Subgroups — C₁₃₉×#35742 #48030338

Order 35584.

1898 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2650×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2618×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2588×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2574×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2569×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2521×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2520×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2498×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2481×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2474×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2469×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2436×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2396×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₂×#395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2364×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	#2359×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	2	yes	—
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#399×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	1	yes	characteristic
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	1	yes	characteristic
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#397×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#396×C₁₃₉	C₂²	1	2	yes	—
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#395×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	1	yes	characteristic
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#395×C₁₃₉	C₂²	1	1	yes	characteristic
51	#395×C₁₃₉	C₂²	1	1	yes	characteristic
52	#394×C₁₃₉	C₂²	1	1	yes	characteristic
53	#394×C₁₃₉	C₂²	1	1	yes	characteristic
54	#393×C₁₃₉	C₂²	1	2	yes	—
55	#393×C₁₃₉	C₂²	1	2	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	2	yes	—
72	#387×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#386×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	2	yes	—
82	#386×C₁₃₉	C₂²	1	2	yes	—
83	#386×C₁₃₉	C₂²	1	2	yes	—
84	#386×C₁₃₉	C₂²	1	2	yes	—
85	#385×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#382×C₁₃₉	C₂²	1	2	yes	—
88	#380×C₁₃₉	C₂²	1	2	yes	—
89	#380×C₁₃₉	C₂²	1	1	yes	characteristic
90	#380×C₁₃₉	C₂²	1	2	yes	—
91	#380×C₁₃₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	2	yes	—
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	—	2	4	no	—
108	C₂²×Q₈×C₁₃₉	—	4	4	no	—
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	#126×C₁₃₉	—	4	4	no	—
121	#124×C₁₃₉	—	4	4	no	—
122	#123×C₁₃₉	—	2	8	no	—
123	#121×C₁₃₉	—	2	4	no	—
124	C₄×Q₈×C₁₃₉	—	4	4	no	—
125	C₄×D₄×C₁₃₉	—	2	8	no	—
126	#117×C₁₃₉	—	2	4	no	—
127	#117×C₁₃₉	—	2	4	no	—
128	#117×C₁₃₉	—	4	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊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	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊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	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	1	yes	characteristic
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	1	yes	characteristic
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
197	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂×Q₈×C₁₃₉	—	2	2	no	—
210	C₂×Q₈×C₁₃₉	—	2	4	no	—
211	C₂×Q₈×C₁₃₉	—	2	2	no	—
212	C₂×Q₈×C₁₃₉	—	2	4	no	—
213	C₂×Q₈×C₁₃₉	—	2	4	no	—
214	C₂×Q₈×C₁₃₉	—	4	2	no	—
215	C₂×Q₈×C₁₃₉	—	4	2	no	—
216	C₂×Q₈×C₁₃₉	—	4	16	no	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	4	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	4	2	no	—
233	C₂²×C₄×C₁₃₉	—	4	2	no	—
234	C₂²×C₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
237	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₁₃₉	—	2	2	no	—
256	C₄⋊C₄×C₁₃₉	—	2	2	no	—
257	C₄⋊C₄×C₁₃₉	—	2	2	no	—
258	C₄⋊C₄×C₁₃₉	—	2	2	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	2	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	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	—
293	C₄²×C₁₃₉	—	2	4	no	—
294	C₄²×C₁₃₉	—	2	4	no	—
295	C₄²×C₁₃₉	—	2	4	no	—
296	C₄²×C₁₃₉	—	2	4	no	—
297	C₄²×C₁₃₉	—	4	2	no	—
298	C₄²×C₁₃₉	—	4	2	no	—
299	C₄²×C₁₃₉	—	4	2	no	—
300	C₄²×C₁₃₉	—	4	2	no	—
301	C₄²×C₁₃₉	—	4	2	no	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	2	2	no	—
311	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
312	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
313	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
314	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
315	Q₈×C₁₃₉	—	2	8	no	—
316	Q₈×C₁₃₉	—	4	8	no	—
317	Q₈×C₁₃₉	—	4	4	no	—
318	D₄×C₁₃₉	—	4	8	no	—
319	D₄×C₁₃₉	—	8	2	no	—
320	C₂×C₄×C₁₃₉	—	2	8	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	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	—	4	4	no	—
362	C₂×C₄×C₁₃₉	—	4	8	no	—
363	C₂×C₄×C₁₃₉	—	4	8	no	—
364	C₂×C₄×C₁₃₉	—	4	8	no	—
365	C₂×C₄×C₁₃₉	—	8	2	no	—
366	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
368	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
369	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
370	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
371	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
372	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
373	C₂²×C₁₃₉	—	2	2	no	—
374	C₂²×C₁₃₉	—	2	2	no	—
375	C₂²×C₁₃₉	—	2	4	no	—
376	C₂²×C₁₃₉	—	2	4	no	—
377	C₂²×C₁₃₉	—	4	2	no	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	2	no	—
380	C₂²×C₁₃₉	—	4	2	no	—
381	C₂²×C₁₃₉	—	4	2	no	—
382	C₂²×C₁₃₉	—	4	2	no	—
383	C₂²×C₁₃₉	—	4	2	no	—
384	C₂²×C₁₃₉	#529	1	4	yes	—
385	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
386	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
387	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
389	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
390	C₄×C₁₃₉	—	2	2	no	—
391	C₄×C₁₃₉	—	2	2	no	—
392	C₄×C₁₃₉	—	2	2	no	—
393	C₄×C₁₃₉	—	2	2	no	—
394	C₄×C₁₃₉	—	2	4	no	—
395	C₄×C₁₃₉	—	2	4	no	—
396	C₄×C₁₃₉	—	2	4	no	—
397	C₄×C₁₃₉	—	4	2	no	—
398	C₄×C₁₃₉	—	4	2	no	—
399	C₄×C₁₃₉	—	4	1	no	—
400	C₄×C₁₃₉	—	4	1	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	2	no	—
403	C₄×C₁₃₉	—	4	2	no	—
404	C₄×C₁₃₉	—	4	2	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₂×C₁₃₉	—	2	4	no	—
408	C₂×C₁₃₉	—	8	2	no	—
409	C₂×C₁₃₉	C₂×#529	1	1	yes	characteristic
410	C₂×C₁₃₉	#3490	1	1	yes	characteristic
411	C₂×C₁₃₉	#3509	1	1	yes	characteristic
412	C₂×C₁₃₉	#3511	1	2	yes	—
413	C₂×C₁₃₉	#3520	1	2	yes	—
414	#35742	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₁₃₉	#35742	1	1	yes	characteristic, direct product factor, Sylow
416	#2650	C₂×C₁₃₉	1	2	yes	complemented
417	#2618	C₂×C₁₃₉	1	1	yes	characteristic
418	#2588	C₂×C₁₃₉	1	2	yes	complemented
419	#2574	C₂×C₁₃₉	1	2	yes	complemented
420	#2569	C₂×C₁₃₉	1	1	yes	characteristic, complemented
421	#2521	C₂×C₁₃₉	1	2	yes	complemented
422	#2520	C₂×C₁₃₉	1	2	yes	complemented
423	#2498	C₂×C₁₃₉	1	2	yes	complemented
424	#2481	C₂×C₁₃₉	1	2	yes	complemented
425	#2474	C₂×C₁₃₉	1	2	yes	complemented
426	#2469	C₂×C₁₃₉	1	2	yes	complemented
427	#2436	C₂×C₁₃₉	1	1	yes	characteristic
428	#2396	C₂×C₁₃₉	1	2	yes	complemented
429	C₂×#395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
430	#2364	C₂×C₁₃₉	1	1	yes	characteristic
431	#2359	C₂×C₁₃₉	1	2	yes	complemented
432	#2352	C₂×C₁₃₉	1	2	yes	complemented
433	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
434	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
435	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
437	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
438	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
439	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
442	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
445	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
447	#400	C₂²×C₁₃₉	1	2	yes	—
448	#400	C₂²×C₁₃₉	1	2	yes	—
449	#400	C₂²×C₁₃₉	1	2	yes	—
450	#400	C₂²×C₁₃₉	1	2	yes	—
451	#399	C₂²×C₁₃₉	1	2	yes	—
452	#398	C₂²×C₁₃₉	1	2	yes	—
453	#398	C₂²×C₁₃₉	1	1	yes	characteristic
454	#398	C₂²×C₁₃₉	1	1	yes	characteristic
455	#398	C₂²×C₁₃₉	1	2	yes	—
456	#397	C₂²×C₁₃₉	1	2	yes	—
457	#397	C₂²×C₁₃₉	1	2	yes	—
458	#396	C₂²×C₁₃₉	1	2	yes	—
459	#396	C₂²×C₁₃₉	1	2	yes	—
460	#396	C₂²×C₁₃₉	1	2	yes	—
461	#395	C₂²×C₁₃₉	1	1	yes	characteristic
462	#395	C₂²×C₁₃₉	1	2	yes	—
463	#395	C₂²×C₁₃₉	1	1	yes	characteristic
464	#395	C₂²×C₁₃₉	1	1	yes	characteristic
465	#395	C₂²×C₁₃₉	1	1	yes	characteristic
466	#395	C₂²×C₁₃₉	1	2	yes	—
467	#394	C₂²×C₁₃₉	1	1	yes	characteristic
468	#394	C₂²×C₁₃₉	1	1	yes	characteristic
469	#393	C₂²×C₁₃₉	1	2	yes	—
470	#393	C₂²×C₁₃₉	1	2	yes	—
471	#391	C₂²×C₁₃₉	1	2	yes	—
472	#391	C₂²×C₁₃₉	1	2	yes	—
473	#391	C₂²×C₁₃₉	1	2	yes	—
474	#391	C₂²×C₁₃₉	1	2	yes	—
475	#389	C₂²×C₁₃₉	1	2	yes	—
476	#388	C₂²×C₁₃₉	1	2	yes	—
477	#388	C₂²×C₁₃₉	1	2	yes	—
478	#388	C₂²×C₁₃₉	1	2	yes	—
479	#388	C₂²×C₁₃₉	1	2	yes	—
480	#388	C₂²×C₁₃₉	1	2	yes	—
481	#388	C₂²×C₁₃₉	1	2	yes	—
482	#388	C₂²×C₁₃₉	1	2	yes	—
483	#388	C₂²×C₁₃₉	1	2	yes	—
484	#387	C₂²×C₁₃₉	1	2	yes	—
485	#387	C₂²×C₁₃₉	1	2	yes	—
486	#387	C₂²×C₁₃₉	1	2	yes	—
487	#387	C₂²×C₁₃₉	1	2	yes	—
488	#387	C₂²×C₁₃₉	1	2	yes	—
489	#387	C₂²×C₁₃₉	1	2	yes	—
490	#387	C₂²×C₁₃₉	1	2	yes	—
491	#387	C₂²×C₁₃₉	1	2	yes	—
492	#387	C₂²×C₁₃₉	1	2	yes	—
493	#387	C₂²×C₁₃₉	1	2	yes	—
494	#387	C₂²×C₁₃₉	1	2	yes	—
495	#386	C₂²×C₁₃₉	1	2	yes	—
496	#386	C₂²×C₁₃₉	1	2	yes	—
497	#386	C₂²×C₁₃₉	1	2	yes	—
498	#386	C₂²×C₁₃₉	1	2	yes	—
499	#386	C₂²×C₁₃₉	1	2	yes	—
500	#385	C₂²×C₁₃₉	1	2	yes	—
501	#385	C₂²×C₁₃₉	1	2	yes	—
502	#382	C₂²×C₁₃₉	1	2	yes	—
503	#380	C₂²×C₁₃₉	1	1	yes	characteristic
504	#380	C₂²×C₁₃₉	1	2	yes	—
505	#380	C₂²×C₁₃₉	1	2	yes	—
506	#380	C₂²×C₁₃₉	1	2	yes	—
507	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
508	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
509	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
510	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
513	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
514	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
515	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
516	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
517	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
518	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
520	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
521	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
522	C₂²×Q₈	—	2	4	no	—
523	C₂²×Q₈	—	4	4	no	—
524	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
526	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	#126	—	4	4	no	—
536	#124	—	4	4	no	—
537	#123	—	2	8	no	—
538	#121	—	2	4	no	—
539	C₄×Q₈	—	4	4	no	—
540	C₄×D₄	—	2	8	no	—
541	#117	—	2	4	no	—
542	#117	—	2	4	no	—
543	#117	—	4	4	no	—
544	C₂×C₄⋊C₄	—	2	4	no	—
545	C₂×C₄⋊C₄	—	4	4	no	—
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	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	1	yes	characteristic
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	2	yes	—
596	#95	C₂³×C₁₃₉	1	2	yes	—
597	#95	C₂³×C₁₃₉	1	2	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	1	yes	characteristic
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	2	yes	—
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	1	yes	characteristic
614	#95	C₂³×C₁₃₉	1	1	yes	characteristic
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
622	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
623	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	4	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	2	4	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	4	2	no	—
631	C₂×Q₈	—	4	16	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
652	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	2	4	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₄²	—	4	2	no	—
716	C₄²	—	4	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
727	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
728	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
729	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
730	Q₈	—	2	8	no	—
731	Q₈	—	4	8	no	—
732	Q₈	—	4	4	no	—
733	D₄	—	4	8	no	—
734	D₄	—	8	2	no	—
735	C₂×C₄	—	2	8	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	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	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	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	—	4	4	no	—
777	C₂×C₄	—	4	8	no	—
778	C₂×C₄	—	4	8	no	—
779	C₂×C₄	—	4	8	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
782	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
783	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
784	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
785	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
786	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
787	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	#529×C₁₃₉	1	4	yes	—
800	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
801	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
802	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
803	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
804	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	4	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	4	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₂	—	2	4	no	—
823	C₂	—	8	2	no	—
824	C₂	C₂×#529×C₁₃₉	1	1	yes	characteristic
825	C₂	#3490×C₁₃₉	1	1	yes	characteristic
826	C₂	#3509×C₁₃₉	1	1	yes	characteristic
827	C₂	#3511×C₁₃₉	1	2	yes	—
828	C₂	#3520×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. #2650×C₁₃₉	C₂	semidirect
3. #2588×C₁₃₉	C₂	semidirect
4. #2574×C₁₃₉	C₂	semidirect
5. #2569×C₁₃₉	C₂	semidirect
6. #2521×C₁₃₉	C₂	semidirect
7. #2520×C₁₃₉	C₂	semidirect
8. #2498×C₁₃₉	C₂	semidirect
9. #2481×C₁₃₉	C₂	semidirect
10. #2474×C₁₃₉	C₂	semidirect
11. #2469×C₁₃₉	C₂	semidirect
13. #2396×C₁₃₉	C₂	semidirect
14. C₂×#395×C₁₃₉	C₂	semidirect
16. #2359×C₁₃₉	C₂	semidirect
17. #2352×C₁₃₉	C₂	semidirect
18. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
19. #2274×C₁₃₉	C₂	semidirect
414. #35742	C₁₃₉	direct (N × H)
415. C₁₃₉	#35742	direct (N × H)
416. #2650	C₂×C₁₃₉	semidirect
418. #2588	C₂×C₁₃₉	semidirect
419. #2574	C₂×C₁₃₉	semidirect
420. #2569	C₂×C₁₃₉	semidirect
421. #2521	C₂×C₁₃₉	semidirect
422. #2520	C₂×C₁₃₉	semidirect
423. #2498	C₂×C₁₃₉	semidirect
424. #2481	C₂×C₁₃₉	semidirect
425. #2474	C₂×C₁₃₉	semidirect
426. #2469	C₂×C₁₃₉	semidirect
428. #2396	C₂×C₁₃₉	semidirect
429. C₂×#395	C₂×C₁₃₉	semidirect
431. #2359	C₂×C₁₃₉	semidirect
432. #2352	C₂×C₁₃₉	semidirect
433. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
434. #2274	C₂×C₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#2650×C₁₃₉	2
#2618×C₁₃₉	2
#2588×C₁₃₉	2
#2574×C₁₃₉	2
#2569×C₁₃₉	2
#2521×C₁₃₉	2
#2520×C₁₃₉	2
#2498×C₁₃₉	2
#2481×C₁₃₉	2
#2474×C₁₃₉	2
#2469×C₁₃₉	2
#2436×C₁₃₉	2
#2396×C₁₃₉	2
C₂×#395×C₁₃₉	2
#2364×C₁₃₉	2
#2359×C₁₃₉	2
#2352×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
#2274×C₁₃₉	2
#35742	139

Subgroups — C139×#35742 #48030338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35742 #48030338