Subgroups — C₁₃₉×#36426 #48031022

Order 35584.

2806 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2847×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2504×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2477×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2471×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2439×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2411×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2404×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	#547×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#117×C₁₃₉	—	2	8	no	—
34	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#117×C₁₃₉	C₂²	1	4	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×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
43	#400×C₁₃₉	C₂²	1	2	yes	complemented
44	#399×C₁₃₉	C₂²	1	2	yes	complemented
45	#397×C₁₃₉	C₂²	1	4	yes	complemented
46	#396×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#393×C₁₃₉	C₂²	1	4	yes	—
49	#392×C₁₃₉	C₂²	1	4	yes	—
50	#391×C₁₃₉	C₂²	1	4	yes	complemented
51	#390×C₁₃₉	C₂²	1	4	yes	—
52	#390×C₁₃₉	C₂²	1	4	yes	complemented
53	#390×C₁₃₉	C₂²	1	2	yes	complemented
54	#389×C₁₃₉	C₂²	1	2	yes	complemented
55	#389×C₁₃₉	C₂²	1	2	yes	complemented
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	complemented
58	#388×C₁₃₉	C₂²	1	4	yes	complemented
59	#387×C₁₃₉	C₂²	1	4	yes	complemented
60	#387×C₁₃₉	C₂²	1	4	yes	complemented
61	#387×C₁₃₉	C₂²	1	4	yes	complemented
62	#386×C₁₃₉	C₂²	1	1	yes	characteristic
63	#386×C₁₃₉	C₂²	1	2	yes	—
64	#386×C₁₃₉	C₂²	1	2	yes	—
65	#386×C₁₃₉	C₂²	1	2	yes	—
66	#386×C₁₃₉	C₂²	1	2	yes	—
67	#386×C₁₃₉	C₂²	1	4	yes	—
68	#386×C₁₃₉	C₂²	1	2	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	—
70	#386×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	1	yes	characteristic
72	#385×C₁₃₉	C₂²	1	2	yes	—
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#382×C₁₃₉	C₂²	1	2	yes	complemented
75	#381×C₁₃₉	C₂²	1	2	yes	—
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	complemented
79	#379×C₁₃₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂×#41×C₁₃₉	—	4	4	no	—
89	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃₉	—	2	4	no	—
97	C₂³×C₄×C₁₃₉	—	2	8	no	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
108	#123×C₁₃₉	—	2	8	no	—
109	#123×C₁₃₉	—	2	8	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
111	#121×C₁₃₉	—	2	4	no	—
112	#121×C₁₃₉	—	2	8	no	—
113	#121×C₁₃₉	—	2	4	no	—
114	#120×C₁₃₉	—	2	4	no	—
115	#120×C₁₃₉	—	4	4	no	—
116	C₄×D₄×C₁₃₉	—	2	4	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	#117×C₁₃₉	—	2	8	no	—
120	#117×C₁₃₉	—	2	8	no	—
121	#117×C₁₃₉	—	2	16	no	—
122	#117×C₁₃₉	—	4	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃₉	—	2	8	no	—
160	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	—	2	2	no	—
177	C₂⁴×C₁₃₉	—	2	4	no	—
178	C₂⁴×C₁₃₉	—	2	2	no	—
179	C₂⁴×C₁₃₉	—	2	2	no	—
180	C₂⁴×C₁₃₉	—	4	2	no	—
181	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
185	#41×C₁₃₉	—	4	32	no	—
186	C₂×Q₈×C₁₃₉	—	2	4	no	—
187	C₂×Q₈×C₁₃₉	—	2	4	no	—
188	C₂×Q₈×C₁₃₉	—	4	2	no	—
189	C₂×D₄×C₁₃₉	—	2	2	no	—
190	C₂×D₄×C₁₃₉	—	2	2	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	—	2	8	no	—
198	C₂×D₄×C₁₃₉	—	2	2	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	4	2	no	—
202	C₂×D₄×C₁₃₉	—	4	2	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂×D₄×C₁₃₉	—	4	4	no	—
205	C₂×D₄×C₁₃₉	#41	1	4	yes	—
206	C₂²×C₄×C₁₃₉	—	2	32	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	4	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	4	no	—
219	C₂²×C₄×C₁₃₉	—	2	2	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	4	no	—
223	C₂²×C₄×C₁₃₉	—	2	4	no	—
224	C₂²×C₄×C₁₃₉	—	4	4	no	—
225	C₂²×C₄×C₁₃₉	—	4	2	no	—
226	C₂²×C₄×C₁₃₉	—	4	2	no	—
227	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
228	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₁₃₉	#41	1	8	yes	complemented
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	2	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	4	4	no	—
252	C₄⋊C₄×C₁₃₉	—	4	4	no	—
253	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
256	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
275	C₄²×C₁₃₉	—	2	8	no	—
276	C₄²×C₁₃₉	—	2	8	no	—
277	C₄²×C₁₃₉	—	2	2	no	—
278	C₄²×C₁₃₉	—	2	4	no	—
279	C₄²×C₁₃₉	—	4	4	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	8	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	4	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	—	2	4	no	—
298	C₂³×C₁₃₉	—	4	8	no	—
299	C₂³×C₁₃₉	—	4	8	no	—
300	C₂³×C₁₃₉	—	4	4	no	—
301	C₂³×C₁₃₉	—	4	4	no	—
302	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
303	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
304	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
305	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
306	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
307	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
308	Q₈×C₁₃₉	—	4	8	no	—
309	D₄×C₁₃₉	—	2	8	no	—
310	D₄×C₁₃₉	—	4	8	no	—
311	D₄×C₁₃₉	—	4	8	no	—
312	D₄×C₁₃₉	—	4	8	no	—
313	D₄×C₁₃₉	—	4	4	no	—
314	D₄×C₁₃₉	—	8	8	no	—
315	C₂×C₄×C₁₃₉	—	2	16	no	—
316	C₂×C₄×C₁₃₉	—	2	8	no	—
317	C₂×C₄×C₁₃₉	—	2	16	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	8	no	—
328	C₂×C₄×C₁₃₉	—	2	16	no	—
329	C₂×C₄×C₁₃₉	—	2	4	no	—
330	C₂×C₄×C₁₃₉	—	2	1	no	—
331	C₂×C₄×C₁₃₉	—	2	1	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	4	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	4	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	4	no	—
344	C₂×C₄×C₁₃₉	—	2	2	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	—	4	8	no	—
349	C₂×C₄×C₁₃₉	—	4	8	no	—
350	C₂×C₄×C₁₃₉	—	4	8	no	—
351	C₂×C₄×C₁₃₉	—	4	4	no	—
352	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
353	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
357	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
359	C₂²×C₁₃₉	—	2	2	no	—
360	C₂²×C₁₃₉	—	2	4	no	—
361	C₂²×C₁₃₉	—	2	2	no	—
362	C₂²×C₁₃₉	—	2	4	no	—
363	C₂²×C₁₃₉	—	2	4	no	—
364	C₂²×C₁₃₉	—	2	2	no	—
365	C₂²×C₁₃₉	—	2	4	no	—
366	C₂²×C₁₃₉	—	2	4	no	—
367	C₂²×C₁₃₉	—	2	4	no	—
368	C₂²×C₁₃₉	—	4	16	no	—
369	C₂²×C₁₃₉	—	4	1	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	1	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	4	no	—
379	C₂²×C₁₃₉	—	4	2	no	—
380	C₂²×C₁₃₉	—	4	4	no	—
381	C₂²×C₁₃₉	#546	1	4	yes	—
382	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
383	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
384	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
385	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂²×C₁₃₉	#585	1	2	yes	—
387	C₄×C₁₃₉	—	2	2	no	—
388	C₄×C₁₃₉	—	2	4	no	—
389	C₄×C₁₃₉	—	2	4	no	—
390	C₄×C₁₃₉	—	2	4	no	—
391	C₄×C₁₃₉	—	2	2	no	—
392	C₄×C₁₃₉	—	4	1	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₄×C₁₃₉	—	4	1	no	—
396	C₄×C₁₃₉	—	4	4	no	—
397	C₄×C₁₃₉	—	4	2	no	—
398	C₄×C₁₃₉	—	4	4	no	—
399	C₄×C₁₃₉	#525	1	4	yes	—
400	C₂×C₁₃₉	—	2	4	no	—
401	C₂×C₁₃₉	—	4	2	no	—
402	C₂×C₁₃₉	—	4	4	no	—
403	C₂×C₁₃₉	—	8	2	no	—
404	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
405	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
406	C₂×C₁₃₉	#3475	1	2	yes	—
407	C₂×C₁₃₉	#3487	1	1	yes	characteristic
408	C₂×C₁₃₉	#3494	1	2	yes	—
409	#36426	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
410	C₁₃₉	#36426	1	1	yes	characteristic, direct product factor, Sylow
411	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2853	C₂×C₁₃₉	1	2	yes	complemented
414	#2847	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	#2504	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#2477	C₂×C₁₃₉	1	4	yes	complemented
418	#2471	C₂×C₁₃₉	1	4	yes	complemented
419	#2439	C₂×C₁₃₉	1	2	yes	complemented
420	#2414	C₂×C₁₃₉	1	2	yes	complemented
421	#2411	C₂×C₁₃₉	1	2	yes	complemented
422	#2404	C₂×C₁₃₉	1	2	yes	complemented
423	#2363	C₂×C₁₃₉	1	2	yes	complemented
424	#2352	C₂×C₁₃₉	1	2	yes	complemented
425	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic, complemented
427	#2297	C₂×C₁₃₉	1	2	yes	complemented
428	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
429	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	#547	—	2	8	no	—
431	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
432	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
434	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
435	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
436	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
438	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
443	C₂×#117	—	2	8	no	—
444	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
445	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
446	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
447	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
448	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
449	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
450	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
451	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
452	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
453	#400	C₂²×C₁₃₉	1	2	yes	complemented
454	#399	C₂²×C₁₃₉	1	2	yes	complemented
455	#397	C₂²×C₁₃₉	1	4	yes	complemented
456	#396	C₂²×C₁₃₉	1	4	yes	—
457	#394	C₂²×C₁₃₉	1	4	yes	—
458	#393	C₂²×C₁₃₉	1	4	yes	—
459	#392	C₂²×C₁₃₉	1	4	yes	—
460	#391	C₂²×C₁₃₉	1	4	yes	complemented
461	#390	C₂²×C₁₃₉	1	4	yes	—
462	#390	C₂²×C₁₃₉	1	2	yes	complemented
463	#390	C₂²×C₁₃₉	1	4	yes	complemented
464	#389	C₂²×C₁₃₉	1	2	yes	complemented
465	#389	C₂²×C₁₃₉	1	2	yes	complemented
466	#388	C₂²×C₁₃₉	1	4	yes	—
467	#388	C₂²×C₁₃₉	1	4	yes	complemented
468	#388	C₂²×C₁₃₉	1	4	yes	complemented
469	#387	C₂²×C₁₃₉	1	4	yes	complemented
470	#387	C₂²×C₁₃₉	1	4	yes	complemented
471	#387	C₂²×C₁₃₉	1	4	yes	complemented
472	#386	C₂²×C₁₃₉	1	2	yes	—
473	#386	C₂²×C₁₃₉	1	4	yes	—
474	#386	C₂²×C₁₃₉	1	2	yes	—
475	#386	C₂²×C₁₃₉	1	4	yes	—
476	#386	C₂²×C₁₃₉	1	4	yes	—
477	#386	C₂²×C₁₃₉	1	2	yes	—
478	#386	C₂²×C₁₃₉	1	2	yes	—
479	#386	C₂²×C₁₃₉	1	2	yes	—
480	#386	C₂²×C₁₃₉	1	1	yes	characteristic
481	#385	C₂²×C₁₃₉	1	1	yes	characteristic
482	#385	C₂²×C₁₃₉	1	2	yes	—
483	#385	C₂²×C₁₃₉	1	2	yes	—
484	#382	C₂²×C₁₃₉	1	2	yes	complemented
485	#381	C₂²×C₁₃₉	1	2	yes	—
486	#380	C₂²×C₁₃₉	1	1	yes	characteristic
487	#380	C₂²×C₁₃₉	1	2	yes	—
488	#380	C₂²×C₁₃₉	1	2	yes	complemented
489	#379	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
491	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
492	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
494	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
495	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×#41	—	2	8	no	—
497	C₂×#41	—	2	8	no	—
498	C₂×#41	—	4	4	no	—
499	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
500	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂³×C₄	—	2	4	no	—
507	C₂³×C₄	—	2	8	no	—
508	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
512	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₄⋊Q₈	—	2	4	no	—
518	#123	—	2	8	no	—
519	#123	—	2	8	no	—
520	C₂²⋊Q₈	—	2	8	no	—
521	#121	—	2	4	no	—
522	#121	—	2	8	no	—
523	#121	—	2	4	no	—
524	#120	—	2	4	no	—
525	#120	—	4	4	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	4	no	—
529	#117	—	2	8	no	—
530	#117	—	2	8	no	—
531	#117	—	2	16	no	—
532	#117	—	4	4	no	—
533	C₂×C₄⋊C₄	—	2	4	no	—
534	C₂×C₄⋊C₄	—	2	4	no	—
535	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	—	2	8	no	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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×C₄²	—	2	8	no	—
570	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
571	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
572	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	4	yes	—
579	#95	C₂³×C₁₃₉	1	4	yes	—
580	#95	C₂³×C₁₃₉	1	4	yes	—
581	#95	C₂³×C₁₃₉	1	4	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	4	yes	—
584	#95	C₂³×C₁₃₉	1	4	yes	—
585	#95	C₂³×C₁₃₉	1	4	yes	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	4	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
594	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
595	#41	—	4	32	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	4	no	—
598	C₂×Q₈	—	4	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	8	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	#41×C₁₃₉	1	4	yes	—
616	C₂²×C₄	—	2	32	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	4	4	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
638	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
639	C₂²×C₄	#41×C₁₃₉	1	8	yes	complemented
640	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
642	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	4	4	no	—
662	C₄⋊C₄	—	4	4	no	—
663	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
664	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
665	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	8	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	—	4	4	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₄²	—	2	8	no	—
686	C₄²	—	2	8	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	4	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	8	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	4	4	no	—
711	C₂³	—	4	4	no	—
712	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
713	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
714	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
715	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
716	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
717	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
718	Q₈	—	4	8	no	—
719	D₄	—	2	8	no	—
720	D₄	—	4	8	no	—
721	D₄	—	4	8	no	—
722	D₄	—	4	8	no	—
723	D₄	—	4	4	no	—
724	D₄	—	8	8	no	—
725	C₂×C₄	—	2	16	no	—
726	C₂×C₄	—	2	8	no	—
727	C₂×C₄	—	2	16	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	8	no	—
738	C₂×C₄	—	2	16	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	8	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
764	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
765	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
766	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
767	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
768	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	16	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	4	no	—
791	C₂²	#546×C₁₃₉	1	4	yes	—
792	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
793	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
794	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
795	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
796	C₂²	#585×C₁₃₉	1	2	yes	—
797	C₄	—	2	2	no	—
798	C₄	—	2	4	no	—
799	C₄	—	2	4	no	—
800	C₄	—	2	4	no	—
801	C₄	—	2	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	4	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	2	no	—
809	C₄	#525×C₁₃₉	1	4	yes	—
810	C₂	—	2	4	no	—
811	C₂	—	4	4	no	—
812	C₂	—	4	2	no	—
813	C₂	—	8	2	no	—
814	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
815	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
816	C₂	#3475×C₁₃₉	1	2	yes	—
817	C₂	#3487×C₁₃₉	1	1	yes	characteristic
818	C₂	#3494×C₁₃₉	1	2	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×#547×C₁₃₉	C₂	semidirect
2. C₂²×#117×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2847×C₁₃₉	C₂	semidirect
5. #2504×C₁₃₉	C₂	semidirect
6. #2487×C₁₃₉	C₂	semidirect
7. #2477×C₁₃₉	C₂	semidirect
8. #2471×C₁₃₉	C₂	semidirect
9. #2439×C₁₃₉	C₂	semidirect
10. #2414×C₁₃₉	C₂	semidirect
11. #2411×C₁₃₉	C₂	semidirect
12. #2404×C₁₃₉	C₂	semidirect
13. #2363×C₁₃₉	C₂	semidirect
14. #2352×C₁₃₉	C₂	semidirect
15. #2344×C₁₃₉	C₂	semidirect
16. C₄×#120×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
23. C₂×#123×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
43. #400×C₁₃₉	C₂²	semidirect
44. #399×C₁₃₉	C₂²	semidirect
45. #397×C₁₃₉	C₂²	semidirect
50. #391×C₁₃₉	C₂²	semidirect
52. #390×C₁₃₉	C₂²	semidirect
53. #390×C₁₃₉	C₂²	semidirect
54. #389×C₁₃₉	C₂²	semidirect
55. #389×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #388×C₁₃₉	C₂²	semidirect
59. #387×C₁₃₉	C₂²	semidirect
60. #387×C₁₃₉	C₂²	semidirect
61. #387×C₁₃₉	C₂²	semidirect
74. #382×C₁₃₉	C₂²	semidirect
78. #380×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
125. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
229. C₂²×C₄×C₁₃₉	#41	semidirect
409. #36426	C₁₃₉	direct (N × H)
410. C₁₃₉	#36426	direct (N × H)
411. C₂×#547	C₂×C₁₃₉	semidirect
412. C₂²×#117	C₂×C₁₃₉	semidirect
413. #2853	C₂×C₁₃₉	semidirect
414. #2847	C₂×C₁₃₉	semidirect
415. #2504	C₂×C₁₃₉	semidirect
416. #2487	C₂×C₁₃₉	semidirect
417. #2477	C₂×C₁₃₉	semidirect
418. #2471	C₂×C₁₃₉	semidirect
419. #2439	C₂×C₁₃₉	semidirect
420. #2414	C₂×C₁₃₉	semidirect
421. #2411	C₂×C₁₃₉	semidirect
422. #2404	C₂×C₁₃₉	semidirect
423. #2363	C₂×C₁₃₉	semidirect
424. #2352	C₂×C₁₃₉	semidirect
425. #2344	C₂×C₁₃₉	semidirect
426. C₄×#120	C₂×C₁₃₉	semidirect
427. #2297	C₂×C₁₃₉	semidirect
431. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
433. C₂×#123	C₂²×C₁₃₉	semidirect
434. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
437. C₂×#121	C₂²×C₁₃₉	semidirect
442. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
450. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
453. #400	C₂²×C₁₃₉	semidirect
454. #399	C₂²×C₁₃₉	semidirect
455. #397	C₂²×C₁₃₉	semidirect
460. #391	C₂²×C₁₃₉	semidirect
462. #390	C₂²×C₁₃₉	semidirect
463. #390	C₂²×C₁₃₉	semidirect
464. #389	C₂²×C₁₃₉	semidirect
465. #389	C₂²×C₁₃₉	semidirect
467. #388	C₂²×C₁₃₉	semidirect
468. #388	C₂²×C₁₃₉	semidirect
469. #387	C₂²×C₁₃₉	semidirect
470. #387	C₂²×C₁₃₉	semidirect
471. #387	C₂²×C₁₃₉	semidirect
484. #382	C₂²×C₁₃₉	semidirect
488. #380	C₂²×C₁₃₉	semidirect
490. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
493. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
494. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
535. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
639. C₂²×C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂²×#117×C₁₃₉	2
#2853×C₁₃₉	2
#2847×C₁₃₉	2
#2504×C₁₃₉	2
#2487×C₁₃₉	2
#2477×C₁₃₉	2
#2471×C₁₃₉	2
#2439×C₁₃₉	2
#2414×C₁₃₉	2
#2411×C₁₃₉	2
#2404×C₁₃₉	2
#2363×C₁₃₉	2
#2352×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#120×C₁₃₉	2
#2297×C₁₃₉	2
#36426	139

Subgroups — C139×#36426 #48031022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36426 #48031022