Subgroups — C₁₃₉×#24527 #48019123

Order 35584.

1182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#450×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2073×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2055×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1892×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1877×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#1823×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1804×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
20	#450×C₁₃₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#103×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂×#102×C₁₃₉	—	2	4	no	—
24	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	#400×C₁₃₉	—	2	2	no	—
30	#391×C₁₃₉	C₂²	1	2	yes	complemented
31	#390×C₁₃₉	C₂²	1	2	yes	—
32	#386×C₁₃₉	—	2	2	no	—
33	#382×C₁₃₉	C₂²	1	2	yes	complemented
34	#381×C₁₃₉	—	2	1	no	—
35	#381×C₁₃₉	—	2	1	no	—
36	#380×C₁₃₉	C₂²	1	1	yes	characteristic
37	#379×C₁₃₉	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	#340×C₁₃₉	C₂²	1	2	yes	complemented
40	#340×C₁₃₉	C₂²	1	2	yes	complemented
41	#340×C₁₃₉	C₂²	1	2	yes	complemented
42	#336×C₁₃₉	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₃₉	—	2	1	no	—
44	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₉	—	2	4	no	—
46	C₂²×D₄×C₁₃₉	—	2	1	no	—
47	C₂²×D₄×C₁₃₉	—	2	2	no	—
48	C₂²×D₄×C₁₃₉	—	4	2	no	—
49	C₂²×D₄×C₁₃₉	D₄	1	4	yes	—
50	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃₉	—	2	1	no	—
53	C₂³×C₄×C₁₃₉	—	2	2	no	—
54	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₃₉	—	4	2	no	—
59	C₂²×C₈×C₁₃₉	—	2	2	no	—
60	C₂²×C₈×C₁₃₉	—	4	2	no	—
61	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
64	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
65	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
66	C₄×D₄×C₁₃₉	—	2	4	no	—
67	C₄×D₄×C₁₃₉	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
81	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
84	C₄⋊C₈×C₁₃₉	—	4	2	no	—
85	#103×C₁₃₉	—	4	2	no	—
86	#102×C₁₃₉	—	2	4	no	—
87	#102×C₁₃₉	—	2	4	no	—
88	#102×C₁₃₉	—	2	2	no	—
89	#102×C₁₃₉	—	2	2	no	—
90	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
91	#95×C₁₃₉	—	2	2	no	—
92	#95×C₁₃₉	—	2	2	no	—
93	#95×C₁₃₉	—	2	2	no	—
94	#95×C₁₃₉	—	2	2	no	—
95	#95×C₁₃₉	—	2	1	no	—
96	#95×C₁₃₉	D₄	1	2	yes	—
97	C₂⁴×C₁₃₉	—	2	1	no	—
98	C₂⁴×C₁₃₉	—	2	1	no	—
99	C₂⁴×C₁₃₉	—	2	4	no	—
100	C₂⁴×C₁₃₉	—	4	4	no	—
101	C₂⁴×C₁₃₉	—	4	2	no	—
102	C₂⁴×C₁₃₉	—	4	2	no	—
103	C₂⁴×C₁₃₉	—	8	2	no	—
104	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₃₉	—	2	1	no	—
106	C₂×Q₈×C₁₃₉	—	2	1	no	—
107	C₂×Q₈×C₁₃₉	—	2	2	no	—
108	C₂×Q₈×C₁₃₉	—	2	2	no	—
109	C₂×D₄×C₁₃₉	—	2	8	no	—
110	C₂×D₄×C₁₃₉	—	2	4	no	—
111	C₂×D₄×C₁₃₉	—	2	1	no	—
112	C₂×D₄×C₁₃₉	—	2	2	no	—
113	C₂×D₄×C₁₃₉	—	2	1	no	—
114	C₂×D₄×C₁₃₉	—	2	2	no	—
115	C₂×D₄×C₁₃₉	—	2	2	no	—
116	C₂×D₄×C₁₃₉	—	4	4	no	—
117	C₂×D₄×C₁₃₉	—	4	8	no	—
118	C₂×D₄×C₁₃₉	—	4	4	no	—
119	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₃₉	#41	1	4	yes	—
122	C₂²×C₄×C₁₃₉	—	2	2	no	—
123	C₂²×C₄×C₁₃₉	—	2	2	no	—
124	C₂²×C₄×C₁₃₉	—	2	1	no	—
125	C₂²×C₄×C₁₃₉	—	2	1	no	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	2	no	—
128	C₂²×C₄×C₁₃₉	—	4	4	no	—
129	C₂²×C₄×C₁₃₉	—	4	4	no	—
130	C₂²×C₄×C₁₃₉	—	4	2	no	—
131	C₂²×C₄×C₁₃₉	—	4	2	no	—
132	C₂²×C₄×C₁₃₉	—	4	2	no	—
133	C₂²×C₄×C₁₃₉	—	8	2	no	—
134	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₁₃₉	—	4	4	no	—
141	SD₁₆×C₁₃₉	—	4	4	no	—
142	C₂×C₈×C₁₃₉	—	2	1	no	—
143	C₂×C₈×C₁₃₉	—	2	1	no	—
144	C₂×C₈×C₁₃₉	—	2	2	no	—
145	C₂×C₈×C₁₃₉	—	2	2	no	—
146	C₂×C₈×C₁₃₉	—	2	2	no	—
147	C₂×C₈×C₁₃₉	—	2	2	no	—
148	C₂×C₈×C₁₃₉	—	2	2	no	—
149	C₂×C₈×C₁₃₉	—	4	4	no	—
150	C₄⋊C₄×C₁₃₉	—	2	2	no	—
151	C₄⋊C₄×C₁₃₉	—	2	1	no	—
152	C₄⋊C₄×C₁₃₉	—	2	2	no	—
153	C₄⋊C₄×C₁₃₉	—	2	2	no	—
154	C₄⋊C₄×C₁₃₉	—	2	1	no	—
155	C₄⋊C₄×C₁₃₉	—	2	2	no	—
156	C₄⋊C₄×C₁₃₉	—	4	2	no	—
157	C₄⋊C₄×C₁₃₉	—	4	2	no	—
158	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
163	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
164	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
165	C₄²×C₁₃₉	—	2	2	no	—
166	C₄²×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	2	no	—
168	C₂³×C₁₃₉	—	2	2	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	4	no	—
171	C₂³×C₁₃₉	—	2	2	no	—
172	C₂³×C₁₃₉	—	4	8	no	—
173	C₂³×C₁₃₉	—	4	1	no	—
174	C₂³×C₁₃₉	—	4	1	no	—
175	C₂³×C₁₃₉	—	4	2	no	—
176	C₂³×C₁₃₉	—	4	2	no	—
177	C₂³×C₁₃₉	—	4	1	no	—
178	C₂³×C₁₃₉	—	4	1	no	—
179	C₂³×C₁₃₉	—	4	2	no	—
180	C₂³×C₁₃₉	—	4	8	no	—
181	C₂³×C₁₃₉	—	8	4	no	—
182	C₂³×C₁₃₉	—	8	8	no	—
183	C₂³×C₁₃₉	—	8	8	no	—
184	C₂³×C₁₃₉	#121	1	2	yes	—
185	C₂³×C₁₃₉	#135	1	2	yes	—
186	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
187	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃₉	—	4	1	no	—
189	Q₈×C₁₃₉	—	4	1	no	—
190	Q₈×C₁₃₉	—	4	2	no	—
191	D₄×C₁₃₉	—	2	2	no	—
192	D₄×C₁₃₉	—	2	2	no	—
193	D₄×C₁₃₉	—	2	2	no	—
194	D₄×C₁₃₉	—	2	4	no	—
195	D₄×C₁₃₉	—	4	8	no	—
196	D₄×C₁₃₉	—	4	2	no	—
197	D₄×C₁₃₉	#123	1	4	yes	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	2	2	no	—
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	2	no	—
204	C₂×C₄×C₁₃₉	—	2	2	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	4	1	no	—
209	C₂×C₄×C₁₃₉	—	4	1	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	—	8	8	no	—
219	C₂×C₄×C₁₃₉	—	8	4	no	—
220	C₂×C₄×C₁₃₉	#121	1	2	yes	—
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
225	C₈×C₁₃₉	—	4	1	no	—
226	C₈×C₁₃₉	—	4	2	no	—
227	C₈×C₁₃₉	—	4	1	no	—
228	C₂²×C₁₃₉	—	2	2	no	—
229	C₂²×C₁₃₉	—	2	4	no	—
230	C₂²×C₁₃₉	—	2	2	no	—
231	C₂²×C₁₃₉	—	2	4	no	—
232	C₂²×C₁₃₉	—	2	4	no	—
233	C₂²×C₁₃₉	—	4	2	no	—
234	C₂²×C₁₃₉	—	4	4	no	—
235	C₂²×C₁₃₉	—	4	2	no	—
236	C₂²×C₁₃₉	—	4	4	no	—
237	C₂²×C₁₃₉	—	4	2	no	—
238	C₂²×C₁₃₉	—	4	2	no	—
239	C₂²×C₁₃₉	—	4	2	no	—
240	C₂²×C₁₃₉	—	8	16	no	—
241	C₂²×C₁₃₉	—	8	2	no	—
242	C₂²×C₁₃₉	—	8	2	no	—
243	C₂²×C₁₃₉	#463	1	4	yes	—
244	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
245	C₂²×C₁₃₉	#546	1	2	yes	—
246	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
247	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂²×C₁₃₉	#577	1	2	yes	—
249	C₄×C₁₃₉	—	2	2	no	—
250	C₄×C₁₃₉	—	4	2	no	—
251	C₄×C₁₃₉	—	4	2	no	—
252	C₄×C₁₃₉	—	8	1	no	—
253	C₄×C₁₃₉	—	8	2	no	—
254	C₄×C₁₃₉	—	8	1	no	—
255	C₄×C₁₃₉	—	8	2	no	—
256	C₄×C₁₃₉	C₂×#123	1	1	yes	characteristic
257	C₄×C₁₃₉	#534	1	1	yes	characteristic
258	C₄×C₁₃₉	#551	1	2	yes	—
259	C₂×C₁₃₉	—	2	4	no	—
260	C₂×C₁₃₉	—	4	4	no	—
261	C₂×C₁₃₉	—	8	2	no	—
262	C₂×C₁₃₉	#2412	1	1	yes	characteristic
263	C₂×C₁₃₉	C₂×#463	1	1	yes	characteristic
264	C₂×C₁₃₉	#3042	1	1	yes	characteristic
265	C₂×C₁₃₉	#3296	1	2	yes	—
266	C₂×C₁₃₉	#3310	1	2	yes	—
267	#24527	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₁₃₉	#24527	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#450	C₂×C₁₃₉	1	1	yes	characteristic
270	C₂²×#102	C₂×C₁₃₉	1	1	yes	characteristic
271	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
272	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
273	#2073	C₂×C₁₃₉	1	2	yes	complemented
274	#2055	C₂×C₁₃₉	1	2	yes	complemented
275	#1892	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	#1877	C₂×C₁₃₉	1	2	yes	complemented
277	#1850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
278	#1823	C₂×C₁₃₉	1	1	yes	characteristic, complemented
279	#1804	C₂×C₁₃₉	1	2	yes	complemented
280	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
281	C₂²×SD₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂²×SD₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
283	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
284	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
286	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂²×C₂²⋊C₄	—	2	1	no	—
288	#450	—	2	4	no	—
289	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	complemented
290	C₂×#103	C₂²×C₁₃₉	1	2	yes	complemented
291	C₂×#102	—	2	4	no	—
292	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
293	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
294	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
295	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
297	#400	—	2	2	no	—
298	#391	C₂²×C₁₃₉	1	2	yes	complemented
299	#390	C₂²×C₁₃₉	1	2	yes	—
300	#386	—	2	2	no	—
301	#382	C₂²×C₁₃₉	1	2	yes	complemented
302	#381	—	2	1	no	—
303	#381	—	2	1	no	—
304	#380	C₂²×C₁₃₉	1	1	yes	characteristic
305	#379	—	2	1	no	—
306	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
307	#340	C₂²×C₁₃₉	1	2	yes	complemented
308	#340	C₂²×C₁₃₉	1	2	yes	complemented
309	#340	C₂²×C₁₃₉	1	2	yes	complemented
310	#336	C₂²×C₁₃₉	1	2	yes	complemented
311	C₂⁵	—	2	1	no	—
312	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	4	2	no	—
317	C₂²×D₄	D₄×C₁₃₉	1	4	yes	—
318	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	4	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	4	2	no	—
329	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	4	4	no	—
349	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
352	C₄⋊C₈	—	4	2	no	—
353	#103	—	4	2	no	—
354	#102	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	2	2	no	—
357	#102	—	2	2	no	—
358	C₂²⋊C₈	—	2	2	no	—
359	#95	—	2	1	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	#95	—	2	2	no	—
363	#95	—	2	2	no	—
364	#95	D₄×C₁₃₉	1	2	yes	—
365	C₂⁴	—	2	1	no	—
366	C₂⁴	—	2	1	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	4	4	no	—
369	C₂⁴	—	4	2	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	8	2	no	—
372	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
388	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
389	C₂×D₄	#41×C₁₃₉	1	4	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
406	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
408	SD₁₆	—	4	4	no	—
409	SD₁₆	—	4	4	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	8	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	8	4	no	—
450	C₂³	—	8	8	no	—
451	C₂³	—	8	8	no	—
452	C₂³	#121×C₁₃₉	1	2	yes	—
453	C₂³	#135×C₁₃₉	1	2	yes	—
454	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
455	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	4	8	no	—
464	D₄	—	4	2	no	—
465	D₄	#123×C₁₃₉	1	4	yes	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	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	—	8	8	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	#121×C₁₃₉	1	2	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
491	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
493	C₈	—	4	1	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	1	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	16	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	#463×C₁₃₉	1	4	yes	—
512	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
513	C₂²	#546×C₁₃₉	1	2	yes	—
514	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
515	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
516	C₂²	#577×C₁₃₉	1	2	yes	—
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	2	no	—
523	C₄	—	8	1	no	—
524	C₄	C₂×#123×C₁₃₉	1	1	yes	characteristic
525	C₄	#534×C₁₃₉	1	1	yes	characteristic
526	C₄	#551×C₁₃₉	1	2	yes	—
527	C₂	—	2	4	no	—
528	C₂	—	4	4	no	—
529	C₂	—	8	2	no	—
530	C₂	#2412×C₁₃₉	1	1	yes	characteristic
531	C₂	C₂×#463×C₁₃₉	1	1	yes	characteristic
532	C₂	#3042×C₁₃₉	1	1	yes	characteristic
533	C₂	#3296×C₁₃₉	1	2	yes	—
534	C₂	#3310×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₄×C₂²⋊C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2503×C₁₃₉	C₂	semidirect
5. #2073×C₁₃₉	C₂	semidirect
6. #2055×C₁₃₉	C₂	semidirect
7. #1892×C₁₃₉	C₂	semidirect
8. #1877×C₁₃₉	C₂	semidirect
9. #1850×C₁₃₉	C₂	semidirect
10. #1823×C₁₃₉	C₂	semidirect
11. #1804×C₁₃₉	C₂	semidirect
21. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
22. C₂×#103×C₁₃₉	C₂²	semidirect
30. #391×C₁₃₉	C₂²	semidirect
33. #382×C₁₃₉	C₂²	semidirect
39. #340×C₁₃₉	C₂²	semidirect
40. #340×C₁₃₉	C₂²	semidirect
41. #340×C₁₃₉	C₂²	semidirect
42. #336×C₁₃₉	C₂²	semidirect
267. #24527	C₁₃₉	direct (N × H)
268. C₁₃₉	#24527	direct (N × H)
271. #2503	C₂×C₁₃₉	semidirect
273. #2073	C₂×C₁₃₉	semidirect
274. #2055	C₂×C₁₃₉	semidirect
275. #1892	C₂×C₁₃₉	semidirect
276. #1877	C₂×C₁₃₉	semidirect
277. #1850	C₂×C₁₃₉	semidirect
278. #1823	C₂×C₁₃₉	semidirect
279. #1804	C₂×C₁₃₉	semidirect
289. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
290. C₂×#103	C₂²×C₁₃₉	semidirect
298. #391	C₂²×C₁₃₉	semidirect
301. #382	C₂²×C₁₃₉	semidirect
307. #340	C₂²×C₁₃₉	semidirect
308. #340	C₂²×C₁₃₉	semidirect
309. #340	C₂²×C₁₃₉	semidirect
310. #336	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#450×C₁₃₉	2
C₂²×#102×C₁₃₉	2
#2503×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#2073×C₁₃₉	2
#2055×C₁₃₉	2
#1892×C₁₃₉	2
#1877×C₁₃₉	2
#1850×C₁₃₉	2
#1823×C₁₃₉	2
#1804×C₁₃₉	2
#24527	139

Subgroups — C139×#24527 #48019123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#24527 #48019123