Subgroups — C₁₃₉×#36505 #48031101

Order 35584.

2372 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2851×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2562×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2536×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2475×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2460×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2446×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2432×C₁₃₉	C₂	1	2	yes	maximal
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2355×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	#557×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₄×#41×C₁₃₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
42	#400×C₁₃₉	C₂²	1	4	yes	—
43	#398×C₁₃₉	C₂²	1	4	yes	—
44	#397×C₁₃₉	C₂²	1	4	yes	—
45	#396×C₁₃₉	C₂²	1	4	yes	—
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#391×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	1	yes	characteristic
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	1	yes	characteristic
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#388×C₁₃₉	C₂²	1	4	yes	—
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#387×C₁₃₉	C₂²	1	4	yes	—
62	#387×C₁₃₉	C₂²	1	2	yes	—
63	#387×C₁₃₉	C₂²	1	4	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#385×C₁₃₉	C₂²	1	4	yes	—
67	#385×C₁₃₉	C₂²	1	2	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#384×C₁₃₉	C₂²	1	1	yes	characteristic
71	#382×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	2	yes	—
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
85	C₂×#41×C₁₃₉	—	2	4	no	—
86	C₂×#41×C₁₃₉	—	2	4	no	—
87	C₂×#41×C₁₃₉	—	2	4	no	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
100	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
101	#125×C₁₃₉	—	2	16	no	—
102	#125×C₁₃₉	—	2	8	no	—
103	#124×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
107	C₄×Q₈×C₁₃₉	—	2	4	no	—
108	C₄×Q₈×C₁₃₉	—	2	8	no	—
109	C₄×Q₈×C₁₃₉	—	2	8	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	#117×C₁₃₉	—	2	4	no	—
117	#117×C₁₃₉	—	2	8	no	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
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	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	—	2	8	no	—
149	C₂×C₄²×C₁₃₉	—	2	4	no	—
150	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	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	4	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	#41×C₁₃₉	—	2	32	no	—
177	C₂×Q₈×C₁₃₉	—	2	2	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	2	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	2	4	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×Q₈×C₁₃₉	—	2	2	no	—
184	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
185	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
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	2	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	#41	1	4	yes	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	2	no	—
201	C₂²×C₄×C₁₃₉	—	2	2	no	—
202	C₂²×C₄×C₁₃₉	—	2	4	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	2	no	—
205	C₂²×C₄×C₁₃₉	—	2	2	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	4	2	no	—
208	C₂²×C₄×C₁₃₉	—	4	1	no	—
209	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	2	no	—
229	C₄⋊C₄×C₁₃₉	—	2	8	no	—
230	C₄⋊C₄×C₁₃₉	—	2	8	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	8	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	8	no	—
238	C₄⋊C₄×C₁₃₉	—	2	8	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	2	no	—
242	C₄⋊C₄×C₁₃₉	—	4	2	no	—
243	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	—	2	4	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	2	4	no	—
259	C₄²×C₁₃₉	—	2	2	no	—
260	C₄²×C₁₃₉	—	2	8	no	—
261	C₄²×C₁₃₉	—	2	4	no	—
262	C₄²×C₁₃₉	—	2	4	no	—
263	C₄²×C₁₃₉	—	4	4	no	—
264	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
265	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	1	no	—
268	C₂³×C₁₃₉	—	2	1	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	1	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	1	no	—
274	C₂³×C₁₃₉	—	2	1	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
279	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
280	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
281	Q₈×C₁₃₉	—	2	8	no	—
282	Q₈×C₁₃₉	—	2	8	no	—
283	Q₈×C₁₃₉	—	4	8	no	—
284	D₄×C₁₃₉	—	2	16	no	—
285	D₄×C₁₃₉	—	2	8	no	—
286	C₂×C₄×C₁₃₉	—	2	16	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	1	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	1	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	1	no	—
299	C₂×C₄×C₁₃₉	—	2	8	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	4	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	4	8	no	—
322	C₂×C₄×C₁₃₉	—	4	4	no	—
323	C₂×C₄×C₁₃₉	—	4	4	no	—
324	C₂×C₄×C₁₃₉	—	4	8	no	—
325	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
331	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
332	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
333	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
334	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
335	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
336	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
337	C₂²×C₁₃₉	—	2	4	no	—
338	C₂²×C₁₃₉	—	2	2	no	—
339	C₂²×C₁₃₉	—	2	2	no	—
340	C₂²×C₁₃₉	—	2	4	no	—
341	C₂²×C₁₃₉	—	2	2	no	—
342	C₂²×C₁₃₉	—	2	4	no	—
343	C₂²×C₁₃₉	—	4	1	no	—
344	C₂²×C₁₃₉	—	4	2	no	—
345	C₂²×C₁₃₉	—	4	2	no	—
346	C₂²×C₁₃₉	—	4	1	no	—
347	C₂²×C₁₃₉	—	4	1	no	—
348	C₂²×C₁₃₉	—	4	2	no	—
349	C₂²×C₁₃₉	—	4	2	no	—
350	C₂²×C₁₃₉	—	4	1	no	—
351	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
352	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
353	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
357	C₂²×C₁₃₉	#585	1	1	yes	characteristic
358	C₄×C₁₃₉	—	2	2	no	—
359	C₄×C₁₃₉	—	2	4	no	—
360	C₄×C₁₃₉	—	2	4	no	—
361	C₄×C₁₃₉	—	2	2	no	—
362	C₄×C₁₃₉	—	2	4	no	—
363	C₄×C₁₃₉	—	2	2	no	—
364	C₄×C₁₃₉	—	4	4	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₄×C₁₃₉	—	4	1	no	—
367	C₄×C₁₃₉	—	4	4	no	—
368	C₄×C₁₃₉	—	4	2	no	—
369	C₄×C₁₃₉	—	4	2	no	—
370	C₄×C₁₃₉	—	4	2	no	—
371	C₄×C₁₃₉	#525	1	4	yes	—
372	C₄×C₁₃₉	#548	1	4	yes	—
373	C₂×C₁₃₉	—	4	2	no	—
374	C₂×C₁₃₉	—	4	4	no	—
375	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
376	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
377	C₂×C₁₃₉	#3480	1	1	yes	characteristic
378	C₂×C₁₃₉	#3482	1	1	yes	characteristic
379	C₂×C₁₃₉	#3489	1	1	yes	characteristic
380	C₂×C₁₃₉	#3509	1	1	yes	characteristic
381	C₂×C₁₃₉	#3515	1	1	yes	characteristic
382	#36505	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₁₃₉	#36505	1	1	yes	characteristic, direct product factor, Sylow
384	C₂×#557	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
386	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
387	#2851	C₂×C₁₃₉	1	2	yes	complemented
388	#2562	C₂×C₁₃₉	1	2	yes	complemented
389	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
390	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	#2536	C₂×C₁₃₉	1	2	yes	complemented
392	#2475	C₂×C₁₃₉	1	4	yes	complemented
393	#2460	C₂×C₁₃₉	1	4	yes	complemented
394	#2446	C₂×C₁₃₉	1	2	yes	complemented
395	#2432	C₂×C₁₃₉	1	2	yes	—
396	#2367	C₂×C₁₃₉	1	2	yes	complemented
397	#2362	C₂×C₁₃₉	1	2	yes	complemented
398	#2355	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
400	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
401	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
402	#557	—	2	8	no	—
403	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
405	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
406	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
407	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
408	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
410	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
411	C₄×#41	—	2	8	no	—
412	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
413	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
415	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
423	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
424	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
425	#400	C₂²×C₁₃₉	1	4	yes	—
426	#398	C₂²×C₁₃₉	1	4	yes	—
427	#397	C₂²×C₁₃₉	1	4	yes	—
428	#396	C₂²×C₁₃₉	1	4	yes	—
429	#394	C₂²×C₁₃₉	1	4	yes	—
430	#394	C₂²×C₁₃₉	1	4	yes	—
431	#391	C₂²×C₁₃₉	1	2	yes	—
432	#391	C₂²×C₁₃₉	1	2	yes	—
433	#391	C₂²×C₁₃₉	1	2	yes	—
434	#391	C₂²×C₁₃₉	1	1	yes	characteristic
435	#390	C₂²×C₁₃₉	1	2	yes	—
436	#389	C₂²×C₁₃₉	1	1	yes	characteristic
437	#389	C₂²×C₁₃₉	1	2	yes	—
438	#389	C₂²×C₁₃₉	1	2	yes	—
439	#389	C₂²×C₁₃₉	1	2	yes	—
440	#388	C₂²×C₁₃₉	1	4	yes	—
441	#388	C₂²×C₁₃₉	1	4	yes	—
442	#388	C₂²×C₁₃₉	1	4	yes	—
443	#388	C₂²×C₁₃₉	1	4	yes	—
444	#387	C₂²×C₁₃₉	1	4	yes	—
445	#387	C₂²×C₁₃₉	1	4	yes	—
446	#387	C₂²×C₁₃₉	1	4	yes	—
447	#387	C₂²×C₁₃₉	1	4	yes	—
448	#387	C₂²×C₁₃₉	1	2	yes	—
449	#385	C₂²×C₁₃₉	1	4	yes	—
450	#385	C₂²×C₁₃₉	1	4	yes	—
451	#385	C₂²×C₁₃₉	1	4	yes	—
452	#385	C₂²×C₁₃₉	1	2	yes	—
453	#384	C₂²×C₁₃₉	1	1	yes	characteristic
454	#382	C₂²×C₁₃₉	1	2	yes	—
455	#380	C₂²×C₁₃₉	1	1	yes	characteristic
456	#380	C₂²×C₁₃₉	1	2	yes	—
457	#380	C₂²×C₁₃₉	1	2	yes	—
458	#380	C₂²×C₁₃₉	1	2	yes	—
459	#380	C₂²×C₁₃₉	1	2	yes	—
460	#380	C₂²×C₁₃₉	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	2	4	no	—
470	C₂×#41	—	2	4	no	—
471	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
472	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₄⋊Q₈	—	2	8	no	—
483	C₄⋊Q₈	—	2	4	no	—
484	#125	—	2	16	no	—
485	#125	—	2	8	no	—
486	#124	—	2	8	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	C₂²⋊Q₈	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	C₄×Q₈	—	2	4	no	—
491	C₄×Q₈	—	2	8	no	—
492	C₄×Q₈	—	2	8	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	4	no	—
499	#117	—	2	4	no	—
500	#117	—	2	8	no	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
531	C₂×C₄²	—	2	8	no	—
532	C₂×C₄²	—	2	4	no	—
533	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
538	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
544	#95	C₂³×C₁₃₉	1	2	yes	—
545	#95	C₂³×C₁₃₉	1	2	yes	—
546	#95	C₂³×C₁₃₉	1	4	yes	—
547	#95	C₂³×C₁₃₉	1	2	yes	—
548	#95	C₂³×C₁₃₉	1	2	yes	—
549	#95	C₂³×C₁₃₉	1	4	yes	—
550	#95	C₂³×C₁₃₉	1	4	yes	—
551	#95	C₂³×C₁₃₉	1	2	yes	—
552	#95	C₂³×C₁₃₉	1	4	yes	—
553	#95	C₂³×C₁₃₉	1	4	yes	—
554	#95	C₂³×C₁₃₉	1	4	yes	—
555	#95	C₂³×C₁₃₉	1	4	yes	—
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
558	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
559	#41	—	2	32	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	4	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
568	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	#41×C₁₃₉	1	4	yes	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	8	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	8	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
627	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	8	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	4	no	—
647	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
648	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	2	no	—
661	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
662	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
663	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
664	Q₈	—	2	8	no	—
665	Q₈	—	2	8	no	—
666	Q₈	—	4	8	no	—
667	D₄	—	2	16	no	—
668	D₄	—	2	8	no	—
669	C₂×C₄	—	2	16	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	8	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
711	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
713	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
714	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
715	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
716	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
717	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
718	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
719	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	1	no	—
734	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
735	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
736	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
737	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
738	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
739	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
740	C₂²	#585×C₁₃₉	1	1	yes	characteristic
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	2	no	—
747	C₄	—	4	4	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	4	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	#525×C₁₃₉	1	4	yes	—
755	C₄	#548×C₁₃₉	1	4	yes	—
756	C₂	—	4	2	no	—
757	C₂	—	4	4	no	—
758	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
759	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
760	C₂	#3480×C₁₃₉	1	1	yes	characteristic
761	C₂	#3482×C₁₃₉	1	1	yes	characteristic
762	C₂	#3489×C₁₃₉	1	1	yes	characteristic
763	C₂	#3509×C₁₃₉	1	1	yes	characteristic
764	C₂	#3515×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
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×#557×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2851×C₁₃₉	C₂	semidirect
5. #2562×C₁₃₉	C₂	semidirect
6. #2547×C₁₃₉	C₂	semidirect
7. #2538×C₁₃₉	C₂	semidirect
8. #2536×C₁₃₉	C₂	semidirect
9. #2475×C₁₃₉	C₂	semidirect
10. #2460×C₁₃₉	C₂	semidirect
11. #2446×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2362×C₁₃₉	C₂	semidirect
15. #2355×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
185. C₂×Q₈×C₁₃₉	#41	semidirect
382. #36505	C₁₃₉	direct (N × H)
383. C₁₃₉	#36505	direct (N × H)
384. C₂×#557	C₂×C₁₃₉	semidirect
386. #2857	C₂×C₁₃₉	semidirect
387. #2851	C₂×C₁₃₉	semidirect
388. #2562	C₂×C₁₃₉	semidirect
389. #2547	C₂×C₁₃₉	semidirect
390. #2538	C₂×C₁₃₉	semidirect
391. #2536	C₂×C₁₃₉	semidirect
392. #2475	C₂×C₁₃₉	semidirect
393. #2460	C₂×C₁₃₉	semidirect
394. #2446	C₂×C₁₃₉	semidirect
396. #2367	C₂×C₁₃₉	semidirect
397. #2362	C₂×C₁₃₉	semidirect
398. #2355	C₂×C₁₃₉	semidirect
399. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
400. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
568. C₂×Q₈	#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×#557×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2857×C₁₃₉	2
#2851×C₁₃₉	2
#2562×C₁₃₉	2
#2547×C₁₃₉	2
#2538×C₁₃₉	2
#2536×C₁₃₉	2
#2475×C₁₃₉	2
#2460×C₁₃₉	2
#2446×C₁₃₉	2
#2432×C₁₃₉	2
#2367×C₁₃₉	2
#2362×C₁₃₉	2
#2355×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#36505	139

Subgroups — C139×#36505 #48031101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36505 #48031101