Subgroups — C₁₃₉×#36596 #48031192

Order 35584.

2612 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2554×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2543×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2512×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2416×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2366×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#553×C₁₃₉	—	2	16	no	—
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	4	yes	—
43	#397×C₁₃₉	C₂²	1	4	yes	—
44	#396×C₁₃₉	C₂²	1	4	yes	—
45	#394×C₁₃₉	C₂²	1	4	yes	—
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#392×C₁₃₉	C₂²	1	4	yes	—
48	#390×C₁₃₉	C₂²	1	2	yes	—
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	2	yes	—
51	#390×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	4	yes	—
53	#390×C₁₃₉	C₂²	1	4	yes	—
54	#390×C₁₃₉	C₂²	1	1	yes	characteristic
55	#390×C₁₃₉	C₂²	1	2	yes	—
56	#390×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	1	yes	characteristic
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#386×C₁₃₉	C₂²	1	2	yes	—
66	#386×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	4	yes	—
69	#384×C₁₃₉	C₂²	1	2	yes	—
70	#384×C₁₃₉	C₂²	1	1	yes	characteristic
71	#380×C₁₃₉	C₂²	1	1	yes	characteristic
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	#127×C₁₃₉	—	2	4	no	—
100	#127×C₁₃₉	—	4	4	no	—
101	#126×C₁₃₉	—	2	16	no	—
102	#125×C₁₃₉	—	2	8	no	—
103	#123×C₁₃₉	—	2	16	no	—
104	#121×C₁₃₉	—	2	16	no	—
105	#121×C₁₃₉	—	2	8	no	—
106	#121×C₁₃₉	—	2	8	no	—
107	#121×C₁₃₉	—	2	4	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	8	no	—
110	#121×C₁₃₉	—	4	4	no	—
111	#121×C₁₃₉	—	4	8	no	—
112	C₄×D₄×C₁₃₉	—	2	16	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	4	4	no	—
117	#117×C₁₃₉	—	2	8	no	—
118	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
119	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	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	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	—	2	4	no	—
152	C₂×C₄²×C₁₃₉	—	4	4	no	—
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	2	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂×D₄×C₁₃₉	—	2	8	no	—
176	C₂×D₄×C₁₃₉	—	2	4	no	—
177	C₂×D₄×C₁₃₉	—	2	8	no	—
178	C₂×D₄×C₁₃₉	—	2	4	no	—
179	C₂×D₄×C₁₃₉	—	2	8	no	—
180	C₂×D₄×C₁₃₉	—	2	4	no	—
181	C₂×D₄×C₁₃₉	—	2	4	no	—
182	C₂×D₄×C₁₃₉	—	2	8	no	—
183	C₂×D₄×C₁₃₉	—	2	2	no	—
184	C₂×D₄×C₁₃₉	—	2	4	no	—
185	C₂×D₄×C₁₃₉	—	2	2	no	—
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	2	no	—
193	C₂×D₄×C₁₃₉	—	4	4	no	—
194	C₂×D₄×C₁₃₉	—	4	2	no	—
195	C₂×D₄×C₁₃₉	—	4	4	no	—
196	C₂×D₄×C₁₃₉	—	4	4	no	—
197	C₂×D₄×C₁₃₉	—	4	4	no	—
198	C₂×D₄×C₁₃₉	—	4	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	2	no	—
200	C₂²×C₄×C₁₃₉	—	2	2	no	—
201	C₂²×C₄×C₁₃₉	—	2	2	no	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	8	no	—
211	C₂²×C₄×C₁₃₉	—	4	2	no	—
212	C₂²×C₄×C₁₃₉	—	4	2	no	—
213	C₂²×C₄×C₁₃₉	—	4	2	no	—
214	C₂²×C₄×C₁₃₉	—	4	1	no	—
215	C₂²×C₄×C₁₃₉	—	4	4	no	—
216	C₂²×C₄×C₁₃₉	—	4	4	no	—
217	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
219	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	8	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	8	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	2	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	—	4	4	no	—
245	C₄⋊C₄×C₁₃₉	—	4	2	no	—
246	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
249	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
250	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
261	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₄²×C₁₃₉	—	2	8	no	—
266	C₄²×C₁₃₉	—	2	4	no	—
267	C₄²×C₁₃₉	—	2	2	no	—
268	C₄²×C₁₃₉	—	2	2	no	—
269	C₄²×C₁₃₉	—	2	2	no	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	4	2	no	—
273	C₄²×C₁₃₉	—	4	2	no	—
274	C₄²×C₁₃₉	#41	1	4	yes	—
275	C₂³×C₁₃₉	—	2	1	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	1	no	—
278	C₂³×C₁₃₉	—	2	1	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	4	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	4	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	4	no	—
287	C₂³×C₁₃₉	—	2	4	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	4	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
294	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
295	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
296	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
297	D₄×C₁₃₉	—	4	16	no	—
298	D₄×C₁₃₉	—	4	8	no	—
299	D₄×C₁₃₉	—	4	8	no	—
300	D₄×C₁₃₉	—	4	4	no	—
301	D₄×C₁₃₉	—	4	8	no	—
302	D₄×C₁₃₉	—	8	4	no	—
303	D₄×C₁₃₉	—	8	8	no	—
304	D₄×C₁₃₉	—	8	8	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	1	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	1	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	1	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	8	no	—
318	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	4	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	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	4	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	4	8	no	—
338	C₂×C₄×C₁₃₉	—	4	4	no	—
339	C₂×C₄×C₁₃₉	—	4	8	no	—
340	C₂×C₄×C₁₃₉	—	4	8	no	—
341	C₂×C₄×C₁₃₉	—	8	8	no	—
342	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
351	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
354	C₂²×C₁₃₉	—	2	2	no	—
355	C₂²×C₁₃₉	—	2	2	no	—
356	C₂²×C₁₃₉	—	2	2	no	—
357	C₂²×C₁₃₉	—	2	2	no	—
358	C₂²×C₁₃₉	—	2	2	no	—
359	C₂²×C₁₃₉	—	2	2	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	4	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	4	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	4	no	—
366	C₂²×C₁₃₉	—	4	4	no	—
367	C₂²×C₁₃₉	—	4	2	no	—
368	C₂²×C₁₃₉	—	4	4	no	—
369	C₂²×C₁₃₉	—	4	2	no	—
370	C₂²×C₁₃₉	—	4	4	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	4	4	no	—
374	C₂²×C₁₃₉	#550	1	4	yes	—
375	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
376	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
378	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂²×C₁₃₉	#585	1	1	yes	characteristic
382	C₄×C₁₃₉	—	2	2	no	—
383	C₄×C₁₃₉	—	2	2	no	—
384	C₄×C₁₃₉	—	2	2	no	—
385	C₄×C₁₃₉	—	2	4	no	—
386	C₄×C₁₃₉	—	2	4	no	—
387	C₄×C₁₃₉	—	2	4	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	—	4	4	no	—
390	C₄×C₁₃₉	—	4	2	no	—
391	C₄×C₁₃₉	—	4	1	no	—
392	C₄×C₁₃₉	—	4	2	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	#532	1	4	yes	—
395	C₄×C₁₃₉	#553	1	4	yes	complemented
396	C₂×C₁₃₉	—	2	4	no	—
397	C₂×C₁₃₉	—	8	2	no	—
398	C₂×C₁₃₉	—	8	4	no	—
399	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
400	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
401	C₂×C₁₃₉	C₂×#553	1	1	yes	characteristic
402	C₂×C₁₃₉	#3480	1	1	yes	characteristic
403	C₂×C₁₃₉	#3494	1	1	yes	characteristic
404	C₂×C₁₃₉	#3496	1	1	yes	characteristic
405	C₂×C₁₃₉	#3519	1	1	yes	characteristic
406	#36596	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₁₃₉	#36596	1	1	yes	characteristic, direct product factor, Sylow
408	C₂×#553	C₂×C₁₃₉	1	2	yes	complemented
409	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	#2856	C₂×C₁₃₉	1	2	yes	complemented
411	#2554	C₂×C₁₃₉	1	4	yes	complemented
412	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2543	C₂×C₁₃₉	1	4	yes	complemented
414	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	#2512	C₂×C₁₃₉	1	2	yes	complemented
416	#2490	C₂×C₁₃₉	1	2	yes	complemented
417	#2445	C₂×C₁₃₉	1	2	yes	complemented
418	#2416	C₂×C₁₃₉	1	2	yes	complemented
419	#2366	C₂×C₁₃₉	1	1	yes	characteristic, complemented
420	#2363	C₂×C₁₃₉	1	2	yes	complemented
421	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
422	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
423	C₄×#121	C₂×C₁₃₉	1	2	yes	complemented
424	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	#553	—	2	16	no	—
426	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
428	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
429	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
430	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
431	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
434	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
435	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
436	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
437	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
438	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
443	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
444	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
445	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
449	#398	C₂²×C₁₃₉	1	4	yes	—
450	#397	C₂²×C₁₃₉	1	4	yes	—
451	#396	C₂²×C₁₃₉	1	4	yes	—
452	#394	C₂²×C₁₃₉	1	4	yes	—
453	#394	C₂²×C₁₃₉	1	4	yes	—
454	#392	C₂²×C₁₃₉	1	4	yes	—
455	#390	C₂²×C₁₃₉	1	2	yes	—
456	#390	C₂²×C₁₃₉	1	2	yes	—
457	#390	C₂²×C₁₃₉	1	4	yes	—
458	#390	C₂²×C₁₃₉	1	2	yes	—
459	#390	C₂²×C₁₃₉	1	2	yes	—
460	#390	C₂²×C₁₃₉	1	4	yes	—
461	#390	C₂²×C₁₃₉	1	2	yes	—
462	#390	C₂²×C₁₃₉	1	2	yes	—
463	#390	C₂²×C₁₃₉	1	1	yes	characteristic
464	#390	C₂²×C₁₃₉	1	2	yes	—
465	#389	C₂²×C₁₃₉	1	2	yes	—
466	#389	C₂²×C₁₃₉	1	2	yes	—
467	#389	C₂²×C₁₃₉	1	1	yes	characteristic
468	#388	C₂²×C₁₃₉	1	4	yes	—
469	#388	C₂²×C₁₃₉	1	4	yes	—
470	#388	C₂²×C₁₃₉	1	4	yes	—
471	#388	C₂²×C₁₃₉	1	2	yes	—
472	#386	C₂²×C₁₃₉	1	4	yes	—
473	#386	C₂²×C₁₃₉	1	4	yes	—
474	#386	C₂²×C₁₃₉	1	4	yes	—
475	#386	C₂²×C₁₃₉	1	2	yes	—
476	#384	C₂²×C₁₃₉	1	1	yes	characteristic
477	#384	C₂²×C₁₃₉	1	2	yes	—
478	#380	C₂²×C₁₃₉	1	2	yes	—
479	#380	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
490	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
506	#127	—	2	4	no	—
507	#127	—	4	4	no	—
508	#126	—	2	16	no	—
509	#125	—	2	8	no	—
510	#123	—	2	16	no	—
511	#121	—	2	16	no	—
512	#121	—	2	8	no	—
513	#121	—	2	4	no	—
514	#121	—	2	8	no	—
515	#121	—	2	8	no	—
516	#121	—	2	8	no	—
517	#121	—	4	8	no	—
518	#121	—	4	4	no	—
519	C₄×D₄	—	2	16	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	4	4	no	—
524	#117	—	2	8	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄²	—	2	4	no	—
559	C₂×C₄²	—	4	4	no	—
560	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	4	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	4	yes	—
578	#95	C₂³×C₁₃₉	1	2	yes	—
579	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
580	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
581	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
626	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	8	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	8	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	4	no	—
653	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
654	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
655	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
656	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	8	no	—
659	C₂²⋊C₄	—	2	8	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	8	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	8	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	4	no	—
669	C₂²⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	—	4	4	no	—
672	C₄²	—	2	8	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	4	2	no	—
680	C₄²	—	4	2	no	—
681	C₄²	#41×C₁₃₉	1	4	yes	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	4	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
701	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
702	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
703	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
704	D₄	—	4	16	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	8	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	8	no	—
711	D₄	—	8	8	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	8	no	—
725	C₂×C₄	—	2	8	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	8	8	no	—
749	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
752	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
753	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
754	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
755	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
756	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
757	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
758	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
759	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
760	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	#550×C₁₃₉	1	4	yes	—
782	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
783	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
784	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
785	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
786	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
787	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
788	C₂²	#585×C₁₃₉	1	1	yes	characteristic
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	4	no	—
794	C₄	—	2	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	4	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	#532×C₁₃₉	1	4	yes	—
802	C₄	#553×C₁₃₉	1	4	yes	complemented
803	C₂	—	2	4	no	—
804	C₂	—	8	2	no	—
805	C₂	—	8	4	no	—
806	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
807	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
808	C₂	C₂×#553×C₁₃₉	1	1	yes	characteristic
809	C₂	#3480×C₁₃₉	1	1	yes	characteristic
810	C₂	#3494×C₁₃₉	1	1	yes	characteristic
811	C₂	#3496×C₁₃₉	1	1	yes	characteristic
812	C₂	#3519×C₁₃₉	1	1	yes	characteristic

	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×#553×C₁₃₉	C₂	semidirect
2. #2856×C₁₃₉	C₂	semidirect
3. #2856×C₁₃₉	C₂	semidirect
4. #2554×C₁₃₉	C₂	semidirect
5. #2552×C₁₃₉	C₂	semidirect
6. #2543×C₁₃₉	C₂	semidirect
7. #2541×C₁₃₉	C₂	semidirect
8. #2512×C₁₃₉	C₂	semidirect
9. #2490×C₁₃₉	C₂	semidirect
10. #2445×C₁₃₉	C₂	semidirect
11. #2416×C₁₃₉	C₂	semidirect
12. #2366×C₁₃₉	C₂	semidirect
13. #2363×C₁₃₉	C₂	semidirect
14. #2354×C₁₃₉	C₂	semidirect
15. C₄×#121×C₁₃₉	C₂	semidirect
16. C₄×#121×C₁₃₉	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
119. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
395. C₄×C₁₃₉	#553	semidirect
406. #36596	C₁₃₉	direct (N × H)
407. C₁₃₉	#36596	direct (N × H)
408. C₂×#553	C₂×C₁₃₉	semidirect
409. #2856	C₂×C₁₃₉	semidirect
410. #2856	C₂×C₁₃₉	semidirect
411. #2554	C₂×C₁₃₉	semidirect
412. #2552	C₂×C₁₃₉	semidirect
413. #2543	C₂×C₁₃₉	semidirect
414. #2541	C₂×C₁₃₉	semidirect
415. #2512	C₂×C₁₃₉	semidirect
416. #2490	C₂×C₁₃₉	semidirect
417. #2445	C₂×C₁₃₉	semidirect
418. #2416	C₂×C₁₃₉	semidirect
419. #2366	C₂×C₁₃₉	semidirect
420. #2363	C₂×C₁₃₉	semidirect
421. #2354	C₂×C₁₃₉	semidirect
422. C₄×#121	C₂×C₁₃₉	semidirect
423. C₄×#121	C₂×C₁₃₉	semidirect
424. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
526. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
802. C₄	#553×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
#2856×C₁₃₉	2
#2554×C₁₃₉	2
#2552×C₁₃₉	2
#2543×C₁₃₉	2
#2541×C₁₃₉	2
#2512×C₁₃₉	2
#2490×C₁₃₉	2
#2445×C₁₃₉	2
#2416×C₁₃₉	2
#2366×C₁₃₉	2
#2363×C₁₃₉	2
#2354×C₁₃₉	2
C₄×#121×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36596	139

Subgroups — C139×#36596 #48031192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36596 #48031192