Subgroups — C₁₃₉×#36237 #48030833

Order 35584.

3072 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2483×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2447×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2443×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2419×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2412×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2339×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#385×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
21	#546×C₁₃₉	—	2	8	no	—
22	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
43	#400×C₁₃₉	C₂²	1	2	yes	complemented
44	#399×C₁₃₉	C₂²	1	2	yes	complemented
45	#398×C₁₃₉	C₂²	1	4	yes	complemented
46	#397×C₁₃₉	C₂²	1	4	yes	complemented
47	#397×C₁₃₉	C₂²	1	4	yes	complemented
48	#397×C₁₃₉	C₂²	1	4	yes	complemented
49	#394×C₁₃₉	C₂²	1	4	yes	complemented
50	#391×C₁₃₉	C₂²	1	2	yes	complemented
51	#391×C₁₃₉	C₂²	1	2	yes	complemented
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	complemented
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#388×C₁₃₉	C₂²	1	2	yes	complemented
56	#387×C₁₃₉	C₂²	1	2	yes	complemented
57	#387×C₁₃₉	C₂²	1	4	yes	complemented
58	#386×C₁₃₉	C₂²	1	1	yes	characteristic
59	#386×C₁₃₉	C₂²	1	2	yes	—
60	#386×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	complemented
62	#386×C₁₃₉	C₂²	1	4	yes	complemented
63	#385×C₁₃₉	C₂²	1	1	yes	characteristic
64	#385×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	2	yes	—
66	#385×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	2	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	complemented
69	#385×C₁₃₉	C₂²	1	4	yes	complemented
70	#385×C₁₃₉	C₂²	1	4	yes	complemented
71	#385×C₁₃₉	C₂²	1	4	yes	complemented
72	#384×C₁₃₉	C₂²	1	2	yes	complemented
73	#381×C₁₃₉	C₂²	1	1	yes	characteristic
74	#381×C₁₃₉	C₂²	1	2	yes	—
75	#381×C₁₃₉	C₂²	1	4	yes	complemented
76	#381×C₁₃₉	C₂²	1	4	yes	complemented
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	#380×C₁₃₉	C₂²	1	2	yes	complemented
79	#380×C₁₃₉	C₂²	1	4	yes	complemented
80	#379×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂×#41×C₁₃₉	—	2	4	no	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	—	2	8	no	—
90	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	—	2	8	no	—
98	C₂³×C₄×C₁₃₉	—	4	8	no	—
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	#124×C₁₃₉	—	2	4	no	—
110	#123×C₁₃₉	—	2	8	no	—
111	#123×C₁₃₉	—	2	4	no	—
112	#123×C₁₃₉	—	4	8	no	—
113	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
114	#121×C₁₃₉	—	2	4	no	—
115	#121×C₁₃₉	—	2	8	no	—
116	#120×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	16	no	—
118	C₄×D₄×C₁₃₉	—	2	8	no	—
119	C₄×D₄×C₁₃₉	—	2	8	no	—
120	C₄×D₄×C₁₃₉	—	2	4	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
138	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
139	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	—	2	4	no	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	C₂⁴×C₁₃₉	—	2	4	no	—
177	C₂⁴×C₁₃₉	—	2	8	no	—
178	C₂⁴×C₁₃₉	—	2	4	no	—
179	C₂⁴×C₁₃₉	—	4	4	no	—
180	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
185	#41×C₁₃₉	—	4	16	no	—
186	C₂×Q₈×C₁₃₉	—	2	2	no	—
187	C₂×Q₈×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	8	no	—
189	C₂×D₄×C₁₃₉	—	2	32	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	2	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	2	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	4	4	no	—
198	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
199	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
200	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
201	C₂×D₄×C₁₃₉	#41	1	8	yes	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	4	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	8	no	—
209	C₂²×C₄×C₁₃₉	—	2	8	no	—
210	C₂²×C₄×C₁₃₉	—	2	8	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	8	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	8	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	8	no	—
219	C₂²×C₄×C₁₃₉	—	2	8	no	—
220	C₂²×C₄×C₁₃₉	—	4	4	no	—
221	C₂²×C₄×C₁₃₉	—	4	4	no	—
222	C₂²×C₄×C₁₃₉	—	4	4	no	—
223	C₂²×C₄×C₁₃₉	—	4	4	no	—
224	C₂²×C₄×C₁₃₉	—	4	4	no	—
225	C₂²×C₄×C₁₃₉	—	4	32	no	—
226	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	4	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	8	no	—
249	C₄⋊C₄×C₁₃₉	—	4	4	no	—
250	C₄⋊C₄×C₁₃₉	—	4	4	no	—
251	C₄⋊C₄×C₁₃₉	—	4	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	complemented
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	2	2	no	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	4	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	16	no	—
280	C₂³×C₁₃₉	—	2	16	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	4	no	—
283	C₂³×C₁₃₉	—	2	4	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	1	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	4	8	no	—
291	C₂³×C₁₃₉	—	4	16	no	—
292	C₂³×C₁₃₉	—	4	16	no	—
293	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
294	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
295	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
296	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
297	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
298	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
299	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
300	Q₈×C₁₃₉	—	4	4	no	—
301	D₄×C₁₃₉	—	2	16	no	—
302	D₄×C₁₃₉	—	2	8	no	—
303	D₄×C₁₃₉	—	4	8	no	—
304	D₄×C₁₃₉	—	4	4	no	—
305	D₄×C₁₃₉	—	8	4	no	—
306	D₄×C₁₃₉	#123	1	16	yes	complemented
307	C₂×C₄×C₁₃₉	—	2	8	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	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	8	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	4	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	4	no	—
330	C₂×C₄×C₁₃₉	—	2	4	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	4	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	4	16	no	—
338	C₂×C₄×C₁₃₉	—	4	16	no	—
339	C₂×C₄×C₁₃₉	—	4	16	no	—
340	C₂×C₄×C₁₃₉	—	4	8	no	—
341	C₂×C₄×C₁₃₉	—	4	8	no	—
342	C₂×C₄×C₁₃₉	—	4	4	no	—
343	C₂×C₄×C₁₃₉	—	4	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	C₂×#41	1	4	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
349	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
350	C₂²×C₁₃₉	—	2	2	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	2	8	no	—
353	C₂²×C₁₃₉	—	2	4	no	—
354	C₂²×C₁₃₉	—	2	2	no	—
355	C₂²×C₁₃₉	—	2	4	no	—
356	C₂²×C₁₃₉	—	2	4	no	—
357	C₂²×C₁₃₉	—	2	8	no	—
358	C₂²×C₁₃₉	—	2	4	no	—
359	C₂²×C₁₃₉	—	2	4	no	—
360	C₂²×C₁₃₉	—	2	4	no	—
361	C₂²×C₁₃₉	—	4	32	no	—
362	C₂²×C₁₃₉	—	4	4	no	—
363	C₂²×C₁₃₉	—	4	4	no	—
364	C₂²×C₁₃₉	—	4	1	no	—
365	C₂²×C₁₃₉	—	4	1	no	—
366	C₂²×C₁₃₉	—	4	2	no	—
367	C₂²×C₁₃₉	—	4	1	no	—
368	C₂²×C₁₃₉	—	4	2	no	—
369	C₂²×C₁₃₉	C₂×#123	1	8	yes	—
370	C₂²×C₁₃₉	#547	1	4	yes	—
371	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
372	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
373	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
375	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	C₄×C₁₃₉	—	2	2	no	—
377	C₄×C₁₃₉	—	2	4	no	—
378	C₄×C₁₃₉	—	2	4	no	—
379	C₄×C₁₃₉	—	4	1	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	1	no	—
383	C₄×C₁₃₉	—	4	4	no	—
384	C₄×C₁₃₉	—	4	4	no	—
385	C₄×C₁₃₉	—	4	1	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	C₂×#123	1	4	yes	—
389	C₂×C₁₃₉	—	2	4	no	—
390	C₂×C₁₃₉	—	2	8	no	—
391	C₂×C₁₃₉	—	4	4	no	—
392	C₂×C₁₃₉	—	8	1	no	—
393	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
394	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
395	C₂×C₁₃₉	#3481	1	2	yes	—
396	C₂×C₁₃₉	#3484	1	1	yes	characteristic
397	C₂×C₁₃₉	#3520	1	2	yes	—
398	#36237	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₁₃₉	#36237	1	1	yes	characteristic, direct product factor, Sylow
400	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic
401	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	#2849	C₂×C₁₃₉	1	2	yes	complemented
404	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2483	C₂×C₁₃₉	1	2	yes	complemented
407	#2447	C₂×C₁₃₉	1	2	yes	complemented
408	#2443	C₂×C₁₃₉	1	4	yes	complemented
409	#2422	C₂×C₁₃₉	1	2	yes	complemented
410	#2419	C₂×C₁₃₉	1	4	yes	complemented
411	#2412	C₂×C₁₃₉	1	2	yes	complemented
412	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
413	#2339	C₂×C₁₃₉	1	2	yes	complemented
414	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	C₂×#385	C₂×C₁₃₉	1	2	yes	complemented
417	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
420	#546	—	2	8	no	—
421	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
425	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
428	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
429	C₂×C₄×D₄	—	2	8	no	—
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
434	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
438	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
439	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
440	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
442	#400	C₂²×C₁₃₉	1	2	yes	complemented
443	#399	C₂²×C₁₃₉	1	2	yes	complemented
444	#398	C₂²×C₁₃₉	1	4	yes	complemented
445	#397	C₂²×C₁₃₉	1	4	yes	complemented
446	#397	C₂²×C₁₃₉	1	4	yes	complemented
447	#397	C₂²×C₁₃₉	1	4	yes	complemented
448	#394	C₂²×C₁₃₉	1	4	yes	complemented
449	#391	C₂²×C₁₃₉	1	2	yes	complemented
450	#391	C₂²×C₁₃₉	1	2	yes	complemented
451	#390	C₂²×C₁₃₉	1	2	yes	—
452	#389	C₂²×C₁₃₉	1	2	yes	complemented
453	#389	C₂²×C₁₃₉	1	2	yes	complemented
454	#388	C₂²×C₁₃₉	1	2	yes	complemented
455	#387	C₂²×C₁₃₉	1	4	yes	complemented
456	#387	C₂²×C₁₃₉	1	2	yes	complemented
457	#386	C₂²×C₁₃₉	1	1	yes	characteristic
458	#386	C₂²×C₁₃₉	1	2	yes	—
459	#386	C₂²×C₁₃₉	1	4	yes	—
460	#386	C₂²×C₁₃₉	1	4	yes	complemented
461	#386	C₂²×C₁₃₉	1	4	yes	complemented
462	#385	C₂²×C₁₃₉	1	2	yes	—
463	#385	C₂²×C₁₃₉	1	2	yes	—
464	#385	C₂²×C₁₃₉	1	2	yes	—
465	#385	C₂²×C₁₃₉	1	2	yes	—
466	#385	C₂²×C₁₃₉	1	1	yes	characteristic
467	#385	C₂²×C₁₃₉	1	4	yes	complemented
468	#385	C₂²×C₁₃₉	1	4	yes	complemented
469	#385	C₂²×C₁₃₉	1	4	yes	complemented
470	#385	C₂²×C₁₃₉	1	4	yes	complemented
471	#384	C₂²×C₁₃₉	1	2	yes	complemented
472	#381	C₂²×C₁₃₉	1	2	yes	—
473	#381	C₂²×C₁₃₉	1	1	yes	characteristic
474	#381	C₂²×C₁₃₉	1	4	yes	complemented
475	#381	C₂²×C₁₃₉	1	4	yes	complemented
476	#380	C₂²×C₁₃₉	1	1	yes	characteristic
477	#380	C₂²×C₁₃₉	1	2	yes	complemented
478	#380	C₂²×C₁₃₉	1	4	yes	complemented
479	#379	C₂²×C₁₃₉	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
481	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
483	C₂×#95	C₂²×C₁₃₉	1	4	yes	complemented
484	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
485	C₂×#41	—	2	4	no	—
486	C₂×#41	—	2	8	no	—
487	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	—	2	8	no	—
489	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
490	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂³×C₄	—	2	8	no	—
497	C₂³×C₄	—	4	8	no	—
498	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
504	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
508	#124	—	2	4	no	—
509	#123	—	2	8	no	—
510	#123	—	2	4	no	—
511	#123	—	4	8	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	#121	—	2	4	no	—
514	#121	—	2	8	no	—
515	#120	—	2	8	no	—
516	C₄×D₄	—	2	16	no	—
517	C₄×D₄	—	2	8	no	—
518	C₄×D₄	—	2	8	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	4	no	—
522	C₂×C₄⋊C₄	—	2	4	no	—
523	C₂×C₄⋊C₄	—	4	8	no	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
536	C₂×C₂²⋊C₄	—	2	8	no	—
537	C₂×C₂²⋊C₄	—	2	8	no	—
538	C₂×C₂²⋊C₄	—	2	8	no	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄²	—	2	4	no	—
558	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	4	yes	—
572	#95	C₂³×C₁₃₉	1	4	yes	—
573	#95	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	4	yes	—
575	C₂⁴	—	2	4	no	—
576	C₂⁴	—	2	8	no	—
577	C₂⁴	—	2	4	no	—
578	C₂⁴	—	4	4	no	—
579	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
580	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
582	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
583	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	#41	—	4	16	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	32	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
598	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
599	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
600	C₂×D₄	#41×C₁₃₉	1	8	yes	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	8	no	—
608	C₂²×C₄	—	2	8	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	32	no	—
625	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
632	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	4	no	—
640	C₄⋊C₄	—	2	4	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	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	8	no	—
648	C₄⋊C₄	—	4	4	no	—
649	C₄⋊C₄	—	4	4	no	—
650	C₄⋊C₄	—	4	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	8	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	complemented
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	16	no	—
679	C₂³	—	2	16	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	4	8	no	—
690	C₂³	—	4	16	no	—
691	C₂³	—	4	16	no	—
692	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
693	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
694	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
695	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
696	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
697	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
698	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
699	Q₈	—	4	4	no	—
700	D₄	—	2	16	no	—
701	D₄	—	2	8	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	4	no	—
704	D₄	—	8	4	no	—
705	D₄	#123×C₁₃₉	1	16	yes	complemented
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	8	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	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	4	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	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	4	16	no	—
737	C₂×C₄	—	4	16	no	—
738	C₂×C₄	—	4	16	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	8	4	no	—
744	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
746	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
747	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
748	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	8	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	8	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	32	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	2	no	—
768	C₂²	C₂×#123×C₁₃₉	1	8	yes	—
769	C₂²	#547×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×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
774	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
775	C₄	—	2	2	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	4	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	4	no	—
783	C₄	—	4	4	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	C₂×#123×C₁₃₉	1	4	yes	—
788	C₂	—	2	4	no	—
789	C₂	—	2	8	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	1	no	—
792	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
793	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
794	C₂	#3481×C₁₃₉	1	2	yes	—
795	C₂	#3484×C₁₃₉	1	1	yes	characteristic
796	C₂	#3520×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#546×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. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2849×C₁₃₉	C₂	semidirect
5. #2502×C₁₃₉	C₂	semidirect
6. #2487×C₁₃₉	C₂	semidirect
7. #2483×C₁₃₉	C₂	semidirect
8. #2447×C₁₃₉	C₂	semidirect
9. #2443×C₁₃₉	C₂	semidirect
10. #2422×C₁₃₉	C₂	semidirect
11. #2419×C₁₃₉	C₂	semidirect
12. #2412×C₁₃₉	C₂	semidirect
13. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
14. #2339×C₁₃₉	C₂	semidirect
15. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
16. C₄×#123×C₁₃₉	C₂	semidirect
17. C₂×#385×C₁₃₉	C₂	semidirect
25. C₂×#123×C₁₃₉	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
43. #400×C₁₃₉	C₂²	semidirect
44. #399×C₁₃₉	C₂²	semidirect
45. #398×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
47. #397×C₁₃₉	C₂²	semidirect
48. #397×C₁₃₉	C₂²	semidirect
49. #394×C₁₃₉	C₂²	semidirect
50. #391×C₁₃₉	C₂²	semidirect
51. #391×C₁₃₉	C₂²	semidirect
53. #389×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #388×C₁₃₉	C₂²	semidirect
56. #387×C₁₃₉	C₂²	semidirect
57. #387×C₁₃₉	C₂²	semidirect
61. #386×C₁₃₉	C₂²	semidirect
62. #386×C₁₃₉	C₂²	semidirect
68. #385×C₁₃₉	C₂²	semidirect
69. #385×C₁₃₉	C₂²	semidirect
70. #385×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #384×C₁₃₉	C₂²	semidirect
75. #381×C₁₃₉	C₂²	semidirect
76. #381×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
79. #380×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₂×#95×C₁₃₉	C₂²	semidirect
269. C₂²⋊C₄×C₁₃₉	#41	semidirect
306. D₄×C₁₃₉	#123	semidirect
398. #36237	C₁₃₉	direct (N × H)
399. C₁₃₉	#36237	direct (N × H)
401. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
402. #2855	C₂×C₁₃₉	semidirect
403. #2849	C₂×C₁₃₉	semidirect
404. #2502	C₂×C₁₃₉	semidirect
405. #2487	C₂×C₁₃₉	semidirect
406. #2483	C₂×C₁₃₉	semidirect
407. #2447	C₂×C₁₃₉	semidirect
408. #2443	C₂×C₁₃₉	semidirect
409. #2422	C₂×C₁₃₉	semidirect
410. #2419	C₂×C₁₃₉	semidirect
411. #2412	C₂×C₁₃₉	semidirect
412. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
413. #2339	C₂×C₁₃₉	semidirect
414. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
415. C₄×#123	C₂×C₁₃₉	semidirect
416. C₂×#385	C₂×C₁₃₉	semidirect
424. C₂×#123	C₂²×C₁₃₉	semidirect
437. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
442. #400	C₂²×C₁₃₉	semidirect
443. #399	C₂²×C₁₃₉	semidirect
444. #398	C₂²×C₁₃₉	semidirect
445. #397	C₂²×C₁₃₉	semidirect
446. #397	C₂²×C₁₃₉	semidirect
447. #397	C₂²×C₁₃₉	semidirect
448. #394	C₂²×C₁₃₉	semidirect
449. #391	C₂²×C₁₃₉	semidirect
450. #391	C₂²×C₁₃₉	semidirect
452. #389	C₂²×C₁₃₉	semidirect
453. #389	C₂²×C₁₃₉	semidirect
454. #388	C₂²×C₁₃₉	semidirect
455. #387	C₂²×C₁₃₉	semidirect
456. #387	C₂²×C₁₃₉	semidirect
460. #386	C₂²×C₁₃₉	semidirect
461. #386	C₂²×C₁₃₉	semidirect
467. #385	C₂²×C₁₃₉	semidirect
468. #385	C₂²×C₁₃₉	semidirect
469. #385	C₂²×C₁₃₉	semidirect
470. #385	C₂²×C₁₃₉	semidirect
471. #384	C₂²×C₁₃₉	semidirect
474. #381	C₂²×C₁₃₉	semidirect
475. #381	C₂²×C₁₃₉	semidirect
477. #380	C₂²×C₁₃₉	semidirect
478. #380	C₂²×C₁₃₉	semidirect
480. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
482. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
483. C₂×#95	C₂²×C₁₃₉	semidirect
668. C₂²⋊C₄	#41×C₁₃₉	semidirect
705. D₄	#123×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2855×C₁₃₉	2
#2849×C₁₃₉	2
#2502×C₁₃₉	2
#2487×C₁₃₉	2
#2483×C₁₃₉	2
#2447×C₁₃₉	2
#2443×C₁₃₉	2
#2422×C₁₃₉	2
#2419×C₁₃₉	2
#2412×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2339×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#123×C₁₃₉	2
C₂×#385×C₁₃₉	2
#36237	139

Subgroups — C139×#36237 #48030833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36237 #48030833