Subgroups — C₁₃₉×#33526 #48028122

Order 35584.

1150 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#508×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#3061×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2189×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2187×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2186×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2184×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2139×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#357×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2113×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₁₃₉	—	2	1	no	—
13	#576×C₁₃₉	—	2	4	no	—
14	#576×C₁₃₉	—	2	4	no	—
15	C₂×AGL(1,ℤ/8)×C₁₃₉	—	2	1	no	—
16	C₂×AGL(1,ℤ/8)×C₁₃₉	—	2	2	no	—
17	C₂×#135×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₁₃₉	C₂²	1	1	yes	characteristic
23	#537×C₁₃₉	—	2	1	no	—
24	#509×C₁₃₉	—	2	4	no	—
25	#508×C₁₃₉	—	2	4	no	—
26	C₂×Q₃₂×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×SD₃₂×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×SD₃₂×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×D₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₁₆×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×M₃₂×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	#468×C₁₃₉	—	2	2	no	—
35	#467×C₁₃₉	C₂²	1	2	yes	complemented
36	#466×C₁₃₉	C₂²	1	2	yes	complemented
37	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	#417×C₁₃₉	—	2	1	no	—
39	#358×C₁₃₉	C₂²	1	2	yes	complemented
40	#357×C₁₃₉	C₂²	1	2	yes	complemented
41	#357×C₁₃₉	C₂²	1	2	yes	complemented
42	#357×C₁₃₉	C₂²	1	2	yes	complemented
43	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	complemented
44	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	complemented
45	H(5,𝔽₂)×C₁₃₉	—	2	8	no	—
46	H(5,𝔽₂)×C₁₃₉	—	4	4	no	—
47	C₂×#41×C₁₃₉	—	2	2	no	—
48	C₂×#41×C₁₃₉	—	2	1	no	—
49	C₂×#41×C₁₃₉	—	2	1	no	—
50	C₂×#41×C₁₃₉	—	4	1	no	—
51	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₃₉	—	2	2	no	—
53	C₂²×D₄×C₁₃₉	—	2	1	no	—
54	C₂²×D₄×C₁₃₉	—	4	2	no	—
55	C₂²×D₄×C₁₃₉	—	4	1	no	—
56	AGL(1,ℤ/8)×C₁₃₉	—	2	8	no	—
57	AGL(1,ℤ/8)×C₁₃₉	—	2	16	no	—
58	#135×C₁₃₉	—	2	4	no	—
59	#135×C₁₃₉	—	2	4	no	—
60	#135×C₁₃₉	—	2	2	no	—
61	#135×C₁₃₉	—	2	2	no	—
62	#135×C₁₃₉	—	2	2	no	—
63	#135×C₁₃₉	D₄	1	4	yes	complemented
64	C₂×Q₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
67	C₂×SD₁₆×C₁₃₉	—	2	1	no	—
68	C₂×SD₁₆×C₁₃₉	—	2	1	no	—
69	C₂×D₈×C₁₃₉	—	2	4	no	—
70	C₂×D₈×C₁₃₉	—	2	4	no	—
71	C₂×D₈×C₁₃₉	—	2	2	no	—
72	C₂×D₈×C₁₃₉	—	2	1	no	—
73	C₂×D₈×C₁₃₉	—	2	2	no	—
74	C₂×D₈×C₁₃₉	D₄	1	4	yes	complemented
75	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂×D₈×C₁₃₉	C₂³	1	2	yes	—
78	#131×C₁₃₉	—	2	2	no	—
79	#131×C₁₃₉	—	2	2	no	—
80	C₂×M₁₆×C₁₃₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₁₃₉	D₄	1	2	yes	—
82	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
85	C₂²⋊Q₈×C₁₃₉	—	4	1	no	—
86	#121×C₁₃₉	—	2	2	no	—
87	#121×C₁₃₉	—	4	1	no	—
88	#121×C₁₃₉	—	4	2	no	—
89	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
90	Q₃₂×C₁₃₉	—	2	2	no	—
91	SD₃₂×C₁₃₉	—	2	2	no	—
92	SD₃₂×C₁₃₉	—	2	2	no	—
93	SD₃₂×C₁₃₉	—	2	4	no	—
94	D₁₆×C₁₃₉	—	2	2	no	—
95	D₁₆×C₁₃₉	—	2	4	no	—
96	M₃₂×C₁₃₉	—	2	2	no	—
97	C₂×C₁₆×C₁₃₉	—	2	2	no	—
98	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
101	#107×C₁₃₉	—	2	1	no	—
102	#107×C₁₃₉	C₂³	1	2	yes	—
103	#103×C₁₃₉	—	2	2	no	—
104	#102×C₁₃₉	—	2	2	no	—
105	C₂⁴×C₁₃₉	—	4	2	no	—
106	C₂⁴×C₁₃₉	—	4	1	no	—
107	#41×C₁₃₉	—	2	2	no	—
108	#41×C₁₃₉	—	2	2	no	—
109	#41×C₁₃₉	—	2	8	no	—
110	#41×C₁₃₉	—	2	4	no	—
111	#41×C₁₃₉	—	4	4	no	—
112	#41×C₁₃₉	—	4	8	no	—
113	#41×C₁₃₉	—	4	2	no	—
114	#41×C₁₃₉	—	4	2	no	—
115	#41×C₁₃₉	—	4	2	no	—
116	C₂×Q₈×C₁₃₉	—	2	1	no	—
117	C₂×Q₈×C₁₃₉	—	2	1	no	—
118	C₂×Q₈×C₁₃₉	D₈	1	1	yes	characteristic
119	C₂×D₄×C₁₃₉	—	2	8	no	—
120	C₂×D₄×C₁₃₉	—	2	4	no	—
121	C₂×D₄×C₁₃₉	—	2	1	no	—
122	C₂×D₄×C₁₃₉	—	2	2	no	—
123	C₂×D₄×C₁₃₉	—	2	1	no	—
124	C₂×D₄×C₁₃₉	—	4	4	no	—
125	C₂×D₄×C₁₃₉	—	4	16	no	—
126	C₂×D₄×C₁₃₉	—	4	8	no	—
127	C₂×D₄×C₁₃₉	—	4	2	no	—
128	C₂×D₄×C₁₃₉	—	4	1	no	—
129	C₂×D₄×C₁₃₉	—	4	1	no	—
130	C₂×D₄×C₁₃₉	—	4	2	no	—
131	C₂×D₄×C₁₃₉	—	4	2	no	—
132	C₂×D₄×C₁₃₉	—	4	1	no	—
133	C₂×D₄×C₁₃₉	—	4	2	no	—
134	C₂×D₄×C₁₃₉	D₈	1	2	yes	—
135	C₂×D₄×C₁₃₉	D₈	1	1	yes	characteristic
136	C₂²×C₄×C₁₃₉	—	4	2	no	—
137	C₂²×C₄×C₁₃₉	—	4	1	no	—
138	C₂²×C₄×C₁₃₉	—	4	1	no	—
139	C₂²×C₄×C₁₃₉	—	4	1	no	—
140	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
142	Q₁₆×C₁₃₉	—	2	1	no	—
143	Q₁₆×C₁₃₉	—	2	1	no	—
144	Q₁₆×C₁₃₉	—	2	1	no	—
145	Q₁₆×C₁₃₉	C₂×D₄	1	2	yes	—
146	SD₁₆×C₁₃₉	—	2	8	no	—
147	SD₁₆×C₁₃₉	—	2	4	no	—
148	SD₁₆×C₁₃₉	—	4	2	no	—
149	D₈×C₁₃₉	—	2	8	no	—
150	D₈×C₁₃₉	—	2	4	no	—
151	D₈×C₁₃₉	—	2	2	no	—
152	D₈×C₁₃₉	—	2	1	no	—
153	D₈×C₁₃₉	—	2	1	no	—
154	D₈×C₁₃₉	—	2	1	no	—
155	D₈×C₁₃₉	C₂×D₄	1	2	yes	—
156	D₈×C₁₃₉	C₂×D₄	1	4	yes	—
157	M₁₆×C₁₃₉	—	2	2	no	—
158	M₁₆×C₁₃₉	—	2	4	no	—
159	C₂×C₈×C₁₃₉	—	2	2	no	—
160	C₂×C₈×C₁₃₉	—	2	2	no	—
161	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
166	C₄⋊C₄×C₁₃₉	—	2	2	no	—
167	C₄⋊C₄×C₁₃₉	—	4	1	no	—
168	C₄⋊C₄×C₁₃₉	—	4	2	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
171	C₁₆×C₁₃₉	—	2	1	no	—
172	C₁₆×C₁₃₉	—	2	1	no	—
173	C₁₆×C₁₃₉	—	2	2	no	—
174	C₂³×C₁₃₉	—	4	8	no	—
175	C₂³×C₁₃₉	—	4	2	no	—
176	C₂³×C₁₃₉	—	4	1	no	—
177	C₂³×C₁₃₉	—	4	4	no	—
178	C₂³×C₁₃₉	—	4	1	no	—
179	C₂³×C₁₃₉	—	16	1	no	—
180	C₂³×C₁₃₉	—	16	1	no	—
181	C₂³×C₁₃₉	—	16	2	no	—
182	C₂³×C₁₃₉	—	16	2	no	—
183	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
184	C₂³×C₁₃₉	C₂×D₈	1	1	yes	characteristic
185	Q₈×C₁₃₉	—	2	2	no	—
186	Q₈×C₁₃₉	—	2	2	no	—
187	Q₈×C₁₃₉	—	4	1	no	—
188	Q₈×C₁₃₉	—	4	1	no	—
189	Q₈×C₁₃₉	—	4	1	no	—
190	D₄×C₁₃₉	—	2	4	no	—
191	D₄×C₁₃₉	—	2	2	no	—
192	D₄×C₁₃₉	—	2	4	no	—
193	D₄×C₁₃₉	—	2	2	no	—
194	D₄×C₁₃₉	—	4	8	no	—
195	D₄×C₁₃₉	—	4	8	no	—
196	D₄×C₁₃₉	—	4	4	no	—
197	D₄×C₁₃₉	—	4	1	no	—
198	D₄×C₁₃₉	—	4	1	no	—
199	D₄×C₁₃₉	—	4	2	no	—
200	D₄×C₁₃₉	—	4	1	no	—
201	D₄×C₁₃₉	—	4	4	no	—
202	D₄×C₁₃₉	—	8	2	no	—
203	D₄×C₁₃₉	—	16	2	no	—
204	C₂×C₄×C₁₃₉	—	2	2	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	4	8	no	—
207	C₂×C₄×C₁₃₉	—	4	1	no	—
208	C₂×C₄×C₁₃₉	—	4	4	no	—
209	C₂×C₄×C₁₃₉	—	4	2	no	—
210	C₂×C₄×C₁₃₉	—	4	1	no	—
211	C₂×C₄×C₁₃₉	—	8	2	no	—
212	C₂×C₄×C₁₃₉	—	16	1	no	—
213	C₂×C₄×C₁₃₉	#120	1	2	yes	—
214	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
218	C₈×C₁₃₉	—	2	2	no	—
219	C₈×C₁₃₉	#120	1	2	yes	—
220	C₈×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
222	C₂²×C₁₃₉	—	2	1	no	—
223	C₂²×C₁₃₉	—	2	1	no	—
224	C₂²×C₁₃₉	—	2	2	no	—
225	C₂²×C₁₃₉	—	2	2	no	—
226	C₂²×C₁₃₉	—	2	2	no	—
227	C₂²×C₁₃₉	—	4	4	no	—
228	C₂²×C₁₃₉	—	4	2	no	—
229	C₂²×C₁₃₉	—	8	2	no	—
230	C₂²×C₁₃₉	—	8	1	no	—
231	C₂²×C₁₃₉	—	8	2	no	—
232	C₂²×C₁₃₉	—	8	1	no	—
233	C₂²×C₁₃₉	—	8	1	no	—
234	C₂²×C₁₃₉	—	8	1	no	—
235	C₂²×C₁₃₉	—	8	1	no	—
236	C₂²×C₁₃₉	—	16	4	no	—
237	C₂²×C₁₃₉	—	16	8	no	—
238	C₂²×C₁₃₉	#447	1	2	yes	—
239	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
240	C₄×C₁₃₉	—	2	2	no	—
241	C₄×C₁₃₉	—	4	2	no	—
242	C₄×C₁₃₉	—	8	2	no	—
243	C₄×C₁₃₉	—	8	1	no	—
244	C₄×C₁₃₉	#447	1	2	yes	—
245	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
246	C₄×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₂×C₁₃₉	—	2	2	no	—
248	C₂×C₁₃₉	—	4	2	no	—
249	C₂×C₁₃₉	—	8	4	no	—
250	C₂×C₁₃₉	—	8	2	no	—
251	C₂×C₁₃₉	—	16	1	no	—
252	C₂×C₁₃₉	C₂×#447	1	1	yes	characteristic
253	C₂×C₁₃₉	#3415	1	1	yes	characteristic
254	C₂×C₁₃₉	#3416	1	1	yes	characteristic
255	#33526	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₁₃₉	#33526	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#576	C₂×C₁₃₉	1	1	yes	characteristic, complemented
258	C₂×#509	C₂×C₁₃₉	1	1	yes	characteristic, complemented
259	C₂×#508	C₂×C₁₃₉	1	1	yes	characteristic, complemented
260	#3061	C₂×C₁₃₉	1	1	yes	characteristic, complemented
261	#2189	C₂×C₁₃₉	1	2	yes	complemented
262	#2187	C₂×C₁₃₉	1	2	yes	complemented
263	#2186	C₂×C₁₃₉	1	2	yes	complemented
264	#2184	C₂×C₁₃₉	1	2	yes	complemented
265	#2139	C₂×C₁₃₉	1	1	yes	characteristic, complemented
266	C₂×#357	C₂×C₁₃₉	1	1	yes	characteristic, complemented
267	#2113	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	C₂×H(5,𝔽₂)	—	2	1	no	—
269	#576	—	2	4	no	—
270	#576	—	2	4	no	—
271	C₂×AGL(1,ℤ/8)	—	2	1	no	—
272	C₂×AGL(1,ℤ/8)	—	2	2	no	—
273	C₂×#135	C₂²×C₁₃₉	1	2	yes	—
274	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic
275	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
276	C₂²×D₈	C₂²×C₁₃₉	1	2	yes	—
277	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
278	C₂×#131	C₂²×C₁₃₉	1	1	yes	characteristic
279	#537	—	2	1	no	—
280	#509	—	2	4	no	—
281	#508	—	2	4	no	—
282	C₂×Q₃₂	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
283	C₂×SD₃₂	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
284	C₂×SD₃₂	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
285	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	complemented
286	C₂×D₁₆	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
287	C₂×D₁₆	C₂²×C₁₃₉	1	2	yes	complemented
288	C₂×M₃₂	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
289	C₂²×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
290	#468	—	2	2	no	—
291	#467	C₂²×C₁₃₉	1	2	yes	complemented
292	#466	C₂²×C₁₃₉	1	2	yes	complemented
293	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
294	#417	—	2	1	no	—
295	#358	C₂²×C₁₃₉	1	2	yes	complemented
296	#357	C₂²×C₁₃₉	1	2	yes	complemented
297	#357	C₂²×C₁₃₉	1	2	yes	complemented
298	#357	C₂²×C₁₃₉	1	2	yes	complemented
299	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	complemented
300	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	complemented
301	H(5,𝔽₂)	—	2	8	no	—
302	H(5,𝔽₂)	—	4	4	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	4	1	no	—
307	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	4	2	no	—
311	C₂²×D₄	—	4	1	no	—
312	AGL(1,ℤ/8)	—	2	8	no	—
313	AGL(1,ℤ/8)	—	2	16	no	—
314	#135	—	2	4	no	—
315	#135	—	2	4	no	—
316	#135	—	2	2	no	—
317	#135	—	2	2	no	—
318	#135	—	2	2	no	—
319	#135	D₄×C₁₃₉	1	4	yes	complemented
320	C₂×Q₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
321	C₂×Q₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	1	no	—
324	C₂×SD₁₆	—	2	1	no	—
325	C₂×D₈	—	2	4	no	—
326	C₂×D₈	—	2	4	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	1	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×D₈	D₄×C₁₃₉	1	4	yes	complemented
331	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
332	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
333	C₂×D₈	C₂³×C₁₃₉	1	2	yes	—
334	#131	—	2	2	no	—
335	#131	—	2	2	no	—
336	C₂×M₁₆	D₄×C₁₃₉	1	1	yes	characteristic
337	C₂×M₁₆	D₄×C₁₃₉	1	2	yes	—
338	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
339	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	4	1	no	—
342	#121	—	2	2	no	—
343	#121	—	4	1	no	—
344	#121	—	4	2	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	Q₃₂	—	2	2	no	—
347	SD₃₂	—	2	2	no	—
348	SD₃₂	—	2	2	no	—
349	SD₃₂	—	2	4	no	—
350	D₁₆	—	2	2	no	—
351	D₁₆	—	2	4	no	—
352	M₃₂	—	2	2	no	—
353	C₂×C₁₆	—	2	2	no	—
354	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
355	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
356	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
357	#107	—	2	1	no	—
358	#107	C₂³×C₁₃₉	1	2	yes	—
359	#103	—	2	2	no	—
360	#102	—	2	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	1	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	8	no	—
366	#41	—	2	4	no	—
367	#41	—	4	4	no	—
368	#41	—	4	8	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	D₈×C₁₃₉	1	1	yes	characteristic
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	16	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	1	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	D₈×C₁₃₉	1	2	yes	—
391	C₂×D₄	D₈×C₁₃₉	1	1	yes	characteristic
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
398	Q₁₆	—	2	1	no	—
399	Q₁₆	—	2	1	no	—
400	Q₁₆	—	2	1	no	—
401	Q₁₆	C₂×D₄×C₁₃₉	1	2	yes	—
402	SD₁₆	—	2	8	no	—
403	SD₁₆	—	2	4	no	—
404	SD₁₆	—	4	2	no	—
405	D₈	—	2	8	no	—
406	D₈	—	2	4	no	—
407	D₈	—	2	2	no	—
408	D₈	—	2	1	no	—
409	D₈	—	2	1	no	—
410	D₈	—	2	1	no	—
411	D₈	C₂×D₄×C₁₃₉	1	2	yes	—
412	D₈	C₂×D₄×C₁₃₉	1	4	yes	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	2	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
418	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
419	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
421	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₁₆	—	2	1	no	—
428	C₁₆	—	2	1	no	—
429	C₁₆	—	2	2	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	16	1	no	—
436	C₂³	—	16	1	no	—
437	C₂³	—	16	2	no	—
438	C₂³	—	16	2	no	—
439	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
440	C₂³	C₂×D₈×C₁₃₉	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	1	no	—
458	D₄	—	8	2	no	—
459	D₄	—	16	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	16	1	no	—
469	C₂×C₄	#120×C₁₃₉	1	2	yes	—
470	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
471	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
472	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	#120×C₁₃₉	1	2	yes	—
476	C₈	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
477	C₈	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	16	4	no	—
493	C₂²	—	16	8	no	—
494	C₂²	#447×C₁₃₉	1	2	yes	—
495	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	2	no	—
499	C₄	—	8	1	no	—
500	C₄	#447×C₁₃₉	1	2	yes	—
501	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
502	C₄	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	4	no	—
506	C₂	—	8	2	no	—
507	C₂	—	16	1	no	—
508	C₂	C₂×#447×C₁₃₉	1	1	yes	characteristic
509	C₂	#3415×C₁₃₉	1	1	yes	characteristic
510	C₂	#3416×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×#41×C₁₃₉ ◁ C₂×#131×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#576×C₁₃₉	C₂	semidirect
2. C₂×#509×C₁₃₉	C₂	semidirect
3. C₂×#508×C₁₃₉	C₂	semidirect
4. #3061×C₁₃₉	C₂	semidirect
5. #2189×C₁₃₉	C₂	semidirect
6. #2187×C₁₃₉	C₂	semidirect
7. #2186×C₁₃₉	C₂	semidirect
8. #2184×C₁₃₉	C₂	semidirect
9. #2139×C₁₃₉	C₂	semidirect
10. C₂×#357×C₁₃₉	C₂	semidirect
11. #2113×C₁₃₉	C₂	semidirect
19. C₂×#135×C₁₃₉	C₂²	semidirect
26. C₂×Q₃₂×C₁₃₉	C₂²	semidirect
27. C₂×SD₃₂×C₁₃₉	C₂²	semidirect
28. C₂×SD₃₂×C₁₃₉	C₂²	semidirect
29. C₂×SD₃₂×C₁₃₉	C₂²	semidirect
30. C₂×D₁₆×C₁₃₉	C₂²	semidirect
31. C₂×D₁₆×C₁₃₉	C₂²	semidirect
32. C₂×M₃₂×C₁₃₉	C₂²	semidirect
33. C₂²×C₁₆×C₁₃₉	C₂²	semidirect
35. #467×C₁₃₉	C₂²	semidirect
36. #466×C₁₃₉	C₂²	semidirect
37. C₂×#107×C₁₃₉	C₂²	semidirect
39. #358×C₁₃₉	C₂²	semidirect
40. #357×C₁₃₉	C₂²	semidirect
41. #357×C₁₃₉	C₂²	semidirect
42. #357×C₁₃₉	C₂²	semidirect
43. C₂²⋊C₁₆×C₁₃₉	C₂²	semidirect
44. C₂²⋊C₁₆×C₁₃₉	C₂²	semidirect
63. #135×C₁₃₉	D₄	semidirect
74. C₂×D₈×C₁₃₉	D₄	semidirect
255. #33526	C₁₃₉	direct (N × H)
256. C₁₃₉	#33526	direct (N × H)
257. C₂×#576	C₂×C₁₃₉	semidirect
258. C₂×#509	C₂×C₁₃₉	semidirect
259. C₂×#508	C₂×C₁₃₉	semidirect
260. #3061	C₂×C₁₃₉	semidirect
261. #2189	C₂×C₁₃₉	semidirect
262. #2187	C₂×C₁₃₉	semidirect
263. #2186	C₂×C₁₃₉	semidirect
264. #2184	C₂×C₁₃₉	semidirect
265. #2139	C₂×C₁₃₉	semidirect
266. C₂×#357	C₂×C₁₃₉	semidirect
267. #2113	C₂×C₁₃₉	semidirect
275. C₂×#135	C₂²×C₁₃₉	semidirect
282. C₂×Q₃₂	C₂²×C₁₃₉	semidirect
283. C₂×SD₃₂	C₂²×C₁₃₉	semidirect
284. C₂×SD₃₂	C₂²×C₁₃₉	semidirect
285. C₂×SD₃₂	C₂²×C₁₃₉	semidirect
286. C₂×D₁₆	C₂²×C₁₃₉	semidirect
287. C₂×D₁₆	C₂²×C₁₃₉	semidirect
288. C₂×M₃₂	C₂²×C₁₃₉	semidirect
289. C₂²×C₁₆	C₂²×C₁₃₉	semidirect
291. #467	C₂²×C₁₃₉	semidirect
292. #466	C₂²×C₁₃₉	semidirect
293. C₂×#107	C₂²×C₁₃₉	semidirect
295. #358	C₂²×C₁₃₉	semidirect
296. #357	C₂²×C₁₃₉	semidirect
297. #357	C₂²×C₁₃₉	semidirect
298. #357	C₂²×C₁₃₉	semidirect
299. C₂²⋊C₁₆	C₂²×C₁₃₉	semidirect
300. C₂²⋊C₁₆	C₂²×C₁₃₉	semidirect
319. #135	D₄×C₁₃₉	semidirect
330. C₂×D₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#576×C₁₃₉	2
C₂×#509×C₁₃₉	2
C₂×#508×C₁₃₉	2
#3061×C₁₃₉	2
#2189×C₁₃₉	2
#2187×C₁₃₉	2
#2186×C₁₃₉	2
#2184×C₁₃₉	2
#2139×C₁₃₉	2
C₂×#357×C₁₃₉	2
#2113×C₁₃₉	2
#33526	139

Subgroups — C139×#33526 #48028122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33526 #48028122