Subgroups — C₁₃₉×#36547 #48031143

Order 35584.

2354 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2855×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2855×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2583×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2579×C₁₃₉	C₂	1	2	yes	maximal
7	#2465×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2462×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2434×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2429×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2409×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2365×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2345×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₁₃₉	C₂	1	2	yes	maximal
17	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	#554×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	—	2	8	no	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
41	#398×C₁₃₉	C₂²	1	4	yes	—
42	#398×C₁₃₉	C₂²	1	4	yes	—
43	#396×C₁₃₉	C₂²	1	4	yes	—
44	#395×C₁₃₉	C₂²	1	4	yes	—
45	#395×C₁₃₉	C₂²	1	2	yes	—
46	#395×C₁₃₉	C₂²	1	4	yes	—
47	#393×C₁₃₉	C₂²	1	2	yes	—
48	#391×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	4	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	4	yes	—
53	#389×C₁₃₉	C₂²	1	4	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	4	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	2	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#387×C₁₃₉	C₂²	1	2	yes	—
61	#387×C₁₃₉	C₂²	1	4	yes	—
62	#387×C₁₃₉	C₂²	1	4	yes	—
63	#387×C₁₃₉	C₂²	1	4	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	1	yes	characteristic
67	#386×C₁₃₉	C₂²	1	2	yes	—
68	#385×C₁₃₉	C₂²	1	1	yes	characteristic
69	#385×C₁₃₉	C₂²	1	2	yes	—
70	#385×C₁₃₉	C₂²	1	2	yes	—
71	#385×C₁₃₉	C₂²	1	2	yes	—
72	#385×C₁₃₉	C₂²	1	4	yes	—
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#381×C₁₃₉	C₂²	1	1	yes	characteristic
75	#381×C₁₃₉	C₂²	1	2	yes	—
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
85	C₂²×Q₈×C₁₃₉	—	2	8	no	—
86	C₂²×Q₈×C₁₃₉	—	2	4	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
100	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
101	#125×C₁₃₉	—	2	8	no	—
102	#123×C₁₃₉	Q₈	1	8	yes	complemented
103	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
107	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
108	C₄×Q₈×C₁₃₉	—	2	8	no	—
109	C₄×Q₈×C₁₃₉	—	2	16	no	—
110	C₄×Q₈×C₁₃₉	—	2	8	no	—
111	C₄×Q₈×C₁₃₉	—	2	4	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	2	4	no	—
114	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
115	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
116	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	—	2	8	no	—
148	C₂×C₄²×C₁₃₉	—	2	4	no	—
149	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
173	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂×Q₈×C₁₃₉	—	2	32	no	—
175	C₂×Q₈×C₁₃₉	—	2	4	no	—
176	C₂×Q₈×C₁₃₉	—	2	4	no	—
177	C₂×Q₈×C₁₃₉	—	2	2	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	8	no	—
180	C₂×Q₈×C₁₃₉	—	2	4	no	—
181	C₂×Q₈×C₁₃₉	—	2	4	no	—
182	C₂×Q₈×C₁₃₉	—	4	4	no	—
183	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
184	C₂×D₄×C₁₃₉	—	2	2	no	—
185	C₂×D₄×C₁₃₉	—	2	2	no	—
186	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	4	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	8	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	2	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	4	4	no	—
197	C₂²×C₄×C₁₃₉	—	4	2	no	—
198	C₂²×C₄×C₁₃₉	—	4	4	no	—
199	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
201	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₁₃₉	—	2	8	no	—
218	C₄⋊C₄×C₁₃₉	—	2	8	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	8	no	—
228	C₄⋊C₄×C₁₃₉	—	2	8	no	—
229	C₄⋊C₄×C₁₃₉	—	2	8	no	—
230	C₄⋊C₄×C₁₃₉	—	4	2	no	—
231	C₄⋊C₄×C₁₃₉	—	4	4	no	—
232	C₄⋊C₄×C₁₃₉	—	4	4	no	—
233	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
234	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
235	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
236	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
237	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
245	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
246	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
247	C₄²×C₁₃₉	—	2	8	no	—
248	C₄²×C₁₃₉	—	2	8	no	—
249	C₄²×C₁₃₉	—	2	4	no	—
250	C₄²×C₁₃₉	—	2	4	no	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₄²×C₁₃₉	—	2	2	no	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	4	4	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	1	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	1	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
262	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
263	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
264	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
265	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
266	Q₈×C₁₃₉	—	2	16	no	—
267	Q₈×C₁₃₉	—	2	16	no	—
268	Q₈×C₁₃₉	—	4	4	no	—
269	Q₈×C₁₃₉	—	8	4	no	—
270	D₄×C₁₃₉	—	2	8	no	—
271	C₂×C₄×C₁₃₉	—	2	16	no	—
272	C₂×C₄×C₁₃₉	—	2	8	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	4	no	—
283	C₂×C₄×C₁₃₉	—	2	4	no	—
284	C₂×C₄×C₁₃₉	—	2	8	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	1	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	4	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	4	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	4	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	4	8	no	—
303	C₂×C₄×C₁₃₉	—	4	4	no	—
304	C₂×C₄×C₁₃₉	—	4	4	no	—
305	C₂×C₄×C₁₃₉	—	8	4	no	—
306	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
307	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
308	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
311	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
312	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
313	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
314	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
315	C₂²×C₁₃₉	—	2	2	no	—
316	C₂²×C₁₃₉	—	2	4	no	—
317	C₂²×C₁₃₉	—	2	2	no	—
318	C₂²×C₁₃₉	—	2	4	no	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	2	4	no	—
321	C₂²×C₁₃₉	—	4	1	no	—
322	C₂²×C₁₃₉	—	4	1	no	—
323	C₂²×C₁₃₉	—	4	2	no	—
324	C₂²×C₁₃₉	D₄×Q₈	1	4	yes	—
325	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
326	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
327	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
328	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	C₂²×C₁₃₉	#585	1	2	yes	—
330	C₄×C₁₃₉	—	2	2	no	—
331	C₄×C₁₃₉	—	2	8	no	—
332	C₄×C₁₃₉	—	2	4	no	—
333	C₄×C₁₃₉	—	2	2	no	—
334	C₄×C₁₃₉	—	2	4	no	—
335	C₄×C₁₃₉	—	2	4	no	—
336	C₄×C₁₃₉	—	2	4	no	—
337	C₄×C₁₃₉	—	4	1	no	—
338	C₄×C₁₃₉	—	4	2	no	—
339	C₄×C₁₃₉	—	4	2	no	—
340	C₄×C₁₃₉	—	4	2	no	—
341	C₄×C₁₃₉	—	4	1	no	—
342	C₄×C₁₃₉	—	4	2	no	—
343	C₄×C₁₃₉	—	4	4	no	—
344	C₄×C₁₃₉	#525	1	4	yes	—
345	C₂×C₁₃₉	—	2	4	no	—
346	C₂×C₁₃₉	—	4	2	no	—
347	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
348	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
349	C₂×C₁₃₉	Q₈×#41	1	2	yes	—
350	C₂×C₁₃₉	#3485	1	1	yes	characteristic
351	C₂×C₁₃₉	#3516	1	2	yes	—
352	#36547	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₁₃₉	#36547	1	1	yes	characteristic, direct product factor, Sylow
354	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
355	C₂²×C₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	#2855	C₂×C₁₃₉	1	2	yes	complemented
357	#2855	C₂×C₁₃₉	1	1	yes	characteristic, complemented
358	#2583	C₂×C₁₃₉	1	2	yes	complemented
359	#2579	C₂×C₁₃₉	1	2	yes	—
360	#2465	C₂×C₁₃₉	1	4	yes	complemented
361	#2462	C₂×C₁₃₉	1	4	yes	complemented
362	#2451	C₂×C₁₃₉	1	2	yes	complemented
363	#2434	C₂×C₁₃₉	1	1	yes	characteristic, complemented
364	#2429	C₂×C₁₃₉	1	2	yes	complemented
365	#2409	C₂×C₁₃₉	1	1	yes	characteristic
366	#2365	C₂×C₁₃₉	1	2	yes	complemented
367	#2360	C₂×C₁₃₉	1	2	yes	complemented
368	#2345	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	C₄×#123	C₂×C₁₃₉	1	2	yes	—
370	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic
371	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
372	#554	—	2	8	no	—
373	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
374	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
376	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
379	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
380	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
382	C₂×C₄×Q₈	—	2	8	no	—
383	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
384	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
386	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
387	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
388	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
390	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
391	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
393	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
394	#398	C₂²×C₁₃₉	1	4	yes	—
395	#398	C₂²×C₁₃₉	1	4	yes	—
396	#396	C₂²×C₁₃₉	1	4	yes	—
397	#395	C₂²×C₁₃₉	1	4	yes	—
398	#395	C₂²×C₁₃₉	1	2	yes	—
399	#395	C₂²×C₁₃₉	1	4	yes	—
400	#393	C₂²×C₁₃₉	1	2	yes	—
401	#391	C₂²×C₁₃₉	1	2	yes	—
402	#391	C₂²×C₁₃₉	1	4	yes	—
403	#391	C₂²×C₁₃₉	1	2	yes	—
404	#391	C₂²×C₁₃₉	1	2	yes	—
405	#389	C₂²×C₁₃₉	1	4	yes	—
406	#389	C₂²×C₁₃₉	1	4	yes	—
407	#389	C₂²×C₁₃₉	1	2	yes	—
408	#389	C₂²×C₁₃₉	1	4	yes	—
409	#389	C₂²×C₁₃₉	1	2	yes	—
410	#388	C₂²×C₁₃₉	1	4	yes	—
411	#388	C₂²×C₁₃₉	1	2	yes	—
412	#387	C₂²×C₁₃₉	1	4	yes	—
413	#387	C₂²×C₁₃₉	1	4	yes	—
414	#387	C₂²×C₁₃₉	1	4	yes	—
415	#387	C₂²×C₁₃₉	1	4	yes	—
416	#387	C₂²×C₁₃₉	1	4	yes	—
417	#387	C₂²×C₁₃₉	1	4	yes	—
418	#387	C₂²×C₁₃₉	1	2	yes	—
419	#386	C₂²×C₁₃₉	1	1	yes	characteristic
420	#386	C₂²×C₁₃₉	1	2	yes	—
421	#385	C₂²×C₁₃₉	1	2	yes	—
422	#385	C₂²×C₁₃₉	1	2	yes	—
423	#385	C₂²×C₁₃₉	1	4	yes	—
424	#385	C₂²×C₁₃₉	1	1	yes	characteristic
425	#385	C₂²×C₁₃₉	1	2	yes	—
426	#385	C₂²×C₁₃₉	1	2	yes	—
427	#381	C₂²×C₁₃₉	1	1	yes	characteristic
428	#381	C₂²×C₁₃₉	1	2	yes	—
429	#380	C₂²×C₁₃₉	1	2	yes	—
430	#380	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
438	C₂²×Q₈	—	2	8	no	—
439	C₂²×Q₈	—	2	4	no	—
440	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
441	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
443	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
444	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
451	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₄⋊Q₈	—	2	8	no	—
453	C₄⋊Q₈	—	2	4	no	—
454	#125	—	2	8	no	—
455	#123	Q₈×C₁₃₉	1	8	yes	complemented
456	C₂²⋊Q₈	—	2	8	no	—
457	C₂²⋊Q₈	—	2	8	no	—
458	C₂²⋊Q₈	—	2	4	no	—
459	C₂²⋊Q₈	—	2	8	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₄×Q₈	—	2	8	no	—
462	C₄×Q₈	—	2	16	no	—
463	C₄×Q₈	—	2	8	no	—
464	C₄×Q₈	—	2	4	no	—
465	C₄×D₄	—	2	8	no	—
466	C₄×D₄	—	2	4	no	—
467	C₂×C₄⋊C₄	—	2	8	no	—
468	C₂×C₄⋊C₄	—	2	4	no	—
469	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄²	—	2	8	no	—
501	C₂×C₄²	—	2	4	no	—
502	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
505	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
510	#95	C₂³×C₁₃₉	1	2	yes	—
511	#95	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	2	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	2	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	#95	C₂³×C₁₃₉	1	4	yes	—
518	#95	C₂³×C₁₃₉	1	2	yes	—
519	#95	C₂³×C₁₃₉	1	2	yes	—
520	#95	C₂³×C₁₃₉	1	4	yes	—
521	#95	C₂³×C₁₃₉	1	2	yes	—
522	#95	C₂³×C₁₃₉	1	4	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	4	yes	—
525	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
526	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
527	C₂×Q₈	—	2	32	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	8	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	4	4	no	—
536	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
553	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
554	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₄⋊C₄	—	2	8	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
587	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
588	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
589	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
599	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
600	C₄²	—	2	8	no	—
601	C₄²	—	2	8	no	—
602	C₄²	—	2	4	no	—
603	C₄²	—	2	4	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	4	4	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	2	no	—
614	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
615	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
616	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
617	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
618	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
619	Q₈	—	2	16	no	—
620	Q₈	—	2	16	no	—
621	Q₈	—	4	4	no	—
622	Q₈	—	8	4	no	—
623	D₄	—	2	8	no	—
624	C₂×C₄	—	2	16	no	—
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	4	8	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	8	4	no	—
659	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
660	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
661	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
663	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
664	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
665	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
666	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
667	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	2	no	—
677	C₂²	D₄×Q₈×C₁₃₉	1	4	yes	—
678	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
679	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
680	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
681	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
682	C₂²	#585×C₁₃₉	1	2	yes	—
683	C₄	—	2	2	no	—
684	C₄	—	2	8	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	4	no	—
697	C₄	#525×C₁₃₉	1	4	yes	—
698	C₂	—	2	4	no	—
699	C₂	—	4	2	no	—
700	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
701	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
702	C₂	Q₈×#41×C₁₃₉	1	2	yes	—
703	C₂	#3485×C₁₃₉	1	1	yes	characteristic
704	C₂	#3516×C₁₃₉	1	2	yes	—

	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
2. C₂²×C₄×Q₈×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2855×C₁₃₉	C₂	semidirect
5. #2583×C₁₃₉	C₂	semidirect
7. #2465×C₁₃₉	C₂	semidirect
8. #2462×C₁₃₉	C₂	semidirect
9. #2451×C₁₃₉	C₂	semidirect
10. #2434×C₁₃₉	C₂	semidirect
11. #2429×C₁₃₉	C₂	semidirect
13. #2365×C₁₃₉	C₂	semidirect
14. #2360×C₁₃₉	C₂	semidirect
15. #2345×C₁₃₉	C₂	semidirect
102. #123×C₁₃₉	Q₈	semidirect
236. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
246. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
352. #36547	C₁₃₉	direct (N × H)
353. C₁₃₉	#36547	direct (N × H)
355. C₂²×C₄×Q₈	C₂×C₁₃₉	semidirect
356. #2855	C₂×C₁₃₉	semidirect
357. #2855	C₂×C₁₃₉	semidirect
358. #2583	C₂×C₁₃₉	semidirect
360. #2465	C₂×C₁₃₉	semidirect
361. #2462	C₂×C₁₃₉	semidirect
362. #2451	C₂×C₁₃₉	semidirect
363. #2434	C₂×C₁₃₉	semidirect
364. #2429	C₂×C₁₃₉	semidirect
366. #2365	C₂×C₁₃₉	semidirect
367. #2360	C₂×C₁₃₉	semidirect
368. #2345	C₂×C₁₃₉	semidirect
455. #123	Q₈×C₁₃₉	semidirect
589. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect
599. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂²×C₄×Q₈×C₁₃₉	2
#2855×C₁₃₉	2
#2583×C₁₃₉	2
#2579×C₁₃₉	2
#2465×C₁₃₉	2
#2462×C₁₃₉	2
#2451×C₁₃₉	2
#2434×C₁₃₉	2
#2429×C₁₃₉	2
#2409×C₁₃₉	2
#2365×C₁₃₉	2
#2360×C₁₃₉	2
#2345×C₁₃₉	2
C₄×#123×C₁₃₉	2
#36547	139

Subgroups — C139×#36547 #48031143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36547 #48031143