Subgroups — C₁₃₉×#20606 #48015202

Order 35584.

3722 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#421×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×#104×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2879×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1789×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#585×C₁₃₉	—	2	8	no	—
8	#585×C₁₃₉	—	2	8	no	—
9	C₂×2₋¹⁺⁴×C₁₃₉	—	2	1	no	—
10	C₂×2₋¹⁺⁴×C₁₃₉	C₄	1	4	yes	complemented
11	C₂×H(5,𝔽₂)×C₁₃₉	—	2	2	no	—
12	C₂×H(5,𝔽₂)×C₁₃₉	—	2	1	no	—
13	C₂×H(5,𝔽₂)×C₁₃₉	C₄	1	4	yes	complemented
14	C₂²×#41×C₁₃₉	—	2	4	no	—
15	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
17	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	#421×C₁₃₉	—	2	8	no	—
22	C₂×#104×C₁₃₉	—	2	8	no	—
23	C₂×#104×C₁₃₉	C₂²	1	8	yes	complemented
24	C₂×#104×C₁₃₉	C₂²	1	8	yes	complemented
25	#408×C₁₃₉	—	2	4	no	—
26	#407×C₁₃₉	C₂²	1	4	yes	complemented
27	#391×C₁₃₉	—	2	1	no	—
28	#390×C₁₃₉	—	2	1	no	—
29	#386×C₁₃₉	—	2	2	no	—
30	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
31	2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
32	2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
33	2₋¹⁺⁴×C₁₃₉	—	2	16	no	—
34	2₋¹⁺⁴×C₁₃₉	—	2	16	no	—
35	H(5,𝔽₂)×C₁₃₉	—	2	8	no	—
36	H(5,𝔽₂)×C₁₃₉	—	2	8	no	—
37	H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
38	H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
39	H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
40	H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
41	C₂×#41×C₁₃₉	—	2	32	no	—
42	C₂×#41×C₁₃₉	—	2	32	no	—
43	C₂×#41×C₁₃₉	—	2	16	no	—
44	C₂×#41×C₁₃₉	—	2	16	no	—
45	C₂×#41×C₁₃₉	—	2	4	no	—
46	C₂×#41×C₁₃₉	—	2	8	no	—
47	C₂×#41×C₁₃₉	—	2	4	no	—
48	C₂×#41×C₁₃₉	—	2	4	no	—
49	C₂×#41×C₁₃₉	—	2	2	no	—
50	C₂×#41×C₁₃₉	—	2	2	no	—
51	C₂×#41×C₁₃₉	—	2	4	no	—
52	C₂×#41×C₁₃₉	—	2	4	no	—
53	C₂×#41×C₁₃₉	—	2	4	no	—
54	C₂×#41×C₁₃₉	—	2	4	no	—
55	C₂×#41×C₁₃₉	—	2	4	no	—
56	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
57	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
58	C₂×#41×C₁₃₉	C₂×C₄	1	8	yes	complemented
59	C₂×#41×C₁₃₉	D₄	1	8	yes	—
60	C₂×#41×C₁₃₉	D₄	1	8	yes	—
61	C₂×#41×C₁₃₉	D₄	1	4	yes	—
62	C₂×#41×C₁₃₉	C₂³	1	4	yes	—
63	C₂²×Q₈×C₁₃₉	—	2	4	no	—
64	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
66	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₁₃₉	—	2	2	no	—
68	C₂²×D₄×C₁₃₉	—	2	4	no	—
69	C₂²×D₄×C₁₃₉	—	2	4	no	—
70	C₂²×D₄×C₁₃₉	—	2	8	no	—
71	C₂²×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	complemented
73	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
74	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₁₃₉	—	2	4	no	—
76	C₂³×C₄×C₁₃₉	—	2	2	no	—
77	C₂³×C₄×C₁₃₉	—	2	1	no	—
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₁₃₉	—	2	2	no	—
81	C₂×M₁₆×C₁₃₉	—	2	4	no	—
82	C₂×M₁₆×C₁₃₉	—	2	4	no	—
83	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
84	C₂²×C₈×C₁₃₉	—	2	2	no	—
85	#117×C₁₃₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
89	C₂×C₄²×C₁₃₉	—	2	4	no	—
90	C₂×C₄²×C₁₃₉	—	2	1	no	—
91	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
93	#104×C₁₃₉	—	2	16	no	—
94	#104×C₁₃₉	—	2	16	no	—
95	C₂²⋊C₈×C₁₃₉	—	2	8	no	—
96	#95×C₁₃₉	—	2	4	no	—
97	C₂⁴×C₁₃₉	—	2	2	no	—
98	C₂⁴×C₁₃₉	—	2	4	no	—
99	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
100	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
101	#41×C₁₃₉	—	2	32	no	—
102	#41×C₁₃₉	—	2	16	no	—
103	#41×C₁₃₉	—	2	16	no	—
104	#41×C₁₃₉	—	2	64	no	—
105	#41×C₁₃₉	—	2	32	no	—
106	#41×C₁₃₉	—	2	32	no	—
107	#41×C₁₃₉	—	2	16	no	—
108	#41×C₁₃₉	—	2	16	no	—
109	#41×C₁₃₉	—	2	8	no	—
110	#41×C₁₃₉	—	2	8	no	—
111	#41×C₁₃₉	—	2	8	no	—
112	#41×C₁₃₉	—	2	8	no	—
113	#41×C₁₃₉	—	2	8	no	—
114	#41×C₁₃₉	—	2	8	no	—
115	#41×C₁₃₉	—	2	8	no	—
116	#41×C₁₃₉	—	2	8	no	—
117	#41×C₁₃₉	—	2	8	no	—
118	#41×C₁₃₉	—	2	4	no	—
119	#41×C₁₃₉	—	2	4	no	—
120	#41×C₁₃₉	C₂²⋊C₄	1	16	yes	complemented
121	#41×C₁₃₉	C₂×D₄	1	8	yes	—
122	#41×C₁₃₉	C₂×D₄	1	8	yes	—
123	C₂×Q₈×C₁₃₉	—	2	32	no	—
124	C₂×Q₈×C₁₃₉	—	2	16	no	—
125	C₂×Q₈×C₁₃₉	—	2	2	no	—
126	C₂×Q₈×C₁₃₉	—	2	4	no	—
127	C₂×Q₈×C₁₃₉	—	2	4	no	—
128	C₂×Q₈×C₁₃₉	—	2	2	no	—
129	C₂×Q₈×C₁₃₉	—	2	2	no	—
130	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	4	yes	—
131	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
132	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₁₃₉	—	2	16	no	—
134	C₂×D₄×C₁₃₉	—	2	16	no	—
135	C₂×D₄×C₁₃₉	—	2	64	no	—
136	C₂×D₄×C₁₃₉	—	2	32	no	—
137	C₂×D₄×C₁₃₉	—	2	4	no	—
138	C₂×D₄×C₁₃₉	—	2	8	no	—
139	C₂×D₄×C₁₃₉	—	2	8	no	—
140	C₂×D₄×C₁₃₉	—	2	8	no	—
141	C₂×D₄×C₁₃₉	—	2	4	no	—
142	C₂×D₄×C₁₃₉	—	2	4	no	—
143	C₂×D₄×C₁₃₉	—	2	4	no	—
144	C₂×D₄×C₁₃₉	—	2	16	no	—
145	C₂×D₄×C₁₃₉	—	2	2	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	2	4	no	—
148	C₂×D₄×C₁₃₉	—	2	2	no	—
149	C₂×D₄×C₁₃₉	—	2	2	no	—
150	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
151	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
152	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
153	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₃₉	—	2	32	no	—
155	C₂²×C₄×C₁₃₉	—	2	2	no	—
156	C₂²×C₄×C₁₃₉	—	2	4	no	—
157	C₂²×C₄×C₁₃₉	—	2	4	no	—
158	C₂²×C₄×C₁₃₉	—	2	8	no	—
159	C₂²×C₄×C₁₃₉	—	2	8	no	—
160	C₂²×C₄×C₁₃₉	—	2	8	no	—
161	C₂²×C₄×C₁₃₉	—	2	4	no	—
162	C₂²×C₄×C₁₃₉	—	2	4	no	—
163	C₂²×C₄×C₁₃₉	—	2	4	no	—
164	C₂²×C₄×C₁₃₉	—	2	2	no	—
165	C₂²×C₄×C₁₃₉	—	2	2	no	—
166	C₂²×C₄×C₁₃₉	—	4	4	no	—
167	C₂²×C₄×C₁₃₉	—	4	2	no	—
168	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	M₁₆×C₁₃₉	—	2	4	no	—
178	M₁₆×C₁₃₉	—	2	4	no	—
179	M₁₆×C₁₃₉	—	4	4	no	—
180	C₂×C₈×C₁₃₉	—	2	4	no	—
181	C₂×C₈×C₁₃₉	—	4	4	no	—
182	C₄⋊C₄×C₁₃₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
185	C₄²×C₁₃₉	—	2	4	no	—
186	C₄²×C₁₃₉	—	2	4	no	—
187	C₄²×C₁₃₉	—	4	2	no	—
188	C₂³×C₁₃₉	—	2	16	no	—
189	C₂³×C₁₃₉	—	2	4	no	—
190	C₂³×C₁₃₉	—	2	2	no	—
191	C₂³×C₁₃₉	—	2	2	no	—
192	C₂³×C₁₃₉	—	2	8	no	—
193	C₂³×C₁₃₉	—	4	2	no	—
194	C₂³×C₁₃₉	—	4	4	no	—
195	C₂³×C₁₃₉	—	8	4	no	—
196	C₂³×C₁₃₉	—	8	8	no	—
197	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂³×C₁₃₉	#120	1	2	yes	—
200	C₂³×C₁₃₉	#120	1	2	yes	—
201	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₁₃₉	—	2	16	no	—
203	Q₈×C₁₃₉	—	2	4	no	—
204	Q₈×C₁₃₉	—	2	8	no	—
205	Q₈×C₁₃₉	—	2	8	no	—
206	Q₈×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	—
207	D₄×C₁₃₉	—	2	32	no	—
208	D₄×C₁₃₉	—	2	16	no	—
209	D₄×C₁₃₉	—	2	8	no	—
210	D₄×C₁₃₉	—	2	8	no	—
211	D₄×C₁₃₉	—	2	16	no	—
212	D₄×C₁₃₉	—	2	16	no	—
213	D₄×C₁₃₉	—	2	4	no	—
214	D₄×C₁₃₉	—	2	8	no	—
215	D₄×C₁₃₉	—	2	8	no	—
216	D₄×C₁₃₉	C₂×C₂²⋊C₄	1	8	yes	—
217	C₂×C₄×C₁₃₉	—	2	16	no	—
218	C₂×C₄×C₁₃₉	—	2	32	no	—
219	C₂×C₄×C₁₃₉	—	2	4	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	8	no	—
223	C₂×C₄×C₁₃₉	—	2	8	no	—
224	C₂×C₄×C₁₃₉	—	2	8	no	—
225	C₂×C₄×C₁₃₉	—	2	8	no	—
226	C₂×C₄×C₁₃₉	—	2	8	no	—
227	C₂×C₄×C₁₃₉	—	2	16	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	4	2	no	—
230	C₂×C₄×C₁₃₉	—	4	8	no	—
231	C₂×C₄×C₁₃₉	—	4	2	no	—
232	C₂×C₄×C₁₃₉	—	4	4	no	—
233	C₂×C₄×C₁₃₉	—	4	2	no	—
234	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
235	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
237	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₁₃₉	#120	1	4	yes	—
239	C₂×C₄×C₁₃₉	#120	1	4	yes	—
240	C₂×C₄×C₁₃₉	#120	1	2	yes	—
241	C₂×C₄×C₁₃₉	#120	1	2	yes	—
242	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₁₃₉	—	4	4	no	—
247	C₂²×C₁₃₉	—	2	2	no	—
248	C₂²×C₁₃₉	—	2	4	no	—
249	C₂²×C₁₃₉	—	2	8	no	—
250	C₂²×C₁₃₉	—	2	4	no	—
251	C₂²×C₁₃₉	—	2	8	no	—
252	C₂²×C₁₃₉	—	4	2	no	—
253	C₂²×C₁₃₉	—	4	2	no	—
254	C₂²×C₁₃₉	—	4	8	no	—
255	C₂²×C₁₃₉	—	8	2	no	—
256	C₂²×C₁₃₉	—	8	2	no	—
257	C₂²×C₁₃₉	—	8	8	no	—
258	C₂²×C₁₃₉	—	8	16	no	—
259	C₂²×C₁₃₉	#379	1	4	yes	—
260	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
262	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
263	C₄×C₁₃₉	—	2	8	no	—
264	C₄×C₁₃₉	—	2	4	no	—
265	C₄×C₁₃₉	—	4	4	no	—
266	C₄×C₁₃₉	—	8	2	no	—
267	C₄×C₁₃₉	#379	1	4	yes	—
268	C₄×C₁₃₉	C₂²×C₂²⋊C₄	1	2	yes	—
269	C₄×C₁₃₉	C₂×#120	1	2	yes	—
270	C₂×C₁₃₉	—	2	1	no	—
271	C₂×C₁₃₉	—	2	1	no	—
272	C₂×C₁₃₉	—	2	4	no	—
273	C₂×C₁₃₉	—	4	4	no	—
274	C₂×C₁₃₉	—	4	8	no	—
275	C₂×C₁₃₉	C₂×#379	1	1	yes	characteristic
276	C₂×C₁₃₉	#2901	1	2	yes	—
277	#20606	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₁₃₉	#20606	1	1	yes	characteristic, direct product factor, Sylow
279	C₂×#585	C₂×C₁₃₉	1	1	yes	characteristic
280	C₂×#421	C₂×C₁₃₉	1	2	yes	complemented
281	C₂²×#104	C₂×C₁₃₉	1	2	yes	complemented
282	#2879	C₂×C₁₃₉	1	1	yes	characteristic, complemented
283	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
284	#1789	C₂×C₁₃₉	1	8	yes	complemented
285	#585	—	2	8	no	—
286	#585	—	2	8	no	—
287	C₂×2₋¹⁺⁴	—	2	1	no	—
288	C₂×2₋¹⁺⁴	C₄×C₁₃₉	1	4	yes	complemented
289	C₂×H(5,𝔽₂)	—	2	2	no	—
290	C₂×H(5,𝔽₂)	—	2	1	no	—
291	C₂×H(5,𝔽₂)	C₄×C₁₃₉	1	4	yes	complemented
292	C₂²×#41	—	2	4	no	—
293	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
294	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
295	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	complemented
297	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
298	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
299	#421	—	2	8	no	—
300	C₂×#104	—	2	8	no	—
301	C₂×#104	C₂²×C₁₃₉	1	8	yes	complemented
302	C₂×#104	C₂²×C₁₃₉	1	8	yes	complemented
303	#408	—	2	4	no	—
304	#407	C₂²×C₁₃₉	1	4	yes	complemented
305	#391	—	2	1	no	—
306	#390	—	2	1	no	—
307	#386	—	2	2	no	—
308	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
309	2₋¹⁺⁴	—	2	8	no	—
310	2₋¹⁺⁴	—	2	8	no	—
311	2₋¹⁺⁴	—	2	16	no	—
312	2₋¹⁺⁴	—	2	16	no	—
313	H(5,𝔽₂)	—	2	8	no	—
314	H(5,𝔽₂)	—	2	8	no	—
315	H(5,𝔽₂)	—	2	16	no	—
316	H(5,𝔽₂)	—	2	16	no	—
317	H(5,𝔽₂)	—	2	16	no	—
318	H(5,𝔽₂)	—	2	16	no	—
319	C₂×#41	—	2	32	no	—
320	C₂×#41	—	2	32	no	—
321	C₂×#41	—	2	16	no	—
322	C₂×#41	—	2	16	no	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	—	2	8	no	—
325	C₂×#41	—	2	4	no	—
326	C₂×#41	—	2	4	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	—	2	4	no	—
331	C₂×#41	—	2	4	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	2	4	no	—
334	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
335	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
336	C₂×#41	C₂×C₄×C₁₃₉	1	8	yes	complemented
337	C₂×#41	D₄×C₁₃₉	1	8	yes	—
338	C₂×#41	D₄×C₁₃₉	1	8	yes	—
339	C₂×#41	D₄×C₁₃₉	1	4	yes	—
340	C₂×#41	C₂³×C₁₃₉	1	4	yes	—
341	C₂²×Q₈	—	2	4	no	—
342	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
343	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
344	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	4	no	—
347	C₂²×D₄	—	2	4	no	—
348	C₂²×D₄	—	2	8	no	—
349	C₂²×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
350	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	complemented
351	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
352	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
353	C₂³×C₄	—	2	4	no	—
354	C₂³×C₄	—	2	2	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	4	no	—
360	C₂×M₁₆	—	2	4	no	—
361	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
362	C₂²×C₈	—	2	2	no	—
363	#117	—	2	4	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₄²	—	2	4	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
370	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
371	#104	—	2	16	no	—
372	#104	—	2	16	no	—
373	C₂²⋊C₈	—	2	8	no	—
374	#95	—	2	4	no	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
378	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
379	#41	—	2	32	no	—
380	#41	—	2	16	no	—
381	#41	—	2	16	no	—
382	#41	—	2	64	no	—
383	#41	—	2	32	no	—
384	#41	—	2	32	no	—
385	#41	—	2	16	no	—
386	#41	—	2	16	no	—
387	#41	—	2	8	no	—
388	#41	—	2	8	no	—
389	#41	—	2	8	no	—
390	#41	—	2	8	no	—
391	#41	—	2	8	no	—
392	#41	—	2	8	no	—
393	#41	—	2	8	no	—
394	#41	—	2	8	no	—
395	#41	—	2	8	no	—
396	#41	—	2	4	no	—
397	#41	—	2	4	no	—
398	#41	C₂²⋊C₄×C₁₃₉	1	16	yes	complemented
399	#41	C₂×D₄×C₁₃₉	1	8	yes	—
400	#41	C₂×D₄×C₁₃₉	1	8	yes	—
401	C₂×Q₈	—	2	32	no	—
402	C₂×Q₈	—	2	16	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	4	yes	—
409	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
410	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	64	no	—
414	C₂×D₄	—	2	32	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	16	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
429	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
430	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
431	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
432	C₂²×C₄	—	2	32	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	8	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
447	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
450	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
455	M₁₆	—	2	4	no	—
456	M₁₆	—	2	4	no	—
457	M₁₆	—	4	4	no	—
458	C₂×C₈	—	2	4	no	—
459	C₂×C₈	—	4	4	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	8	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	4	2	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	8	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	8	4	no	—
474	C₂³	—	8	8	no	—
475	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
476	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
477	C₂³	#120×C₁₃₉	1	2	yes	—
478	C₂³	#120×C₁₃₉	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
480	Q₈	—	2	16	no	—
481	Q₈	—	2	4	no	—
482	Q₈	—	2	8	no	—
483	Q₈	—	2	8	no	—
484	Q₈	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	—
485	D₄	—	2	32	no	—
486	D₄	—	2	16	no	—
487	D₄	—	2	8	no	—
488	D₄	—	2	8	no	—
489	D₄	—	2	16	no	—
490	D₄	—	2	16	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	8	no	—
493	D₄	—	2	8	no	—
494	D₄	C₂×C₂²⋊C₄×C₁₃₉	1	8	yes	—
495	C₂×C₄	—	2	16	no	—
496	C₂×C₄	—	2	32	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	16	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
513	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
515	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
516	C₂×C₄	#120×C₁₃₉	1	4	yes	—
517	C₂×C₄	#120×C₁₃₉	1	4	yes	—
518	C₂×C₄	#120×C₁₃₉	1	2	yes	—
519	C₂×C₄	#120×C₁₃₉	1	2	yes	—
520	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
524	C₈	—	4	4	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	8	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	8	8	no	—
536	C₂²	—	8	16	no	—
537	C₂²	#379×C₁₃₉	1	4	yes	—
538	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
539	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
540	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
541	C₄	—	2	8	no	—
542	C₄	—	2	4	no	—
543	C₄	—	4	4	no	—
544	C₄	—	8	2	no	—
545	C₄	#379×C₁₃₉	1	4	yes	—
546	C₄	C₂²×C₂²⋊C₄×C₁₃₉	1	2	yes	—
547	C₄	C₂×#120×C₁₃₉	1	2	yes	—
548	C₂	—	2	1	no	—
549	C₂	—	2	1	no	—
550	C₂	—	2	4	no	—
551	C₂	—	4	4	no	—
552	C₂	—	4	8	no	—
553	C₂	C₂×#379×C₁₃₉	1	1	yes	characteristic
554	C₂	#2901×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
prime radical	C₂×#585×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂²×#41×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#421×C₁₃₉	C₂	semidirect
3. C₂²×#104×C₁₃₉	C₂	semidirect
4. #2879×C₁₃₉	C₂	semidirect
5. #2297×C₁₃₉	C₂	semidirect
6. #1789×C₁₃₉	C₂	semidirect
10. C₂×2₋¹⁺⁴×C₁₃₉	C₄	semidirect
13. C₂×H(5,𝔽₂)×C₁₃₉	C₄	semidirect
18. C₂²×M₁₆×C₁₃₉	C₂²	semidirect
19. C₂×#117×C₁₃₉	C₂²	semidirect
20. C₂²×C₄²×C₁₃₉	C₂²	semidirect
23. C₂×#104×C₁₃₉	C₂²	semidirect
24. C₂×#104×C₁₃₉	C₂²	semidirect
26. #407×C₁₃₉	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
58. C₂×#41×C₁₃₉	C₂×C₄	semidirect
65. C₂²×Q₈×C₁₃₉	C₂×C₄	semidirect
72. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
120. #41×C₁₃₉	C₂²⋊C₄	semidirect
131. C₂×Q₈×C₁₃₉	C₂²⋊C₄	semidirect
152. C₂×D₄×C₁₃₉	C₂²⋊C₄	semidirect
277. #20606	C₁₃₉	direct (N × H)
278. C₁₃₉	#20606	direct (N × H)
280. C₂×#421	C₂×C₁₃₉	semidirect
281. C₂²×#104	C₂×C₁₃₉	semidirect
282. #2879	C₂×C₁₃₉	semidirect
283. #2297	C₂×C₁₃₉	semidirect
284. #1789	C₂×C₁₃₉	semidirect
288. C₂×2₋¹⁺⁴	C₄×C₁₃₉	semidirect
291. C₂×H(5,𝔽₂)	C₄×C₁₃₉	semidirect
296. C₂²×M₁₆	C₂²×C₁₃₉	semidirect
297. C₂×#117	C₂²×C₁₃₉	semidirect
298. C₂²×C₄²	C₂²×C₁₃₉	semidirect
301. C₂×#104	C₂²×C₁₃₉	semidirect
302. C₂×#104	C₂²×C₁₃₉	semidirect
304. #407	C₂²×C₁₃₉	semidirect
308. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
336. C₂×#41	C₂×C₄×C₁₃₉	semidirect
343. C₂²×Q₈	C₂×C₄×C₁₃₉	semidirect
350. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
398. #41	C₂²⋊C₄×C₁₃₉	semidirect
409. C₂×Q₈	C₂²⋊C₄×C₁₃₉	semidirect
430. C₂×D₄	C₂²⋊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×#585×C₁₃₉	2
C₂×#421×C₁₃₉	2
C₂²×#104×C₁₃₉	2
#2879×C₁₃₉	2
#2297×C₁₃₉	2
#1789×C₁₃₉	2
#20606	139

Subgroups — C139×#20606 #48015202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20606 #48015202