₂²	1	2	yes	—
76	#388×C₁₃₉	C₂²	1	2	yes	—
77	#388×C₁₃₉	C₂²	1	2	yes	—
78	#388×C₁₃₉	C₂²	1	2	yes	—
79	#388×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#386×C₁₃₉	C₂²	1	2	yes	—
86	#386×C₁₃₉	C₂²	1	2	yes	—
87	#386×C₁₃₉	C₂²	1	2	yes	—
88	#385×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#384×C₁₃₉	C₂²	1	2	yes	—
91	#382×C₁₃₉	C₂²	1	2	yes	—
92	#381×C₁₃₉	C₂²	1	2	yes	—
93	#380×C₁₃₉	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
106	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	#126×C₁₃₉	—	2	8	no	—
118	#126×C₁₃₉	—	2	8	no	—
119	#125×C₁₃₉	—	2	8	no	—
120	#125×C₁₃₉	—	2	8	no	—
121	#125×C₁₃₉	—	2	8	no	—
122	#123×C₁₃₉	—	2	8	no	—
123	#123×C₁₃₉	—	2	8	no	—
124	#123×C₁₃₉	—	2	8	no	—
125	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
126	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
127	#121×C₁₃₉	—	2	4	no	—
128	C₄×Q₈×C₁₃₉	—	2	8	no	—
129	C₄×D₄×C₁₃₉	—	2	8	no	—
130	#117×C₁₃₉	—	2	8	no	—
131	#117×C₁₃₉	—	2	4	no	—
132	#117×C₁₃₉	—	2	8	no	—
133	#117×C₁₃₉	D₄	1	8	yes	complemented
134	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
135	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	1	yes	characteristic
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	1	yes	characteristic
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	1	yes	characteristic
212	#95×C₁₃₉	C₂³	1	1	yes	characteristic
213	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂×Q₈×C₁₃₉	—	2	4	no	—
218	C₂×Q₈×C₁₃₉	—	2	4	no	—
219	C₂×Q₈×C₁₃₉	—	4	2	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂×D₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	—	2	2	no	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	4	no	—
228	C₂²×C₄×C₁₃₉	—	2	4	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	4	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	4	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	2	2	no	—
273	C₄⋊C₄×C₁₃₉	—	2	2	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	2	2	no	—
276	C₄⋊C₄×C₁₃₉	—	2	2	no	—
277	C₄⋊C₄×C₁₃₉	—	2	2	no	—
278	C₄⋊C₄×C₁₃₉	—	2	4	no	—
279	C₄⋊C₄×C₁₃₉	—	2	4	no	—
280	C₄⋊C₄×C₁₃₉	—	2	2	no	—
281	C₄⋊C₄×C₁₃₉	—	2	4	no	—
282	C₄⋊C₄×C₁₃₉	—	2	4	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	4	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
302	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
303	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
304	C₄²×C₁₃₉	—	2	4	no	—
305	C₄²×C₁₃₉	—	2	4	no	—
306	C₄²×C₁₃₉	—	2	4	no	—
307	C₄²×C₁₃₉	—	2	4	no	—
308	C₄²×C₁₃₉	—	4	2	no	—
309	C₄²×C₁₃₉	—	4	2	no	—
310	C₄²×C₁₃₉	—	4	2	no	—
311	C₄²×C₁₃₉	—	4	2	no	—
312	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
324	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
325	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃₉	—	4	8	no	—
327	D₄×C₁₃₉	—	4	8	no	—
328	D₄×C₁₃₉	—	8	2	no	—
329	C₂×C₄×C₁₃₉	—	2	8	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	4	4	no	—
370	C₂×C₄×C₁₃₉	—	4	8	no	—
371	C₂×C₄×C₁₃₉	—	4	8	no	—
372	C₂×C₄×C₁₃₉	—	4	8	no	—
373	C₂×C₄×C₁₃₉	—	8	2	no	—
374	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
379	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
381	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	2	no	—
384	C₂²×C₁₃₉	—	2	2	no	—
385	C₂²×C₁₃₉	—	2	4	no	—
386	C₂²×C₁₃₉	—	4	2	no	—
387	C₂²×C₁₃₉	—	4	2	no	—
388	C₂²×C₁₃₉	—	4	2	no	—
389	C₂²×C₁₃₉	—	4	2	no	—
390	C₂²×C₁₃₉	—	4	2	no	—
391	C₂²×C₁₃₉	—	4	2	no	—
392	C₂²×C₁₃₉	—	4	2	no	—
393	C₂²×C₁₃₉	#532	1	4	yes	—
394	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
395	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
398	C₂²×C₁₃₉	#585	1	2	yes	—
399	C₄×C₁₃₉	—	2	2	no	—
400	C₄×C₁₃₉	—	2	2	no	—
401	C₄×C₁₃₉	—	2	4	no	—
402	C₄×C₁₃₉	—	2	4	no	—
403	C₄×C₁₃₉	—	2	4	no	—
404	C₄×C₁₃₉	—	2	2	no	—
405	C₄×C₁₃₉	—	2	2	no	—
406	C₄×C₁₃₉	—	2	4	no	—
407	C₄×C₁₃₉	—	4	2	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₄×C₁₃₉	—	4	2	no	—
411	C₄×C₁₃₉	—	4	2	no	—
412	C₄×C₁₃₉	—	4	2	no	—
413	C₄×C₁₃₉	—	4	1	no	—
414	C₄×C₁₃₉	—	4	1	no	—
415	C₄×C₁₃₉	—	4	2	no	—
416	C₂×C₁₃₉	—	2	4	no	—
417	C₂×C₁₃₉	—	8	2	no	—
418	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
419	C₂×C₁₃₉	#3489	1	2	yes	—
420	C₂×C₁₃₉	#3491	1	1	yes	characteristic
421	C₂×C₁₃₉	#3509	1	1	yes	characteristic
422	C₂×C₁₃₉	#3515	1	2	yes	—
423	#36024	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₁₃₉	#36024	1	1	yes	characteristic, direct product factor, Sylow
425	C₂×#552	C₂×C₁₃₉	1	2	yes	complemented
426	#2664	C₂×C₁₃₉	1	2	yes	complemented
427	#2618	C₂×C₁₃₉	1	1	yes	characteristic
428	#2601	C₂×C₁₃₉	1	2	yes	complemented
429	#2565	C₂×C₁₃₉	1	2	yes	complemented
430	#2560	C₂×C₁₃₉	1	2	yes	complemented
431	#2556	C₂×C₁₃₉	1	2	yes	complemented
432	#2549	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	#2519	C₂×C₁₃₉	1	2	yes	complemented
434	#2506	C₂×C₁₃₉	1	2	yes	complemented
435	#2501	C₂×C₁₃₉	1	1	yes	characteristic
436	#2488	C₂×C₁₃₉	1	2	yes	complemented
437	#2413	C₂×C₁₃₉	1	2	yes	complemented
438	#2396	C₂×C₁₃₉	1	2	yes	complemented
439	C₂×#398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	#2364	C₂×C₁₃₉	1	1	yes	characteristic
441	#2359	C₂×C₁₃₉	1	2	yes	complemented
442	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
443	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
444	#552	—	2	16	no	—
445	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
446	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
447	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
448	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
450	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
451	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
452	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
454	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
455	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
458	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
459	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
460	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
465	#400	C₂²×C₁₃₉	1	2	yes	—
466	#400	C₂²×C₁₃₉	1	2	yes	—
467	#399	C₂²×C₁₃₉	1	2	yes	—
468	#399	C₂²×C₁₃₉	1	2	yes	—
469	#398	C₂²×C₁₃₉	1	2	yes	—
470	#398	C₂²×C₁₃₉	1	1	yes	characteristic
471	#398	C₂²×C₁₃₉	1	2	yes	—
472	#398	C₂²×C₁₃₉	1	2	yes	—
473	#398	C₂²×C₁₃₉	1	2	yes	—
474	#398	C₂²×C₁₃₉	1	1	yes	characteristic
475	#398	C₂²×C₁₃₉	1	1	yes	characteristic
476	#398	C₂²×C₁₃₉	1	1	yes	characteristic
477	#398	C₂²×C₁₃₉	1	1	yes	characteristic
478	#398	C₂²×C₁₃₉	1	1	yes	characteristic
479	#398	C₂²×C₁₃₉	1	2	yes	—
480	#397	C₂²×C₁₃₉	1	2	yes	—
481	#396	C₂²×C₁₃₉	1	2	yes	—
482	#396	C₂²×C₁₃₉	1	2	yes	—
483	#396	C₂²×C₁₃₉	1	2	yes	—
484	#396	C₂²×C₁₃₉	1	2	yes	—
485	#395	C₂²×C₁₃₉	1	2	yes	—
486	#394	C₂²×C₁₃₉	1	1	yes	characteristic
487	#394	C₂²×C₁₃₉	1	1	yes	characteristic
488	#393	C₂²×C₁₃₉	1	2	yes	—
489	#391	C₂²×C₁₃₉	1	2	yes	—
490	#391	C₂²×C₁₃₉	1	2	yes	—
491	#390	C₂²×C₁₃₉	1	2	yes	—
492	#389	C₂²×C₁₃₉	1	2	yes	—
493	#389	C₂²×C₁₃₉	1	2	yes	—
494	#389	C₂²×C₁₃₉	1	2	yes	—
495	#389	C₂²×C₁₃₉	1	2	yes	—
496	#389	C₂²×C₁₃₉	1	2	yes	—
497	#388	C₂²×C₁₃₉	1	2	yes	—
498	#388	C₂²×C₁₃₉	1	2	yes	—
499	#388	C₂²×C₁₃₉	1	2	yes	—
500	#388	C₂²×C₁₃₉	1	2	yes	—
501	#388	C₂²×C₁₃₉	1	2	yes	—
502	#388	C₂²×C₁₃₉	1	2	yes	—
503	#388	C₂²×C₁₃₉	1	2	yes	—
504	#387	C₂²×C₁₃₉	1	2	yes	—
505	#387	C₂²×C₁₃₉	1	2	yes	—
506	#387	C₂²×C₁₃₉	1	2	yes	—
507	#387	C₂²×C₁₃₉	1	2	yes	—
508	#387	C₂²×C₁₃₉	1	2	yes	—
509	#386	C₂²×C₁₃₉	1	2	yes	—
510	#386	C₂²×C₁₃₉	1	2	yes	—
511	#386	C₂²×C₁₃₉	1	2	yes	—
512	#385	C₂²×C₁₃₉	1	2	yes	—
513	#385	C₂²×C₁₃₉	1	2	yes	—
514	#384	C₂²×C₁₃₉	1	2	yes	—
515	#382	C₂²×C₁₃₉	1	2	yes	—
516	#381	C₂²×C₁₃₉	1	2	yes	—
517	#380	C₂²×C₁₃₉	1	1	yes	characteristic
518	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
519	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
530	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
531	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
533	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	#126	—	2	8	no	—
542	#126	—	2	8	no	—
543	#125	—	2	8	no	—
544	#125	—	2	8	no	—
545	#125	—	2	8	no	—
546	#123	—	2	8	no	—
547	#123	—	2	8	no	—
548	#123	—	2	8	no	—
549	C₂²⋊Q₈	—	2	8	no	—
550	C₂²⋊Q₈	—	2	8	no	—
551	#121	—	2	4	no	—
552	C₄×Q₈	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	#117	—	2	8	no	—
555	#117	—	2	4	no	—
556	#117	—	2	8	no	—
557	#117	D₄×C₁₃₉	1	8	yes	complemented
558	C₂×C₄⋊C₄	—	2	8	no	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	—	2	4	no	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	1	yes	characteristic
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	#95	C₂³×C₁₃₉	1	2	yes	—
620	#95	C₂³×C₁₃₉	1	2	yes	—
621	#95	C₂³×C₁₃₉	1	1	yes	characteristic
622	#95	C₂³×C₁₃₉	1	2	yes	—
623	#95	C₂³×C₁₃₉	1	2	yes	—
624	#95	C₂³×C₁₃₉	1	2	yes	—
625	#95	C₂³×C₁₃₉	1	2	yes	—
626	#95	C₂³×C₁₃₉	1	2	yes	—
627	#95	C₂³×C₁₃₉	1	2	yes	—
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	2	yes	—
631	#95	C₂³×C₁₃₉	1	2	yes	—
632	#95	C₂³×C₁₃₉	1	1	yes	characteristic
633	#95	C₂³×C₁₃₉	1	1	yes	characteristic
634	#95	C₂³×C₁₃₉	1	2	yes	—
635	#95	C₂³×C₁₃₉	1	2	yes	—
636	#95	C₂³×C₁₃₉	1	2	yes	—
637	#95	C₂³×C₁₃₉	1	2	yes	—
638	#95	C₂³×C₁₃₉	1	2	yes	—
639	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
640	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
664	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
726	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
727	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	4	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
747	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
748	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
749	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
750	Q₈	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	8	2	no	—
753	C₂×C₄	—	2	8	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	8	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
799	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
801	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
802	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
803	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
804	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
805	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	#532×C₁₃₉	1	4	yes	—
818	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
819	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
820	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
821	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
822	C₂²	#585×C₁₃₉	1	2	yes	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	2	4	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	4	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₂	—	2	4	no	—
841	C₂	—	8	2	no	—
842	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
843	C₂	#3489×C₁₃₉	1	2	yes	—
844	C₂	#3491×C₁₃₉	1	1	yes	characteristic
845	C₂	#3509×C₁₃₉	1	1	yes	characteristic
846	C₂	#3515×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×C₁₃₉	C₂²
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×#552×C₁₃₉	C₂	semidirect
2. #2664×C₁₃₉	C₂	semidirect
4. #2601×C₁₃₉	C₂	semidirect
5. #2565×C₁₃₉	C₂	semidirect
6. #2560×C₁₃₉	C₂	semidirect
7. #2556×C₁₃₉	C₂	semidirect
8. #2549×C₁₃₉	C₂	semidirect
9. #2519×C₁₃₉	C₂	semidirect
10. #2506×C₁₃₉	C₂	semidirect
12. #2488×C₁₃₉	C₂	semidirect
13. #2413×C₁₃₉	C₂	semidirect
14. #2396×C₁₃₉	C₂	semidirect
15. C₂×#398×C₁₃₉	C₂	semidirect
17. #2359×C₁₃₉	C₂	semidirect
18. #2344×C₁₃₉	C₂	semidirect
19. #2274×C₁₃₉	C₂	semidirect
133. #117×C₁₃₉	D₄	semidirect
423. #36024	C₁₃₉	direct (N × H)
424. C₁₃₉	#36024	direct (N × H)
425. C₂×#552	C₂×C₁₃₉	semidirect
426. #2664	C₂×C₁₃₉	semidirect
428. #2601	C₂×C₁₃₉	semidirect
429. #2565	C₂×C₁₃₉	semidirect
430. #2560	C₂×C₁₃₉	semidirect
431. #2556	C₂×C₁₃₉	semidirect
432. #2549	C₂×C₁₃₉	semidirect
433. #2519	C₂×C₁₃₉	semidirect
434. #2506	C₂×C₁₃₉	semidirect
436. #2488	C₂×C₁₃₉	semidirect
437. #2413	C₂×C₁₃₉	semidirect
438. #2396	C₂×C₁₃₉	semidirect
439. C₂×#398	C₂×C₁₃₉	semidirect
441. #2359	C₂×C₁₃₉	semidirect
442. #2344	C₂×C₁₃₉	semidirect
443. #2274	C₂×C₁₃₉	semidirect
557. #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×#552×C₁₃₉	2
#2664×C₁₃₉	2
#2618×C₁₃₉	2
#2601×C₁₃₉	2
#2565×C₁₃₉	2
#2560×C₁₃₉	2
#2556×C₁₃₉	2
#2549×C₁₃₉	2
#2519×C₁₃₉	2
#2506×C₁₃₉	2
#2501×C₁₃₉	2
#2488×C₁₃₉	2
#2413×C₁₃₉	2
#2396×C₁₃₉	2
C₂×#398×C₁₃₉	2
#2364×C₁₃₉	2
#2359×C₁₃₉	2
#2344×C₁₃₉	2
#2274×C₁₃₉	2
#36024	139

Subgroups — C139×#36024 #48030620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36024 #48030620