Subgroups — C₁₃₉×#37131 #48031727

Order 35584.

2048 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2726×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2724×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2718×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2706×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2704×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2701×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2698×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2682×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2680×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2664×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2602×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2583×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2293×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#539×C₁₃₉	—	2	16	no	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	#400×C₁₃₉	C₂²	1	2	yes	—
40	#399×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#397×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#397×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#396×C₁₃₉	C₂²	1	2	yes	—
55	#396×C₁₃₉	C₂²	1	2	yes	—
56	#395×C₁₃₉	C₂²	1	2	yes	—
57	#395×C₁₃₉	C₂²	1	2	yes	—
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#394×C₁₃₉	C₂²	1	2	yes	—
60	#394×C₁₃₉	C₂²	1	2	yes	—
61	#394×C₁₃₉	C₂²	1	2	yes	—
62	#392×C₁₃₉	C₂²	1	2	yes	—
63	#391×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#390×C₁₃₉	C₂²	1	1	yes	characteristic
68	#390×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	1	yes	characteristic
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	2	yes	—
73	#389×C₁₃₉	C₂²	1	2	yes	—
74	#389×C₁₃₉	C₂²	1	2	yes	—
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic
77	#389×C₁₃₉	C₂²	1	1	yes	characteristic
78	#389×C₁₃₉	C₂²	1	1	yes	characteristic
79	#389×C₁₃₉	C₂²	1	2	yes	—
80	#389×C₁₃₉	C₂²	1	1	yes	characteristic
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic
82	#389×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#388×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#386×C₁₃₉	C₂²	1	2	yes	—
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	2	yes	—
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#384×C₁₃₉	C₂²	1	1	yes	characteristic
101	#384×C₁₃₉	C₂²	1	1	yes	characteristic
102	#382×C₁₃₉	C₂²	1	2	yes	—
103	#381×C₁₃₉	C₂²	1	2	yes	—
104	#380×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
107	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
117	#126×C₁₃₉	—	2	8	no	—
118	#126×C₁₃₉	—	2	8	no	—
119	#125×C₁₃₉	—	2	8	no	—
120	#125×C₁₃₉	—	2	8	no	—
121	#123×C₁₃₉	—	2	8	no	—
122	#123×C₁₃₉	—	2	8	no	—
123	#123×C₁₃₉	—	2	8	no	—
124	#123×C₁₃₉	—	2	8	no	—
125	#123×C₁₃₉	—	4	4	no	—
126	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
127	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
128	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
129	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
130	#121×C₁₃₉	—	2	8	no	—
131	C₄×D₄×C₁₃₉	—	2	8	no	—
132	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
133	#117×C₁₃₉	—	4	4	no	—
134	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	#95×C₁₃₉	C₂³	1	2	yes	—
211	#95×C₁₃₉	C₂³	1	2	yes	—
212	#95×C₁₃₉	C₂³	1	2	yes	—
213	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₁₃₉	—	2	4	no	—
216	C₂×Q₈×C₁₃₉	—	4	2	no	—
217	C₂×Q₈×C₁₃₉	—	4	2	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	4	1	no	—
222	C₂×D₄×C₁₃₉	—	4	1	no	—
223	C₂×D₄×C₁₃₉	—	4	2	no	—
224	C₂×D₄×C₁₃₉	—	4	2	no	—
225	C₂×D₄×C₁₃₉	—	4	2	no	—
226	C₂×D₄×C₁₃₉	—	4	1	no	—
227	C₂×D₄×C₁₃₉	—	4	1	no	—
228	C₂×D₄×C₁₃₉	—	4	2	no	—
229	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	4	no	—
233	C₂²×C₄×C₁₃₉	—	4	2	no	—
234	C₂²×C₄×C₁₃₉	—	4	2	no	—
235	C₂²×C₄×C₁₃₉	—	4	2	no	—
236	C₂²×C₄×C₁₃₉	—	4	2	no	—
237	C₂²×C₄×C₁₃₉	—	4	2	no	—
238	C₂²×C₄×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	—	4	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	4	no	—
261	C₄⋊C₄×C₁₃₉	—	2	4	no	—
262	C₄⋊C₄×C₁₃₉	—	2	4	no	—
263	C₄⋊C₄×C₁₃₉	—	2	4	no	—
264	C₄⋊C₄×C₁₃₉	—	2	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	4	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	2	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	2	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	1	no	—
277	C₄⋊C₄×C₁₃₉	—	4	2	no	—
278	C₄⋊C₄×C₁₃₉	—	4	1	no	—
279	C₄⋊C₄×C₁₃₉	—	4	2	no	—
280	C₄⋊C₄×C₁₃₉	—	4	1	no	—
281	C₄⋊C₄×C₁₃₉	—	4	1	no	—
282	C₄⋊C₄×C₁₃₉	—	4	1	no	—
283	C₄⋊C₄×C₁₃₉	—	4	1	no	—
284	C₄⋊C₄×C₁₃₉	—	4	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	2	no	—
286	C₄⋊C₄×C₁₃₉	—	4	2	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
306	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
310	C₄²×C₁₃₉	—	2	4	no	—
311	C₄²×C₁₃₉	—	2	2	no	—
312	C₄²×C₁₃₉	—	2	2	no	—
313	C₄²×C₁₃₉	—	2	2	no	—
314	C₄²×C₁₃₉	—	4	1	no	—
315	C₄²×C₁₃₉	—	4	1	no	—
316	C₄²×C₁₃₉	—	4	1	no	—
317	C₄²×C₁₃₉	—	4	2	no	—
318	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
333	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
334	Q₈×C₁₃₉	—	8	4	no	—
335	D₄×C₁₃₉	—	4	4	no	—
336	D₄×C₁₃₉	—	4	8	no	—
337	D₄×C₁₃₉	—	8	2	no	—
338	D₄×C₁₃₉	—	8	4	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	1	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	1	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	1	no	—
349	C₂×C₄×C₁₃₉	—	2	1	no	—
350	C₂×C₄×C₁₃₉	—	2	1	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	1	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	1	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	2	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	2	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	4	8	no	—
384	C₂×C₄×C₁₃₉	—	4	8	no	—
385	C₂×C₄×C₁₃₉	—	8	4	no	—
386	C₂×C₄×C₁₃₉	—	8	4	no	—
387	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
392	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
394	C₂²×C₁₃₉	—	2	4	no	—
395	C₂²×C₁₃₉	—	2	4	no	—
396	C₂²×C₁₃₉	—	2	4	no	—
397	C₂²×C₁₃₉	—	4	2	no	—
398	C₂²×C₁₃₉	—	4	2	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	2	no	—
401	C₂²×C₁₃₉	—	4	2	no	—
402	C₂²×C₁₃₉	—	4	2	no	—
403	C₂²×C₁₃₉	—	4	2	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	2	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	2	no	—
408	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
409	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂²×C₁₃₉	#585	1	1	yes	characteristic
413	C₂²×C₁₃₉	#585	1	1	yes	characteristic
414	C₂²×C₁₃₉	#585	1	1	yes	characteristic
415	C₄×C₁₃₉	—	2	2	no	—
416	C₄×C₁₃₉	—	2	2	no	—
417	C₄×C₁₃₉	—	2	4	no	—
418	C₄×C₁₃₉	—	2	2	no	—
419	C₄×C₁₃₉	—	2	2	no	—
420	C₄×C₁₃₉	—	2	2	no	—
421	C₄×C₁₃₉	—	2	2	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	2	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	2	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	—	4	1	no	—
430	C₄×C₁₃₉	—	4	2	no	—
431	C₄×C₁₃₉	—	4	2	no	—
432	C₂×C₁₃₉	—	4	4	no	—
433	C₂×C₁₃₉	—	8	2	no	—
434	C₂×C₁₃₉	#3449	1	1	yes	characteristic
435	C₂×C₁₃₉	#3496	1	1	yes	characteristic
436	C₂×C₁₃₉	#3499	1	1	yes	characteristic
437	C₂×C₁₃₉	#3553	1	1	yes	characteristic
438	C₂×C₁₃₉	#3554	1	1	yes	characteristic
439	C₂×C₁₃₉	#3559	1	1	yes	characteristic
440	C₂×C₁₃₉	#3564	1	1	yes	characteristic
441	#37131	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₁₃₉	#37131	1	1	yes	characteristic, direct product factor, Sylow
443	C₂×#539	C₂×C₁₃₉	1	2	yes	complemented
444	#2860	C₂×C₁₃₉	1	1	yes	characteristic, complemented
445	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2726	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	#2724	C₂×C₁₃₉	1	1	yes	characteristic, complemented
448	#2718	C₂×C₁₃₉	1	2	yes	complemented
449	#2706	C₂×C₁₃₉	1	2	yes	complemented
450	#2704	C₂×C₁₃₉	1	2	yes	complemented
451	#2701	C₂×C₁₃₉	1	2	yes	complemented
452	#2698	C₂×C₁₃₉	1	2	yes	complemented
453	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	#2682	C₂×C₁₃₉	1	1	yes	characteristic
455	#2680	C₂×C₁₃₉	1	2	yes	complemented
456	#2664	C₂×C₁₃₉	1	2	yes	complemented
457	#2602	C₂×C₁₃₉	1	2	yes	complemented
458	#2583	C₂×C₁₃₉	1	2	yes	complemented
459	#2415	C₂×C₁₃₉	1	2	yes	complemented
460	#2413	C₂×C₁₃₉	1	2	yes	complemented
461	#2293	C₂×C₁₃₉	1	1	yes	characteristic, complemented
462	#539	—	2	16	no	—
463	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
464	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
466	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
467	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
469	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
470	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
471	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
472	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
474	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
475	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
476	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
477	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
479	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
480	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
481	#400	C₂²×C₁₃₉	1	2	yes	—
482	#399	C₂²×C₁₃₉	1	2	yes	—
483	#398	C₂²×C₁₃₉	1	2	yes	—
484	#398	C₂²×C₁₃₉	1	2	yes	—
485	#398	C₂²×C₁₃₉	1	2	yes	—
486	#398	C₂²×C₁₃₉	1	2	yes	—
487	#398	C₂²×C₁₃₉	1	2	yes	—
488	#398	C₂²×C₁₃₉	1	2	yes	—
489	#398	C₂²×C₁₃₉	1	2	yes	—
490	#397	C₂²×C₁₃₉	1	2	yes	—
491	#397	C₂²×C₁₃₉	1	2	yes	—
492	#397	C₂²×C₁₃₉	1	2	yes	—
493	#397	C₂²×C₁₃₉	1	2	yes	—
494	#396	C₂²×C₁₃₉	1	2	yes	—
495	#396	C₂²×C₁₃₉	1	2	yes	—
496	#396	C₂²×C₁₃₉	1	2	yes	—
497	#396	C₂²×C₁₃₉	1	2	yes	—
498	#395	C₂²×C₁₃₉	1	2	yes	—
499	#395	C₂²×C₁₃₉	1	2	yes	—
500	#394	C₂²×C₁₃₉	1	2	yes	—
501	#394	C₂²×C₁₃₉	1	2	yes	—
502	#394	C₂²×C₁₃₉	1	2	yes	—
503	#394	C₂²×C₁₃₉	1	2	yes	—
504	#392	C₂²×C₁₃₉	1	2	yes	—
505	#391	C₂²×C₁₃₉	1	2	yes	—
506	#390	C₂²×C₁₃₉	1	1	yes	characteristic
507	#390	C₂²×C₁₃₉	1	1	yes	characteristic
508	#390	C₂²×C₁₃₉	1	1	yes	characteristic
509	#390	C₂²×C₁₃₉	1	1	yes	characteristic
510	#390	C₂²×C₁₃₉	1	1	yes	characteristic
511	#389	C₂²×C₁₃₉	1	1	yes	characteristic
512	#389	C₂²×C₁₃₉	1	2	yes	—
513	#389	C₂²×C₁₃₉	1	2	yes	—
514	#389	C₂²×C₁₃₉	1	2	yes	—
515	#389	C₂²×C₁₃₉	1	1	yes	characteristic
516	#389	C₂²×C₁₃₉	1	1	yes	characteristic
517	#389	C₂²×C₁₃₉	1	1	yes	characteristic
518	#389	C₂²×C₁₃₉	1	1	yes	characteristic
519	#389	C₂²×C₁₃₉	1	2	yes	—
520	#389	C₂²×C₁₃₉	1	1	yes	characteristic
521	#389	C₂²×C₁₃₉	1	1	yes	characteristic
522	#389	C₂²×C₁₃₉	1	2	yes	—
523	#389	C₂²×C₁₃₉	1	1	yes	characteristic
524	#389	C₂²×C₁₃₉	1	1	yes	characteristic
525	#388	C₂²×C₁₃₉	1	2	yes	—
526	#388	C₂²×C₁₃₉	1	2	yes	—
527	#388	C₂²×C₁₃₉	1	2	yes	—
528	#388	C₂²×C₁₃₉	1	2	yes	—
529	#388	C₂²×C₁₃₉	1	2	yes	—
530	#388	C₂²×C₁₃₉	1	2	yes	—
531	#388	C₂²×C₁₃₉	1	2	yes	—
532	#388	C₂²×C₁₃₉	1	2	yes	—
533	#387	C₂²×C₁₃₉	1	2	yes	—
534	#386	C₂²×C₁₃₉	1	2	yes	—
535	#386	C₂²×C₁₃₉	1	2	yes	—
536	#385	C₂²×C₁₃₉	1	2	yes	—
537	#385	C₂²×C₁₃₉	1	2	yes	—
538	#385	C₂²×C₁₃₉	1	2	yes	—
539	#385	C₂²×C₁₃₉	1	2	yes	—
540	#385	C₂²×C₁₃₉	1	2	yes	—
541	#385	C₂²×C₁₃₉	1	2	yes	—
542	#384	C₂²×C₁₃₉	1	1	yes	characteristic
543	#384	C₂²×C₁₃₉	1	1	yes	characteristic
544	#382	C₂²×C₁₃₉	1	2	yes	—
545	#381	C₂²×C₁₃₉	1	2	yes	—
546	#380	C₂²×C₁₃₉	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
548	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
549	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
551	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
559	#126	—	2	8	no	—
560	#126	—	2	8	no	—
561	#125	—	2	8	no	—
562	#125	—	2	8	no	—
563	#123	—	2	8	no	—
564	#123	—	2	8	no	—
565	#123	—	2	8	no	—
566	#123	—	2	8	no	—
567	#123	—	4	4	no	—
568	C₂²⋊Q₈	—	2	8	no	—
569	C₂²⋊Q₈	—	2	8	no	—
570	C₂²⋊Q₈	—	2	8	no	—
571	C₂²⋊Q₈	—	4	4	no	—
572	#121	—	2	8	no	—
573	C₄×D₄	—	2	8	no	—
574	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
575	#117	—	4	4	no	—
576	C₂×C₄⋊C₄	—	2	8	no	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
637	#95	C₂³×C₁₃₉	1	2	yes	—
638	#95	C₂³×C₁₃₉	1	2	yes	—
639	#95	C₂³×C₁₃₉	1	2	yes	—
640	#95	C₂³×C₁₃₉	1	2	yes	—
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	2	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	2	yes	—
646	#95	C₂³×C₁₃₉	1	2	yes	—
647	#95	C₂³×C₁₃₉	1	2	yes	—
648	#95	C₂³×C₁₃₉	1	2	yes	—
649	#95	C₂³×C₁₃₉	1	2	yes	—
650	#95	C₂³×C₁₃₉	1	2	yes	—
651	#95	C₂³×C₁₃₉	1	2	yes	—
652	#95	C₂³×C₁₃₉	1	2	yes	—
653	#95	C₂³×C₁₃₉	1	2	yes	—
654	#95	C₂³×C₁₃₉	1	2	yes	—
655	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
656	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	4	1	no	—
664	C₂×D₄	—	4	1	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	—	4	1	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	4	1	no	—
757	C₄²	—	4	1	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	2	no	—
760	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
775	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
776	Q₈	—	8	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	8	no	—
779	D₄	—	8	2	no	—
780	D₄	—	8	4	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	8	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	4	no	—
829	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
830	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
833	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
834	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
835	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
851	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
852	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
853	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
854	C₂²	#585×C₁₃₉	1	1	yes	characteristic
855	C₂²	#585×C₁₃₉	1	1	yes	characteristic
856	C₂²	#585×C₁₃₉	1	1	yes	characteristic
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₂	—	4	4	no	—
875	C₂	—	8	2	no	—
876	C₂	#3449×C₁₃₉	1	1	yes	characteristic
877	C₂	#3496×C₁₃₉	1	1	yes	characteristic
878	C₂	#3499×C₁₃₉	1	1	yes	characteristic
879	C₂	#3553×C₁₃₉	1	1	yes	characteristic
880	C₂	#3554×C₁₃₉	1	1	yes	characteristic
881	C₂	#3559×C₁₃₉	1	1	yes	characteristic
882	C₂	#3564×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2682×C₁₃₉	C₂
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×#539×C₁₃₉	C₂	semidirect
2. #2860×C₁₃₉	C₂	semidirect
3. #2859×C₁₃₉	C₂	semidirect
4. #2726×C₁₃₉	C₂	semidirect
5. #2724×C₁₃₉	C₂	semidirect
6. #2718×C₁₃₉	C₂	semidirect
7. #2706×C₁₃₉	C₂	semidirect
8. #2704×C₁₃₉	C₂	semidirect
9. #2701×C₁₃₉	C₂	semidirect
10. #2698×C₁₃₉	C₂	semidirect
11. #2683×C₁₃₉	C₂	semidirect
13. #2680×C₁₃₉	C₂	semidirect
14. #2664×C₁₃₉	C₂	semidirect
15. #2602×C₁₃₉	C₂	semidirect
16. #2583×C₁₃₉	C₂	semidirect
17. #2415×C₁₃₉	C₂	semidirect
18. #2413×C₁₃₉	C₂	semidirect
19. #2293×C₁₃₉	C₂	semidirect
132. C₄×D₄×C₁₃₉	D₄	semidirect
441. #37131	C₁₃₉	direct (N × H)
442. C₁₃₉	#37131	direct (N × H)
443. C₂×#539	C₂×C₁₃₉	semidirect
444. #2860	C₂×C₁₃₉	semidirect
445. #2859	C₂×C₁₃₉	semidirect
446. #2726	C₂×C₁₃₉	semidirect
447. #2724	C₂×C₁₃₉	semidirect
448. #2718	C₂×C₁₃₉	semidirect
449. #2706	C₂×C₁₃₉	semidirect
450. #2704	C₂×C₁₃₉	semidirect
451. #2701	C₂×C₁₃₉	semidirect
452. #2698	C₂×C₁₃₉	semidirect
453. #2683	C₂×C₁₃₉	semidirect
455. #2680	C₂×C₁₃₉	semidirect
456. #2664	C₂×C₁₃₉	semidirect
457. #2602	C₂×C₁₃₉	semidirect
458. #2583	C₂×C₁₃₉	semidirect
459. #2415	C₂×C₁₃₉	semidirect
460. #2413	C₂×C₁₃₉	semidirect
461. #2293	C₂×C₁₃₉	semidirect
574. C₄×D₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₁₃₉	2
#2860×C₁₃₉	2
#2859×C₁₃₉	2
#2726×C₁₃₉	2
#2724×C₁₃₉	2
#2718×C₁₃₉	2
#2706×C₁₃₉	2
#2704×C₁₃₉	2
#2701×C₁₃₉	2
#2698×C₁₃₉	2
#2683×C₁₃₉	2
#2682×C₁₃₉	2
#2680×C₁₃₉	2
#2664×C₁₃₉	2
#2602×C₁₃₉	2
#2583×C₁₃₉	2
#2415×C₁₃₉	2
#2413×C₁₃₉	2
#2293×C₁₃₉	2
#37131	139

Subgroups — C139×#37131 #48031727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37131 #48031727