Subgroups — C₁₃₉×#37216 #48031812

Order 35584.

1804 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2860×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2809×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2782×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2733×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2733×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2718×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2714×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2682×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2635×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2526×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2464×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2326×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
15	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
23	#400×C₁₃₉	C₂²	1	4	yes	—
24	#400×C₁₃₉	C₂²	1	2	yes	—
25	#399×C₁₃₉	C₂²	1	2	yes	—
26	#398×C₁₃₉	C₂²	1	4	yes	—
27	#397×C₁₃₉	C₂²	1	4	yes	—
28	#396×C₁₃₉	C₂²	1	4	yes	—
29	#394×C₁₃₉	C₂²	1	4	yes	—
30	#394×C₁₃₉	C₂²	1	2	yes	—
31	#394×C₁₃₉	C₂²	1	4	yes	—
32	#394×C₁₃₉	C₂²	1	4	yes	—
33	#392×C₁₃₉	C₂²	1	4	yes	—
34	#392×C₁₃₉	C₂²	1	2	yes	—
35	#392×C₁₃₉	C₂²	1	4	yes	—
36	#392×C₁₃₉	C₂²	1	4	yes	—
37	#391×C₁₃₉	C₂²	1	1	yes	characteristic
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	4	yes	—
40	#390×C₁₃₉	C₂²	1	1	yes	characteristic
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×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	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#387×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	4	yes	—
57	#386×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#385×C₁₃₉	C₂²	1	4	yes	—
60	#385×C₁₃₉	C₂²	1	4	yes	—
61	#384×C₁₃₉	C₂²	1	2	yes	—
62	#382×C₁₃₉	C₂²	1	1	yes	characteristic
63	#381×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
65	#376×C₁₃₉	C₂²	1	2	yes	—
66	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
76	#126×C₁₃₉	—	4	8	no	—
77	#124×C₁₃₉	—	2	4	no	—
78	#124×C₁₃₉	—	2	8	no	—
79	#123×C₁₃₉	—	4	8	no	—
80	#121×C₁₃₉	—	4	4	no	—
81	#121×C₁₃₉	—	4	8	no	—
82	C₄×Q₈×C₁₃₉	—	4	2	no	—
83	C₄×D₄×C₁₃₉	—	4	4	no	—
84	C₄×D₄×C₁₃₉	—	4	2	no	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	#95×C₁₃₉	C₂³	1	4	yes	—
120	#95×C₁₃₉	C₂³	1	2	yes	—
121	#95×C₁₃₉	C₂³	1	4	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
130	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
131	C₂×Q₈×C₁₃₉	—	4	1	no	—
132	C₂×Q₈×C₁₃₉	—	4	1	no	—
133	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
134	C₂×D₄×C₁₃₉	—	2	2	no	—
135	C₂×D₄×C₁₃₉	—	2	4	no	—
136	C₂×D₄×C₁₃₉	—	2	4	no	—
137	C₂×D₄×C₁₃₉	—	4	2	no	—
138	C₂×D₄×C₁₃₉	—	4	1	no	—
139	C₂×D₄×C₁₃₉	—	4	2	no	—
140	C₂×D₄×C₁₃₉	—	4	1	no	—
141	C₂×D₄×C₁₃₉	—	4	4	no	—
142	C₂×D₄×C₁₃₉	—	4	4	no	—
143	C₂×D₄×C₁₃₉	—	4	4	no	—
144	C₂×D₄×C₁₃₉	—	4	2	no	—
145	C₂×D₄×C₁₃₉	—	4	4	no	—
146	C₂×D₄×C₁₃₉	—	4	2	no	—
147	C₂×D₄×C₁₃₉	—	4	2	no	—
148	C₂×D₄×C₁₃₉	—	4	4	no	—
149	C₂×D₄×C₁₃₉	—	4	4	no	—
150	C₂×D₄×C₁₃₉	—	4	4	no	—
151	C₂²×C₄×C₁₃₉	—	2	4	no	—
152	C₂²×C₄×C₁₃₉	—	4	4	no	—
153	C₂²×C₄×C₁₃₉	—	4	4	no	—
154	C₂²×C₄×C₁₃₉	—	4	4	no	—
155	C₂²×C₄×C₁₃₉	—	4	4	no	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₁₃₉	—	2	8	no	—
168	C₄⋊C₄×C₁₃₉	—	2	4	no	—
169	C₄⋊C₄×C₁₃₉	—	4	2	no	—
170	C₄⋊C₄×C₁₃₉	—	4	2	no	—
171	C₄⋊C₄×C₁₃₉	—	4	2	no	—
172	C₄⋊C₄×C₁₃₉	—	4	1	no	—
173	C₄⋊C₄×C₁₃₉	—	4	2	no	—
174	C₄⋊C₄×C₁₃₉	—	4	1	no	—
175	C₄⋊C₄×C₁₃₉	—	4	2	no	—
176	C₄⋊C₄×C₁₃₉	—	4	4	no	—
177	C₄⋊C₄×C₁₃₉	—	4	4	no	—
178	C₄⋊C₄×C₁₃₉	—	4	4	no	—
179	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
182	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
191	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
192	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
193	C₄²×C₁₃₉	—	2	2	no	—
194	C₄²×C₁₃₉	—	2	4	no	—
195	C₄²×C₁₃₉	—	2	2	no	—
196	C₄²×C₁₃₉	—	2	4	no	—
197	C₄²×C₁₃₉	—	2	4	no	—
198	C₄²×C₁₃₉	—	4	1	no	—
199	C₄²×C₁₃₉	—	4	2	no	—
200	C₄²×C₁₃₉	—	4	2	no	—
201	C₂³×C₁₃₉	—	2	4	no	—
202	C₂³×C₁₃₉	—	2	2	no	—
203	C₂³×C₁₃₉	—	2	4	no	—
204	C₂³×C₁₃₉	—	2	4	no	—
205	C₂³×C₁₃₉	—	2	4	no	—
206	C₂³×C₁₃₉	—	2	2	no	—
207	C₂³×C₁₃₉	—	2	4	no	—
208	C₂³×C₁₃₉	—	2	4	no	—
209	C₂³×C₁₃₉	—	2	4	no	—
210	C₂³×C₁₃₉	—	2	4	no	—
211	C₂³×C₁₃₉	—	2	2	no	—
212	C₂³×C₁₃₉	—	2	4	no	—
213	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
214	Q₈×C₁₃₉	—	4	4	no	—
215	D₄×C₁₃₉	—	4	8	no	—
216	D₄×C₁₃₉	—	4	4	no	—
217	D₄×C₁₃₉	—	8	4	no	—
218	D₄×C₁₃₉	—	8	4	no	—
219	D₄×C₁₃₉	—	8	8	no	—
220	D₄×C₁₃₉	—	8	8	no	—
221	C₂×C₄×C₁₃₉	—	2	1	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	1	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	2	4	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	1	no	—
232	C₂×C₄×C₁₃₉	—	2	2	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	4	no	—
236	C₂×C₄×C₁₃₉	—	2	4	no	—
237	C₂×C₄×C₁₃₉	—	2	4	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	4	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	4	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	2	4	no	—
246	C₂×C₄×C₁₃₉	—	8	4	no	—
247	C₂×C₄×C₁₃₉	—	8	8	no	—
248	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
252	C₂²×C₁₃₉	—	4	4	no	—
253	C₂²×C₁₃₉	—	4	2	no	—
254	C₂²×C₁₃₉	—	4	4	no	—
255	C₂²×C₁₃₉	—	4	4	no	—
256	C₂²×C₁₃₉	—	4	4	no	—
257	C₂²×C₁₃₉	—	4	2	no	—
258	C₂²×C₁₃₉	—	4	4	no	—
259	C₂²×C₁₃₉	—	4	4	no	—
260	C₂²×C₁₃₉	—	4	2	no	—
261	C₂²×C₁₃₉	—	4	4	no	—
262	C₂²×C₁₃₉	—	4	4	no	—
263	C₂²×C₁₃₉	—	4	4	no	—
264	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
265	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
266	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
267	C₂²×C₁₃₉	#585	1	1	yes	characteristic
268	C₂²×C₁₃₉	#585	1	2	yes	—
269	C₄×C₁₃₉	—	2	2	no	—
270	C₄×C₁₃₉	—	2	4	no	—
271	C₄×C₁₃₉	—	2	2	no	—
272	C₄×C₁₃₉	—	2	4	no	—
273	C₄×C₁₃₉	—	4	2	no	—
274	C₄×C₁₃₉	—	4	4	no	—
275	C₄×C₁₃₉	—	4	2	no	—
276	C₄×C₁₃₉	—	4	1	no	—
277	C₄×C₁₃₉	—	4	2	no	—
278	C₄×C₁₃₉	—	4	4	no	—
279	C₄×C₁₃₉	—	4	4	no	—
280	C₂×C₁₃₉	—	8	2	no	—
281	C₂×C₁₃₉	—	8	4	no	—
282	C₂×C₁₃₉	#3459	1	1	yes	characteristic
283	C₂×C₁₃₉	#3517	1	2	yes	—
284	C₂×C₁₃₉	#3545	1	1	yes	characteristic
285	C₂×C₁₃₉	#3549	1	1	yes	characteristic
286	C₂×C₁₃₉	#3560	1	2	yes	—
287	#37216	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₁₃₉	#37216	1	1	yes	characteristic, direct product factor, Sylow
289	#2860	C₂×C₁₃₉	1	2	yes	complemented
290	#2809	C₂×C₁₃₉	1	1	yes	characteristic, complemented
291	#2782	C₂×C₁₃₉	1	2	yes	complemented
292	#2733	C₂×C₁₃₉	1	1	yes	characteristic, complemented
293	#2733	C₂×C₁₃₉	1	2	yes	complemented
294	#2718	C₂×C₁₃₉	1	4	yes	complemented
295	#2714	C₂×C₁₃₉	1	4	yes	complemented
296	#2682	C₂×C₁₃₉	1	2	yes	complemented
297	#2635	C₂×C₁₃₉	1	2	yes	complemented
298	#2526	C₂×C₁₃₉	1	4	yes	complemented
299	#2464	C₂×C₁₃₉	1	4	yes	complemented
300	#2326	C₂×C₁₃₉	1	2	yes	complemented
301	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
302	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
303	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
304	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
306	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
307	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
308	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
311	#400	C₂²×C₁₃₉	1	2	yes	—
312	#400	C₂²×C₁₃₉	1	4	yes	—
313	#399	C₂²×C₁₃₉	1	2	yes	—
314	#398	C₂²×C₁₃₉	1	4	yes	—
315	#397	C₂²×C₁₃₉	1	4	yes	—
316	#396	C₂²×C₁₃₉	1	4	yes	—
317	#394	C₂²×C₁₃₉	1	4	yes	—
318	#394	C₂²×C₁₃₉	1	2	yes	—
319	#394	C₂²×C₁₃₉	1	4	yes	—
320	#394	C₂²×C₁₃₉	1	4	yes	—
321	#392	C₂²×C₁₃₉	1	4	yes	—
322	#392	C₂²×C₁₃₉	1	2	yes	—
323	#392	C₂²×C₁₃₉	1	4	yes	—
324	#392	C₂²×C₁₃₉	1	4	yes	—
325	#391	C₂²×C₁₃₉	1	2	yes	—
326	#391	C₂²×C₁₃₉	1	1	yes	characteristic
327	#390	C₂²×C₁₃₉	1	2	yes	—
328	#390	C₂²×C₁₃₉	1	2	yes	—
329	#390	C₂²×C₁₃₉	1	2	yes	—
330	#390	C₂²×C₁₃₉	1	2	yes	—
331	#390	C₂²×C₁₃₉	1	1	yes	characteristic
332	#390	C₂²×C₁₃₉	1	4	yes	—
333	#389	C₂²×C₁₃₉	1	2	yes	—
334	#389	C₂²×C₁₃₉	1	2	yes	—
335	#389	C₂²×C₁₃₉	1	2	yes	—
336	#388	C₂²×C₁₃₉	1	4	yes	—
337	#388	C₂²×C₁₃₉	1	4	yes	—
338	#388	C₂²×C₁₃₉	1	4	yes	—
339	#388	C₂²×C₁₃₉	1	4	yes	—
340	#388	C₂²×C₁₃₉	1	4	yes	—
341	#388	C₂²×C₁₃₉	1	4	yes	—
342	#388	C₂²×C₁₃₉	1	4	yes	—
343	#387	C₂²×C₁₃₉	1	4	yes	—
344	#386	C₂²×C₁₃₉	1	4	yes	—
345	#386	C₂²×C₁₃₉	1	4	yes	—
346	#385	C₂²×C₁₃₉	1	4	yes	—
347	#385	C₂²×C₁₃₉	1	4	yes	—
348	#385	C₂²×C₁₃₉	1	4	yes	—
349	#384	C₂²×C₁₃₉	1	2	yes	—
350	#382	C₂²×C₁₃₉	1	1	yes	characteristic
351	#381	C₂²×C₁₃₉	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
353	#376	C₂²×C₁₃₉	1	2	yes	—
354	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
355	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
357	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
359	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
360	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
361	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
364	#126	—	4	8	no	—
365	#124	—	2	8	no	—
366	#124	—	2	4	no	—
367	#123	—	4	8	no	—
368	#121	—	4	4	no	—
369	#121	—	4	8	no	—
370	C₄×Q₈	—	4	2	no	—
371	C₄×D₄	—	4	4	no	—
372	C₄×D₄	—	4	2	no	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
407	#95	C₂³×C₁₃₉	1	4	yes	—
408	#95	C₂³×C₁₃₉	1	4	yes	—
409	#95	C₂³×C₁₃₉	1	4	yes	—
410	#95	C₂³×C₁₃₉	1	4	yes	—
411	#95	C₂³×C₁₃₉	1	2	yes	—
412	#95	C₂³×C₁₃₉	1	2	yes	—
413	#95	C₂³×C₁₃₉	1	4	yes	—
414	#95	C₂³×C₁₃₉	1	4	yes	—
415	#95	C₂³×C₁₃₉	1	4	yes	—
416	#95	C₂³×C₁₃₉	1	4	yes	—
417	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
418	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	4	no	—
465	C₄⋊C₄	—	4	4	no	—
466	C₄⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	4	4	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	4	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	4	no	—
480	C₂²⋊C₄	—	4	4	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	4	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	4	no	—
486	C₄²	—	4	1	no	—
487	C₄²	—	4	2	no	—
488	C₄²	—	4	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
502	Q₈	—	4	4	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	4	no	—
505	D₄	—	8	4	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	8	no	—
508	D₄	—	8	8	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	8	4	no	—
535	C₂×C₄	—	8	8	no	—
536	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
537	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
538	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
539	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
553	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
554	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
555	C₂²	#585×C₁₃₉	1	2	yes	—
556	C₂²	#585×C₁₃₉	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	4	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	4	no	—
568	C₂	—	8	2	no	—
569	C₂	—	8	4	no	—
570	C₂	#3459×C₁₃₉	1	1	yes	characteristic
571	C₂	#3517×C₁₃₉	1	2	yes	—
572	C₂	#3545×C₁₃₉	1	1	yes	characteristic
573	C₂	#3549×C₁₃₉	1	1	yes	characteristic
574	C₂	#3560×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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. #2860×C₁₃₉	C₂	semidirect
2. #2809×C₁₃₉	C₂	semidirect
3. #2782×C₁₃₉	C₂	semidirect
4. #2733×C₁₃₉	C₂	semidirect
5. #2733×C₁₃₉	C₂	semidirect
6. #2718×C₁₃₉	C₂	semidirect
7. #2714×C₁₃₉	C₂	semidirect
8. #2682×C₁₃₉	C₂	semidirect
9. #2635×C₁₃₉	C₂	semidirect
10. #2526×C₁₃₉	C₂	semidirect
11. #2464×C₁₃₉	C₂	semidirect
12. #2326×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
287. #37216	C₁₃₉	direct (N × H)
288. C₁₃₉	#37216	direct (N × H)
289. #2860	C₂×C₁₃₉	semidirect
290. #2809	C₂×C₁₃₉	semidirect
291. #2782	C₂×C₁₃₉	semidirect
292. #2733	C₂×C₁₃₉	semidirect
293. #2733	C₂×C₁₃₉	semidirect
294. #2718	C₂×C₁₃₉	semidirect
295. #2714	C₂×C₁₃₉	semidirect
296. #2682	C₂×C₁₃₉	semidirect
297. #2635	C₂×C₁₃₉	semidirect
298. #2526	C₂×C₁₃₉	semidirect
299. #2464	C₂×C₁₃₉	semidirect
300. #2326	C₂×C₁₃₉	semidirect
301. C₄×#124	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2860×C₁₃₉	2
#2809×C₁₃₉	2
#2782×C₁₃₉	2
#2733×C₁₃₉	2
#2718×C₁₃₉	2
#2714×C₁₃₉	2
#2682×C₁₃₉	2
#2635×C₁₃₉	2
#2526×C₁₃₉	2
#2464×C₁₃₉	2
#2326×C₁₃₉	2
C₄×#124×C₁₃₉	2
#37216	139

Subgroups — C139×#37216 #48031812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37216 #48031812