Subgroups — C₁₃₉×#35982 #48030578

Order 35584.

2568 conjugacy classes of subgroups.

The subgroup lattice has 758 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	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2633×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2625×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2598×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2562×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2480×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2454×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2427×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2418×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#552×C₁₃₉	—	2	8	no	—
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
29	#518×C₁₃₉	—	2	8	no	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
42	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
43	#400×C₁₃₉	C₂²	1	2	yes	complemented
44	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	#399×C₁₃₉	C₂²	1	4	yes	complemented
46	#398×C₁₃₉	C₂²	1	2	yes	complemented
47	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	#397×C₁₃₉	C₂²	1	4	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	4	yes	complemented
51	#397×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	#396×C₁₃₉	C₂²	1	4	yes	complemented
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#394×C₁₃₉	C₂²	1	2	yes	—
57	#394×C₁₃₉	C₂²	1	4	yes	complemented
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	complemented
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#389×C₁₃₉	C₂²	1	2	yes	complemented
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#388×C₁₃₉	C₂²	1	4	yes	complemented
68	#386×C₁₃₉	C₂²	1	4	yes	complemented
69	#386×C₁₃₉	C₂²	1	4	yes	complemented
70	#385×C₁₃₉	C₂²	1	4	yes	complemented
71	#385×C₁₃₉	C₂²	1	4	yes	complemented
72	#385×C₁₃₉	C₂²	1	4	yes	complemented
73	#383×C₁₃₉	C₂²	1	2	yes	complemented
74	#380×C₁₃₉	C₂²	1	1	yes	characteristic
75	#380×C₁₃₉	C₂²	1	4	yes	complemented
76	#380×C₁₃₉	C₂²	1	4	yes	complemented
77	#379×C₁₃₉	C₂²	1	2	yes	—
78	#379×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₉	—	2	8	no	—
88	C₂²×D₄×C₁₃₉	—	2	4	no	—
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	#126×C₁₃₉	—	2	8	no	—
99	#125×C₁₃₉	—	2	4	no	—
100	#125×C₁₃₉	—	2	8	no	—
101	#124×C₁₃₉	—	2	8	no	—
102	#123×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
105	#121×C₁₃₉	—	2	8	no	—
106	#120×C₁₃₉	—	4	4	no	—
107	C₄×Q₈×C₁₃₉	—	2	4	no	—
108	C₄×D₄×C₁₃₉	—	2	4	no	—
109	C₄×D₄×C₁₃₉	—	2	8	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	4	8	no	—
114	#117×C₁₃₉	—	2	4	no	—
115	#117×C₁₃₉	—	2	8	no	—
116	#117×C₁₃₉	D₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
169	#95×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	C₂⁴×C₁₃₉	—	2	4	no	—
174	C₂⁴×C₁₃₉	—	2	8	no	—
175	C₂⁴×C₁₃₉	—	4	2	no	—
176	C₂⁴×C₁₃₉	—	4	2	no	—
177	C₂⁴×C₁₃₉	—	4	4	no	—
178	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
180	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
181	C₂×Q₈×C₁₃₉	—	2	2	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	32	no	—
184	C₂×D₄×C₁₃₉	—	2	8	no	—
185	C₂×D₄×C₁₃₉	—	2	2	no	—
186	C₂×D₄×C₁₃₉	—	2	8	no	—
187	C₂×D₄×C₁₃₉	—	2	8	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	4	4	no	—
193	C₂×D₄×C₁₃₉	—	4	1	no	—
194	C₂×D₄×C₁₃₉	#41	1	8	yes	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	8	no	—
201	C₂²×C₄×C₁₃₉	—	2	8	no	—
202	C₂²×C₄×C₁₃₉	—	4	2	no	—
203	C₂²×C₄×C₁₃₉	—	4	4	no	—
204	C₂²×C₄×C₁₃₉	—	4	4	no	—
205	C₂²×C₄×C₁₃₉	—	4	4	no	—
206	C₂²×C₄×C₁₃₉	—	4	4	no	—
207	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	2	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	2	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	4	no	—
233	C₄⋊C₄×C₁₃₉	—	4	4	no	—
234	C₄⋊C₄×C₁₃₉	—	4	2	no	—
235	C₄⋊C₄×C₁₃₉	—	4	2	no	—
236	C₄⋊C₄×C₁₃₉	—	4	4	no	—
237	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
238	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
239	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
252	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
256	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
257	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
258	C₄²×C₁₃₉	—	2	4	no	—
259	C₄²×C₁₃₉	—	2	4	no	—
260	C₄²×C₁₃₉	—	2	2	no	—
261	C₄²×C₁₃₉	—	2	4	no	—
262	C₄²×C₁₃₉	—	4	4	no	—
263	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
264	C₂³×C₁₃₉	—	2	16	no	—
265	C₂³×C₁₃₉	—	2	1	no	—
266	C₂³×C₁₃₉	—	2	4	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	2	no	—
269	C₂³×C₁₃₉	—	2	4	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	1	no	—
272	C₂³×C₁₃₉	—	2	4	no	—
273	C₂³×C₁₃₉	—	2	4	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	4	no	—
278	C₂³×C₁₃₉	—	2	1	no	—
279	C₂³×C₁₃₉	—	8	4	no	—
280	C₂³×C₁₃₉	—	8	4	no	—
281	C₂³×C₁₃₉	—	8	8	no	—
282	C₂³×C₁₃₉	—	8	8	no	—
283	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
284	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
285	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
286	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
287	Q₈×C₁₃₉	—	4	4	no	—
288	D₄×C₁₃₉	—	2	16	no	—
289	D₄×C₁₃₉	—	2	16	no	—
290	D₄×C₁₃₉	—	4	4	no	—
291	D₄×C₁₃₉	—	4	16	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	8	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	4	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	4	8	no	—
325	C₂×C₄×C₁₃₉	—	4	4	no	—
326	C₂×C₄×C₁₃₉	—	8	8	no	—
327	C₂×C₄×C₁₃₉	—	8	8	no	—
328	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
329	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
333	C₂²×C₁₃₉	—	2	2	no	—
334	C₂²×C₁₃₉	—	2	8	no	—
335	C₂²×C₁₃₉	—	2	2	no	—
336	C₂²×C₁₃₉	—	2	2	no	—
337	C₂²×C₁₃₉	—	2	2	no	—
338	C₂²×C₁₃₉	—	2	4	no	—
339	C₂²×C₁₃₉	—	2	8	no	—
340	C₂²×C₁₃₉	—	2	8	no	—
341	C₂²×C₁₃₉	—	4	1	no	—
342	C₂²×C₁₃₉	—	4	4	no	—
343	C₂²×C₁₃₉	—	4	4	no	—
344	C₂²×C₁₃₉	—	4	1	no	—
345	C₂²×C₁₃₉	—	4	4	no	—
346	C₂²×C₁₃₉	—	4	2	no	—
347	C₂²×C₁₃₉	—	4	2	no	—
348	C₂²×C₁₃₉	—	4	4	no	—
349	C₂²×C₁₃₉	—	4	2	no	—
350	C₂²×C₁₃₉	—	8	16	no	—
351	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
352	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
353	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₁₃₉	#585	1	1	yes	characteristic
355	C₂²×C₁₃₉	#585	1	2	yes	—
356	C₄×C₁₃₉	—	2	2	no	—
357	C₄×C₁₃₉	—	2	4	no	—
358	C₄×C₁₃₉	—	2	4	no	—
359	C₄×C₁₃₉	—	4	1	no	—
360	C₄×C₁₃₉	—	4	2	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	2	no	—
363	C₄×C₁₃₉	—	4	1	no	—
364	C₄×C₁₃₉	—	4	1	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	2	no	—
367	C₄×C₁₃₉	—	4	4	no	—
368	C₄×C₁₃₉	—	4	2	no	—
369	C₄×C₁₃₉	#525	1	4	yes	—
370	C₂×C₁₃₉	—	4	2	no	—
371	C₂×C₁₃₉	—	4	8	no	—
372	C₂×C₁₃₉	—	4	2	no	—
373	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
374	C₂×C₁₃₉	#3488	1	1	yes	characteristic
375	C₂×C₁₃₉	#3500	1	1	yes	characteristic
376	C₂×C₁₃₉	#3513	1	2	yes	—
377	C₂×C₁₃₉	#3521	1	2	yes	—
378	#35982	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₁₃₉	#35982	1	1	yes	characteristic, direct product factor, Sylow
380	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	#2633	C₂×C₁₃₉	1	2	yes	complemented
383	#2625	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	#2598	C₂×C₁₃₉	1	2	yes	complemented
385	#2562	C₂×C₁₃₉	1	2	yes	complemented
386	#2480	C₂×C₁₃₉	1	4	yes	complemented
387	#2454	C₂×C₁₃₉	1	2	yes	complemented
388	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
389	#2427	C₂×C₁₃₉	1	2	yes	complemented
390	#2418	C₂×C₁₃₉	1	4	yes	complemented
391	#2408	C₂×C₁₃₉	1	1	yes	characteristic
392	#2395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2392	C₂×C₁₃₉	1	2	yes	complemented
394	#2367	C₂×C₁₃₉	1	2	yes	complemented
395	#2361	C₂×C₁₃₉	1	2	yes	complemented
396	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
398	#552	—	2	8	no	—
399	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
400	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
401	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
402	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
403	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
406	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
407	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
408	#518	—	2	8	no	—
409	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
410	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
415	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
416	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
419	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
420	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
421	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
422	#400	C₂²×C₁₃₉	1	2	yes	complemented
423	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
424	#399	C₂²×C₁₃₉	1	4	yes	complemented
425	#398	C₂²×C₁₃₉	1	2	yes	complemented
426	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
427	#397	C₂²×C₁₃₉	1	4	yes	—
428	#397	C₂²×C₁₃₉	1	2	yes	—
429	#397	C₂²×C₁₃₉	1	4	yes	complemented
430	#397	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
431	#396	C₂²×C₁₃₉	1	4	yes	complemented
432	#394	C₂²×C₁₃₉	1	2	yes	—
433	#394	C₂²×C₁₃₉	1	2	yes	—
434	#394	C₂²×C₁₃₉	1	2	yes	—
435	#394	C₂²×C₁₃₉	1	2	yes	—
436	#394	C₂²×C₁₃₉	1	4	yes	complemented
437	#392	C₂²×C₁₃₉	1	2	yes	—
438	#391	C₂²×C₁₃₉	1	2	yes	complemented
439	#390	C₂²×C₁₃₉	1	2	yes	—
440	#390	C₂²×C₁₃₉	1	2	yes	—
441	#389	C₂²×C₁₃₉	1	2	yes	complemented
442	#389	C₂²×C₁₃₉	1	2	yes	complemented
443	#388	C₂²×C₁₃₉	1	4	yes	—
444	#388	C₂²×C₁₃₉	1	4	yes	complemented
445	#388	C₂²×C₁₃₉	1	4	yes	complemented
446	#388	C₂²×C₁₃₉	1	4	yes	complemented
447	#386	C₂²×C₁₃₉	1	4	yes	complemented
448	#386	C₂²×C₁₃₉	1	4	yes	complemented
449	#385	C₂²×C₁₃₉	1	4	yes	complemented
450	#385	C₂²×C₁₃₉	1	4	yes	complemented
451	#385	C₂²×C₁₃₉	1	4	yes	complemented
452	#383	C₂²×C₁₃₉	1	2	yes	complemented
453	#380	C₂²×C₁₃₉	1	1	yes	characteristic
454	#380	C₂²×C₁₃₉	1	4	yes	complemented
455	#380	C₂²×C₁₃₉	1	4	yes	complemented
456	#379	C₂²×C₁₃₉	1	2	yes	—
457	#379	C₂²×C₁₃₉	1	4	yes	—
458	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
459	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
460	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
461	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
463	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
464	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
465	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂²×D₄	—	2	8	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
469	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
476	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
477	#126	—	2	8	no	—
478	#125	—	2	4	no	—
479	#125	—	2	8	no	—
480	#124	—	2	8	no	—
481	#123	—	2	8	no	—
482	C₂²⋊Q₈	—	2	4	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	#121	—	2	8	no	—
485	#120	—	4	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×D₄	—	2	4	no	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	8	no	—
492	C₄×D₄	—	4	8	no	—
493	#117	—	2	4	no	—
494	#117	—	2	8	no	—
495	#117	D₄×C₁₃₉	1	8	yes	complemented
496	C₂×C₄⋊C₄	—	2	4	no	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	—	2	16	no	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
539	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
540	#95	C₂³×C₁₃₉	1	1	yes	characteristic
541	#95	C₂³×C₁₃₉	1	1	yes	characteristic
542	#95	C₂³×C₁₃₉	1	2	yes	—
543	#95	C₂³×C₁₃₉	1	2	yes	—
544	#95	C₂³×C₁₃₉	1	2	yes	—
545	#95	C₂³×C₁₃₉	1	4	yes	—
546	#95	C₂³×C₁₃₉	1	2	yes	—
547	#95	C₂³×C₁₃₉	1	2	yes	—
548	#95	C₂³×C₁₃₉	1	4	yes	—
549	#95	C₂³×C₁₃₉	1	4	yes	—
550	#95	C₂³×C₁₃₉	1	4	yes	—
551	#95	C₂³×C₁₃₉	1	4	yes	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	8	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	4	no	—
557	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
558	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
559	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×D₄	—	2	32	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	1	no	—
573	C₂×D₄	#41×C₁₃₉	1	8	yes	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
589	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	4	4	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
617	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	8	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	4	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	4	4	no	—
642	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
643	C₂³	—	2	16	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	8	4	no	—
659	C₂³	—	8	4	no	—
660	C₂³	—	8	8	no	—
661	C₂³	—	8	8	no	—
662	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
663	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
664	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
665	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
666	Q₈	—	4	4	no	—
667	D₄	—	2	16	no	—
668	D₄	—	2	16	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	16	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	8	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
708	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
711	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	8	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	8	no	—
719	C₂²	—	2	8	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	8	16	no	—
730	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
731	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
732	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
733	C₂²	#585×C₁₃₉	1	1	yes	characteristic
734	C₂²	#585×C₁₃₉	1	2	yes	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	#525×C₁₃₉	1	4	yes	—
749	C₂	—	4	2	no	—
750	C₂	—	4	8	no	—
751	C₂	—	4	2	no	—
752	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
753	C₂	#3488×C₁₃₉	1	1	yes	characteristic
754	C₂	#3500×C₁₃₉	1	1	yes	characteristic
755	C₂	#3513×C₁₃₉	1	2	yes	—
756	C₂	#3521×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2408×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×#552×C₁₃₉	C₂	semidirect
2. C₂×#518×C₁₃₉	C₂	semidirect
3. #2633×C₁₃₉	C₂	semidirect
4. #2625×C₁₃₉	C₂	semidirect
5. #2598×C₁₃₉	C₂	semidirect
6. #2562×C₁₃₉	C₂	semidirect
7. #2480×C₁₃₉	C₂	semidirect
8. #2454×C₁₃₉	C₂	semidirect
9. #2435×C₁₃₉	C₂	semidirect
10. #2427×C₁₃₉	C₂	semidirect
11. #2418×C₁₃₉	C₂	semidirect
13. #2395×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. #2367×C₁₃₉	C₂	semidirect
16. #2361×C₁₃₉	C₂	semidirect
17. #2347×C₁₃₉	C₂	semidirect
21. C₂×#125×C₁₃₉	C₂²	semidirect
22. C₂×#125×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
39. C₂×#117×C₁₃₉	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
42. #400×C₁₃₉	C₂²	semidirect
43. #400×C₁₃₉	C₂²	semidirect
44. #399×C₁₃₉	C₂²	semidirect
45. #399×C₁₃₉	C₂²	semidirect
46. #398×C₁₃₉	C₂²	semidirect
47. #398×C₁₃₉	C₂²	semidirect
50. #397×C₁₃₉	C₂²	semidirect
51. #397×C₁₃₉	C₂²	semidirect
52. #396×C₁₃₉	C₂²	semidirect
57. #394×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
63. #389×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #388×C₁₃₉	C₂²	semidirect
68. #386×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
70. #385×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #385×C₁₃₉	C₂²	semidirect
73. #383×C₁₃₉	C₂²	semidirect
75. #380×C₁₃₉	C₂²	semidirect
76. #380×C₁₃₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
116. #117×C₁₃₉	D₄	semidirect
378. #35982	C₁₃₉	direct (N × H)
379. C₁₃₉	#35982	direct (N × H)
380. C₂×#552	C₂×C₁₃₉	semidirect
381. C₂×#518	C₂×C₁₃₉	semidirect
382. #2633	C₂×C₁₃₉	semidirect
383. #2625	C₂×C₁₃₉	semidirect
384. #2598	C₂×C₁₃₉	semidirect
385. #2562	C₂×C₁₃₉	semidirect
386. #2480	C₂×C₁₃₉	semidirect
387. #2454	C₂×C₁₃₉	semidirect
388. #2435	C₂×C₁₃₉	semidirect
389. #2427	C₂×C₁₃₉	semidirect
390. #2418	C₂×C₁₃₉	semidirect
392. #2395	C₂×C₁₃₉	semidirect
393. #2392	C₂×C₁₃₉	semidirect
394. #2367	C₂×C₁₃₉	semidirect
395. #2361	C₂×C₁₃₉	semidirect
396. #2347	C₂×C₁₃₉	semidirect
400. C₂×#125	C₂²×C₁₃₉	semidirect
401. C₂×#125	C₂²×C₁₃₉	semidirect
405. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
409. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
415. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
418. C₂×#117	C₂²×C₁₃₉	semidirect
419. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
421. #400	C₂²×C₁₃₉	semidirect
422. #400	C₂²×C₁₃₉	semidirect
423. #399	C₂²×C₁₃₉	semidirect
424. #399	C₂²×C₁₃₉	semidirect
425. #398	C₂²×C₁₃₉	semidirect
426. #398	C₂²×C₁₃₉	semidirect
429. #397	C₂²×C₁₃₉	semidirect
430. #397	C₂²×C₁₃₉	semidirect
431. #396	C₂²×C₁₃₉	semidirect
436. #394	C₂²×C₁₃₉	semidirect
438. #391	C₂²×C₁₃₉	semidirect
441. #389	C₂²×C₁₃₉	semidirect
442. #389	C₂²×C₁₃₉	semidirect
444. #388	C₂²×C₁₃₉	semidirect
445. #388	C₂²×C₁₃₉	semidirect
446. #388	C₂²×C₁₃₉	semidirect
447. #386	C₂²×C₁₃₉	semidirect
448. #386	C₂²×C₁₃₉	semidirect
449. #385	C₂²×C₁₃₉	semidirect
450. #385	C₂²×C₁₃₉	semidirect
451. #385	C₂²×C₁₃₉	semidirect
452. #383	C₂²×C₁₃₉	semidirect
454. #380	C₂²×C₁₃₉	semidirect
455. #380	C₂²×C₁₃₉	semidirect
458. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
459. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
460. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
462. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
463. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
495. #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
C₂×#518×C₁₃₉	2
#2633×C₁₃₉	2
#2625×C₁₃₉	2
#2598×C₁₃₉	2
#2562×C₁₃₉	2
#2480×C₁₃₉	2
#2454×C₁₃₉	2
#2435×C₁₃₉	2
#2427×C₁₃₉	2
#2418×C₁₃₉	2
#2408×C₁₃₉	2
#2395×C₁₃₉	2
#2392×C₁₃₉	2
#2367×C₁₃₉	2
#2361×C₁₃₉	2
#2347×C₁₃₉	2
#35982	139

Subgroups — C139×#35982 #48030578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35982 #48030578