Subgroups — C₁₃₉×#35622 #48030218

Order 35584.

2246 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2565×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2475×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2473×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2468×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2466×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2327×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2326×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	#541×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	#520×C₁₃₉	—	2	8	no	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	#400×C₁₃₉	C₂²	1	4	yes	—
48	#398×C₁₃₉	C₂²	1	4	yes	—
49	#398×C₁₃₉	C₂²	1	4	yes	—
50	#398×C₁₃₉	C₂²	1	4	yes	—
51	#397×C₁₃₉	C₂²	1	4	yes	—
52	#396×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	—
55	#391×C₁₃₉	C₂²	1	1	yes	characteristic
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic
60	#391×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	4	yes	—
64	#389×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	4	yes	—
72	#387×C₁₃₉	C₂²	1	4	yes	—
73	#387×C₁₃₉	C₂²	1	4	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	#385×C₁₃₉	C₂²	1	4	yes	—
77	#385×C₁₃₉	C₂²	1	4	yes	—
78	#385×C₁₃₉	C₂²	1	4	yes	—
79	#384×C₁₃₉	C₂²	1	1	yes	characteristic
80	#384×C₁₃₉	C₂²	1	1	yes	characteristic
81	#382×C₁₃₉	C₂²	1	1	yes	characteristic
82	#382×C₁₃₉	C₂²	1	1	yes	characteristic
83	#381×C₁₃₉	C₂²	1	4	yes	—
84	#380×C₁₃₉	C₂²	1	4	yes	—
85	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
91	#376×C₁₃₉	C₂²	1	1	yes	characteristic
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₃₉	—	2	4	no	—
94	C₂×#41×C₁₃₉	—	2	4	no	—
95	C₂×#41×C₁₃₉	—	2	4	no	—
96	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
107	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
108	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
109	#126×C₁₃₉	—	2	8	no	—
110	#126×C₁₃₉	—	2	8	no	—
111	#125×C₁₃₉	—	2	8	no	—
112	#125×C₁₃₉	—	2	8	no	—
113	#125×C₁₃₉	—	2	4	no	—
114	#124×C₁₃₉	—	2	4	no	—
115	#124×C₁₃₉	—	2	4	no	—
116	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
118	C₄×Q₈×C₁₃₉	—	2	4	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×Q₈×C₁₃₉	—	2	4	no	—
121	C₄×Q₈×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	—	2	4	no	—
126	#117×C₁₃₉	—	2	8	no	—
127	#117×C₁₃₉	D₄	1	8	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	#95×C₁₃₉	C₂³	1	4	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	4	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	4	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	4	yes	—
185	#95×C₁₃₉	C₂³	1	4	yes	—
186	#95×C₁₃₉	C₂³	1	4	yes	—
187	#95×C₁₃₉	C₂³	1	4	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
193	#41×C₁₃₉	—	2	32	no	—
194	C₂×Q₈×C₁₃₉	—	2	2	no	—
195	C₂×Q₈×C₁₃₉	—	2	2	no	—
196	C₂×Q₈×C₁₃₉	—	2	2	no	—
197	C₂×Q₈×C₁₃₉	—	2	2	no	—
198	C₂×Q₈×C₁₃₉	—	2	2	no	—
199	C₂×Q₈×C₁₃₉	—	2	2	no	—
200	C₂×Q₈×C₁₃₉	—	2	2	no	—
201	C₂×Q₈×C₁₃₉	—	2	2	no	—
202	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
203	C₂×D₄×C₁₃₉	—	2	4	no	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	2	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	2	no	—
208	C₂×D₄×C₁₃₉	#41	1	4	yes	—
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	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	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	—	4	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	4	no	—
219	C₂²×C₄×C₁₃₉	—	4	4	no	—
220	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	2	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	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₁₃₉	—	2	4	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	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	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	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	8	no	—
254	C₄⋊C₄×C₁₃₉	—	2	8	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	4	4	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	4	no	—
259	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	—	2	8	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	2	4	no	—
275	C₄²×C₁₃₉	—	2	4	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	—	2	2	no	—
278	C₄²×C₁₃₉	—	2	2	no	—
279	C₄²×C₁₃₉	—	2	2	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	4	2	no	—
283	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
284	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	1	no	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	4	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	4	yes	—
295	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
296	Q₈×C₁₃₉	—	2	8	no	—
297	Q₈×C₁₃₉	—	4	4	no	—
298	Q₈×C₁₃₉	—	4	4	no	—
299	D₄×C₁₃₉	—	2	16	no	—
300	D₄×C₁₃₉	—	2	8	no	—
301	C₂×C₄×C₁₃₉	—	2	16	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
312	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
327	C₂×C₄×C₁₃₉	—	2	4	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	4	no	—
335	C₂×C₄×C₁₃₉	—	2	4	no	—
336	C₂×C₄×C₁₃₉	—	8	4	no	—
337	C₂×C₄×C₁₃₉	—	8	4	no	—
338	C₂×C₄×C₁₃₉	—	8	4	no	—
339	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
346	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
349	C₂²×C₁₃₉	—	2	2	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	2	8	no	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	4	no	—
359	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
360	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
363	C₂²×C₁₃₉	#585	1	2	yes	—
364	C₄×C₁₃₉	—	2	2	no	—
365	C₄×C₁₃₉	—	2	4	no	—
366	C₄×C₁₃₉	—	2	2	no	—
367	C₄×C₁₃₉	—	2	2	no	—
368	C₄×C₁₃₉	—	2	2	no	—
369	C₄×C₁₃₉	—	2	2	no	—
370	C₄×C₁₃₉	—	2	4	no	—
371	C₄×C₁₃₉	—	4	2	no	—
372	C₄×C₁₃₉	—	4	2	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	2	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	#525	1	4	yes	—
381	C₂×C₁₃₉	—	4	2	no	—
382	C₂×C₁₃₉	—	4	4	no	—
383	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
384	C₂×C₁₃₉	#3499	1	1	yes	characteristic
385	C₂×C₁₃₉	#3500	1	1	yes	characteristic
386	C₂×C₁₃₉	#3515	1	2	yes	—
387	C₂×C₁₃₉	#3516	1	2	yes	—
388	#35622	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₁₃₉	#35622	1	1	yes	characteristic, direct product factor, Sylow
390	C₂×#541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic
392	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2565	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
396	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
397	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
398	#2475	C₂×C₁₃₉	1	4	yes	complemented
399	#2473	C₂×C₁₃₉	1	4	yes	complemented
400	#2468	C₂×C₁₃₉	1	4	yes	complemented
401	#2466	C₂×C₁₃₉	1	4	yes	complemented
402	#2432	C₂×C₁₃₉	1	1	yes	characteristic
403	#2432	C₂×C₁₃₉	1	1	yes	characteristic
404	#2327	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2326	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
410	#541	—	2	8	no	—
411	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
415	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
416	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
418	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
419	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
423	#520	—	2	8	no	—
424	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
432	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
435	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	#400	C₂²×C₁₃₉	1	4	yes	—
437	#398	C₂²×C₁₃₉	1	4	yes	—
438	#398	C₂²×C₁₃₉	1	4	yes	—
439	#398	C₂²×C₁₃₉	1	4	yes	—
440	#397	C₂²×C₁₃₉	1	4	yes	—
441	#396	C₂²×C₁₃₉	1	4	yes	—
442	#394	C₂²×C₁₃₉	1	4	yes	—
443	#394	C₂²×C₁₃₉	1	4	yes	—
444	#391	C₂²×C₁₃₉	1	1	yes	characteristic
445	#391	C₂²×C₁₃₉	1	1	yes	characteristic
446	#391	C₂²×C₁₃₉	1	1	yes	characteristic
447	#391	C₂²×C₁₃₉	1	1	yes	characteristic
448	#391	C₂²×C₁₃₉	1	1	yes	characteristic
449	#391	C₂²×C₁₃₉	1	1	yes	characteristic
450	#390	C₂²×C₁₃₉	1	1	yes	characteristic
451	#390	C₂²×C₁₃₉	1	1	yes	characteristic
452	#389	C₂²×C₁₃₉	1	4	yes	—
453	#389	C₂²×C₁₃₉	1	4	yes	—
454	#388	C₂²×C₁₃₉	1	4	yes	—
455	#388	C₂²×C₁₃₉	1	2	yes	—
456	#388	C₂²×C₁₃₉	1	2	yes	—
457	#388	C₂²×C₁₃₉	1	4	yes	—
458	#387	C₂²×C₁₃₉	1	4	yes	—
459	#387	C₂²×C₁₃₉	1	4	yes	—
460	#387	C₂²×C₁₃₉	1	4	yes	—
461	#387	C₂²×C₁₃₉	1	2	yes	—
462	#387	C₂²×C₁₃₉	1	2	yes	—
463	#385	C₂²×C₁₃₉	1	4	yes	—
464	#385	C₂²×C₁₃₉	1	4	yes	—
465	#385	C₂²×C₁₃₉	1	4	yes	—
466	#385	C₂²×C₁₃₉	1	4	yes	—
467	#385	C₂²×C₁₃₉	1	4	yes	—
468	#384	C₂²×C₁₃₉	1	1	yes	characteristic
469	#384	C₂²×C₁₃₉	1	1	yes	characteristic
470	#382	C₂²×C₁₃₉	1	1	yes	characteristic
471	#382	C₂²×C₁₃₉	1	1	yes	characteristic
472	#381	C₂²×C₁₃₉	1	4	yes	—
473	#380	C₂²×C₁₃₉	1	4	yes	—
474	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
475	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
480	#376	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	4	no	—
485	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₄⋊Q₈	—	2	4	no	—
496	C₄⋊Q₈	—	2	4	no	—
497	C₄⋊Q₈	—	2	4	no	—
498	#126	—	2	8	no	—
499	#126	—	2	8	no	—
500	#125	—	2	8	no	—
501	#125	—	2	8	no	—
502	#125	—	2	4	no	—
503	#124	—	2	4	no	—
504	#124	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₄×Q₈	—	2	4	no	—
508	C₄×Q₈	—	2	4	no	—
509	C₄×Q₈	—	2	4	no	—
510	C₄×Q₈	—	2	4	no	—
511	C₄×D₄	—	2	8	no	—
512	C₄×D₄	—	2	8	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	#117	—	2	8	no	—
516	#117	D₄×C₁₃₉	1	8	yes	—
517	C₂×C₄⋊C₄	—	2	4	no	—
518	C₂×C₄⋊C₄	—	2	8	no	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	2	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	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	4	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	4	yes	—
572	#95	C₂³×C₁₃₉	1	4	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	4	yes	—
575	#95	C₂³×C₁₃₉	1	2	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	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
582	#41	—	2	32	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	#41×C₁₃₉	1	4	yes	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	8	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	4	4	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
649	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	8	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	4	no	—
660	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
661	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	2	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	4	2	no	—
672	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
673	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
683	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
684	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
685	Q₈	—	2	8	no	—
686	Q₈	—	4	4	no	—
687	Q₈	—	4	4	no	—
688	D₄	—	2	16	no	—
689	D₄	—	2	8	no	—
690	C₂×C₄	—	2	16	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	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	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	—	8	4	no	—
728	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
734	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
735	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
736	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
737	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	4	no	—
748	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
750	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
751	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
752	C₂²	#585×C₁₃₉	1	2	yes	—
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	#525×C₁₃₉	1	4	yes	—
770	C₂	—	4	2	no	—
771	C₂	—	4	4	no	—
772	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
773	C₂	#3499×C₁₃₉	1	1	yes	characteristic
774	C₂	#3500×C₁₃₉	1	1	yes	characteristic
775	C₂	#3515×C₁₃₉	1	2	yes	—
776	C₂	#3516×C₁₃₉	1	2	yes	—

	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×#541×C₁₃₉	C₂	semidirect
3. #2566×C₁₃₉	C₂	semidirect
4. #2565×C₁₃₉	C₂	semidirect
5. #2547×C₁₃₉	C₂	semidirect
6. #2546×C₁₃₉	C₂	semidirect
7. #2503×C₁₃₉	C₂	semidirect
8. #2502×C₁₃₉	C₂	semidirect
9. #2475×C₁₃₉	C₂	semidirect
10. #2473×C₁₃₉	C₂	semidirect
11. #2468×C₁₃₉	C₂	semidirect
12. #2466×C₁₃₉	C₂	semidirect
15. #2327×C₁₃₉	C₂	semidirect
16. #2326×C₁₃₉	C₂	semidirect
17. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
18. C₄×#124×C₁₃₉	C₂	semidirect
19. #2298×C₁₃₉	C₂	semidirect
388. #35622	C₁₃₉	direct (N × H)
389. C₁₃₉	#35622	direct (N × H)
390. C₂×#541	C₂×C₁₃₉	semidirect
392. #2566	C₂×C₁₃₉	semidirect
393. #2565	C₂×C₁₃₉	semidirect
394. #2547	C₂×C₁₃₉	semidirect
395. #2546	C₂×C₁₃₉	semidirect
396. #2503	C₂×C₁₃₉	semidirect
397. #2502	C₂×C₁₃₉	semidirect
398. #2475	C₂×C₁₃₉	semidirect
399. #2473	C₂×C₁₃₉	semidirect
400. #2468	C₂×C₁₃₉	semidirect
401. #2466	C₂×C₁₃₉	semidirect
404. #2327	C₂×C₁₃₉	semidirect
405. #2326	C₂×C₁₃₉	semidirect
406. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
407. C₄×#124	C₂×C₁₃₉	semidirect
408. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#541×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2566×C₁₃₉	2
#2565×C₁₃₉	2
#2547×C₁₃₉	2
#2546×C₁₃₉	2
#2503×C₁₃₉	2
#2502×C₁₃₉	2
#2475×C₁₃₉	2
#2473×C₁₃₉	2
#2468×C₁₃₉	2
#2466×C₁₃₉	2
#2432×C₁₃₉	2
#2327×C₁₃₉	2
#2326×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2298×C₁₃₉	2
#35622	139

Subgroups — C139×#35622 #48030218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35622 #48030218