Subgroups — C₁₃₉×#37152 #48031748

Order 35584.

1608 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2781×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2727×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2726×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2725×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2724×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2722×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2705×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2694×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2691×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2651×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2587×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2554×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2522×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2335×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₄×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	#400×C₁₃₉	C₂²	1	2	yes	—
29	#399×C₁₃₉	C₂²	1	2	yes	—
30	#399×C₁₃₉	C₂²	1	2	yes	—
31	#398×C₁₃₉	C₂²	1	2	yes	—
32	#398×C₁₃₉	C₂²	1	2	yes	—
33	#398×C₁₃₉	C₂²	1	2	yes	—
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#397×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#396×C₁₃₉	C₂²	1	2	yes	—
42	#396×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	#394×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	2	yes	—
48	#394×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#392×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	1	yes	characteristic
53	#390×C₁₃₉	C₂²	1	2	yes	—
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	1	yes	characteristic
56	#390×C₁₃₉	C₂²	1	1	yes	characteristic
57	#390×C₁₃₉	C₂²	1	1	yes	characteristic
58	#390×C₁₃₉	C₂²	1	1	yes	characteristic
59	#390×C₁₃₉	C₂²	1	1	yes	characteristic
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	1	yes	characteristic
64	#389×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	1	yes	characteristic
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
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	#388×C₁₃₉	C₂²	1	2	yes	—
81	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#386×C₁₃₉	C₂²	1	2	yes	—
91	#386×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#385×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	1	yes	characteristic
97	#380×C₁₃₉	C₂²	1	2	yes	—
98	#380×C₁₃₉	C₂²	1	2	yes	—
99	#380×C₁₃₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊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	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	#126×C₁₃₉	—	4	4	no	—
114	#126×C₁₃₉	—	4	4	no	—
115	#126×C₁₃₉	—	4	4	no	—
116	#125×C₁₃₉	—	2	4	no	—
117	#125×C₁₃₉	—	4	4	no	—
118	#123×C₁₃₉	—	2	8	no	—
119	#123×C₁₃₉	—	4	4	no	—
120	#121×C₁₃₉	—	4	4	no	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	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	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	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	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	2	no	—
206	C₂×D₄×C₁₃₉	—	2	2	no	—
207	C₂×D₄×C₁₃₉	—	4	2	no	—
208	C₂×D₄×C₁₃₉	—	4	2	no	—
209	C₂×D₄×C₁₃₉	—	4	1	no	—
210	C₂×D₄×C₁₃₉	—	4	1	no	—
211	C₂×D₄×C₁₃₉	—	4	1	no	—
212	C₂×D₄×C₁₃₉	—	4	1	no	—
213	C₂×D₄×C₁₃₉	—	4	2	no	—
214	C₂×D₄×C₁₃₉	—	4	2	no	—
215	C₂×D₄×C₁₃₉	—	4	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	4	2	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	no	—
219	C₂²×C₄×C₁₃₉	—	4	2	no	—
220	C₂²×C₄×C₁₃₉	—	4	2	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	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	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	2	no	—
249	C₄⋊C₄×C₁₃₉	—	4	1	no	—
250	C₄⋊C₄×C₁₃₉	—	4	1	no	—
251	C₄⋊C₄×C₁₃₉	—	4	1	no	—
252	C₄⋊C₄×C₁₃₉	—	4	1	no	—
253	C₄⋊C₄×C₁₃₉	—	4	1	no	—
254	C₄⋊C₄×C₁₃₉	—	4	1	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	2	no	—
266	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
281	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
282	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
283	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄²×C₁₃₉	—	2	2	no	—
290	C₄²×C₁₃₉	—	2	2	no	—
291	C₄²×C₁₃₉	—	2	2	no	—
292	C₄²×C₁₃₉	—	2	2	no	—
293	C₄²×C₁₃₉	—	4	1	no	—
294	C₄²×C₁₃₉	—	4	1	no	—
295	C₄²×C₁₃₉	—	4	2	no	—
296	C₄²×C₁₃₉	—	4	2	no	—
297	C₄²×C₁₃₉	—	4	1	no	—
298	C₄²×C₁₃₉	—	4	2	no	—
299	C₄²×C₁₃₉	—	4	2	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	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	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
315	D₄×C₁₃₉	—	8	4	no	—
316	D₄×C₁₃₉	—	8	2	no	—
317	D₄×C₁₃₉	—	8	2	no	—
318	D₄×C₁₃₉	—	8	4	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	1	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
327	C₂×C₄×C₁₃₉	—	2	1	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	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	—	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	—	8	4	no	—
366	C₂×C₄×C₁₃₉	—	8	4	no	—
367	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
368	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
369	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
370	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
371	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	4	2	no	—
374	C₂²×C₁₃₉	—	4	2	no	—
375	C₂²×C₁₃₉	—	4	2	no	—
376	C₂²×C₁₃₉	—	4	2	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	—	4	2	no	—
385	C₂²×C₁₃₉	—	4	2	no	—
386	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
387	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
390	C₂²×C₁₃₉	#585	1	1	yes	characteristic
391	C₂²×C₁₃₉	#585	1	1	yes	characteristic
392	C₂²×C₁₃₉	#585	1	1	yes	characteristic
393	C₄×C₁₃₉	—	2	2	no	—
394	C₄×C₁₃₉	—	2	4	no	—
395	C₄×C₁₃₉	—	2	2	no	—
396	C₄×C₁₃₉	—	2	2	no	—
397	C₄×C₁₃₉	—	2	2	no	—
398	C₄×C₁₃₉	—	4	1	no	—
399	C₄×C₁₃₉	—	4	2	no	—
400	C₄×C₁₃₉	—	4	1	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	2	no	—
403	C₄×C₁₃₉	—	4	1	no	—
404	C₄×C₁₃₉	—	4	2	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₄×C₁₃₉	—	4	2	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	—	4	2	no	—
410	C₂×C₁₃₉	—	8	2	no	—
411	C₂×C₁₃₉	—	8	2	no	—
412	C₂×C₁₃₉	#3461	1	1	yes	characteristic
413	C₂×C₁₃₉	#3514	1	1	yes	characteristic
414	C₂×C₁₃₉	#3517	1	1	yes	characteristic
415	C₂×C₁₃₉	#3548	1	1	yes	characteristic
416	C₂×C₁₃₉	#3553	1	1	yes	characteristic
417	C₂×C₁₃₉	#3560	1	1	yes	characteristic
418	C₂×C₁₃₉	#3560	1	1	yes	characteristic
419	#37152	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₁₃₉	#37152	1	1	yes	characteristic, direct product factor, Sylow
421	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
423	#2781	C₂×C₁₃₉	1	2	yes	complemented
424	#2727	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	#2726	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	#2725	C₂×C₁₃₉	1	2	yes	complemented
427	#2724	C₂×C₁₃₉	1	1	yes	characteristic, complemented
428	#2722	C₂×C₁₃₉	1	2	yes	complemented
429	#2705	C₂×C₁₃₉	1	2	yes	complemented
430	#2694	C₂×C₁₃₉	1	2	yes	complemented
431	#2691	C₂×C₁₃₉	1	2	yes	complemented
432	#2682	C₂×C₁₃₉	1	1	yes	characteristic
433	#2651	C₂×C₁₃₉	1	2	yes	complemented
434	#2587	C₂×C₁₃₉	1	2	yes	complemented
435	#2554	C₂×C₁₃₉	1	2	yes	complemented
436	#2522	C₂×C₁₃₉	1	2	yes	complemented
437	#2490	C₂×C₁₃₉	1	2	yes	complemented
438	#2335	C₂×C₁₃₉	1	2	yes	complemented
439	C₄×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
440	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
441	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
442	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
443	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
445	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
446	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
447	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
448	#400	C₂²×C₁₃₉	1	2	yes	—
449	#399	C₂²×C₁₃₉	1	2	yes	—
450	#399	C₂²×C₁₃₉	1	2	yes	—
451	#398	C₂²×C₁₃₉	1	2	yes	—
452	#398	C₂²×C₁₃₉	1	2	yes	—
453	#398	C₂²×C₁₃₉	1	2	yes	—
454	#398	C₂²×C₁₃₉	1	2	yes	—
455	#398	C₂²×C₁₃₉	1	2	yes	—
456	#398	C₂²×C₁₃₉	1	2	yes	—
457	#397	C₂²×C₁₃₉	1	2	yes	—
458	#397	C₂²×C₁₃₉	1	2	yes	—
459	#397	C₂²×C₁₃₉	1	2	yes	—
460	#397	C₂²×C₁₃₉	1	2	yes	—
461	#396	C₂²×C₁₃₉	1	2	yes	—
462	#396	C₂²×C₁₃₉	1	2	yes	—
463	#396	C₂²×C₁₃₉	1	2	yes	—
464	#396	C₂²×C₁₃₉	1	2	yes	—
465	#396	C₂²×C₁₃₉	1	2	yes	—
466	#394	C₂²×C₁₃₉	1	2	yes	—
467	#394	C₂²×C₁₃₉	1	2	yes	—
468	#394	C₂²×C₁₃₉	1	2	yes	—
469	#394	C₂²×C₁₃₉	1	2	yes	—
470	#394	C₂²×C₁₃₉	1	2	yes	—
471	#392	C₂²×C₁₃₉	1	2	yes	—
472	#390	C₂²×C₁₃₉	1	2	yes	—
473	#390	C₂²×C₁₃₉	1	1	yes	characteristic
474	#390	C₂²×C₁₃₉	1	1	yes	characteristic
475	#390	C₂²×C₁₃₉	1	1	yes	characteristic
476	#390	C₂²×C₁₃₉	1	1	yes	characteristic
477	#390	C₂²×C₁₃₉	1	1	yes	characteristic
478	#390	C₂²×C₁₃₉	1	1	yes	characteristic
479	#390	C₂²×C₁₃₉	1	2	yes	—
480	#390	C₂²×C₁₃₉	1	2	yes	—
481	#389	C₂²×C₁₃₉	1	1	yes	characteristic
482	#389	C₂²×C₁₃₉	1	1	yes	characteristic
483	#389	C₂²×C₁₃₉	1	1	yes	characteristic
484	#389	C₂²×C₁₃₉	1	2	yes	—
485	#389	C₂²×C₁₃₉	1	2	yes	—
486	#389	C₂²×C₁₃₉	1	2	yes	—
487	#389	C₂²×C₁₃₉	1	1	yes	characteristic
488	#389	C₂²×C₁₃₉	1	1	yes	characteristic
489	#389	C₂²×C₁₃₉	1	1	yes	characteristic
490	#389	C₂²×C₁₃₉	1	1	yes	characteristic
491	#389	C₂²×C₁₃₉	1	1	yes	characteristic
492	#389	C₂²×C₁₃₉	1	2	yes	—
493	#388	C₂²×C₁₃₉	1	2	yes	—
494	#388	C₂²×C₁₃₉	1	2	yes	—
495	#388	C₂²×C₁₃₉	1	2	yes	—
496	#388	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	#387	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	#385	C₂²×C₁₃₉	1	2	yes	—
515	#385	C₂²×C₁₃₉	1	2	yes	—
516	#382	C₂²×C₁₃₉	1	1	yes	characteristic
517	#380	C₂²×C₁₃₉	1	2	yes	—
518	#380	C₂²×C₁₃₉	1	2	yes	—
519	#380	C₂²×C₁₃₉	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
526	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
533	#126	—	4	4	no	—
534	#126	—	4	4	no	—
535	#126	—	4	4	no	—
536	#125	—	2	4	no	—
537	#125	—	4	4	no	—
538	#123	—	2	8	no	—
539	#123	—	4	4	no	—
540	#121	—	4	4	no	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
601	C₂×C₄²	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	2	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	1	no	—
672	C₄⋊C₄	—	4	1	no	—
673	C₄⋊C₄	—	4	1	no	—
674	C₄⋊C₄	—	4	1	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	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	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	2	no	—
712	C₄²	—	2	2	no	—
713	C₄²	—	4	1	no	—
714	C₄²	—	4	1	no	—
715	C₄²	—	4	2	no	—
716	C₄²	—	4	2	no	—
717	C₄²	—	4	1	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	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	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
735	D₄	—	8	2	no	—
736	D₄	—	8	2	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	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	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	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	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
788	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
789	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
790	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
791	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
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	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
807	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
808	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
809	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
810	C₂²	#585×C₁₃₉	1	1	yes	characteristic
811	C₂²	#585×C₁₃₉	1	1	yes	characteristic
812	C₂²	#585×C₁₃₉	1	1	yes	characteristic
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₂	—	8	2	no	—
831	C₂	—	8	2	no	—
832	C₂	#3461×C₁₃₉	1	1	yes	characteristic
833	C₂	#3514×C₁₃₉	1	1	yes	characteristic
834	C₂	#3517×C₁₃₉	1	1	yes	characteristic
835	C₂	#3548×C₁₃₉	1	1	yes	characteristic
836	C₂	#3553×C₁₃₉	1	1	yes	characteristic
837	C₂	#3560×C₁₃₉	1	1	yes	characteristic
838	C₂	#3560×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2682×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. #2860×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2781×C₁₃₉	C₂	semidirect
4. #2727×C₁₃₉	C₂	semidirect
5. #2726×C₁₃₉	C₂	semidirect
6. #2725×C₁₃₉	C₂	semidirect
7. #2724×C₁₃₉	C₂	semidirect
8. #2722×C₁₃₉	C₂	semidirect
9. #2705×C₁₃₉	C₂	semidirect
10. #2694×C₁₃₉	C₂	semidirect
11. #2691×C₁₃₉	C₂	semidirect
13. #2651×C₁₃₉	C₂	semidirect
14. #2587×C₁₃₉	C₂	semidirect
15. #2554×C₁₃₉	C₂	semidirect
16. #2522×C₁₃₉	C₂	semidirect
17. #2490×C₁₃₉	C₂	semidirect
18. #2335×C₁₃₉	C₂	semidirect
19. C₄×#125×C₁₃₉	C₂	semidirect
419. #37152	C₁₃₉	direct (N × H)
420. C₁₃₉	#37152	direct (N × H)
421. #2860	C₂×C₁₃₉	semidirect
422. #2860	C₂×C₁₃₉	semidirect
423. #2781	C₂×C₁₃₉	semidirect
424. #2727	C₂×C₁₃₉	semidirect
425. #2726	C₂×C₁₃₉	semidirect
426. #2725	C₂×C₁₃₉	semidirect
427. #2724	C₂×C₁₃₉	semidirect
428. #2722	C₂×C₁₃₉	semidirect
429. #2705	C₂×C₁₃₉	semidirect
430. #2694	C₂×C₁₃₉	semidirect
431. #2691	C₂×C₁₃₉	semidirect
433. #2651	C₂×C₁₃₉	semidirect
434. #2587	C₂×C₁₃₉	semidirect
435. #2554	C₂×C₁₃₉	semidirect
436. #2522	C₂×C₁₃₉	semidirect
437. #2490	C₂×C₁₃₉	semidirect
438. #2335	C₂×C₁₃₉	semidirect
439. C₄×#125	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2781×C₁₃₉	2
#2727×C₁₃₉	2
#2726×C₁₃₉	2
#2725×C₁₃₉	2
#2724×C₁₃₉	2
#2722×C₁₃₉	2
#2705×C₁₃₉	2
#2694×C₁₃₉	2
#2691×C₁₃₉	2
#2682×C₁₃₉	2
#2651×C₁₃₉	2
#2587×C₁₃₉	2
#2554×C₁₃₉	2
#2522×C₁₃₉	2
#2490×C₁₃₉	2
#2335×C₁₃₉	2
C₄×#125×C₁₃₉	2
#37152	139

Subgroups — C139×#37152 #48031748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37152 #48031748