Subgroups — C₁₃₉×#37034 #48031630

Order 35584.

1864 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2803×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2775×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2749×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2728×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2709×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2697×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2697×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2681×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2669×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2648×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2529×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2518×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2472×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2461×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2328×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2321×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	#400×C₁₃₉	C₂²	1	2	yes	complemented
35	#400×C₁₃₉	C₂²	1	2	yes	complemented
36	#398×C₁₃₉	C₂²	1	2	yes	complemented
37	#397×C₁₃₉	C₂²	1	2	yes	—
38	#397×C₁₃₉	C₂²	1	2	yes	—
39	#397×C₁₃₉	C₂²	1	2	yes	—
40	#397×C₁₃₉	C₂²	1	2	yes	—
41	#397×C₁₃₉	C₂²	1	2	yes	complemented
42	#396×C₁₃₉	C₂²	1	2	yes	—
43	#396×C₁₃₉	C₂²	1	2	yes	—
44	#396×C₁₃₉	C₂²	1	2	yes	—
45	#396×C₁₃₉	C₂²	1	2	yes	complemented
46	#395×C₁₃₉	C₂²	1	2	yes	complemented
47	#394×C₁₃₉	C₂²	1	2	yes	—
48	#394×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	2	yes	—
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	complemented
54	#394×C₁₃₉	C₂²	1	2	yes	complemented
55	#393×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	2	yes	—
57	#392×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	complemented
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
64	#389×C₁₃₉	C₂²	1	2	yes	complemented
65	#389×C₁₃₉	C₂²	1	2	yes	complemented
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#388×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	2	yes	—
70	#388×C₁₃₉	C₂²	1	2	yes	—
71	#388×C₁₃₉	C₂²	1	2	yes	—
72	#388×C₁₃₉	C₂²	1	2	yes	—
73	#388×C₁₃₉	C₂²	1	2	yes	—
74	#388×C₁₃₉	C₂²	1	2	yes	complemented
75	#388×C₁₃₉	C₂²	1	2	yes	complemented
76	#388×C₁₃₉	C₂²	1	2	yes	complemented
77	#388×C₁₃₉	C₂²	1	2	yes	complemented
78	#388×C₁₃₉	C₂²	1	2	yes	complemented
79	#387×C₁₃₉	C₂²	1	2	yes	complemented
80	#387×C₁₃₉	C₂²	1	2	yes	complemented
81	#387×C₁₃₉	C₂²	1	2	yes	complemented
82	#386×C₁₃₉	C₂²	1	2	yes	—
83	#386×C₁₃₉	C₂²	1	1	yes	characteristic
84	#386×C₁₃₉	C₂²	1	2	yes	—
85	#386×C₁₃₉	C₂²	1	1	yes	characteristic
86	#386×C₁₃₉	C₂²	1	2	yes	—
87	#386×C₁₃₉	C₂²	1	2	yes	—
88	#386×C₁₃₉	C₂²	1	2	yes	—
89	#386×C₁₃₉	C₂²	1	2	yes	—
90	#386×C₁₃₉	C₂²	1	2	yes	complemented
91	#386×C₁₃₉	C₂²	1	2	yes	complemented
92	#386×C₁₃₉	C₂²	1	2	yes	complemented
93	#385×C₁₃₉	C₂²	1	1	yes	characteristic
94	#385×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
95	#385×C₁₃₉	C₂²	1	2	yes	complemented
96	#383×C₁₃₉	C₂²	1	2	yes	complemented
97	#382×C₁₃₉	C₂²	1	2	yes	complemented
98	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
99	#381×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
100	#379×C₁₃₉	C₂²	1	1	yes	characteristic
101	#379×C₁₃₉	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
106	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
122	#127×C₁₃₉	—	2	4	no	—
123	#124×C₁₃₉	—	4	4	no	—
124	#123×C₁₃₉	—	2	4	no	—
125	#123×C₁₃₉	—	4	4	no	—
126	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
127	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
128	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
129	#121×C₁₃₉	—	4	4	no	—
130	#120×C₁₃₉	—	2	4	no	—
131	#120×C₁₃₉	—	4	4	no	—
132	C₄×D₄×C₁₃₉	—	4	2	no	—
133	C₄×D₄×C₁₃₉	—	4	2	no	—
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	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	—	4	2	no	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃₉	—	4	2	no	—
181	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
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	C₂⁴×C₁₃₉	—	2	2	no	—
209	C₂⁴×C₁₃₉	—	4	1	no	—
210	C₂⁴×C₁₃₉	—	4	1	no	—
211	C₂⁴×C₁₃₉	—	4	2	no	—
212	C₂⁴×C₁₃₉	—	4	2	no	—
213	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂×Q₈×C₁₃₉	—	2	4	no	—
218	C₂×Q₈×C₁₃₉	—	4	2	no	—
219	C₂×Q₈×C₁₃₉	—	4	2	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	4	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂×D₄×C₁₃₉	—	2	4	no	—
225	C₂×D₄×C₁₃₉	—	4	1	no	—
226	C₂×D₄×C₁₃₉	—	4	1	no	—
227	C₂×D₄×C₁₃₉	—	4	1	no	—
228	C₂×D₄×C₁₃₉	—	4	1	no	—
229	C₂×D₄×C₁₃₉	—	4	2	no	—
230	C₂×D₄×C₁₃₉	—	4	2	no	—
231	C₂×D₄×C₁₃₉	—	4	2	no	—
232	C₂×D₄×C₁₃₉	—	4	2	no	—
233	C₂×D₄×C₁₃₉	—	4	2	no	—
234	C₂×D₄×C₁₃₉	—	4	2	no	—
235	C₂×D₄×C₁₃₉	—	4	2	no	—
236	C₂×D₄×C₁₃₉	—	4	2	no	—
237	C₂×D₄×C₁₃₉	—	4	2	no	—
238	C₂×D₄×C₁₃₉	—	4	2	no	—
239	C₂×D₄×C₁₃₉	—	4	2	no	—
240	C₂×D₄×C₁₃₉	#41	1	4	yes	—
241	C₂²×C₄×C₁₃₉	—	2	2	no	—
242	C₂²×C₄×C₁₃₉	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	2	4	no	—
244	C₂²×C₄×C₁₃₉	—	2	2	no	—
245	C₂²×C₄×C₁₃₉	—	4	1	no	—
246	C₂²×C₄×C₁₃₉	—	4	1	no	—
247	C₂²×C₄×C₁₃₉	—	4	2	no	—
248	C₂²×C₄×C₁₃₉	—	4	1	no	—
249	C₂²×C₄×C₁₃₉	—	4	1	no	—
250	C₂²×C₄×C₁₃₉	—	4	2	no	—
251	C₂²×C₄×C₁₃₉	—	4	2	no	—
252	C₂²×C₄×C₁₃₉	—	4	2	no	—
253	C₂²×C₄×C₁₃₉	—	4	2	no	—
254	C₂²×C₄×C₁₃₉	—	4	2	no	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	4	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	—	4	2	no	—
276	C₄⋊C₄×C₁₃₉	—	4	1	no	—
277	C₄⋊C₄×C₁₃₉	—	4	1	no	—
278	C₄⋊C₄×C₁₃₉	—	4	2	no	—
279	C₄⋊C₄×C₁₃₉	—	4	2	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	2	no	—
282	C₄⋊C₄×C₁₃₉	—	4	2	no	—
283	C₄⋊C₄×C₁₃₉	—	4	2	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
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	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
295	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
301	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
302	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
303	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
304	C₂²⋊C₄×C₁₃₉	—	4	1	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	—	4	2	no	—
310	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
312	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
314	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
315	C₄²×C₁₃₉	—	2	2	no	—
316	C₄²×C₁₃₉	—	2	4	no	—
317	C₄²×C₁₃₉	—	2	2	no	—
318	C₄²×C₁₃₉	—	4	2	no	—
319	C₄²×C₁₃₉	—	4	2	no	—
320	C₄²×C₁₃₉	—	4	1	no	—
321	C₄²×C₁₃₉	—	4	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	1	no	—
325	C₂³×C₁₃₉	—	2	1	no	—
326	C₂³×C₁₃₉	—	2	1	no	—
327	C₂³×C₁₃₉	—	2	1	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	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	2	no	—
335	C₂³×C₁₃₉	—	2	2	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	2	no	—
338	C₂³×C₁₃₉	—	2	2	no	—
339	C₂³×C₁₃₉	—	2	2	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	2	no	—
342	C₂³×C₁₃₉	—	2	2	no	—
343	C₂³×C₁₃₉	—	2	2	no	—
344	C₂³×C₁₃₉	—	4	4	no	—
345	C₂³×C₁₃₉	—	8	4	no	—
346	C₂³×C₁₃₉	—	8	2	no	—
347	C₂³×C₁₃₉	—	8	2	no	—
348	C₂³×C₁₃₉	—	8	4	no	—
349	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
351	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
352	Q₈×C₁₃₉	—	8	4	no	—
353	D₄×C₁₃₉	—	4	4	no	—
354	D₄×C₁₃₉	—	4	4	no	—
355	D₄×C₁₃₉	—	8	4	no	—
356	D₄×C₁₃₉	—	8	4	no	—
357	D₄×C₁₃₉	—	8	4	no	—
358	D₄×C₁₃₉	—	8	4	no	—
359	D₄×C₁₃₉	—	8	4	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	2	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	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	1	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	1	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	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	2	no	—
388	C₂×C₄×C₁₃₉	—	2	2	no	—
389	C₂×C₄×C₁₃₉	—	2	2	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	2	2	no	—
393	C₂×C₄×C₁₃₉	—	2	2	no	—
394	C₂×C₄×C₁₃₉	—	2	2	no	—
395	C₂×C₄×C₁₃₉	—	2	2	no	—
396	C₂×C₄×C₁₃₉	—	2	2	no	—
397	C₂×C₄×C₁₃₉	—	2	2	no	—
398	C₂×C₄×C₁₃₉	—	4	4	no	—
399	C₂×C₄×C₁₃₉	—	4	4	no	—
400	C₂×C₄×C₁₃₉	—	4	4	no	—
401	C₂×C₄×C₁₃₉	—	8	2	no	—
402	C₂×C₄×C₁₃₉	—	8	4	no	—
403	C₂×C₄×C₁₃₉	—	8	2	no	—
404	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
405	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
407	C₂²×C₁₃₉	—	2	2	no	—
408	C₂²×C₁₃₉	—	2	2	no	—
409	C₂²×C₁₃₉	—	2	4	no	—
410	C₂²×C₁₃₉	—	2	4	no	—
411	C₂²×C₁₃₉	—	4	1	no	—
412	C₂²×C₁₃₉	—	4	1	no	—
413	C₂²×C₁₃₉	—	4	1	no	—
414	C₂²×C₁₃₉	—	4	1	no	—
415	C₂²×C₁₃₉	—	4	2	no	—
416	C₂²×C₁₃₉	—	4	2	no	—
417	C₂²×C₁₃₉	—	4	2	no	—
418	C₂²×C₁₃₉	—	4	2	no	—
419	C₂²×C₁₃₉	—	4	2	no	—
420	C₂²×C₁₃₉	—	4	2	no	—
421	C₂²×C₁₃₉	—	4	2	no	—
422	C₂²×C₁₃₉	—	4	2	no	—
423	C₂²×C₁₃₉	—	4	2	no	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	4	2	no	—
426	C₂²×C₁₃₉	—	4	2	no	—
427	C₂²×C₁₃₉	—	4	2	no	—
428	C₂²×C₁₃₉	—	4	2	no	—
429	C₂²×C₁₃₉	—	4	2	no	—
430	C₂²×C₁₃₉	—	4	2	no	—
431	C₂²×C₁₃₉	—	8	8	no	—
432	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
433	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
435	C₂²×C₁₃₉	#585	1	1	yes	characteristic
436	C₂²×C₁₃₉	#585	1	2	yes	—
437	C₄×C₁₃₉	—	2	2	no	—
438	C₄×C₁₃₉	—	2	2	no	—
439	C₄×C₁₃₉	—	2	4	no	—
440	C₄×C₁₃₉	—	4	2	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	2	no	—
443	C₄×C₁₃₉	—	4	2	no	—
444	C₄×C₁₃₉	—	4	1	no	—
445	C₄×C₁₃₉	—	4	1	no	—
446	C₄×C₁₃₉	—	4	1	no	—
447	C₄×C₁₃₉	—	4	2	no	—
448	C₄×C₁₃₉	—	4	2	no	—
449	C₄×C₁₃₉	—	4	2	no	—
450	C₄×C₁₃₉	—	4	2	no	—
451	C₄×C₁₃₉	—	4	2	no	—
452	C₂×C₁₃₉	—	4	2	no	—
453	C₂×C₁₃₉	—	4	2	no	—
454	C₂×C₁₃₉	—	8	2	no	—
455	C₂×C₁₃₉	—	8	2	no	—
456	C₂×C₁₃₉	#3459	1	1	yes	characteristic
457	C₂×C₁₃₉	#3514	1	2	yes	—
458	C₂×C₁₃₉	#3533	1	1	yes	characteristic
459	C₂×C₁₃₉	#3537	1	1	yes	characteristic
460	C₂×C₁₃₉	#3551	1	2	yes	—
461	#37034	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₁₃₉	#37034	1	1	yes	characteristic, direct product factor, Sylow
463	#2850	C₂×C₁₃₉	1	2	yes	complemented
464	#2803	C₂×C₁₃₉	1	2	yes	complemented
465	#2775	C₂×C₁₃₉	1	2	yes	complemented
466	#2749	C₂×C₁₃₉	1	2	yes	complemented
467	#2728	C₂×C₁₃₉	1	2	yes	complemented
468	#2709	C₂×C₁₃₉	1	1	yes	characteristic, complemented
469	#2697	C₂×C₁₃₉	1	1	yes	characteristic, complemented
470	#2697	C₂×C₁₃₉	1	2	yes	complemented
471	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
472	#2681	C₂×C₁₃₉	1	2	yes	complemented
473	#2669	C₂×C₁₃₉	1	1	yes	characteristic
474	#2648	C₂×C₁₃₉	1	2	yes	complemented
475	#2529	C₂×C₁₃₉	1	2	yes	complemented
476	#2518	C₂×C₁₃₉	1	2	yes	complemented
477	#2472	C₂×C₁₃₉	1	2	yes	complemented
478	#2461	C₂×C₁₃₉	1	2	yes	complemented
479	#2328	C₂×C₁₃₉	1	1	yes	characteristic, complemented
480	#2321	C₂×C₁₃₉	1	1	yes	characteristic, complemented
481	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
484	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
486	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
487	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
488	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
489	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
490	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
491	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
494	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
495	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
496	#400	C₂²×C₁₃₉	1	2	yes	complemented
497	#400	C₂²×C₁₃₉	1	2	yes	complemented
498	#398	C₂²×C₁₃₉	1	2	yes	complemented
499	#397	C₂²×C₁₃₉	1	2	yes	—
500	#397	C₂²×C₁₃₉	1	2	yes	—
501	#397	C₂²×C₁₃₉	1	2	yes	—
502	#397	C₂²×C₁₃₉	1	2	yes	—
503	#397	C₂²×C₁₃₉	1	2	yes	complemented
504	#396	C₂²×C₁₃₉	1	2	yes	—
505	#396	C₂²×C₁₃₉	1	2	yes	—
506	#396	C₂²×C₁₃₉	1	2	yes	—
507	#396	C₂²×C₁₃₉	1	2	yes	complemented
508	#395	C₂²×C₁₃₉	1	2	yes	complemented
509	#394	C₂²×C₁₃₉	1	2	yes	—
510	#394	C₂²×C₁₃₉	1	2	yes	—
511	#394	C₂²×C₁₃₉	1	2	yes	—
512	#394	C₂²×C₁₃₉	1	2	yes	—
513	#394	C₂²×C₁₃₉	1	2	yes	—
514	#394	C₂²×C₁₃₉	1	2	yes	—
515	#394	C₂²×C₁₃₉	1	2	yes	complemented
516	#394	C₂²×C₁₃₉	1	2	yes	complemented
517	#393	C₂²×C₁₃₉	1	2	yes	—
518	#392	C₂²×C₁₃₉	1	2	yes	—
519	#392	C₂²×C₁₃₉	1	2	yes	—
520	#391	C₂²×C₁₃₉	1	2	yes	complemented
521	#390	C₂²×C₁₃₉	1	2	yes	—
522	#390	C₂²×C₁₃₉	1	1	yes	characteristic
523	#390	C₂²×C₁₃₉	1	2	yes	—
524	#390	C₂²×C₁₃₉	1	2	yes	—
525	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
526	#389	C₂²×C₁₃₉	1	2	yes	complemented
527	#389	C₂²×C₁₃₉	1	2	yes	complemented
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	#388	C₂²×C₁₃₉	1	2	yes	—
534	#388	C₂²×C₁₃₉	1	2	yes	—
535	#388	C₂²×C₁₃₉	1	2	yes	—
536	#388	C₂²×C₁₃₉	1	2	yes	complemented
537	#388	C₂²×C₁₃₉	1	2	yes	complemented
538	#388	C₂²×C₁₃₉	1	2	yes	complemented
539	#388	C₂²×C₁₃₉	1	2	yes	complemented
540	#388	C₂²×C₁₃₉	1	2	yes	complemented
541	#387	C₂²×C₁₃₉	1	2	yes	complemented
542	#387	C₂²×C₁₃₉	1	2	yes	complemented
543	#387	C₂²×C₁₃₉	1	2	yes	complemented
544	#386	C₂²×C₁₃₉	1	2	yes	—
545	#386	C₂²×C₁₃₉	1	1	yes	characteristic
546	#386	C₂²×C₁₃₉	1	2	yes	—
547	#386	C₂²×C₁₃₉	1	2	yes	—
548	#386	C₂²×C₁₃₉	1	2	yes	—
549	#386	C₂²×C₁₃₉	1	1	yes	characteristic
550	#386	C₂²×C₁₃₉	1	2	yes	—
551	#386	C₂²×C₁₃₉	1	2	yes	—
552	#386	C₂²×C₁₃₉	1	2	yes	complemented
553	#386	C₂²×C₁₃₉	1	2	yes	complemented
554	#386	C₂²×C₁₃₉	1	2	yes	complemented
555	#385	C₂²×C₁₃₉	1	1	yes	characteristic
556	#385	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
557	#385	C₂²×C₁₃₉	1	2	yes	complemented
558	#383	C₂²×C₁₃₉	1	2	yes	complemented
559	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
560	#382	C₂²×C₁₃₉	1	2	yes	complemented
561	#381	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
562	#379	C₂²×C₁₃₉	1	1	yes	characteristic
563	#379	C₂²×C₁₃₉	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
565	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
566	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
568	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
569	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
571	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
584	#127	—	2	4	no	—
585	#124	—	4	4	no	—
586	#123	—	2	4	no	—
587	#123	—	4	4	no	—
588	C₂²⋊Q₈	—	4	4	no	—
589	C₂²⋊Q₈	—	4	4	no	—
590	C₂²⋊Q₈	—	4	4	no	—
591	#121	—	4	4	no	—
592	#120	—	2	4	no	—
593	#120	—	4	4	no	—
594	C₄×D₄	—	4	2	no	—
595	C₄×D₄	—	4	2	no	—
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₂²⋊C₄	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
642	C₂×C₄²	—	4	2	no	—
643	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₄²	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	#95	C₂³×C₁₃₉	1	2	yes	—
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	2	yes	—
660	#95	C₂³×C₁₃₉	1	2	yes	—
661	#95	C₂³×C₁₃₉	1	2	yes	—
662	#95	C₂³×C₁₃₉	1	2	yes	—
663	#95	C₂³×C₁₃₉	1	2	yes	—
664	#95	C₂³×C₁₃₉	1	2	yes	—
665	#95	C₂³×C₁₃₉	1	2	yes	—
666	#95	C₂³×C₁₃₉	1	2	yes	—
667	#95	C₂³×C₁₃₉	1	2	yes	—
668	#95	C₂³×C₁₃₉	1	2	yes	—
669	#95	C₂³×C₁₃₉	1	2	yes	—
670	C₂⁴	—	2	2	no	—
671	C₂⁴	—	4	1	no	—
672	C₂⁴	—	4	1	no	—
673	C₂⁴	—	4	2	no	—
674	C₂⁴	—	4	2	no	—
675	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
676	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
677	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	1	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	#41×C₁₃₉	1	4	yes	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	1	no	—
766	C₂²⋊C₄	—	4	1	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	1	no	—
783	C₄²	—	4	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	8	4	no	—
808	C₂³	—	8	2	no	—
809	C₂³	—	8	4	no	—
810	C₂³	—	8	2	no	—
811	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
812	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
813	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
814	Q₈	—	8	4	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	4	no	—
817	D₄	—	8	4	no	—
818	D₄	—	8	4	no	—
819	D₄	—	8	4	no	—
820	D₄	—	8	4	no	—
821	D₄	—	8	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
867	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
868	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	8	8	no	—
894	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
895	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
896	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
897	C₂²	#585×C₁₃₉	1	1	yes	characteristic
898	C₂²	#585×C₁₃₉	1	2	yes	—
899	C₄	—	2	4	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₂	—	4	2	no	—
915	C₂	—	4	2	no	—
916	C₂	—	8	2	no	—
917	C₂	—	8	2	no	—
918	C₂	#3459×C₁₃₉	1	1	yes	characteristic
919	C₂	#3514×C₁₃₉	1	2	yes	—
920	C₂	#3533×C₁₃₉	1	1	yes	characteristic
921	C₂	#3537×C₁₃₉	1	1	yes	characteristic
922	C₂	#3551×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2669×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. #2850×C₁₃₉	C₂	semidirect
2. #2803×C₁₃₉	C₂	semidirect
3. #2775×C₁₃₉	C₂	semidirect
4. #2749×C₁₃₉	C₂	semidirect
5. #2728×C₁₃₉	C₂	semidirect
6. #2709×C₁₃₉	C₂	semidirect
7. #2697×C₁₃₉	C₂	semidirect
8. #2697×C₁₃₉	C₂	semidirect
9. #2683×C₁₃₉	C₂	semidirect
10. #2681×C₁₃₉	C₂	semidirect
12. #2648×C₁₃₉	C₂	semidirect
13. #2529×C₁₃₉	C₂	semidirect
14. #2518×C₁₃₉	C₂	semidirect
15. #2472×C₁₃₉	C₂	semidirect
16. #2461×C₁₃₉	C₂	semidirect
17. #2328×C₁₃₉	C₂	semidirect
18. #2321×C₁₃₉	C₂	semidirect
19. C₄×#123×C₁₃₉	C₂	semidirect
25. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
33. C₂²×C₄²×C₁₃₉	C₂²	semidirect
34. #400×C₁₃₉	C₂²	semidirect
35. #400×C₁₃₉	C₂²	semidirect
36. #398×C₁₃₉	C₂²	semidirect
41. #397×C₁₃₉	C₂²	semidirect
45. #396×C₁₃₉	C₂²	semidirect
46. #395×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
63. #390×C₁₃₉	C₂²	semidirect
64. #389×C₁₃₉	C₂²	semidirect
65. #389×C₁₃₉	C₂²	semidirect
74. #388×C₁₃₉	C₂²	semidirect
75. #388×C₁₃₉	C₂²	semidirect
76. #388×C₁₃₉	C₂²	semidirect
77. #388×C₁₃₉	C₂²	semidirect
78. #388×C₁₃₉	C₂²	semidirect
79. #387×C₁₃₉	C₂²	semidirect
80. #387×C₁₃₉	C₂²	semidirect
81. #387×C₁₃₉	C₂²	semidirect
90. #386×C₁₃₉	C₂²	semidirect
91. #386×C₁₃₉	C₂²	semidirect
92. #386×C₁₃₉	C₂²	semidirect
94. #385×C₁₃₉	C₂²	semidirect
95. #385×C₁₃₉	C₂²	semidirect
96. #383×C₁₃₉	C₂²	semidirect
97. #382×C₁₃₉	C₂²	semidirect
98. #382×C₁₃₉	C₂²	semidirect
99. #381×C₁₃₉	C₂²	semidirect
102. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
106. #376×C₁₃₉	C₂²	semidirect
461. #37034	C₁₃₉	direct (N × H)
462. C₁₃₉	#37034	direct (N × H)
463. #2850	C₂×C₁₃₉	semidirect
464. #2803	C₂×C₁₃₉	semidirect
465. #2775	C₂×C₁₃₉	semidirect
466. #2749	C₂×C₁₃₉	semidirect
467. #2728	C₂×C₁₃₉	semidirect
468. #2709	C₂×C₁₃₉	semidirect
469. #2697	C₂×C₁₃₉	semidirect
470. #2697	C₂×C₁₃₉	semidirect
471. #2683	C₂×C₁₃₉	semidirect
472. #2681	C₂×C₁₃₉	semidirect
474. #2648	C₂×C₁₃₉	semidirect
475. #2529	C₂×C₁₃₉	semidirect
476. #2518	C₂×C₁₃₉	semidirect
477. #2472	C₂×C₁₃₉	semidirect
478. #2461	C₂×C₁₃₉	semidirect
479. #2328	C₂×C₁₃₉	semidirect
480. #2321	C₂×C₁₃₉	semidirect
481. C₄×#123	C₂×C₁₃₉	semidirect
487. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
488. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
493. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
495. C₂²×C₄²	C₂²×C₁₃₉	semidirect
496. #400	C₂²×C₁₃₉	semidirect
497. #400	C₂²×C₁₃₉	semidirect
498. #398	C₂²×C₁₃₉	semidirect
503. #397	C₂²×C₁₃₉	semidirect
507. #396	C₂²×C₁₃₉	semidirect
508. #395	C₂²×C₁₃₉	semidirect
515. #394	C₂²×C₁₃₉	semidirect
516. #394	C₂²×C₁₃₉	semidirect
520. #391	C₂²×C₁₃₉	semidirect
525. #390	C₂²×C₁₃₉	semidirect
526. #389	C₂²×C₁₃₉	semidirect
527. #389	C₂²×C₁₃₉	semidirect
536. #388	C₂²×C₁₃₉	semidirect
537. #388	C₂²×C₁₃₉	semidirect
538. #388	C₂²×C₁₃₉	semidirect
539. #388	C₂²×C₁₃₉	semidirect
540. #388	C₂²×C₁₃₉	semidirect
541. #387	C₂²×C₁₃₉	semidirect
542. #387	C₂²×C₁₃₉	semidirect
543. #387	C₂²×C₁₃₉	semidirect
552. #386	C₂²×C₁₃₉	semidirect
553. #386	C₂²×C₁₃₉	semidirect
554. #386	C₂²×C₁₃₉	semidirect
556. #385	C₂²×C₁₃₉	semidirect
557. #385	C₂²×C₁₃₉	semidirect
558. #383	C₂²×C₁₃₉	semidirect
559. #382	C₂²×C₁₃₉	semidirect
560. #382	C₂²×C₁₃₉	semidirect
561. #381	C₂²×C₁₃₉	semidirect
564. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
567. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
568. #376	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2850×C₁₃₉	2
#2803×C₁₃₉	2
#2775×C₁₃₉	2
#2749×C₁₃₉	2
#2728×C₁₃₉	2
#2709×C₁₃₉	2
#2697×C₁₃₉	2
#2683×C₁₃₉	2
#2681×C₁₃₉	2
#2669×C₁₃₉	2
#2648×C₁₃₉	2
#2529×C₁₃₉	2
#2518×C₁₃₉	2
#2472×C₁₃₉	2
#2461×C₁₃₉	2
#2328×C₁₃₉	2
#2321×C₁₃₉	2
C₄×#123×C₁₃₉	2
#37034	139

Subgroups — C139×#37034 #48031630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37034 #48031630