Subgroups — C₁₃₉×#37311 #48031907

Order 35584.

1534 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2851×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2802×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2792×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2788×C₁₃₉	C₂	1	2	yes	maximal
6	#2768×C₁₃₉	C₂	1	2	yes	maximal
7	#2755×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2729×C₁₃₉	C₂	1	2	yes	maximal
9	#2720×C₁₃₉	C₂	1	2	yes	maximal
10	#2713×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2571×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2570×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2570×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2551×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#2550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#2314×C₁₃₉	C₂	1	1	yes	maximal, characteristic
22	#2314×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#399×C₁₃₉	C₂²	1	2	yes	—
40	#398×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	#398×C₁₃₉	C₂²	1	2	yes	—
49	#398×C₁₃₉	C₂²	1	2	yes	—
50	#396×C₁₃₉	C₂²	1	2	yes	—
51	#396×C₁₃₉	C₂²	1	2	yes	—
52	#395×C₁₃₉	C₂²	1	2	yes	—
53	#395×C₁₃₉	C₂²	1	2	yes	—
54	#395×C₁₃₉	C₂²	1	2	yes	—
55	#395×C₁₃₉	C₂²	1	2	yes	—
56	#395×C₁₃₉	C₂²	1	2	yes	—
57	#393×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	1	yes	characteristic
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	1	yes	characteristic
71	#389×C₁₃₉	C₂²	1	1	yes	characteristic
72	#389×C₁₃₉	C₂²	1	1	yes	characteristic
73	#389×C₁₃₉	C₂²	1	1	yes	characteristic
74	#389×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
80	#388×C₁₃₉	C₂²	1	2	yes	—
81	#388×C₁₃₉	C₂²	1	2	yes	—
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#387×C₁₃₉	C₂²	1	2	yes	—
85	#387×C₁₃₉	C₂²	1	2	yes	—
86	#387×C₁₃₉	C₂²	1	2	yes	—
87	#387×C₁₃₉	C₂²	1	2	yes	—
88	#387×C₁₃₉	C₂²	1	2	yes	—
89	#387×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#387×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#385×C₁₃₉	C₂²	1	1	yes	characteristic
95	#385×C₁₃₉	C₂²	1	2	yes	—
96	#385×C₁₃₉	C₂²	1	1	yes	characteristic
97	#385×C₁₃₉	C₂²	1	1	yes	characteristic
98	#385×C₁₃₉	C₂²	1	1	yes	characteristic
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#384×C₁₃₉	C₂²	1	2	yes	—
101	#384×C₁₃₉	C₂²	1	1	yes	characteristic
102	#384×C₁₃₉	C₂²	1	1	yes	characteristic
103	#384×C₁₃₉	C₂²	1	1	yes	characteristic
104	#384×C₁₃₉	C₂²	1	1	yes	characteristic
105	#382×C₁₃₉	C₂²	1	2	yes	—
106	#382×C₁₃₉	C₂²	1	1	yes	characteristic
107	#382×C₁₃₉	C₂²	1	1	yes	characteristic
108	#382×C₁₃₉	C₂²	1	1	yes	characteristic
109	#382×C₁₃₉	C₂²	1	1	yes	characteristic
110	#380×C₁₃₉	C₂²	1	2	yes	—
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	#380×C₁₃₉	C₂²	1	1	yes	characteristic
113	#380×C₁₃₉	C₂²	1	1	yes	characteristic
114	#380×C₁₃₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
120	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
121	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
122	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
129	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
130	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
131	#125×C₁₃₉	—	4	2	no	—
132	#125×C₁₃₉	—	4	2	no	—
133	#125×C₁₃₉	—	4	4	no	—
134	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
135	#117×C₁₃₉	—	4	2	no	—
136	#117×C₁₃₉	Q₈	1	8	yes	complemented
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
163	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃₉	—	4	2	no	—
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
195	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	1	yes	characteristic
202	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	#95×C₁₃₉	C₂³	1	2	yes	—
214	#95×C₁₃₉	C₂³	1	2	yes	—
215	#95×C₁₃₉	C₂³	1	2	yes	—
216	#95×C₁₃₉	C₂³	1	1	yes	characteristic
217	#95×C₁₃₉	C₂³	1	1	yes	characteristic
218	#95×C₁₃₉	C₂³	1	1	yes	characteristic
219	#95×C₁₃₉	C₂³	1	1	yes	characteristic
220	#95×C₁₃₉	C₂³	1	2	yes	—
221	#95×C₁₃₉	C₂³	1	2	yes	—
222	#95×C₁₃₉	C₂³	1	2	yes	—
223	#95×C₁₃₉	C₂³	1	2	yes	—
224	#95×C₁₃₉	C₂³	1	2	yes	—
225	#95×C₁₃₉	C₂³	1	2	yes	—
226	#95×C₁₃₉	C₂³	1	2	yes	—
227	#95×C₁₃₉	C₂³	1	2	yes	—
228	#95×C₁₃₉	C₂³	1	2	yes	—
229	#95×C₁₃₉	C₂³	1	1	yes	characteristic
230	#95×C₁₃₉	C₂³	1	1	yes	characteristic
231	#95×C₁₃₉	C₂³	1	2	yes	—
232	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂×Q₈×C₁₃₉	—	2	4	no	—
234	C₂×Q₈×C₁₃₉	—	4	2	no	—
235	C₂×Q₈×C₁₃₉	—	4	2	no	—
236	C₂×Q₈×C₁₃₉	—	4	2	no	—
237	C₂×Q₈×C₁₃₉	—	4	2	no	—
238	C₂×Q₈×C₁₃₉	—	4	2	no	—
239	C₂²×C₄×C₁₃₉	—	2	2	no	—
240	C₂²×C₄×C₁₃₉	—	2	2	no	—
241	C₂²×C₄×C₁₃₉	—	2	2	no	—
242	C₂²×C₄×C₁₃₉	—	2	2	no	—
243	C₂²×C₄×C₁₃₉	—	4	1	no	—
244	C₂²×C₄×C₁₃₉	—	4	1	no	—
245	C₂²×C₄×C₁₃₉	—	4	1	no	—
246	C₂²×C₄×C₁₃₉	—	4	1	no	—
247	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	2	no	—
272	C₄⋊C₄×C₁₃₉	—	2	2	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	2	no	—
275	C₄⋊C₄×C₁₃₉	—	2	2	no	—
276	C₄⋊C₄×C₁₃₉	—	2	2	no	—
277	C₄⋊C₄×C₁₃₉	—	2	2	no	—
278	C₄⋊C₄×C₁₃₉	—	2	2	no	—
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	2	4	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	2	no	—
283	C₄⋊C₄×C₁₃₉	—	2	2	no	—
284	C₄⋊C₄×C₁₃₉	—	2	2	no	—
285	C₄⋊C₄×C₁₃₉	—	4	1	no	—
286	C₄⋊C₄×C₁₃₉	—	4	1	no	—
287	C₄⋊C₄×C₁₃₉	—	4	2	no	—
288	C₄⋊C₄×C₁₃₉	—	4	2	no	—
289	C₄⋊C₄×C₁₃₉	—	4	1	no	—
290	C₄⋊C₄×C₁₃₉	—	4	1	no	—
291	C₄⋊C₄×C₁₃₉	—	4	2	no	—
292	C₄⋊C₄×C₁₃₉	—	4	2	no	—
293	C₄⋊C₄×C₁₃₉	—	4	2	no	—
294	C₄⋊C₄×C₁₃₉	—	4	2	no	—
295	C₄⋊C₄×C₁₃₉	—	4	1	no	—
296	C₄⋊C₄×C₁₃₉	—	4	1	no	—
297	C₄⋊C₄×C₁₃₉	—	4	2	no	—
298	C₄⋊C₄×C₁₃₉	—	4	2	no	—
299	C₄⋊C₄×C₁₃₉	—	4	2	no	—
300	C₄⋊C₄×C₁₃₉	—	4	2	no	—
301	C₄⋊C₄×C₁₃₉	—	4	2	no	—
302	C₄⋊C₄×C₁₃₉	—	4	2	no	—
303	C₄⋊C₄×C₁₃₉	—	4	2	no	—
304	C₄⋊C₄×C₁₃₉	—	4	2	no	—
305	C₄⋊C₄×C₁₃₉	—	4	2	no	—
306	C₄⋊C₄×C₁₃₉	—	4	2	no	—
307	C₄⋊C₄×C₁₃₉	—	4	2	no	—
308	C₄⋊C₄×C₁₃₉	—	4	2	no	—
309	C₄⋊C₄×C₁₃₉	—	4	2	no	—
310	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
311	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
312	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
314	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
315	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
316	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
318	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
319	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
320	C₄²×C₁₃₉	—	2	2	no	—
321	C₄²×C₁₃₉	—	2	2	no	—
322	C₄²×C₁₃₉	—	2	2	no	—
323	C₄²×C₁₃₉	—	2	2	no	—
324	C₄²×C₁₃₉	—	4	1	no	—
325	C₄²×C₁₃₉	—	4	1	no	—
326	C₄²×C₁₃₉	—	4	2	no	—
327	C₄²×C₁₃₉	—	4	2	no	—
328	C₄²×C₁₃₉	—	4	2	no	—
329	C₄²×C₁₃₉	—	4	2	no	—
330	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
331	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
332	C₂³×C₁₃₉	—	2	1	no	—
333	C₂³×C₁₃₉	—	2	1	no	—
334	C₂³×C₁₃₉	—	2	1	no	—
335	C₂³×C₁₃₉	—	2	1	no	—
336	C₂³×C₁₃₉	—	2	1	no	—
337	C₂³×C₁₃₉	—	2	1	no	—
338	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
339	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
340	Q₈×C₁₃₉	—	8	4	no	—
341	Q₈×C₁₃₉	—	8	4	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	1	no	—
353	C₂×C₄×C₁₃₉	—	2	1	no	—
354	C₂×C₄×C₁₃₉	—	2	1	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	8	no	—
357	C₂×C₄×C₁₃₉	—	2	1	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	1	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	1	no	—
362	C₂×C₄×C₁₃₉	—	2	1	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	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	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	1	no	—
376	C₂×C₄×C₁₃₉	—	2	1	no	—
377	C₂×C₄×C₁₃₉	—	2	1	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	—	2	2	no	—
384	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
392	C₂×C₄×C₁₃₉	—	2	1	no	—
393	C₂×C₄×C₁₃₉	—	2	1	no	—
394	C₂×C₄×C₁₃₉	—	2	2	no	—
395	C₂×C₄×C₁₃₉	—	2	1	no	—
396	C₂×C₄×C₁₃₉	—	2	1	no	—
397	C₂×C₄×C₁₃₉	—	2	1	no	—
398	C₂×C₄×C₁₃₉	—	2	2	no	—
399	C₂×C₄×C₁₃₉	—	4	4	no	—
400	C₂×C₄×C₁₃₉	—	4	4	no	—
401	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
402	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
403	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
404	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
405	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
406	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
407	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
409	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
410	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
411	C₂²×C₁₃₉	—	2	2	no	—
412	C₂²×C₁₃₉	—	2	2	no	—
413	C₂²×C₁₃₉	—	2	2	no	—
414	C₂²×C₁₃₉	—	4	1	no	—
415	C₂²×C₁₃₉	—	4	1	no	—
416	C₂²×C₁₃₉	—	4	1	no	—
417	C₂²×C₁₃₉	—	4	1	no	—
418	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
419	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂²×C₁₃₉	#585	1	1	yes	characteristic
424	C₂²×C₁₃₉	#585	1	1	yes	characteristic
425	C₄×C₁₃₉	—	2	2	no	—
426	C₄×C₁₃₉	—	2	2	no	—
427	C₄×C₁₃₉	—	2	2	no	—
428	C₄×C₁₃₉	—	2	2	no	—
429	C₄×C₁₃₉	—	2	2	no	—
430	C₄×C₁₃₉	—	2	2	no	—
431	C₄×C₁₃₉	—	2	2	no	—
432	C₄×C₁₃₉	—	4	1	no	—
433	C₄×C₁₃₉	—	4	1	no	—
434	C₄×C₁₃₉	—	4	2	no	—
435	C₄×C₁₃₉	—	4	1	no	—
436	C₄×C₁₃₉	—	4	1	no	—
437	C₄×C₁₃₉	—	4	1	no	—
438	C₄×C₁₃₉	—	4	2	no	—
439	C₄×C₁₃₉	—	4	2	no	—
440	C₄×C₁₃₉	—	4	1	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	2	no	—
443	C₄×C₁₃₉	—	4	2	no	—
444	C₄×C₁₃₉	—	4	2	no	—
445	C₄×C₁₃₉	—	4	2	no	—
446	C₄×C₁₃₉	#544	1	4	yes	—
447	C₂×C₁₃₉	—	4	2	no	—
448	C₂×C₁₃₉	C₂×#544	1	1	yes	characteristic
449	C₂×C₁₃₉	#3503	1	1	yes	characteristic
450	C₂×C₁₃₉	#3504	1	1	yes	characteristic
451	C₂×C₁₃₉	#3541	1	1	yes	characteristic
452	C₂×C₁₃₉	#3542	1	1	yes	characteristic
453	C₂×C₁₃₉	#3554	1	1	yes	characteristic
454	C₂×C₁₃₉	#3555	1	1	yes	characteristic
455	#37311	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₁₃₉	#37311	1	1	yes	characteristic, direct product factor, Sylow
457	#2857	C₂×C₁₃₉	1	1	yes	characteristic
458	#2851	C₂×C₁₃₉	1	1	yes	characteristic
459	#2802	C₂×C₁₃₉	1	2	yes	complemented
460	#2792	C₂×C₁₃₉	1	2	yes	complemented
461	#2788	C₂×C₁₃₉	1	2	yes	—
462	#2768	C₂×C₁₃₉	1	2	yes	—
463	#2755	C₂×C₁₃₉	1	2	yes	complemented
464	#2729	C₂×C₁₃₉	1	2	yes	—
465	#2720	C₂×C₁₃₉	1	2	yes	—
466	#2713	C₂×C₁₃₉	1	2	yes	complemented
467	#2629	C₂×C₁₃₉	1	1	yes	characteristic
468	#2628	C₂×C₁₃₉	1	1	yes	characteristic
469	#2571	C₂×C₁₃₉	1	1	yes	characteristic, complemented
470	#2570	C₂×C₁₃₉	1	1	yes	characteristic, complemented
471	#2570	C₂×C₁₃₉	1	1	yes	characteristic, complemented
472	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
473	#2552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2551	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
476	#2550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	#2314	C₂×C₁₃₉	1	1	yes	characteristic
478	#2314	C₂×C₁₃₉	1	1	yes	characteristic
479	#2296	C₂×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
483	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
486	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
487	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
488	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
490	#400	C₂²×C₁₃₉	1	2	yes	—
491	#400	C₂²×C₁₃₉	1	2	yes	—
492	#400	C₂²×C₁₃₉	1	2	yes	—
493	#400	C₂²×C₁₃₉	1	2	yes	—
494	#400	C₂²×C₁₃₉	1	2	yes	—
495	#399	C₂²×C₁₃₉	1	2	yes	—
496	#398	C₂²×C₁₃₉	1	2	yes	—
497	#398	C₂²×C₁₃₉	1	2	yes	—
498	#398	C₂²×C₁₃₉	1	2	yes	—
499	#398	C₂²×C₁₃₉	1	2	yes	—
500	#398	C₂²×C₁₃₉	1	2	yes	—
501	#398	C₂²×C₁₃₉	1	2	yes	—
502	#398	C₂²×C₁₃₉	1	2	yes	—
503	#398	C₂²×C₁₃₉	1	2	yes	—
504	#398	C₂²×C₁₃₉	1	2	yes	—
505	#398	C₂²×C₁₃₉	1	2	yes	—
506	#396	C₂²×C₁₃₉	1	2	yes	—
507	#396	C₂²×C₁₃₉	1	2	yes	—
508	#395	C₂²×C₁₃₉	1	2	yes	—
509	#395	C₂²×C₁₃₉	1	2	yes	—
510	#395	C₂²×C₁₃₉	1	2	yes	—
511	#395	C₂²×C₁₃₉	1	2	yes	—
512	#395	C₂²×C₁₃₉	1	2	yes	—
513	#393	C₂²×C₁₃₉	1	2	yes	—
514	#391	C₂²×C₁₃₉	1	2	yes	—
515	#391	C₂²×C₁₃₉	1	2	yes	—
516	#391	C₂²×C₁₃₉	1	2	yes	—
517	#389	C₂²×C₁₃₉	1	1	yes	characteristic
518	#389	C₂²×C₁₃₉	1	1	yes	characteristic
519	#389	C₂²×C₁₃₉	1	1	yes	characteristic
520	#389	C₂²×C₁₃₉	1	1	yes	characteristic
521	#389	C₂²×C₁₃₉	1	1	yes	characteristic
522	#389	C₂²×C₁₃₉	1	1	yes	characteristic
523	#389	C₂²×C₁₃₉	1	2	yes	—
524	#389	C₂²×C₁₃₉	1	1	yes	characteristic
525	#389	C₂²×C₁₃₉	1	2	yes	—
526	#389	C₂²×C₁₃₉	1	1	yes	characteristic
527	#389	C₂²×C₁₃₉	1	1	yes	characteristic
528	#389	C₂²×C₁₃₉	1	2	yes	—
529	#389	C₂²×C₁₃₉	1	1	yes	characteristic
530	#389	C₂²×C₁₃₉	1	2	yes	—
531	#389	C₂²×C₁₃₉	1	2	yes	—
532	#389	C₂²×C₁₃₉	1	2	yes	—
533	#389	C₂²×C₁₃₉	1	2	yes	—
534	#389	C₂²×C₁₃₉	1	1	yes	characteristic
535	#389	C₂²×C₁₃₉	1	1	yes	characteristic
536	#388	C₂²×C₁₃₉	1	2	yes	—
537	#388	C₂²×C₁₃₉	1	2	yes	—
538	#388	C₂²×C₁₃₉	1	2	yes	—
539	#388	C₂²×C₁₃₉	1	2	yes	—
540	#387	C₂²×C₁₃₉	1	2	yes	—
541	#387	C₂²×C₁₃₉	1	2	yes	—
542	#387	C₂²×C₁₃₉	1	2	yes	—
543	#387	C₂²×C₁₃₉	1	2	yes	—
544	#387	C₂²×C₁₃₉	1	2	yes	—
545	#387	C₂²×C₁₃₉	1	2	yes	—
546	#387	C₂²×C₁₃₉	1	2	yes	—
547	#387	C₂²×C₁₃₉	1	2	yes	—
548	#387	C₂²×C₁₃₉	1	2	yes	—
549	#387	C₂²×C₁₃₉	1	2	yes	—
550	#385	C₂²×C₁₃₉	1	2	yes	—
551	#385	C₂²×C₁₃₉	1	2	yes	—
552	#385	C₂²×C₁₃₉	1	1	yes	characteristic
553	#385	C₂²×C₁₃₉	1	1	yes	characteristic
554	#385	C₂²×C₁₃₉	1	1	yes	characteristic
555	#385	C₂²×C₁₃₉	1	1	yes	characteristic
556	#384	C₂²×C₁₃₉	1	1	yes	characteristic
557	#384	C₂²×C₁₃₉	1	1	yes	characteristic
558	#384	C₂²×C₁₃₉	1	1	yes	characteristic
559	#384	C₂²×C₁₃₉	1	1	yes	characteristic
560	#384	C₂²×C₁₃₉	1	2	yes	—
561	#382	C₂²×C₁₃₉	1	1	yes	characteristic
562	#382	C₂²×C₁₃₉	1	1	yes	characteristic
563	#382	C₂²×C₁₃₉	1	1	yes	characteristic
564	#382	C₂²×C₁₃₉	1	1	yes	characteristic
565	#382	C₂²×C₁₃₉	1	2	yes	—
566	#380	C₂²×C₁₃₉	1	1	yes	characteristic
567	#380	C₂²×C₁₃₉	1	1	yes	characteristic
568	#380	C₂²×C₁₃₉	1	1	yes	characteristic
569	#380	C₂²×C₁₃₉	1	1	yes	characteristic
570	#380	C₂²×C₁₃₉	1	2	yes	—
571	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
579	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
580	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
581	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₄⋊Q₈	—	4	2	no	—
585	C₄⋊Q₈	—	4	2	no	—
586	C₄⋊Q₈	—	4	4	no	—
587	#125	—	4	2	no	—
588	#125	—	4	2	no	—
589	#125	—	4	4	no	—
590	C₂²⋊Q₈	—	4	4	no	—
591	#117	—	4	2	no	—
592	#117	Q₈×C₁₃₉	1	8	yes	complemented
593	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	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	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₄²	—	4	2	no	—
644	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
650	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
656	#95	C₂³×C₁₃₉	1	1	yes	characteristic
657	#95	C₂³×C₁₃₉	1	1	yes	characteristic
658	#95	C₂³×C₁₃₉	1	1	yes	characteristic
659	#95	C₂³×C₁₃₉	1	1	yes	characteristic
660	#95	C₂³×C₁₃₉	1	1	yes	characteristic
661	#95	C₂³×C₁₃₉	1	1	yes	characteristic
662	#95	C₂³×C₁₃₉	1	1	yes	characteristic
663	#95	C₂³×C₁₃₉	1	1	yes	characteristic
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	#95	C₂³×C₁₃₉	1	2	yes	—
671	#95	C₂³×C₁₃₉	1	2	yes	—
672	#95	C₂³×C₁₃₉	1	2	yes	—
673	#95	C₂³×C₁₃₉	1	2	yes	—
674	#95	C₂³×C₁₃₉	1	2	yes	—
675	#95	C₂³×C₁₃₉	1	2	yes	—
676	#95	C₂³×C₁₃₉	1	2	yes	—
677	#95	C₂³×C₁₃₉	1	2	yes	—
678	#95	C₂³×C₁₃₉	1	2	yes	—
679	#95	C₂³×C₁₃₉	1	2	yes	—
680	#95	C₂³×C₁₃₉	1	2	yes	—
681	#95	C₂³×C₁₃₉	1	2	yes	—
682	#95	C₂³×C₁₃₉	1	2	yes	—
683	#95	C₂³×C₁₃₉	1	2	yes	—
684	#95	C₂³×C₁₃₉	1	2	yes	—
685	#95	C₂³×C₁₃₉	1	2	yes	—
686	#95	C₂³×C₁₃₉	1	2	yes	—
687	#95	C₂³×C₁₃₉	1	2	yes	—
688	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	—	4	2	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	—	4	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	1	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	1	no	—
752	C₄⋊C₄	—	4	1	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
767	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	1	no	—
771	C₂²⋊C₄	—	4	1	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
775	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	4	1	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
787	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
795	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
796	Q₈	—	8	4	no	—
797	Q₈	—	8	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	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	—	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	1	no	—
831	C₂×C₄	—	2	1	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	1	no	—
841	C₂×C₄	—	2	2	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	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
858	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
859	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
860	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
861	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
862	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
863	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
864	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
865	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
866	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
875	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
876	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
877	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
878	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
879	C₂²	#585×C₁₃₉	1	1	yes	characteristic
880	C₂²	#585×C₁₃₉	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	#544×C₁₃₉	1	4	yes	—
903	C₂	—	4	2	no	—
904	C₂	C₂×#544×C₁₃₉	1	1	yes	characteristic
905	C₂	#3503×C₁₃₉	1	1	yes	characteristic
906	C₂	#3504×C₁₃₉	1	1	yes	characteristic
907	C₂	#3541×C₁₃₉	1	1	yes	characteristic
908	C₂	#3542×C₁₃₉	1	1	yes	characteristic
909	C₂	#3554×C₁₃₉	1	1	yes	characteristic
910	C₂	#3555×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
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
3. #2802×C₁₃₉	C₂	semidirect
4. #2792×C₁₃₉	C₂	semidirect
7. #2755×C₁₃₉	C₂	semidirect
10. #2713×C₁₃₉	C₂	semidirect
13. #2571×C₁₃₉	C₂	semidirect
14. #2570×C₁₃₉	C₂	semidirect
15. #2570×C₁₃₉	C₂	semidirect
16. #2552×C₁₃₉	C₂	semidirect
17. #2552×C₁₃₉	C₂	semidirect
18. #2551×C₁₃₉	C₂	semidirect
19. #2550×C₁₃₉	C₂	semidirect
20. #2550×C₁₃₉	C₂	semidirect
136. #117×C₁₃₉	Q₈	semidirect
455. #37311	C₁₃₉	direct (N × H)
456. C₁₃₉	#37311	direct (N × H)
459. #2802	C₂×C₁₃₉	semidirect
460. #2792	C₂×C₁₃₉	semidirect
463. #2755	C₂×C₁₃₉	semidirect
466. #2713	C₂×C₁₃₉	semidirect
469. #2571	C₂×C₁₃₉	semidirect
470. #2570	C₂×C₁₃₉	semidirect
471. #2570	C₂×C₁₃₉	semidirect
472. #2552	C₂×C₁₃₉	semidirect
473. #2552	C₂×C₁₃₉	semidirect
474. #2551	C₂×C₁₃₉	semidirect
475. #2550	C₂×C₁₃₉	semidirect
476. #2550	C₂×C₁₃₉	semidirect
592. #117	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2857×C₁₃₉	2
#2851×C₁₃₉	2
#2802×C₁₃₉	2
#2792×C₁₃₉	2
#2788×C₁₃₉	2
#2768×C₁₃₉	2
#2755×C₁₃₉	2
#2729×C₁₃₉	2
#2720×C₁₃₉	2
#2713×C₁₃₉	2
#2629×C₁₃₉	2
#2628×C₁₃₉	2
#2571×C₁₃₉	2
#2570×C₁₃₉	2
#2552×C₁₃₉	2
#2551×C₁₃₉	2
#2550×C₁₃₉	2
#2314×C₁₃₉	2
#2296×C₁₃₉	2
#37311	139

Subgroups — C139×#37311 #48031907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37311 #48031907