Subgroups — C₁₃₉×#36715 #48031311

Order 35584.

3034 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2701×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2699×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2682×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2678×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2613×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2483×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2411×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2405×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2405×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2403×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2309×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	#534×C₁₃₉	—	2	8	no	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₁₃₉	—	2	8	no	—
28	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#120×C₁₃₉	C₂²	1	2	yes	complemented
35	C₂×#120×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	#398×C₁₃₉	C₂²	1	4	yes	complemented
42	#397×C₁₃₉	C₂²	1	4	yes	complemented
43	#396×C₁₃₉	C₂²	1	4	yes	complemented
44	#396×C₁₃₉	C₂²	1	4	yes	complemented
45	#394×C₁₃₉	C₂²	1	4	yes	complemented
46	#394×C₁₃₉	C₂²	1	4	yes	complemented
47	#394×C₁₃₉	C₂²	1	4	yes	complemented
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#394×C₁₃₉	C₂²	1	4	yes	complemented
50	#392×C₁₃₉	C₂²	1	4	yes	complemented
51	#392×C₁₃₉	C₂²	1	4	yes	complemented
52	#392×C₁₃₉	C₂²	1	4	yes	complemented
53	#390×C₁₃₉	C₂²	1	4	yes	complemented
54	#390×C₁₃₉	C₂²	1	4	yes	complemented
55	#390×C₁₃₉	C₂²	1	4	yes	complemented
56	#389×C₁₃₉	C₂²	1	4	yes	complemented
57	#388×C₁₃₉	C₂²	1	4	yes	complemented
58	#388×C₁₃₉	C₂²	1	4	yes	complemented
59	#386×C₁₃₉	C₂²	1	2	yes	—
60	#386×C₁₃₉	C₂²	1	2	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	complemented
62	#386×C₁₃₉	C₂²	1	2	yes	complemented
63	#386×C₁₃₉	C₂²	1	2	yes	complemented
64	#385×C₁₃₉	C₂²	1	2	yes	complemented
65	#385×C₁₃₉	C₂²	1	2	yes	complemented
66	#385×C₁₃₉	C₂²	1	4	yes	complemented
67	#385×C₁₃₉	C₂²	1	2	yes	complemented
68	#385×C₁₃₉	C₂²	1	2	yes	complemented
69	#381×C₁₃₉	C₂²	1	4	yes	complemented
70	#381×C₁₃₉	C₂²	1	2	yes	complemented
71	#381×C₁₃₉	C₂²	1	2	yes	complemented
72	#379×C₁₃₉	C₂²	1	1	yes	characteristic
73	#379×C₁₃₉	C₂²	1	1	yes	characteristic
74	#379×C₁₃₉	C₂²	1	2	yes	complemented
75	#379×C₁₃₉	C₂²	1	2	yes	complemented
76	#379×C₁₃₉	C₂²	1	2	yes	complemented
77	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃₉	—	2	4	no	—
82	C₂²×D₄×C₁₃₉	—	2	4	no	—
83	C₂²×D₄×C₁₃₉	—	2	4	no	—
84	C₂²×D₄×C₁₃₉	—	4	4	no	—
85	C₂²×D₄×C₁₃₉	—	4	4	no	—
86	C₂²×D₄×C₁₃₉	—	4	4	no	—
87	C₂²×D₄×C₁₃₉	—	4	4	no	—
88	C₂²×D₄×C₁₃₉	D₄	1	8	yes	complemented
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	—	2	4	no	—
100	C₂³×C₄×C₁₃₉	—	4	4	no	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	#123×C₁₃₉	—	2	8	no	—
110	#123×C₁₃₉	—	2	8	no	—
111	#123×C₁₃₉	—	4	8	no	—
112	#123×C₁₃₉	—	4	4	no	—
113	#123×C₁₃₉	—	4	4	no	—
114	#121×C₁₃₉	—	2	16	no	—
115	#121×C₁₃₉	—	2	16	no	—
116	#121×C₁₃₉	—	2	8	no	—
117	#121×C₁₃₉	—	2	8	no	—
118	#120×C₁₃₉	—	2	8	no	—
119	#120×C₁₃₉	—	2	8	no	—
120	#120×C₁₃₉	—	4	4	no	—
121	#120×C₁₃₉	—	4	4	no	—
122	#117×C₁₃₉	—	4	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	2	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	4	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	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	4	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	C₂⁴×C₁₃₉	—	2	4	no	—
165	C₂⁴×C₁₃₉	—	2	4	no	—
166	C₂⁴×C₁₃₉	—	2	2	no	—
167	C₂⁴×C₁₃₉	—	2	2	no	—
168	C₂⁴×C₁₃₉	—	2	4	no	—
169	C₂⁴×C₁₃₉	—	4	2	no	—
170	C₂⁴×C₁₃₉	—	4	2	no	—
171	C₂⁴×C₁₃₉	—	4	2	no	—
172	C₂⁴×C₁₃₉	—	4	2	no	—
173	C₂⁴×C₁₃₉	—	4	2	no	—
174	C₂⁴×C₁₃₉	—	4	2	no	—
175	C₂⁴×C₁₃₉	—	4	2	no	—
176	C₂⁴×C₁₃₉	—	4	2	no	—
177	C₂⁴×C₁₃₉	—	4	2	no	—
178	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
179	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
180	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
185	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	8	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	4	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	4	16	no	—
198	C₂×D₄×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	—	4	2	no	—
200	C₂×D₄×C₁₃₉	—	4	2	no	—
201	C₂×D₄×C₁₃₉	—	4	2	no	—
202	C₂×D₄×C₁₃₉	—	4	2	no	—
203	C₂×D₄×C₁₃₉	—	4	2	no	—
204	C₂×D₄×C₁₃₉	—	4	2	no	—
205	C₂×D₄×C₁₃₉	—	4	4	no	—
206	C₂×D₄×C₁₃₉	—	4	4	no	—
207	C₂×D₄×C₁₃₉	—	4	2	no	—
208	C₂×D₄×C₁₃₉	—	4	16	no	—
209	C₂×D₄×C₁₃₉	—	4	4	no	—
210	C₂×D₄×C₁₃₉	—	4	4	no	—
211	C₂×D₄×C₁₃₉	—	4	4	no	—
212	C₂×D₄×C₁₃₉	—	4	4	no	—
213	C₂×D₄×C₁₃₉	—	4	4	no	—
214	C₂×D₄×C₁₃₉	—	4	16	no	—
215	C₂×D₄×C₁₃₉	—	4	16	no	—
216	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
217	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
218	C₂²×C₄×C₁₃₉	—	2	2	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	8	no	—
224	C₂²×C₄×C₁₃₉	—	2	2	no	—
225	C₂²×C₄×C₁₃₉	—	2	4	no	—
226	C₂²×C₄×C₁₃₉	—	2	2	no	—
227	C₂²×C₄×C₁₃₉	—	2	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	8	no	—
229	C₂²×C₄×C₁₃₉	—	4	4	no	—
230	C₂²×C₄×C₁₃₉	—	4	2	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	16	no	—
235	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	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	4	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	C₄⋊C₄×C₁₃₉	—	2	8	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	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	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	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
268	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
275	C₄²×C₁₃₉	—	4	4	no	—
276	C₂³×C₁₃₉	—	2	2	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	8	no	—
279	C₂³×C₁₃₉	—	2	4	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	4	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	8	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	4	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	2	no	—
298	C₂³×C₁₃₉	—	2	4	no	—
299	C₂³×C₁₃₉	—	2	4	no	—
300	C₂³×C₁₃₉	—	4	4	no	—
301	C₂³×C₁₃₉	—	4	4	no	—
302	C₂³×C₁₃₉	—	4	4	no	—
303	C₂³×C₁₃₉	—	4	4	no	—
304	C₂³×C₁₃₉	—	4	16	no	—
305	C₂³×C₁₃₉	—	4	4	no	—
306	C₂³×C₁₃₉	—	4	4	no	—
307	C₂³×C₁₃₉	—	4	4	no	—
308	C₂³×C₁₃₉	—	4	4	no	—
309	C₂³×C₁₃₉	—	8	8	no	—
310	C₂³×C₁₃₉	—	8	8	no	—
311	C₂³×C₁₃₉	—	8	2	no	—
312	C₂³×C₁₃₉	—	8	2	no	—
313	C₂³×C₁₃₉	—	8	8	no	—
314	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
315	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
316	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
317	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
318	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
319	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
320	D₄×C₁₃₉	—	4	8	no	—
321	D₄×C₁₃₉	—	4	8	no	—
322	D₄×C₁₃₉	—	4	8	no	—
323	D₄×C₁₃₉	—	4	8	no	—
324	D₄×C₁₃₉	—	4	8	no	—
325	D₄×C₁₃₉	—	4	16	no	—
326	D₄×C₁₃₉	—	4	8	no	—
327	D₄×C₁₃₉	—	8	4	no	—
328	D₄×C₁₃₉	—	8	4	no	—
329	D₄×C₁₃₉	—	8	8	no	—
330	C₂×C₄×C₁₃₉	—	2	8	no	—
331	C₂×C₄×C₁₃₉	—	2	8	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	4	no	—
342	C₂×C₄×C₁₃₉	—	2	4	no	—
343	C₂×C₄×C₁₃₉	—	2	4	no	—
344	C₂×C₄×C₁₃₉	—	2	4	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	4	no	—
347	C₂×C₄×C₁₃₉	—	2	4	no	—
348	C₂×C₄×C₁₃₉	—	2	4	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	4	no	—
351	C₂×C₄×C₁₃₉	—	2	4	no	—
352	C₂×C₄×C₁₃₉	—	2	4	no	—
353	C₂×C₄×C₁₃₉	—	4	16	no	—
354	C₂×C₄×C₁₃₉	—	4	4	no	—
355	C₂×C₄×C₁₃₉	—	4	4	no	—
356	C₂×C₄×C₁₃₉	—	4	4	no	—
357	C₂×C₄×C₁₃₉	—	8	2	no	—
358	C₂×C₄×C₁₃₉	—	8	2	no	—
359	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
361	C₂²×C₁₃₉	—	2	2	no	—
362	C₂²×C₁₃₉	—	2	2	no	—
363	C₂²×C₁₃₉	—	2	8	no	—
364	C₂²×C₁₃₉	—	2	2	no	—
365	C₂²×C₁₃₉	—	2	4	no	—
366	C₂²×C₁₃₉	—	2	2	no	—
367	C₂²×C₁₃₉	—	2	4	no	—
368	C₂²×C₁₃₉	—	2	2	no	—
369	C₂²×C₁₃₉	—	2	2	no	—
370	C₂²×C₁₃₉	—	2	2	no	—
371	C₂²×C₁₃₉	—	2	4	no	—
372	C₂²×C₁₃₉	—	2	2	no	—
373	C₂²×C₁₃₉	—	4	16	no	—
374	C₂²×C₁₃₉	—	4	4	no	—
375	C₂²×C₁₃₉	—	4	4	no	—
376	C₂²×C₁₃₉	—	4	4	no	—
377	C₂²×C₁₃₉	—	4	4	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	4	no	—
385	C₂²×C₁₃₉	—	4	4	no	—
386	C₂²×C₁₃₉	—	4	4	no	—
387	C₂²×C₁₃₉	—	4	4	no	—
388	C₂²×C₁₃₉	—	8	8	no	—
389	C₂²×C₁₃₉	—	8	8	no	—
390	C₂²×C₁₃₉	—	8	8	no	—
391	C₂²×C₁₃₉	#534	1	4	yes	—
392	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
393	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
394	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₁₃₉	#585	1	2	yes	—
396	C₄×C₁₃₉	—	2	4	no	—
397	C₄×C₁₃₉	—	2	4	no	—
398	C₄×C₁₃₉	—	4	2	no	—
399	C₄×C₁₃₉	—	4	2	no	—
400	C₄×C₁₃₉	—	4	2	no	—
401	C₄×C₁₃₉	—	4	2	no	—
402	C₄×C₁₃₉	—	4	2	no	—
403	C₄×C₁₃₉	—	4	4	no	—
404	C₄×C₁₃₉	—	4	4	no	—
405	C₂×C₁₃₉	—	2	4	no	—
406	C₂×C₁₃₉	—	4	4	no	—
407	C₂×C₁₃₉	—	4	2	no	—
408	C₂×C₁₃₉	—	4	2	no	—
409	C₂×C₁₃₉	—	8	2	no	—
410	C₂×C₁₃₉	—	8	2	no	—
411	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
412	C₂×C₁₃₉	#3484	1	1	yes	characteristic
413	C₂×C₁₃₉	#3485	1	1	yes	characteristic
414	C₂×C₁₃₉	#3542	1	4	yes	—
415	#36715	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
416	C₁₃₉	#36715	1	1	yes	characteristic, direct product factor, Sylow
417	C₂×#534	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	C₂²×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
419	#2849	C₂×C₁₃₉	1	2	yes	complemented
420	#2701	C₂×C₁₃₉	1	4	yes	complemented
421	#2699	C₂×C₁₃₉	1	4	yes	complemented
422	#2682	C₂×C₁₃₉	1	4	yes	complemented
423	#2678	C₂×C₁₃₉	1	4	yes	complemented
424	#2613	C₂×C₁₃₉	1	2	yes	complemented
425	#2483	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	#2413	C₂×C₁₃₉	1	2	yes	complemented
427	#2411	C₂×C₁₃₉	1	2	yes	complemented
428	#2405	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2405	C₂×C₁₃₉	1	1	yes	characteristic, complemented
430	#2403	C₂×C₁₃₉	1	1	yes	characteristic, complemented
431	#2309	C₂×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
436	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
437	#534	—	2	8	no	—
438	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
439	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
440	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
441	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
442	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
443	C₂×#121	—	2	8	no	—
444	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
445	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
446	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
447	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
448	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
450	C₂×#120	C₂²×C₁₃₉	1	2	yes	complemented
451	C₂×#120	C₂²×C₁₃₉	1	2	yes	complemented
452	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
453	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
454	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
457	#398	C₂²×C₁₃₉	1	4	yes	complemented
458	#397	C₂²×C₁₃₉	1	4	yes	complemented
459	#396	C₂²×C₁₃₉	1	4	yes	complemented
460	#396	C₂²×C₁₃₉	1	4	yes	complemented
461	#394	C₂²×C₁₃₉	1	4	yes	complemented
462	#394	C₂²×C₁₃₉	1	4	yes	complemented
463	#394	C₂²×C₁₃₉	1	4	yes	complemented
464	#394	C₂²×C₁₃₉	1	4	yes	complemented
465	#394	C₂²×C₁₃₉	1	4	yes	complemented
466	#392	C₂²×C₁₃₉	1	4	yes	complemented
467	#392	C₂²×C₁₃₉	1	4	yes	complemented
468	#392	C₂²×C₁₃₉	1	4	yes	complemented
469	#390	C₂²×C₁₃₉	1	4	yes	complemented
470	#390	C₂²×C₁₃₉	1	4	yes	complemented
471	#390	C₂²×C₁₃₉	1	4	yes	complemented
472	#389	C₂²×C₁₃₉	1	4	yes	complemented
473	#388	C₂²×C₁₃₉	1	4	yes	complemented
474	#388	C₂²×C₁₃₉	1	4	yes	complemented
475	#386	C₂²×C₁₃₉	1	2	yes	—
476	#386	C₂²×C₁₃₉	1	2	yes	—
477	#386	C₂²×C₁₃₉	1	4	yes	complemented
478	#386	C₂²×C₁₃₉	1	2	yes	complemented
479	#386	C₂²×C₁₃₉	1	2	yes	complemented
480	#385	C₂²×C₁₃₉	1	2	yes	complemented
481	#385	C₂²×C₁₃₉	1	2	yes	complemented
482	#385	C₂²×C₁₃₉	1	4	yes	complemented
483	#385	C₂²×C₁₃₉	1	2	yes	complemented
484	#385	C₂²×C₁₃₉	1	2	yes	complemented
485	#381	C₂²×C₁₃₉	1	4	yes	complemented
486	#381	C₂²×C₁₃₉	1	2	yes	complemented
487	#381	C₂²×C₁₃₉	1	2	yes	complemented
488	#379	C₂²×C₁₃₉	1	1	yes	characteristic
489	#379	C₂²×C₁₃₉	1	1	yes	characteristic
490	#379	C₂²×C₁₃₉	1	2	yes	complemented
491	#379	C₂²×C₁₃₉	1	2	yes	complemented
492	#379	C₂²×C₁₃₉	1	2	yes	complemented
493	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	—	2	4	no	—
500	C₂²×D₄	—	4	4	no	—
501	C₂²×D₄	—	4	4	no	—
502	C₂²×D₄	—	4	4	no	—
503	C₂²×D₄	—	4	4	no	—
504	C₂²×D₄	D₄×C₁₃₉	1	8	yes	complemented
505	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂³×C₄	—	2	4	no	—
516	C₂³×C₄	—	4	4	no	—
517	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	#123	—	2	8	no	—
526	#123	—	2	8	no	—
527	#123	—	4	8	no	—
528	#123	—	4	4	no	—
529	#123	—	4	4	no	—
530	#121	—	2	16	no	—
531	#121	—	2	16	no	—
532	#121	—	2	8	no	—
533	#121	—	2	8	no	—
534	#120	—	2	8	no	—
535	#120	—	2	8	no	—
536	#120	—	4	4	no	—
537	#120	—	4	4	no	—
538	#117	—	4	4	no	—
539	C₂×C₄⋊C₄	—	2	4	no	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₂²⋊C₄	—	2	4	no	—
548	C₂×C₂²⋊C₄	—	2	4	no	—
549	C₂×C₂²⋊C₄	—	2	4	no	—
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	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
573	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	4	yes	—
575	#95	C₂³×C₁₃₉	1	4	yes	—
576	#95	C₂³×C₁₃₉	1	4	yes	—
577	#95	C₂³×C₁₃₉	1	4	yes	—
578	#95	C₂³×C₁₃₉	1	4	yes	—
579	#95	C₂³×C₁₃₉	1	4	yes	—
580	C₂⁴	—	2	4	no	—
581	C₂⁴	—	2	4	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	2	2	no	—
584	C₂⁴	—	2	4	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	4	2	no	—
588	C₂⁴	—	4	2	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	—	4	2	no	—
592	C₂⁴	—	4	2	no	—
593	C₂⁴	—	4	2	no	—
594	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
595	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
596	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
599	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	8	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	16	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	16	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	16	no	—
631	C₂×D₄	—	4	16	no	—
632	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
633	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	8	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	8	no	—
645	C₂²×C₄	—	4	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	16	no	—
651	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₉	1	4	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	4	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	C₄⋊C₄	—	2	8	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	4	4	no	—
691	C₄²	—	4	4	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	8	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	8	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	4	no	—
718	C₂³	—	4	4	no	—
719	C₂³	—	4	4	no	—
720	C₂³	—	4	16	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	4	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	8	8	no	—
726	C₂³	—	8	8	no	—
727	C₂³	—	8	2	no	—
728	C₂³	—	8	2	no	—
729	C₂³	—	8	8	no	—
730	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
731	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
732	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
733	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
734	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
735	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
736	D₄	—	4	8	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	16	no	—
742	D₄	—	4	8	no	—
743	D₄	—	8	4	no	—
744	D₄	—	8	4	no	—
745	D₄	—	8	8	no	—
746	C₂×C₄	—	2	8	no	—
747	C₂×C₄	—	2	8	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	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	4	16	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
776	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
777	C₂²	—	2	8	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	4	16	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	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	—	8	8	no	—
805	C₂²	—	8	8	no	—
806	C₂²	—	8	8	no	—
807	C₂²	#534×C₁₃₉	1	4	yes	—
808	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
809	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
810	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
811	C₂²	#585×C₁₃₉	1	2	yes	—
812	C₄	—	2	4	no	—
813	C₄	—	2	4	no	—
814	C₄	—	4	4	no	—
815	C₄	—	4	4	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	C₂	—	2	4	no	—
822	C₂	—	4	4	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	2	no	—
825	C₂	—	8	2	no	—
826	C₂	—	8	2	no	—
827	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
828	C₂	#3484×C₁₃₉	1	1	yes	characteristic
829	C₂	#3485×C₁₃₉	1	1	yes	characteristic
830	C₂	#3542×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#534×C₁₃₉	C₂	semidirect
2. C₂²×#121×C₁₃₉	C₂	semidirect
3. #2849×C₁₃₉	C₂	semidirect
4. #2701×C₁₃₉	C₂	semidirect
5. #2699×C₁₃₉	C₂	semidirect
6. #2682×C₁₃₉	C₂	semidirect
7. #2678×C₁₃₉	C₂	semidirect
8. #2613×C₁₃₉	C₂	semidirect
9. #2483×C₁₃₉	C₂	semidirect
10. #2413×C₁₃₉	C₂	semidirect
11. #2411×C₁₃₉	C₂	semidirect
12. #2405×C₁₃₉	C₂	semidirect
13. #2405×C₁₃₉	C₂	semidirect
14. #2403×C₁₃₉	C₂	semidirect
15. #2309×C₁₃₉	C₂	semidirect
19. C₂³×D₄×C₁₃₉	C₂²	semidirect
20. C₂⁴×C₄×C₁₃₉	C₂²	semidirect
24. C₂×#123×C₁₃₉	C₂²	semidirect
25. C₂×#123×C₁₃₉	C₂²	semidirect
26. C₂×#123×C₁₃₉	C₂²	semidirect
29. C₂×#121×C₁₃₉	C₂²	semidirect
30. C₂×#121×C₁₃₉	C₂²	semidirect
31. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×#120×C₁₃₉	C₂²	semidirect
35. C₂×#120×C₁₃₉	C₂²	semidirect
36. C₂×#117×C₁₃₉	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
41. #398×C₁₃₉	C₂²	semidirect
42. #397×C₁₃₉	C₂²	semidirect
43. #396×C₁₃₉	C₂²	semidirect
44. #396×C₁₃₉	C₂²	semidirect
45. #394×C₁₃₉	C₂²	semidirect
46. #394×C₁₃₉	C₂²	semidirect
47. #394×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
49. #394×C₁₃₉	C₂²	semidirect
50. #392×C₁₃₉	C₂²	semidirect
51. #392×C₁₃₉	C₂²	semidirect
52. #392×C₁₃₉	C₂²	semidirect
53. #390×C₁₃₉	C₂²	semidirect
54. #390×C₁₃₉	C₂²	semidirect
55. #390×C₁₃₉	C₂²	semidirect
56. #389×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #388×C₁₃₉	C₂²	semidirect
61. #386×C₁₃₉	C₂²	semidirect
62. #386×C₁₃₉	C₂²	semidirect
63. #386×C₁₃₉	C₂²	semidirect
64. #385×C₁₃₉	C₂²	semidirect
65. #385×C₁₃₉	C₂²	semidirect
66. #385×C₁₃₉	C₂²	semidirect
67. #385×C₁₃₉	C₂²	semidirect
68. #385×C₁₃₉	C₂²	semidirect
69. #381×C₁₃₉	C₂²	semidirect
70. #381×C₁₃₉	C₂²	semidirect
71. #381×C₁₃₉	C₂²	semidirect
74. #379×C₁₃₉	C₂²	semidirect
75. #379×C₁₃₉	C₂²	semidirect
76. #379×C₁₃₉	C₂²	semidirect
88. C₂²×D₄×C₁₃₉	D₄	semidirect
415. #36715	C₁₃₉	direct (N × H)
416. C₁₃₉	#36715	direct (N × H)
417. C₂×#534	C₂×C₁₃₉	semidirect
418. C₂²×#121	C₂×C₁₃₉	semidirect
419. #2849	C₂×C₁₃₉	semidirect
420. #2701	C₂×C₁₃₉	semidirect
421. #2699	C₂×C₁₃₉	semidirect
422. #2682	C₂×C₁₃₉	semidirect
423. #2678	C₂×C₁₃₉	semidirect
424. #2613	C₂×C₁₃₉	semidirect
425. #2483	C₂×C₁₃₉	semidirect
426. #2413	C₂×C₁₃₉	semidirect
427. #2411	C₂×C₁₃₉	semidirect
428. #2405	C₂×C₁₃₉	semidirect
429. #2405	C₂×C₁₃₉	semidirect
430. #2403	C₂×C₁₃₉	semidirect
431. #2309	C₂×C₁₃₉	semidirect
435. C₂³×D₄	C₂²×C₁₃₉	semidirect
436. C₂⁴×C₄	C₂²×C₁₃₉	semidirect
440. C₂×#123	C₂²×C₁₃₉	semidirect
441. C₂×#123	C₂²×C₁₃₉	semidirect
442. C₂×#123	C₂²×C₁₃₉	semidirect
445. C₂×#121	C₂²×C₁₃₉	semidirect
446. C₂×#121	C₂²×C₁₃₉	semidirect
447. C₂×#121	C₂²×C₁₃₉	semidirect
450. C₂×#120	C₂²×C₁₃₉	semidirect
451. C₂×#120	C₂²×C₁₃₉	semidirect
452. C₂×#117	C₂²×C₁₃₉	semidirect
453. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
456. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
457. #398	C₂²×C₁₃₉	semidirect
458. #397	C₂²×C₁₃₉	semidirect
459. #396	C₂²×C₁₃₉	semidirect
460. #396	C₂²×C₁₃₉	semidirect
461. #394	C₂²×C₁₃₉	semidirect
462. #394	C₂²×C₁₃₉	semidirect
463. #394	C₂²×C₁₃₉	semidirect
464. #394	C₂²×C₁₃₉	semidirect
465. #394	C₂²×C₁₃₉	semidirect
466. #392	C₂²×C₁₃₉	semidirect
467. #392	C₂²×C₁₃₉	semidirect
468. #392	C₂²×C₁₃₉	semidirect
469. #390	C₂²×C₁₃₉	semidirect
470. #390	C₂²×C₁₃₉	semidirect
471. #390	C₂²×C₁₃₉	semidirect
472. #389	C₂²×C₁₃₉	semidirect
473. #388	C₂²×C₁₃₉	semidirect
474. #388	C₂²×C₁₃₉	semidirect
477. #386	C₂²×C₁₃₉	semidirect
478. #386	C₂²×C₁₃₉	semidirect
479. #386	C₂²×C₁₃₉	semidirect
480. #385	C₂²×C₁₃₉	semidirect
481. #385	C₂²×C₁₃₉	semidirect
482. #385	C₂²×C₁₃₉	semidirect
483. #385	C₂²×C₁₃₉	semidirect
484. #385	C₂²×C₁₃₉	semidirect
485. #381	C₂²×C₁₃₉	semidirect
486. #381	C₂²×C₁₃₉	semidirect
487. #381	C₂²×C₁₃₉	semidirect
490. #379	C₂²×C₁₃₉	semidirect
491. #379	C₂²×C₁₃₉	semidirect
492. #379	C₂²×C₁₃₉	semidirect
504. C₂²×D₄	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×#534×C₁₃₉	2
C₂²×#121×C₁₃₉	2
#2849×C₁₃₉	2
#2701×C₁₃₉	2
#2699×C₁₃₉	2
#2682×C₁₃₉	2
#2678×C₁₃₉	2
#2613×C₁₃₉	2
#2483×C₁₃₉	2
#2413×C₁₃₉	2
#2411×C₁₃₉	2
#2405×C₁₃₉	2
#2403×C₁₃₉	2
#2309×C₁₃₉	2
#36715	139

Subgroups — C139×#36715 #48031311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36715 #48031311