Subgroups — C₁₃₉×#37023 #48031619

Order 35584.

1348 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2864×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2805×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2802×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2783×C₁₃₉	C₂	1	2	yes	maximal
5	#2777×C₁₃₉	C₂	1	2	yes	maximal
6	#2775×C₁₃₉	C₂	1	2	yes	maximal
7	#2772×C₁₃₉	C₂	1	2	yes	maximal
8	#2769×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2767×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2652×C₁₃₉	C₂	1	2	yes	maximal
11	#2611×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2606×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2599×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2587×C₁₃₉	C₂	1	2	yes	maximal
15	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2533×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2336×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#2320×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
23	#400×C₁₃₉	C₂²	1	1	yes	characteristic
24	#400×C₁₃₉	C₂²	1	2	yes	—
25	#400×C₁₃₉	C₂²	1	2	yes	—
26	#400×C₁₃₉	C₂²	1	2	yes	—
27	#400×C₁₃₉	C₂²	1	2	yes	—
28	#400×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#399×C₁₃₉	C₂²	1	1	yes	characteristic
33	#398×C₁₃₉	C₂²	1	2	yes	—
34	#398×C₁₃₉	C₂²	1	2	yes	—
35	#398×C₁₃₉	C₂²	1	1	yes	characteristic
36	#398×C₁₃₉	C₂²	1	2	yes	—
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	2	yes	—
39	#398×C₁₃₉	C₂²	1	1	yes	characteristic
40	#397×C₁₃₉	C₂²	1	1	yes	characteristic
41	#397×C₁₃₉	C₂²	1	2	yes	—
42	#397×C₁₃₉	C₂²	1	2	yes	—
43	#397×C₁₃₉	C₂²	1	2	yes	—
44	#397×C₁₃₉	C₂²	1	1	yes	characteristic
45	#396×C₁₃₉	C₂²	1	2	yes	—
46	#396×C₁₃₉	C₂²	1	2	yes	—
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#393×C₁₃₉	C₂²	1	1	yes	characteristic
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×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	#388×C₁₃₉	C₂²	1	2	yes	—
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	#387×C₁₃₉	C₂²	1	2	yes	—
72	#387×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#387×C₁₃₉	C₂²	1	2	yes	—
80	#387×C₁₃₉	C₂²	1	2	yes	—
81	#387×C₁₃₉	C₂²	1	2	yes	—
82	#387×C₁₃₉	C₂²	1	2	yes	—
83	#387×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	#385×C₁₃₉	C₂²	1	2	yes	—
92	#385×C₁₃₉	C₂²	1	2	yes	—
93	#383×C₁₃₉	C₂²	1	2	yes	—
94	#383×C₁₃₉	C₂²	1	2	yes	—
95	#383×C₁₃₉	C₂²	1	1	yes	characteristic
96	#382×C₁₃₉	C₂²	1	2	yes	—
97	#382×C₁₃₉	C₂²	1	2	yes	—
98	#382×C₁₃₉	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
104	#376×C₁₃₉	C₂²	1	1	yes	characteristic
105	#376×C₁₃₉	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	#125×C₁₃₉	—	2	4	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	#117×C₁₃₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	1	yes	characteristic
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	1	yes	characteristic
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	2	yes	—
186	#95×C₁₃₉	C₂³	1	2	yes	—
187	#95×C₁₃₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂×Q₈×C₁₃₉	—	2	2	no	—
199	C₂×Q₈×C₁₃₉	—	4	2	no	—
200	C₂²×C₄×C₁₃₉	—	2	2	no	—
201	C₂²×C₄×C₁₃₉	—	4	1	no	—
202	C₂²×C₄×C₁₃₉	—	4	1	no	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
221	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	2	2	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	4	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	—	4	2	no	—
233	C₄⋊C₄×C₁₃₉	—	4	2	no	—
234	C₄⋊C₄×C₁₃₉	—	4	2	no	—
235	C₄⋊C₄×C₁₃₉	—	4	2	no	—
236	C₄⋊C₄×C₁₃₉	—	4	2	no	—
237	C₄⋊C₄×C₁₃₉	—	4	2	no	—
238	C₄⋊C₄×C₁₃₉	—	4	2	no	—
239	C₄⋊C₄×C₁₃₉	—	4	2	no	—
240	C₄⋊C₄×C₁₃₉	—	4	2	no	—
241	C₄⋊C₄×C₁₃₉	—	4	2	no	—
242	C₄⋊C₄×C₁₃₉	—	4	2	no	—
243	C₄⋊C₄×C₁₃₉	—	4	2	no	—
244	C₄⋊C₄×C₁₃₉	—	4	2	no	—
245	C₄⋊C₄×C₁₃₉	—	4	2	no	—
246	C₄⋊C₄×C₁₃₉	—	4	2	no	—
247	C₄⋊C₄×C₁₃₉	—	4	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	2	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
256	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄²×C₁₃₉	—	2	2	no	—
258	C₄²×C₁₃₉	—	2	4	no	—
259	C₄²×C₁₃₉	—	2	4	no	—
260	C₄²×C₁₃₉	—	4	1	no	—
261	C₄²×C₁₃₉	—	4	1	no	—
262	C₄²×C₁₃₉	—	4	1	no	—
263	C₄²×C₁₃₉	—	4	1	no	—
264	C₄²×C₁₃₉	—	4	2	no	—
265	C₄²×C₁₃₉	—	4	2	no	—
266	C₄²×C₁₃₉	—	4	2	no	—
267	C₄²×C₁₃₉	—	4	2	no	—
268	C₄²×C₁₃₉	#41	1	4	yes	—
269	C₂³×C₁₃₉	—	2	1	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	1	no	—
273	C₂³×C₁₃₉	—	2	1	no	—
274	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
275	Q₈×C₁₃₉	—	4	4	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	1	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	1	no	—
283	C₂×C₄×C₁₃₉	—	2	1	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	1	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	4	4	no	—
323	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
324	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
325	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
327	C₂²×C₁₃₉	—	4	1	no	—
328	C₂²×C₁₃₉	—	4	1	no	—
329	C₂²×C₁₃₉	—	4	1	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	2	no	—
332	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
333	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
334	C₂²×C₁₃₉	#585	1	2	yes	—
335	C₂²×C₁₃₉	#585	1	1	yes	characteristic
336	C₂²×C₁₃₉	#585	1	1	yes	characteristic
337	C₄×C₁₃₉	—	2	2	no	—
338	C₄×C₁₃₉	—	2	2	no	—
339	C₄×C₁₃₉	—	2	2	no	—
340	C₄×C₁₃₉	—	2	4	no	—
341	C₄×C₁₃₉	—	4	1	no	—
342	C₄×C₁₃₉	—	4	2	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	1	no	—
347	C₄×C₁₃₉	—	4	1	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	2	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	—	4	2	no	—
353	C₄×C₁₃₉	—	4	2	no	—
354	C₄×C₁₃₉	—	4	2	no	—
355	C₂×C₁₃₉	—	8	1	no	—
356	C₂×C₁₃₉	#3455	1	1	yes	characteristic
357	C₂×C₁₃₉	#3493	1	1	yes	characteristic
358	C₂×C₁₃₉	#3509	1	1	yes	characteristic
359	C₂×C₁₃₉	#3553	1	2	yes	—
360	C₂×C₁₃₉	#3565	1	2	yes	—
361	#37023	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₁₃₉	#37023	1	1	yes	characteristic, direct product factor, Sylow
363	#2864	C₂×C₁₃₉	1	2	yes	complemented
364	#2805	C₂×C₁₃₉	1	2	yes	complemented
365	#2802	C₂×C₁₃₉	1	2	yes	complemented
366	#2783	C₂×C₁₃₉	1	2	yes	—
367	#2777	C₂×C₁₃₉	1	2	yes	—
368	#2775	C₂×C₁₃₉	1	2	yes	—
369	#2772	C₂×C₁₃₉	1	2	yes	—
370	#2769	C₂×C₁₃₉	1	2	yes	complemented
371	#2767	C₂×C₁₃₉	1	2	yes	complemented
372	#2652	C₂×C₁₃₉	1	2	yes	—
373	#2611	C₂×C₁₃₉	1	1	yes	characteristic
374	#2606	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	#2599	C₂×C₁₃₉	1	1	yes	characteristic
376	#2587	C₂×C₁₃₉	1	2	yes	—
377	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
378	#2533	C₂×C₁₃₉	1	2	yes	complemented
379	#2336	C₂×C₁₃₉	1	1	yes	characteristic, complemented
380	#2320	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	#2298	C₂×C₁₃₉	1	1	yes	characteristic
382	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
384	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
385	#400	C₂²×C₁₃₉	1	2	yes	—
386	#400	C₂²×C₁₃₉	1	1	yes	characteristic
387	#400	C₂²×C₁₃₉	1	2	yes	—
388	#400	C₂²×C₁₃₉	1	2	yes	—
389	#400	C₂²×C₁₃₉	1	2	yes	—
390	#400	C₂²×C₁₃₉	1	2	yes	—
391	#400	C₂²×C₁₃₉	1	2	yes	—
392	#400	C₂²×C₁₃₉	1	2	yes	—
393	#400	C₂²×C₁₃₉	1	2	yes	—
394	#399	C₂²×C₁₃₉	1	1	yes	characteristic
395	#398	C₂²×C₁₃₉	1	2	yes	—
396	#398	C₂²×C₁₃₉	1	2	yes	—
397	#398	C₂²×C₁₃₉	1	1	yes	characteristic
398	#398	C₂²×C₁₃₉	1	2	yes	—
399	#398	C₂²×C₁₃₉	1	2	yes	—
400	#398	C₂²×C₁₃₉	1	1	yes	characteristic
401	#398	C₂²×C₁₃₉	1	2	yes	—
402	#397	C₂²×C₁₃₉	1	1	yes	characteristic
403	#397	C₂²×C₁₃₉	1	1	yes	characteristic
404	#397	C₂²×C₁₃₉	1	2	yes	—
405	#397	C₂²×C₁₃₉	1	2	yes	—
406	#397	C₂²×C₁₃₉	1	2	yes	—
407	#396	C₂²×C₁₃₉	1	2	yes	—
408	#396	C₂²×C₁₃₉	1	2	yes	—
409	#396	C₂²×C₁₃₉	1	2	yes	—
410	#395	C₂²×C₁₃₉	1	2	yes	—
411	#395	C₂²×C₁₃₉	1	1	yes	characteristic
412	#393	C₂²×C₁₃₉	1	1	yes	characteristic
413	#391	C₂²×C₁₃₉	1	2	yes	—
414	#389	C₂²×C₁₃₉	1	2	yes	—
415	#389	C₂²×C₁₃₉	1	2	yes	—
416	#389	C₂²×C₁₃₉	1	2	yes	—
417	#389	C₂²×C₁₃₉	1	2	yes	—
418	#389	C₂²×C₁₃₉	1	2	yes	—
419	#389	C₂²×C₁₃₉	1	2	yes	—
420	#389	C₂²×C₁₃₉	1	2	yes	—
421	#389	C₂²×C₁₃₉	1	2	yes	—
422	#389	C₂²×C₁₃₉	1	2	yes	—
423	#389	C₂²×C₁₃₉	1	2	yes	—
424	#389	C₂²×C₁₃₉	1	2	yes	—
425	#389	C₂²×C₁₃₉	1	2	yes	—
426	#389	C₂²×C₁₃₉	1	2	yes	—
427	#388	C₂²×C₁₃₉	1	2	yes	—
428	#388	C₂²×C₁₃₉	1	2	yes	—
429	#388	C₂²×C₁₃₉	1	2	yes	—
430	#388	C₂²×C₁₃₉	1	2	yes	—
431	#388	C₂²×C₁₃₉	1	2	yes	—
432	#388	C₂²×C₁₃₉	1	2	yes	—
433	#387	C₂²×C₁₃₉	1	2	yes	—
434	#387	C₂²×C₁₃₉	1	2	yes	—
435	#387	C₂²×C₁₃₉	1	2	yes	—
436	#387	C₂²×C₁₃₉	1	2	yes	—
437	#387	C₂²×C₁₃₉	1	2	yes	—
438	#387	C₂²×C₁₃₉	1	2	yes	—
439	#387	C₂²×C₁₃₉	1	2	yes	—
440	#387	C₂²×C₁₃₉	1	2	yes	—
441	#387	C₂²×C₁₃₉	1	2	yes	—
442	#387	C₂²×C₁₃₉	1	2	yes	—
443	#387	C₂²×C₁₃₉	1	2	yes	—
444	#387	C₂²×C₁₃₉	1	2	yes	—
445	#387	C₂²×C₁₃₉	1	2	yes	—
446	#387	C₂²×C₁₃₉	1	2	yes	—
447	#387	C₂²×C₁₃₉	1	2	yes	—
448	#387	C₂²×C₁₃₉	1	2	yes	—
449	#387	C₂²×C₁₃₉	1	2	yes	—
450	#387	C₂²×C₁₃₉	1	2	yes	—
451	#387	C₂²×C₁₃₉	1	2	yes	—
452	#387	C₂²×C₁₃₉	1	2	yes	—
453	#385	C₂²×C₁₃₉	1	2	yes	—
454	#385	C₂²×C₁₃₉	1	2	yes	—
455	#383	C₂²×C₁₃₉	1	2	yes	—
456	#383	C₂²×C₁₃₉	1	1	yes	characteristic
457	#383	C₂²×C₁₃₉	1	2	yes	—
458	#382	C₂²×C₁₃₉	1	2	yes	—
459	#382	C₂²×C₁₃₉	1	2	yes	—
460	#382	C₂²×C₁₃₉	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
466	#376	C₂²×C₁₃₉	1	1	yes	characteristic
467	#376	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
471	#125	—	2	4	no	—
472	C₄×Q₈	—	2	4	no	—
473	#117	—	2	4	no	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
522	#95	C₂³×C₁₃₉	1	1	yes	characteristic
523	#95	C₂³×C₁₃₉	1	1	yes	characteristic
524	#95	C₂³×C₁₃₉	1	2	yes	—
525	#95	C₂³×C₁₃₉	1	2	yes	—
526	#95	C₂³×C₁₃₉	1	2	yes	—
527	#95	C₂³×C₁₃₉	1	2	yes	—
528	#95	C₂³×C₁₃₉	1	2	yes	—
529	#95	C₂³×C₁₃₉	1	2	yes	—
530	#95	C₂³×C₁₃₉	1	2	yes	—
531	#95	C₂³×C₁₃₉	1	2	yes	—
532	#95	C₂³×C₁₃₉	1	2	yes	—
533	#95	C₂³×C₁₃₉	1	2	yes	—
534	#95	C₂³×C₁₃₉	1	2	yes	—
535	#95	C₂³×C₁₃₉	1	2	yes	—
536	#95	C₂³×C₁₃₉	1	2	yes	—
537	#95	C₂³×C₁₃₉	1	2	yes	—
538	#95	C₂³×C₁₃₉	1	2	yes	—
539	#95	C₂³×C₁₃₉	1	2	yes	—
540	#95	C₂³×C₁₃₉	1	2	yes	—
541	#95	C₂³×C₁₃₉	1	2	yes	—
542	#95	C₂³×C₁₃₉	1	2	yes	—
543	#95	C₂³×C₁₃₉	1	2	yes	—
544	#95	C₂³×C₁₃₉	1	1	yes	characteristic
545	#95	C₂³×C₁₃₉	1	1	yes	characteristic
546	#95	C₂³×C₁₃₉	1	2	yes	—
547	#95	C₂³×C₁₃₉	1	2	yes	—
548	#95	C₂³×C₁₃₉	1	2	yes	—
549	#95	C₂³×C₁₃₉	1	2	yes	—
550	#95	C₂³×C₁₃₉	1	2	yes	—
551	#95	C₂³×C₁₃₉	1	2	yes	—
552	#95	C₂³×C₁₃₉	1	2	yes	—
553	#95	C₂³×C₁₃₉	1	2	yes	—
554	#95	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	2	yes	—
559	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	2	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	4	2	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₄⋊C₄	—	4	2	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₄²	—	2	2	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	4	1	no	—
623	C₄²	—	4	1	no	—
624	C₄²	—	4	1	no	—
625	C₄²	—	4	1	no	—
626	C₄²	—	4	2	no	—
627	C₄²	—	4	2	no	—
628	C₄²	—	4	2	no	—
629	C₄²	—	4	2	no	—
630	C₄²	#41×C₁₃₉	1	4	yes	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
637	Q₈	—	4	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
686	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
687	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
688	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
695	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
696	C₂²	#585×C₁₃₉	1	1	yes	characteristic
697	C₂²	#585×C₁₃₉	1	2	yes	—
698	C₂²	#585×C₁₃₉	1	1	yes	characteristic
699	C₄	—	2	4	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₂	—	8	1	no	—
718	C₂	#3455×C₁₃₉	1	1	yes	characteristic
719	C₂	#3493×C₁₃₉	1	1	yes	characteristic
720	C₂	#3509×C₁₃₉	1	1	yes	characteristic
721	C₂	#3553×C₁₃₉	1	2	yes	—
722	C₂	#3565×C₁₃₉	1	2	yes	—

	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
1. #2864×C₁₃₉	C₂	semidirect
2. #2805×C₁₃₉	C₂	semidirect
3. #2802×C₁₃₉	C₂	semidirect
8. #2769×C₁₃₉	C₂	semidirect
9. #2767×C₁₃₉	C₂	semidirect
12. #2606×C₁₃₉	C₂	semidirect
15. #2584×C₁₃₉	C₂	semidirect
16. #2533×C₁₃₉	C₂	semidirect
17. #2336×C₁₃₉	C₂	semidirect
18. #2320×C₁₃₉	C₂	semidirect
361. #37023	C₁₃₉	direct (N × H)
362. C₁₃₉	#37023	direct (N × H)
363. #2864	C₂×C₁₃₉	semidirect
364. #2805	C₂×C₁₃₉	semidirect
365. #2802	C₂×C₁₃₉	semidirect
370. #2769	C₂×C₁₃₉	semidirect
371. #2767	C₂×C₁₃₉	semidirect
374. #2606	C₂×C₁₃₉	semidirect
377. #2584	C₂×C₁₃₉	semidirect
378. #2533	C₂×C₁₃₉	semidirect
379. #2336	C₂×C₁₃₉	semidirect
380. #2320	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2864×C₁₃₉	2
#2805×C₁₃₉	2
#2802×C₁₃₉	2
#2783×C₁₃₉	2
#2777×C₁₃₉	2
#2775×C₁₃₉	2
#2772×C₁₃₉	2
#2769×C₁₃₉	2
#2767×C₁₃₉	2
#2652×C₁₃₉	2
#2611×C₁₃₉	2
#2606×C₁₃₉	2
#2599×C₁₃₉	2
#2587×C₁₃₉	2
#2584×C₁₃₉	2
#2533×C₁₃₉	2
#2336×C₁₃₉	2
#2320×C₁₃₉	2
#2298×C₁₃₉	2
#37023	139

Subgroups — C139×#37023 #48031619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37023 #48031619