Subgroups — C₁₃₉×#13934 #48008530

Order 35584.

1226 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#1445×C₁₃₉	C₂	1	2	yes	maximal
3	#1442×C₁₃₉	C₂	1	2	yes	maximal
4	#1436×C₁₃₉	C₂	1	2	yes	maximal
5	#1436×C₁₃₉	C₂	1	2	yes	maximal
6	C₄⋊#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#1434×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#1434×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#1434×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	#1434×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	C₄×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
20	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₁₃₉	—	2	4	no	—
56	C₂×C₄²×C₁₃₉	—	2	4	no	—
57	C₂×C₄²×C₁₃₉	—	4	2	no	—
58	C₂×C₄²×C₁₃₉	—	4	2	no	—
59	C₂×C₄²×C₁₃₉	—	4	2	no	—
60	C₂×C₄²×C₁₃₉	—	4	2	no	—
61	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
64	#95×C₁₃₉	—	2	4	no	—
65	#95×C₁₃₉	—	2	2	no	—
66	#95×C₁₃₉	—	2	4	no	—
67	#95×C₁₃₉	—	2	4	no	—
68	#95×C₁₃₉	—	2	4	no	—
69	#95×C₁₃₉	—	2	4	no	—
70	#95×C₁₃₉	—	2	4	no	—
71	#95×C₁₃₉	—	2	2	no	—
72	#95×C₁₃₉	—	2	2	no	—
73	#95×C₁₃₉	—	4	2	no	—
74	#95×C₁₃₉	—	4	2	no	—
75	#95×C₁₃₉	—	4	2	no	—
76	#95×C₁₃₉	—	4	2	no	—
77	#95×C₁₃₉	C₂×C₄	1	4	yes	—
78	#95×C₁₃₉	C₂×C₄	1	4	yes	—
79	#95×C₁₃₉	Q₈	1	4	yes	—
80	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	2	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	2	no	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	1	no	—
88	C₂²×C₄×C₁₃₉	—	2	1	no	—
89	C₂²×C₄×C₁₃₉	—	2	1	no	—
90	C₂²×C₄×C₁₃₉	—	2	1	no	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	2	2	no	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	2	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	2	1	no	—
103	C₂²×C₄×C₁₃₉	—	2	1	no	—
104	C₂²×C₄×C₁₃₉	—	2	1	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	1	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	2	no	—
110	C₂²×C₄×C₁₃₉	—	2	2	no	—
111	C₂²×C₄×C₁₃₉	—	2	2	no	—
112	C₂²×C₄×C₁₃₉	—	2	2	no	—
113	C₂²×C₄×C₁₃₉	—	2	2	no	—
114	C₂²×C₄×C₁₃₉	—	2	1	no	—
115	C₂²×C₄×C₁₃₉	—	2	2	no	—
116	C₂²×C₄×C₁₃₉	—	2	2	no	—
117	C₂²×C₄×C₁₃₉	—	2	2	no	—
118	C₂²×C₄×C₁₃₉	—	2	2	no	—
119	C₂²×C₄×C₁₃₉	—	2	2	no	—
120	C₂²×C₄×C₁₃₉	—	2	2	no	—
121	C₂²×C₄×C₁₃₉	—	2	2	no	—
122	C₂²×C₄×C₁₃₉	—	2	2	no	—
123	C₂²×C₄×C₁₃₉	—	2	2	no	—
124	C₂²×C₄×C₁₃₉	—	2	2	no	—
125	C₂²×C₄×C₁₃₉	—	2	2	no	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	2	no	—
128	C₂²×C₄×C₁₃₉	—	2	2	no	—
129	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
139	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
140	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
141	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
142	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
143	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
144	C₄⋊C₄×C₁₃₉	—	2	8	no	—
145	C₄⋊C₄×C₁₃₉	—	2	8	no	—
146	C₄⋊C₄×C₁₃₉	—	4	8	no	—
147	C₄²×C₁₃₉	—	2	8	no	—
148	C₄²×C₁₃₉	—	4	4	no	—
149	C₄²×C₁₃₉	—	4	4	no	—
150	C₄²×C₁₃₉	—	4	8	no	—
151	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
152	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
153	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
154	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
155	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
156	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
157	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
158	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
159	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
160	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	—	2	2	no	—
163	C₂×C₄×C₁₃₉	—	2	2	no	—
164	C₂×C₄×C₁₃₉	—	2	2	no	—
165	C₂×C₄×C₁₃₉	—	2	2	no	—
166	C₂×C₄×C₁₃₉	—	2	2	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	—	2	4	no	—
172	C₂×C₄×C₁₃₉	—	2	4	no	—
173	C₂×C₄×C₁₃₉	—	2	4	no	—
174	C₂×C₄×C₁₃₉	—	2	4	no	—
175	C₂×C₄×C₁₃₉	—	2	4	no	—
176	C₂×C₄×C₁₃₉	—	2	4	no	—
177	C₂×C₄×C₁₃₉	—	2	4	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	2	2	no	—
184	C₂×C₄×C₁₃₉	—	2	2	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	2	4	no	—
189	C₂×C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₄×C₁₃₉	—	2	4	no	—
192	C₂×C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₄×C₁₃₉	—	4	2	no	—
194	C₂×C₄×C₁₃₉	—	4	2	no	—
195	C₂×C₄×C₁₃₉	—	4	2	no	—
196	C₂×C₄×C₁₃₉	—	4	2	no	—
197	C₂×C₄×C₁₃₉	—	4	2	no	—
198	C₂×C₄×C₁₃₉	—	4	2	no	—
199	C₂×C₄×C₁₃₉	—	4	2	no	—
200	C₂×C₄×C₁₃₉	—	4	2	no	—
201	C₂×C₄×C₁₃₉	—	4	2	no	—
202	C₂×C₄×C₁₃₉	—	4	2	no	—
203	C₂×C₄×C₁₃₉	—	4	2	no	—
204	C₂×C₄×C₁₃₉	—	4	2	no	—
205	C₂×C₄×C₁₃₉	—	4	2	no	—
206	C₂×C₄×C₁₃₉	—	4	2	no	—
207	C₂×C₄×C₁₃₉	—	4	2	no	—
208	C₂×C₄×C₁₃₉	—	4	2	no	—
209	C₂×C₄×C₁₃₉	—	4	2	no	—
210	C₂×C₄×C₁₃₉	—	4	2	no	—
211	C₂×C₄×C₁₃₉	—	4	2	no	—
212	C₂×C₄×C₁₃₉	—	4	2	no	—
213	C₂×C₄×C₁₃₉	—	4	2	no	—
214	C₂×C₄×C₁₃₉	—	4	2	no	—
215	C₂×C₄×C₁₃₉	—	4	2	no	—
216	C₂×C₄×C₁₃₉	—	4	2	no	—
217	C₂×C₄×C₁₃₉	—	4	2	no	—
218	C₂×C₄×C₁₃₉	—	4	2	no	—
219	C₂×C₄×C₁₃₉	—	4	2	no	—
220	C₂×C₄×C₁₃₉	—	4	2	no	—
221	C₂×C₄×C₁₃₉	#117	1	4	yes	—
222	C₂×C₄×C₁₃₉	#117	1	4	yes	—
223	C₂×C₄×C₁₃₉	#117	1	4	yes	—
224	C₂×C₄×C₁₃₉	C₄×Q₈	1	4	yes	—
225	C₂²×C₁₃₉	C₂×#117	1	1	yes	characteristic
226	C₂²×C₁₃₉	C₂×#117	1	1	yes	characteristic
227	C₂²×C₁₃₉	C₂×#117	1	1	yes	characteristic
228	C₂²×C₁₃₉	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₂²×C₁₃₉	C₄×#41	1	1	yes	characteristic
230	C₂²×C₁₃₉	#518	1	1	yes	characteristic
231	C₂²×C₁₃₉	#520	1	1	yes	characteristic
232	C₂²×C₁₃₉	#529	1	2	yes	—
233	C₂²×C₁₃₉	#529	1	2	yes	—
234	C₂²×C₁₃₉	#529	1	2	yes	—
235	C₂²×C₁₃₉	#533	1	2	yes	—
236	C₂²×C₁₃₉	#538	1	2	yes	—
237	C₂²×C₁₃₉	#539	1	2	yes	—
238	C₂²×C₁₃₉	#551	1	2	yes	—
239	C₂²×C₁₃₉	#552	1	2	yes	—
240	C₂²×C₁₃₉	#553	1	2	yes	—
241	C₂²×C₁₃₉	#553	1	2	yes	—
242	C₂²×C₁₃₉	#554	1	1	yes	characteristic
243	C₂²×C₁₃₉	#554	1	2	yes	—
244	C₂²×C₁₃₉	#556	1	1	yes	characteristic
245	C₂²×C₁₃₉	#557	1	1	yes	characteristic
246	C₂²×C₁₃₉	#559	1	2	yes	—
247	C₂²×C₁₃₉	#559	1	1	yes	characteristic
248	C₄×C₁₃₉	—	2	4	no	—
249	C₄×C₁₃₉	—	2	4	no	—
250	C₄×C₁₃₉	—	2	4	no	—
251	C₄×C₁₃₉	—	2	4	no	—
252	C₄×C₁₃₉	—	4	2	no	—
253	C₄×C₁₃₉	—	4	4	no	—
254	C₄×C₁₃₉	—	4	4	no	—
255	C₄×C₁₃₉	—	4	2	no	—
256	C₄×C₁₃₉	—	4	2	no	—
257	C₄×C₁₃₉	—	8	2	no	—
258	C₄×C₁₃₉	—	8	2	no	—
259	C₂×C₁₃₉	#2283	1	1	yes	characteristic
260	C₂×C₁₃₉	#2295	1	1	yes	characteristic
261	C₂×C₁₃₉	#2318	1	1	yes	characteristic
262	C₂×C₁₃₉	#2343	1	1	yes	characteristic
263	C₂×C₁₃₉	#2345	1	1	yes	characteristic
264	C₂×C₁₃₉	#2355	1	1	yes	characteristic
265	C₂×C₁₃₉	#2357	1	1	yes	characteristic
266	C₂×C₁₃₉	#2589	1	2	yes	—
267	C₂×C₁₃₉	#2590	1	2	yes	—
268	C₂×C₁₃₉	#2596	1	2	yes	—
269	C₂×C₁₃₉	#2597	1	2	yes	—
270	#13934	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₁₃₉	#13934	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
273	#1445	C₂×C₁₃₉	1	2	yes	—
274	#1442	C₂×C₁₃₉	1	2	yes	—
275	#1436	C₂×C₁₃₉	1	2	yes	—
276	#1436	C₂×C₁₃₉	1	2	yes	—
277	C₄⋊#95	C₂×C₁₃₉	1	1	yes	characteristic
278	#1434	C₂×C₁₃₉	1	1	yes	characteristic
279	#1434	C₂×C₁₃₉	1	1	yes	characteristic
280	#1434	C₂×C₁₃₉	1	1	yes	characteristic
281	#1434	C₂×C₁₃₉	1	1	yes	characteristic
282	C₄×#95	C₂×C₁₃₉	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
284	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
286	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
288	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
291	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
293	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
294	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
295	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
296	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
297	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
298	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
299	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
300	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
301	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
302	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
303	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
304	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
306	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
308	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
309	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	4	2	no	—
324	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
326	C₂×C₄²	—	2	4	no	—
327	C₂×C₄²	—	2	4	no	—
328	C₂×C₄²	—	4	2	no	—
329	C₂×C₄²	—	4	2	no	—
330	C₂×C₄²	—	4	2	no	—
331	C₂×C₄²	—	4	2	no	—
332	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
333	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
334	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
335	#95	—	2	4	no	—
336	#95	—	2	2	no	—
337	#95	—	2	4	no	—
338	#95	—	2	4	no	—
339	#95	—	2	4	no	—
340	#95	—	2	4	no	—
341	#95	—	2	4	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	—	4	2	no	—
345	#95	—	4	2	no	—
346	#95	—	4	2	no	—
347	#95	—	4	2	no	—
348	#95	C₂×C₄×C₁₃₉	1	4	yes	—
349	#95	C₂×C₄×C₁₃₉	1	4	yes	—
350	#95	Q₈×C₁₃₉	1	4	yes	—
351	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
401	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
402	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
403	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
404	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
407	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
408	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
409	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
410	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
411	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
412	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
413	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
414	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	4	8	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	4	4	no	—
420	C₄²	—	4	4	no	—
421	C₄²	—	4	8	no	—
422	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
423	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
424	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
425	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
426	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
427	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
428	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
429	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
430	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
431	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
432	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	#117×C₁₃₉	1	4	yes	—
493	C₂×C₄	#117×C₁₃₉	1	4	yes	—
494	C₂×C₄	#117×C₁₃₉	1	4	yes	—
495	C₂×C₄	C₄×Q₈×C₁₃₉	1	4	yes	—
496	C₂²	C₂×#117×C₁₃₉	1	1	yes	characteristic
497	C₂²	C₂×#117×C₁₃₉	1	1	yes	characteristic
498	C₂²	C₂×#117×C₁₃₉	1	1	yes	characteristic
499	C₂²	C₂×C₄×Q₈×C₁₃₉	1	1	yes	characteristic
500	C₂²	C₄×#41×C₁₃₉	1	1	yes	characteristic
501	C₂²	#518×C₁₃₉	1	1	yes	characteristic
502	C₂²	#520×C₁₃₉	1	1	yes	characteristic
503	C₂²	#529×C₁₃₉	1	2	yes	—
504	C₂²	#529×C₁₃₉	1	2	yes	—
505	C₂²	#529×C₁₃₉	1	2	yes	—
506	C₂²	#533×C₁₃₉	1	2	yes	—
507	C₂²	#538×C₁₃₉	1	2	yes	—
508	C₂²	#539×C₁₃₉	1	2	yes	—
509	C₂²	#551×C₁₃₉	1	2	yes	—
510	C₂²	#552×C₁₃₉	1	2	yes	—
511	C₂²	#553×C₁₃₉	1	2	yes	—
512	C₂²	#553×C₁₃₉	1	2	yes	—
513	C₂²	#554×C₁₃₉	1	1	yes	characteristic
514	C₂²	#554×C₁₃₉	1	2	yes	—
515	C₂²	#556×C₁₃₉	1	1	yes	characteristic
516	C₂²	#557×C₁₃₉	1	1	yes	characteristic
517	C₂²	#559×C₁₃₉	1	2	yes	—
518	C₂²	#559×C₁₃₉	1	1	yes	characteristic
519	C₄	—	2	4	no	—
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	4	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	8	2	no	—
529	C₄	—	8	2	no	—
530	C₂	#2283×C₁₃₉	1	1	yes	characteristic
531	C₂	#2295×C₁₃₉	1	1	yes	characteristic
532	C₂	#2318×C₁₃₉	1	1	yes	characteristic
533	C₂	#2343×C₁₃₉	1	1	yes	characteristic
534	C₂	#2345×C₁₃₉	1	1	yes	characteristic
535	C₂	#2355×C₁₃₉	1	1	yes	characteristic
536	C₂	#2357×C₁₃₉	1	1	yes	characteristic
537	C₂	#2589×C₁₃₉	1	2	yes	—
538	C₂	#2590×C₁₃₉	1	2	yes	—
539	C₂	#2596×C₁₃₉	1	2	yes	—
540	C₂	#2597×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
19. C₄×C₄⋊C₄×C₁₃₉	C₄	semidirect
270. #13934	C₁₃₉	direct (N × H)
271. C₁₃₉	#13934	direct (N × H)
290. C₄×C₄⋊C₄	C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#1445×C₁₃₉	2
#1442×C₁₃₉	2
#1436×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#1434×C₁₃₉	2
C₄×#95×C₁₃₉	2
#13934	139

Subgroups — C139×#13934 #48008530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#13934 #48008530