Subgroups — C₁₃₉×#36189 #48030785

Order 35584.

1918 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2570×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2511×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2507×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2497×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2487×C₁₃₉	C₂	1	2	yes	maximal
9	#2442×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2441×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2423×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2417×C₁₃₉	C₂	1	2	yes	maximal
13	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2352×C₁₃₉	C₂	1	2	yes	maximal
15	#2345×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
34	#400×C₁₃₉	C₂²	1	4	yes	—
35	#400×C₁₃₉	C₂²	1	4	yes	—
36	#399×C₁₃₉	C₂²	1	4	yes	—
37	#398×C₁₃₉	C₂²	1	4	yes	—
38	#398×C₁₃₉	C₂²	1	4	yes	—
39	#396×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#391×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#389×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#387×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#386×C₁₃₉	C₂²	1	4	yes	—
60	#385×C₁₃₉	C₂²	1	4	yes	—
61	#384×C₁₃₉	C₂²	1	2	yes	—
62	#384×C₁₃₉	C₂²	1	1	yes	characteristic
63	#384×C₁₃₉	C₂²	1	2	yes	—
64	#384×C₁₃₉	C₂²	1	1	yes	characteristic
65	#384×C₁₃₉	C₂²	1	2	yes	—
66	#384×C₁₃₉	C₂²	1	1	yes	characteristic
67	#382×C₁₃₉	C₂²	1	2	yes	—
68	#382×C₁₃₉	C₂²	1	2	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	4	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
90	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
101	#125×C₁₃₉	—	4	4	no	—
102	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
103	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
104	C₄×Q₈×C₁₃₉	—	4	4	no	—
105	C₄×D₄×C₁₃₉	—	2	4	no	—
106	C₄×D₄×C₁₃₉	—	2	4	no	—
107	C₄×D₄×C₁₃₉	Q₈	1	8	yes	complemented
108	#117×C₁₃₉	—	4	4	no	—
109	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
110	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
111	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₉	—	2	4	no	—
144	C₂×C₄²×C₁₃₉	—	2	4	no	—
145	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	1	yes	characteristic
162	#95×C₁₃₉	C₂³	1	4	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	1	yes	characteristic
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	1	yes	characteristic
171	#95×C₁₃₉	C₂³	1	1	yes	characteristic
172	#95×C₁₃₉	C₂³	1	1	yes	characteristic
173	#95×C₁₃₉	C₂³	1	1	yes	characteristic
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	2	4	no	—
181	C₂×D₄×C₁₃₉	—	2	2	no	—
182	C₂×D₄×C₁₃₉	—	2	2	no	—
183	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
184	C₂²×C₄×C₁₃₉	—	2	2	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	2	no	—
191	C₂²×C₄×C₁₃₉	—	2	2	no	—
192	C₂²×C₄×C₁₃₉	—	2	8	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	2	no	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	4	4	no	—
200	C₂²×C₄×C₁₃₉	—	4	4	no	—
201	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
202	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
203	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
204	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₁₃₉	—	2	8	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	8	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	4	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	4	4	no	—
238	C₄⋊C₄×C₁₃₉	—	4	4	no	—
239	C₄⋊C₄×C₁₃₉	—	4	4	no	—
240	C₄⋊C₄×C₁₃₉	—	4	4	no	—
241	C₄⋊C₄×C₁₃₉	—	4	4	no	—
242	C₄⋊C₄×C₁₃₉	—	4	4	no	—
243	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
244	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
252	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
253	C₄²×C₁₃₉	—	2	2	no	—
254	C₄²×C₁₃₉	—	2	2	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	—	2	2	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	2	2	no	—
259	C₄²×C₁₃₉	—	2	2	no	—
260	C₄²×C₁₃₉	—	2	2	no	—
261	C₄²×C₁₃₉	—	2	2	no	—
262	C₄²×C₁₃₉	—	2	2	no	—
263	C₄²×C₁₃₉	—	2	2	no	—
264	C₄²×C₁₃₉	—	4	4	no	—
265	C₄²×C₁₃₉	—	4	4	no	—
266	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
267	C₄²×C₁₃₉	#41	1	4	yes	—
268	C₂³×C₁₃₉	—	2	1	no	—
269	C₂³×C₁₃₉	—	2	1	no	—
270	C₂³×C₁₃₉	—	2	1	no	—
271	C₂³×C₁₃₉	—	2	1	no	—
272	C₂³×C₁₃₉	—	2	1	no	—
273	C₂³×C₁₃₉	—	2	1	no	—
274	C₂³×C₁₃₉	—	2	1	no	—
275	C₂³×C₁₃₉	—	2	1	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	1	no	—
278	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
279	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
280	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
281	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
282	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
283	Q₈×C₁₃₉	—	4	8	no	—
284	D₄×C₁₃₉	—	2	8	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	1	no	—
289	C₂×C₄×C₁₃₉	—	2	1	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	1	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	1	no	—
297	C₂×C₄×C₁₃₉	—	2	8	no	—
298	C₂×C₄×C₁₃₉	—	2	8	no	—
299	C₂×C₄×C₁₃₉	—	2	8	no	—
300	C₂×C₄×C₁₃₉	—	2	8	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	4	no	—
311	C₂×C₄×C₁₃₉	—	2	4	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	4	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	2	4	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	4	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	4	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	4	4	no	—
326	C₂×C₄×C₁₃₉	—	4	4	no	—
327	C₂×C₄×C₁₃₉	—	8	8	no	—
328	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
329	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
330	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
331	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
332	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
333	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
334	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
335	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
336	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
341	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
342	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
343	C₂²×C₁₃₉	—	2	2	no	—
344	C₂²×C₁₃₉	—	2	2	no	—
345	C₂²×C₁₃₉	—	2	2	no	—
346	C₂²×C₁₃₉	—	2	2	no	—
347	C₂²×C₁₃₉	—	2	2	no	—
348	C₂²×C₁₃₉	—	2	2	no	—
349	C₂²×C₁₃₉	—	2	2	no	—
350	C₂²×C₁₃₉	—	2	2	no	—
351	C₂²×C₁₃₉	—	2	2	no	—
352	C₂²×C₁₃₉	—	4	1	no	—
353	C₂²×C₁₃₉	—	4	1	no	—
354	C₂²×C₁₃₉	—	4	1	no	—
355	C₂²×C₁₃₉	—	4	1	no	—
356	C₂²×C₁₃₉	#533	1	4	yes	—
357	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
358	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	C₄×C₁₃₉	—	2	2	no	—
365	C₄×C₁₃₉	—	2	2	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	—	4	1	no	—
371	C₄×C₁₃₉	—	4	1	no	—
372	C₄×C₁₃₉	—	4	4	no	—
373	C₄×C₁₃₉	—	4	1	no	—
374	C₄×C₁₃₉	—	4	4	no	—
375	C₄×C₁₃₉	—	4	4	no	—
376	C₄×C₁₃₉	—	4	1	no	—
377	C₄×C₁₃₉	—	4	4	no	—
378	C₄×C₁₃₉	#552	1	4	yes	—
379	C₄×C₁₃₉	#553	1	4	yes	—
380	C₄×C₁₃₉	#554	1	4	yes	—
381	C₂×C₁₃₉	—	2	4	no	—
382	C₂×C₁₃₉	—	4	2	no	—
383	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
384	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
385	C₂×C₁₃₉	C₂×#553	1	1	yes	characteristic
386	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
387	C₂×C₁₃₉	#3503	1	1	yes	characteristic
388	C₂×C₁₃₉	#3508	1	1	yes	characteristic
389	C₂×C₁₃₉	#3511	1	1	yes	characteristic
390	#36189	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₁₃₉	#36189	1	1	yes	characteristic, direct product factor, Sylow
392	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2570	C₂×C₁₃₉	1	2	yes	complemented
396	#2511	C₂×C₁₃₉	1	2	yes	complemented
397	#2507	C₂×C₁₃₉	1	2	yes	complemented
398	#2497	C₂×C₁₃₉	1	2	yes	complemented
399	#2487	C₂×C₁₃₉	1	2	yes	—
400	#2442	C₂×C₁₃₉	1	2	yes	complemented
401	#2441	C₂×C₁₃₉	1	2	yes	complemented
402	#2423	C₂×C₁₃₉	1	2	yes	complemented
403	#2417	C₂×C₁₃₉	1	2	yes	—
404	#2360	C₂×C₁₃₉	1	2	yes	complemented
405	#2352	C₂×C₁₃₉	1	2	yes	—
406	#2345	C₂×C₁₃₉	1	2	yes	complemented
407	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
411	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
415	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
420	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
421	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
422	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
423	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
425	#400	C₂²×C₁₃₉	1	4	yes	—
426	#400	C₂²×C₁₃₉	1	4	yes	—
427	#399	C₂²×C₁₃₉	1	4	yes	—
428	#398	C₂²×C₁₃₉	1	4	yes	—
429	#398	C₂²×C₁₃₉	1	4	yes	—
430	#396	C₂²×C₁₃₉	1	4	yes	—
431	#391	C₂²×C₁₃₉	1	2	yes	—
432	#391	C₂²×C₁₃₉	1	2	yes	—
433	#391	C₂²×C₁₃₉	1	2	yes	—
434	#389	C₂²×C₁₃₉	1	2	yes	—
435	#389	C₂²×C₁₃₉	1	2	yes	—
436	#389	C₂²×C₁₃₉	1	2	yes	—
437	#389	C₂²×C₁₃₉	1	2	yes	—
438	#389	C₂²×C₁₃₉	1	2	yes	—
439	#389	C₂²×C₁₃₉	1	2	yes	—
440	#389	C₂²×C₁₃₉	1	2	yes	—
441	#389	C₂²×C₁₃₉	1	2	yes	—
442	#389	C₂²×C₁₃₉	1	2	yes	—
443	#389	C₂²×C₁₃₉	1	2	yes	—
444	#389	C₂²×C₁₃₉	1	4	yes	—
445	#388	C₂²×C₁₃₉	1	4	yes	—
446	#387	C₂²×C₁₃₉	1	4	yes	—
447	#387	C₂²×C₁₃₉	1	4	yes	—
448	#387	C₂²×C₁₃₉	1	4	yes	—
449	#387	C₂²×C₁₃₉	1	4	yes	—
450	#386	C₂²×C₁₃₉	1	4	yes	—
451	#385	C₂²×C₁₃₉	1	4	yes	—
452	#384	C₂²×C₁₃₉	1	1	yes	characteristic
453	#384	C₂²×C₁₃₉	1	2	yes	—
454	#384	C₂²×C₁₃₉	1	1	yes	characteristic
455	#384	C₂²×C₁₃₉	1	1	yes	characteristic
456	#384	C₂²×C₁₃₉	1	2	yes	—
457	#384	C₂²×C₁₃₉	1	2	yes	—
458	#382	C₂²×C₁₃₉	1	2	yes	—
459	#382	C₂²×C₁₃₉	1	2	yes	—
460	#380	C₂²×C₁₃₉	1	2	yes	—
461	#380	C₂²×C₁₃₉	1	4	yes	—
462	#380	C₂²×C₁₃₉	1	2	yes	—
463	#380	C₂²×C₁₃₉	1	2	yes	—
464	#380	C₂²×C₁₃₉	1	2	yes	—
465	#380	C₂²×C₁₃₉	1	2	yes	—
466	#380	C₂²×C₁₃₉	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
476	C₄×C₂²⋊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	1	yes	characteristic
480	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
483	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₄⋊Q₈	—	2	4	no	—
492	#125	—	4	4	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	C₂²⋊Q₈	—	4	4	no	—
495	C₄×Q₈	—	4	4	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	Q₈×C₁₃₉	1	8	yes	complemented
499	#117	—	4	4	no	—
500	C₂×C₄⋊C₄	—	2	8	no	—
501	C₂×C₄⋊C₄	—	4	4	no	—
502	C₂×C₄⋊C₄	—	4	4	no	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₄²	—	2	4	no	—
535	C₂×C₄²	—	2	4	no	—
536	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
549	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
551	#95	C₂³×C₁₃₉	1	1	yes	characteristic
552	#95	C₂³×C₁₃₉	1	1	yes	characteristic
553	#95	C₂³×C₁₃₉	1	1	yes	characteristic
554	#95	C₂³×C₁₃₉	1	1	yes	characteristic
555	#95	C₂³×C₁₃₉	1	1	yes	characteristic
556	#95	C₂³×C₁₃₉	1	1	yes	characteristic
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	#95	C₂³×C₁₃₉	1	4	yes	—
559	#95	C₂³×C₁₃₉	1	4	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	4	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	8	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
593	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
594	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
595	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	8	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	4	4	no	—
629	C₄⋊C₄	—	4	4	no	—
630	C₄⋊C₄	—	4	4	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	—	4	4	no	—
634	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
643	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	4	4	no	—
656	C₄²	—	4	4	no	—
657	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
658	C₄²	#41×C₁₃₉	1	4	yes	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
670	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
671	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
672	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
673	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
674	Q₈	—	4	8	no	—
675	D₄	—	2	8	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	8	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	8	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	8	no	—
719	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
720	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
721	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
722	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
723	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
724	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
725	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
726	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
727	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
728	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
729	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
730	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
731	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
732	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
733	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	#533×C₁₃₉	1	4	yes	—
748	C₂²	C₂³×Q₈×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	C₂²×#41×C₁₃₉	1	1	yes	characteristic
752	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
753	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
754	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	4	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	4	no	—
769	C₄	#552×C₁₃₉	1	4	yes	—
770	C₄	#553×C₁₃₉	1	4	yes	—
771	C₄	#554×C₁₃₉	1	4	yes	—
772	C₂	—	2	4	no	—
773	C₂	—	4	2	no	—
774	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
775	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic
776	C₂	C₂×#553×C₁₃₉	1	1	yes	characteristic
777	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
778	C₂	#3503×C₁₃₉	1	1	yes	characteristic
779	C₂	#3508×C₁₃₉	1	1	yes	characteristic
780	C₂	#3511×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2859×C₁₃₉	C₂	semidirect
2. #2857×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2570×C₁₃₉	C₂	semidirect
5. #2511×C₁₃₉	C₂	semidirect
6. #2507×C₁₃₉	C₂	semidirect
7. #2497×C₁₃₉	C₂	semidirect
9. #2442×C₁₃₉	C₂	semidirect
10. #2441×C₁₃₉	C₂	semidirect
11. #2423×C₁₃₉	C₂	semidirect
13. #2360×C₁₃₉	C₂	semidirect
15. #2345×C₁₃₉	C₂	semidirect
16. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
17. #2285×C₁₃₉	C₂	semidirect
18. C₂×#384×C₁₃₉	C₂	semidirect
107. C₄×D₄×C₁₃₉	Q₈	semidirect
390. #36189	C₁₃₉	direct (N × H)
391. C₁₃₉	#36189	direct (N × H)
392. #2859	C₂×C₁₃₉	semidirect
393. #2857	C₂×C₁₃₉	semidirect
394. #2857	C₂×C₁₃₉	semidirect
395. #2570	C₂×C₁₃₉	semidirect
396. #2511	C₂×C₁₃₉	semidirect
397. #2507	C₂×C₁₃₉	semidirect
398. #2497	C₂×C₁₃₉	semidirect
400. #2442	C₂×C₁₃₉	semidirect
401. #2441	C₂×C₁₃₉	semidirect
402. #2423	C₂×C₁₃₉	semidirect
404. #2360	C₂×C₁₃₉	semidirect
406. #2345	C₂×C₁₃₉	semidirect
407. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
408. #2285	C₂×C₁₃₉	semidirect
409. C₂×#384	C₂×C₁₃₉	semidirect
498. C₄×D₄	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2859×C₁₃₉	2
#2857×C₁₃₉	2
#2570×C₁₃₉	2
#2511×C₁₃₉	2
#2507×C₁₃₉	2
#2497×C₁₃₉	2
#2487×C₁₃₉	2
#2442×C₁₃₉	2
#2441×C₁₃₉	2
#2423×C₁₃₉	2
#2417×C₁₃₉	2
#2360×C₁₃₉	2
#2352×C₁₃₉	2
#2345×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2285×C₁₃₉	2
C₂×#384×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36189	139

Subgroups — C139×#36189 #48030785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36189 #48030785