Subgroups — C₁₃₉×#33527 #48028123

Order 35584.

1098 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#510×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	#2188×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2186×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2185×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2139×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#358×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2113×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₁₃₉	—	2	1	no	—
13	#578×C₁₃₉	—	2	4	no	—
14	#578×C₁₃₉	—	2	4	no	—
15	C₂×#137×C₁₃₉	—	2	1	no	—
16	C₂×#137×C₁₃₉	—	2	2	no	—
17	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#135×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₁₃₉	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₁₃₉	C₂²	1	1	yes	characteristic
23	#537×C₁₃₉	—	2	1	no	—
24	#510×C₁₃₉	—	2	4	no	—
25	#508×C₁₃₉	—	2	4	no	—
26	C₂×Q₃₂×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×Q₃₂×C₁₃₉	C₂²	1	2	yes	—
28	C₂×SD₃₂×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×SD₃₂×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	—
31	C₂×D₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×M₃₂×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
34	#468×C₁₃₉	—	2	2	no	—
35	#467×C₁₃₉	C₂²	1	2	yes	—
36	#466×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
38	#417×C₁₃₉	—	2	1	no	—
39	#358×C₁₃₉	C₂²	1	2	yes	—
40	#358×C₁₃₉	C₂²	1	2	yes	—
41	#358×C₁₃₉	C₂²	1	2	yes	—
42	#357×C₁₃₉	C₂²	1	2	yes	—
43	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
44	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
45	2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
46	2₋¹⁺⁴×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	—	4	2	no	—
52	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃₉	—	2	2	no	—
54	C₂²×Q₈×C₁₃₉	—	2	1	no	—
55	C₂²×Q₈×C₁₃₉	—	4	1	no	—
56	#137×C₁₃₉	—	2	8	no	—
57	#137×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	—	2	4	no	—
65	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
66	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
67	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
69	C₂×Q₁₆×C₁₃₉	D₄	1	4	yes	complemented
70	C₂×Q₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
73	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
74	C₂×SD₁₆×C₁₃₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₃₉	—	2	1	no	—
76	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
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	Q₃₂×C₁₃₉	—	2	4	no	—
92	SD₃₂×C₁₃₉	—	2	2	no	—
93	SD₃₂×C₁₃₉	—	2	4	no	—
94	SD₃₂×C₁₃₉	—	2	2	no	—
95	D₁₆×C₁₃₉	—	2	2	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	#41×C₁₃₉	—	2	2	no	—
106	#41×C₁₃₉	—	2	2	no	—
107	#41×C₁₃₉	—	2	8	no	—
108	#41×C₁₃₉	—	2	4	no	—
109	#41×C₁₃₉	—	4	4	no	—
110	#41×C₁₃₉	—	4	16	no	—
111	#41×C₁₃₉	—	4	8	no	—
112	#41×C₁₃₉	—	4	2	no	—
113	#41×C₁₃₉	—	4	2	no	—
114	#41×C₁₃₉	—	4	2	no	—
115	C₂×Q₈×C₁₃₉	—	2	8	no	—
116	C₂×Q₈×C₁₃₉	—	2	4	no	—
117	C₂×Q₈×C₁₃₉	—	2	2	no	—
118	C₂×Q₈×C₁₃₉	—	2	1	no	—
119	C₂×Q₈×C₁₃₉	—	2	1	no	—
120	C₂×Q₈×C₁₃₉	—	4	4	no	—
121	C₂×Q₈×C₁₃₉	—	4	8	no	—
122	C₂×Q₈×C₁₃₉	—	4	2	no	—
123	C₂×Q₈×C₁₃₉	—	4	1	no	—
124	C₂×Q₈×C₁₃₉	—	4	2	no	—
125	C₂×Q₈×C₁₃₉	D₈	1	1	yes	characteristic
126	C₂×D₄×C₁₃₉	—	2	1	no	—
127	C₂×D₄×C₁₃₉	—	2	1	no	—
128	C₂×D₄×C₁₃₉	—	4	2	no	—
129	C₂×D₄×C₁₃₉	—	4	1	no	—
130	C₂×D₄×C₁₃₉	—	4	1	no	—
131	C₂×D₄×C₁₃₉	—	4	2	no	—
132	C₂×D₄×C₁₃₉	D₈	1	2	yes	—
133	C₂×D₄×C₁₃₉	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₉	—	4	2	no	—
135	C₂²×C₄×C₁₃₉	—	4	1	no	—
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	8	no	—
143	Q₁₆×C₁₃₉	—	2	4	no	—
144	Q₁₆×C₁₃₉	—	2	1	no	—
145	Q₁₆×C₁₃₉	—	2	2	no	—
146	Q₁₆×C₁₃₉	—	2	1	no	—
147	Q₁₆×C₁₃₉	—	2	1	no	—
148	Q₁₆×C₁₃₉	C₂×D₄	1	2	yes	—
149	Q₁₆×C₁₃₉	C₂×D₄	1	4	yes	—
150	SD₁₆×C₁₃₉	—	2	8	no	—
151	SD₁₆×C₁₃₉	—	2	4	no	—
152	SD₁₆×C₁₃₉	—	4	2	no	—
153	D₈×C₁₃₉	—	2	1	no	—
154	D₈×C₁₃₉	—	2	1	no	—
155	D₈×C₁₃₉	—	2	1	no	—
156	D₈×C₁₃₉	C₂×D₄	1	2	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	1	no	—
175	C₂³×C₁₃₉	—	4	1	no	—
176	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
177	C₂³×C₁₃₉	C₂×D₈	1	1	yes	characteristic
178	Q₈×C₁₃₉	—	2	2	no	—
179	Q₈×C₁₃₉	—	2	4	no	—
180	Q₈×C₁₃₉	—	2	2	no	—
181	Q₈×C₁₃₉	—	4	8	no	—
182	Q₈×C₁₃₉	—	4	1	no	—
183	Q₈×C₁₃₉	—	4	2	no	—
184	Q₈×C₁₃₉	—	4	4	no	—
185	Q₈×C₁₃₉	—	4	1	no	—
186	Q₈×C₁₃₉	—	4	1	no	—
187	D₄×C₁₃₉	—	2	4	no	—
188	D₄×C₁₃₉	—	2	2	no	—
189	D₄×C₁₃₉	—	2	2	no	—
190	D₄×C₁₃₉	—	4	8	no	—
191	D₄×C₁₃₉	—	4	4	no	—
192	D₄×C₁₃₉	—	4	1	no	—
193	D₄×C₁₃₉	—	4	1	no	—
194	D₄×C₁₃₉	—	4	1	no	—
195	D₄×C₁₃₉	—	8	2	no	—
196	D₄×C₁₃₉	—	16	2	no	—
197	C₂×C₄×C₁₃₉	—	2	2	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	4	8	no	—
200	C₂×C₄×C₁₃₉	—	4	8	no	—
201	C₂×C₄×C₁₃₉	—	4	2	no	—
202	C₂×C₄×C₁₃₉	—	4	1	no	—
203	C₂×C₄×C₁₃₉	—	4	4	no	—
204	C₂×C₄×C₁₃₉	—	4	4	no	—
205	C₂×C₄×C₁₃₉	—	4	2	no	—
206	C₂×C₄×C₁₃₉	—	4	1	no	—
207	C₂×C₄×C₁₃₉	—	8	2	no	—
208	C₂×C₄×C₁₃₉	—	16	1	no	—
209	C₂×C₄×C₁₃₉	#120	1	2	yes	—
210	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
211	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
212	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
214	C₈×C₁₃₉	—	2	2	no	—
215	C₈×C₁₃₉	#120	1	2	yes	—
216	C₈×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
218	C₂²×C₁₃₉	—	2	1	no	—
219	C₂²×C₁₃₉	—	2	1	no	—
220	C₂²×C₁₃₉	—	2	2	no	—
221	C₂²×C₁₃₉	—	2	2	no	—
222	C₂²×C₁₃₉	—	2	2	no	—
223	C₂²×C₁₃₉	—	4	2	no	—
224	C₂²×C₁₃₉	—	8	1	no	—
225	C₂²×C₁₃₉	—	8	1	no	—
226	C₂²×C₁₃₉	—	8	1	no	—
227	C₂²×C₁₃₉	—	8	1	no	—
228	C₂²×C₁₃₉	—	8	1	no	—
229	C₂²×C₁₃₉	#447	1	2	yes	—
230	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
231	C₄×C₁₃₉	—	2	2	no	—
232	C₄×C₁₃₉	—	4	4	no	—
233	C₄×C₁₃₉	—	4	2	no	—
234	C₄×C₁₃₉	—	8	2	no	—
235	C₄×C₁₃₉	—	8	1	no	—
236	C₄×C₁₃₉	#447	1	2	yes	—
237	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
238	C₄×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₂×C₁₃₉	—	2	2	no	—
240	C₂×C₁₃₉	—	4	2	no	—
241	C₂×C₁₃₉	—	8	2	no	—
242	C₂×C₁₃₉	—	16	1	no	—
243	C₂×C₁₃₉	C₂×#447	1	1	yes	characteristic
244	C₂×C₁₃₉	#3416	1	1	yes	characteristic
245	C₂×C₁₃₉	#3417	1	1	yes	characteristic
246	#33527	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₁₃₉	#33527	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×#578	C₂×C₁₃₉	1	1	yes	characteristic, complemented
249	C₂×#510	C₂×C₁₃₉	1	1	yes	characteristic, complemented
250	C₂×#508	C₂×C₁₃₉	1	1	yes	characteristic, complemented
251	#3061	C₂×C₁₃₉	1	1	yes	characteristic, complemented
252	#2189	C₂×C₁₃₉	1	2	yes	complemented
253	#2188	C₂×C₁₃₉	1	2	yes	complemented
254	#2186	C₂×C₁₃₉	1	2	yes	complemented
255	#2185	C₂×C₁₃₉	1	2	yes	complemented
256	#2139	C₂×C₁₃₉	1	1	yes	characteristic, complemented
257	C₂×#358	C₂×C₁₃₉	1	1	yes	characteristic, complemented
258	#2113	C₂×C₁₃₉	1	1	yes	characteristic, complemented
259	C₂×2₋¹⁺⁴	—	2	1	no	—
260	#578	—	2	4	no	—
261	#578	—	2	4	no	—
262	C₂×#137	—	2	1	no	—
263	C₂×#137	—	2	2	no	—
264	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×#135	C₂²×C₁₃₉	1	2	yes	—
266	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic
267	C₂²×Q₁₆	C₂²×C₁₃₉	1	2	yes	—
268	C₂²×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂×#131	C₂²×C₁₃₉	1	1	yes	characteristic
270	#537	—	2	1	no	—
271	#510	—	2	4	no	—
272	#508	—	2	4	no	—
273	C₂×Q₃₂	C₂²×C₁₃₉	1	1	yes	characteristic
274	C₂×Q₃₂	C₂²×C₁₃₉	1	2	yes	—
275	C₂×SD₃₂	C₂²×C₁₃₉	1	1	yes	characteristic
276	C₂×SD₃₂	C₂²×C₁₃₉	1	1	yes	characteristic
277	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	—
278	C₂×D₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
279	C₂×M₃₂	C₂²×C₁₃₉	1	1	yes	characteristic
280	C₂²×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
281	#468	—	2	2	no	—
282	#467	C₂²×C₁₃₉	1	2	yes	—
283	#466	C₂²×C₁₃₉	1	2	yes	—
284	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
285	#417	—	2	1	no	—
286	#358	C₂²×C₁₃₉	1	2	yes	—
287	#358	C₂²×C₁₃₉	1	2	yes	—
288	#358	C₂²×C₁₃₉	1	2	yes	—
289	#357	C₂²×C₁₃₉	1	2	yes	—
290	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
291	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
292	2₋¹⁺⁴	—	2	8	no	—
293	2₋¹⁺⁴	—	4	4	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	1	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	4	1	no	—
298	C₂×#41	—	4	2	no	—
299	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	—	4	1	no	—
303	#137	—	2	8	no	—
304	#137	—	2	16	no	—
305	#135	—	2	4	no	—
306	#135	—	2	4	no	—
307	#135	—	2	2	no	—
308	#135	—	2	2	no	—
309	#135	—	2	2	no	—
310	#135	D₄×C₁₃₉	1	4	yes	complemented
311	C₂×Q₁₆	—	2	4	no	—
312	C₂×Q₁₆	—	2	4	no	—
313	C₂×Q₁₆	—	2	2	no	—
314	C₂×Q₁₆	—	2	1	no	—
315	C₂×Q₁₆	—	2	2	no	—
316	C₂×Q₁₆	D₄×C₁₃₉	1	4	yes	complemented
317	C₂×Q₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
318	C₂×Q₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
319	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	1	no	—
322	C₂×SD₁₆	—	2	1	no	—
323	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
324	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
325	#131	—	2	2	no	—
326	#131	—	2	2	no	—
327	C₂×M₁₆	D₄×C₁₃₉	1	1	yes	characteristic
328	C₂×M₁₆	D₄×C₁₃₉	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	4	1	no	—
333	#121	—	2	2	no	—
334	#121	—	4	1	no	—
335	#121	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	Q₃₂	—	2	2	no	—
338	Q₃₂	—	2	4	no	—
339	SD₃₂	—	2	2	no	—
340	SD₃₂	—	2	4	no	—
341	SD₃₂	—	2	2	no	—
342	D₁₆	—	2	2	no	—
343	M₃₂	—	2	2	no	—
344	C₂×C₁₆	—	2	2	no	—
345	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
346	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
347	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
348	#107	—	2	1	no	—
349	#107	C₂³×C₁₃₉	1	2	yes	—
350	#103	—	2	2	no	—
351	#102	—	2	2	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	#41	—	2	8	no	—
355	#41	—	2	4	no	—
356	#41	—	4	4	no	—
357	#41	—	4	16	no	—
358	#41	—	4	8	no	—
359	#41	—	4	2	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	C₂×Q₈	—	2	8	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	8	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	4	1	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	D₈×C₁₃₉	1	1	yes	characteristic
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	D₈×C₁₃₉	1	2	yes	—
380	C₂×D₄	D₈×C₁₃₉	1	1	yes	characteristic
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
389	Q₁₆	—	2	8	no	—
390	Q₁₆	—	2	4	no	—
391	Q₁₆	—	2	1	no	—
392	Q₁₆	—	2	2	no	—
393	Q₁₆	—	2	1	no	—
394	Q₁₆	—	2	1	no	—
395	Q₁₆	C₂×D₄×C₁₃₉	1	2	yes	—
396	Q₁₆	C₂×D₄×C₁₃₉	1	4	yes	—
397	SD₁₆	—	2	8	no	—
398	SD₁₆	—	2	4	no	—
399	SD₁₆	—	4	2	no	—
400	D₈	—	2	1	no	—
401	D₈	—	2	1	no	—
402	D₈	—	2	1	no	—
403	D₈	C₂×D₄×C₁₃₉	1	2	yes	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
410	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
411	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
412	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₁₆	—	2	1	no	—
419	C₁₆	—	2	1	no	—
420	C₁₆	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
424	C₂³	C₂×D₈×C₁₃₉	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	4	8	no	—
429	Q₈	—	4	4	no	—
430	Q₈	—	4	1	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	4	8	no	—
438	D₄	—	4	4	no	—
439	D₄	—	4	1	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	8	2	no	—
443	D₄	—	16	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	16	1	no	—
456	C₂×C₄	#120×C₁₃₉	1	2	yes	—
457	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
458	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
459	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	#120×C₁₃₉	1	2	yes	—
463	C₈	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
464	C₈	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	#447×C₁₃₉	1	2	yes	—
477	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	4	4	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	1	no	—
483	C₄	#447×C₁₃₉	1	2	yes	—
484	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
485	C₄	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
486	C₂	—	2	2	no	—
487	C₂	—	4	2	no	—
488	C₂	—	8	2	no	—
489	C₂	—	16	1	no	—
490	C₂	C₂×#447×C₁₃₉	1	1	yes	characteristic
491	C₂	#3416×C₁₃₉	1	1	yes	characteristic
492	C₂	#3417×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×#578×C₁₃₉	C₂	semidirect
2. C₂×#510×C₁₃₉	C₂	semidirect
3. C₂×#508×C₁₃₉	C₂	semidirect
4. #3061×C₁₃₉	C₂	semidirect
5. #2189×C₁₃₉	C₂	semidirect
6. #2188×C₁₃₉	C₂	semidirect
7. #2186×C₁₃₉	C₂	semidirect
8. #2185×C₁₃₉	C₂	semidirect
9. #2139×C₁₃₉	C₂	semidirect
10. C₂×#358×C₁₃₉	C₂	semidirect
11. #2113×C₁₃₉	C₂	semidirect
63. #135×C₁₃₉	D₄	semidirect
69. C₂×Q₁₆×C₁₃₉	D₄	semidirect
246. #33527	C₁₃₉	direct (N × H)
247. C₁₃₉	#33527	direct (N × H)
248. C₂×#578	C₂×C₁₃₉	semidirect
249. C₂×#510	C₂×C₁₃₉	semidirect
250. C₂×#508	C₂×C₁₃₉	semidirect
251. #3061	C₂×C₁₃₉	semidirect
252. #2189	C₂×C₁₃₉	semidirect
253. #2188	C₂×C₁₃₉	semidirect
254. #2186	C₂×C₁₃₉	semidirect
255. #2185	C₂×C₁₃₉	semidirect
256. #2139	C₂×C₁₃₉	semidirect
257. C₂×#358	C₂×C₁₃₉	semidirect
258. #2113	C₂×C₁₃₉	semidirect
310. #135	D₄×C₁₃₉	semidirect
316. C₂×Q₁₆	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×#578×C₁₃₉	2
C₂×#510×C₁₃₉	2
C₂×#508×C₁₃₉	2
#3061×C₁₃₉	2
#2189×C₁₃₉	2
#2188×C₁₃₉	2
#2186×C₁₃₉	2
#2185×C₁₃₉	2
#2139×C₁₃₉	2
C₂×#358×C₁₃₉	2
#2113×C₁₃₉	2
#33527	139

Subgroups — C139×#33527 #48028123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33527 #48028123