Subgroups — C₂×#2195×C₁₃₉ #48028133

Order 35584.

1078 conjugacy classes of subgroups.

The subgroup lattice has 522 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
2	C₂×#510×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Q₃₂×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#473×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2195×C₁₃₉	C₂	1	8	yes	maximal, direct product factor
6	C₂×#362×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#359×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#350×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×2₋¹⁺⁴×C₁₃₉	—	2	1	no	—
10	#578×C₁₃₉	—	2	2	no	—
11	#578×C₁₃₉	—	2	2	no	—
12	#578×C₁₃₉	—	2	2	no	—
13	#578×C₁₃₉	C₂²	1	4	yes	—
14	C₂×#137×C₁₃₉	—	2	2	no	—
15	C₂×#137×C₁₃₉	—	2	1	no	—
16	C₂×#137×C₁₃₉	—	2	1	no	—
17	C₂×#135×C₁₃₉	—	2	1	no	—
18	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₁₃₉	—	2	1	no	—
20	C₂²×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₁₃₉	C₂²	1	1	yes	characteristic
23	#510×C₁₃₉	—	2	2	no	—
24	#510×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×Q₃₂×C₁₃₉	—	2	2	no	—
26	C₂×Q₃₂×C₁₃₉	—	2	2	no	—
27	C₂×Q₃₂×C₁₃₉	—	2	1	no	—
28	C₂×Q₃₂×C₁₃₉	C₂²	1	4	yes	complemented
29	C₂×SD₃₂×C₁₃₉	—	2	1	no	—
30	C₂×M₃₂×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
32	#473×C₁₃₉	—	2	2	no	—
33	#473×C₁₃₉	C₂²	1	4	yes	complemented
34	C₂×#108×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#101×C₁₃₉	—	2	1	no	—
36	#362×C₁₃₉	C₂²	1	4	yes	complemented
37	#359×C₁₃₉	C₂²	1	4	yes	complemented
38	#350×C₁₃₉	C₂²	1	4	yes	complemented
39	2₋¹⁺⁴×C₁₃₉	—	2	4	no	—
40	2₋¹⁺⁴×C₁₃₉	—	2	4	no	—
41	2₋¹⁺⁴×C₁₃₉	—	4	2	no	—
42	2₋¹⁺⁴×C₁₃₉	—	4	2	no	—
43	C₂×#41×C₁₃₉	—	2	2	no	—
44	C₂×#41×C₁₃₉	—	2	1	no	—
45	C₂×#41×C₁₃₉	—	4	2	no	—
46	C₂×#41×C₁₃₉	—	4	1	no	—
47	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃₉	—	2	2	no	—
49	C₂²×Q₈×C₁₃₉	—	2	1	no	—
50	C₂²×Q₈×C₁₃₉	—	2	1	no	—
51	C₂²×Q₈×C₁₃₉	—	4	1	no	—
52	#137×C₁₃₉	—	2	4	no	—
53	#137×C₁₃₉	—	2	8	no	—
54	#137×C₁₃₉	—	2	8	no	—
55	#137×C₁₃₉	—	2	4	no	—
56	#137×C₁₃₉	—	2	4	no	—
57	#137×C₁₃₉	—	4	2	no	—
58	#135×C₁₃₉	—	2	4	no	—
59	#135×C₁₃₉	—	2	4	no	—
60	#135×C₁₃₉	—	2	1	no	—
61	#135×C₁₃₉	—	2	1	no	—
62	#135×C₁₃₉	D₄	1	2	yes	—
63	#135×C₁₃₉	C₂³	1	2	yes	—
64	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
65	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
66	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
67	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
72	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
73	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
74	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
75	C₂×Q₁₆×C₁₃₉	—	4	1	no	—
76	C₂×Q₁₆×C₁₃₉	D₄	1	1	yes	characteristic
77	C₂×Q₁₆×C₁₃₉	D₄	1	2	yes	—
78	C₂×Q₁₆×C₁₃₉	D₄	1	2	yes	—
79	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
81	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
82	C₂×SD₁₆×C₁₃₉	—	2	1	no	—
83	C₂×SD₁₆×C₁₃₉	—	4	1	no	—
84	C₂×D₈×C₁₃₉	D₄	1	1	yes	characteristic
85	#131×C₁₃₉	—	2	1	no	—
86	#131×C₁₃₉	—	2	1	no	—
87	#131×C₁₃₉	D₄	1	2	yes	—
88	#131×C₁₃₉	C₂³	1	2	yes	—
89	C₂×M₁₆×C₁₃₉	—	2	1	no	—
90	C₂×M₁₆×C₁₃₉	—	2	1	no	—
91	C₂×M₁₆×C₁₃₉	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₁₃₉	—	2	1	no	—
93	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	Q₃₂×C₁₃₉	—	2	8	no	—
95	Q₃₂×C₁₃₉	—	2	4	no	—
96	SD₃₂×C₁₃₉	—	2	4	no	—
97	M₃₂×C₁₃₉	—	2	1	no	—
98	M₃₂×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₁₆×C₁₃₉	—	2	1	no	—
100	C₂×C₁₆×C₁₃₉	—	2	1	no	—
101	C₂×C₁₆×C₁₃₉	—	2	1	no	—
102	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
103	#108×C₁₃₉	—	2	1	no	—
104	#108×C₁₃₉	C₂³	1	2	yes	—
105	#101×C₁₃₉	—	2	4	no	—
106	#41×C₁₃₉	—	2	1	no	—
107	#41×C₁₃₉	—	2	1	no	—
108	#41×C₁₃₉	—	2	8	no	—
109	#41×C₁₃₉	—	2	2	no	—
110	#41×C₁₃₉	—	2	2	no	—
111	#41×C₁₃₉	—	4	4	no	—
112	#41×C₁₃₉	—	4	8	no	—
113	#41×C₁₃₉	—	4	8	no	—
114	#41×C₁₃₉	—	4	4	no	—
115	#41×C₁₃₉	—	4	4	no	—
116	#41×C₁₃₉	—	4	1	no	—
117	#41×C₁₃₉	—	4	1	no	—
118	#41×C₁₃₉	D₈	1	2	yes	—
119	#41×C₁₃₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₃₉	—	2	8	no	—
121	C₂×Q₈×C₁₃₉	—	2	2	no	—
122	C₂×Q₈×C₁₃₉	—	2	1	no	—
123	C₂×Q₈×C₁₃₉	—	2	2	no	—
124	C₂×Q₈×C₁₃₉	—	2	2	no	—
125	C₂×Q₈×C₁₃₉	—	2	2	no	—
126	C₂×Q₈×C₁₃₉	—	4	2	no	—
127	C₂×Q₈×C₁₃₉	—	4	4	no	—
128	C₂×Q₈×C₁₃₉	—	4	4	no	—
129	C₂×Q₈×C₁₃₉	—	4	4	no	—
130	C₂×Q₈×C₁₃₉	—	4	1	no	—
131	C₂×Q₈×C₁₃₉	—	4	1	no	—
132	C₂×Q₈×C₁₃₉	—	4	1	no	—
133	C₂×Q₈×C₁₃₉	—	4	1	no	—
134	C₂×Q₈×C₁₃₉	—	4	1	no	—
135	C₂×Q₈×C₁₃₉	—	4	1	no	—
136	C₂×Q₈×C₁₃₉	—	4	1	no	—
137	C₂×Q₈×C₁₃₉	—	4	1	no	—
138	C₂×Q₈×C₁₃₉	D₈	1	1	yes	characteristic
139	C₂×D₄×C₁₃₉	—	2	1	no	—
140	C₂×D₄×C₁₃₉	—	2	1	no	—
141	C₂×D₄×C₁₃₉	—	4	2	no	—
142	C₂×D₄×C₁₃₉	—	4	1	no	—
143	C₂×D₄×C₁₃₉	D₈	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₉	—	2	1	no	—
145	C₂²×C₄×C₁₃₉	—	4	2	no	—
146	C₂²×C₄×C₁₃₉	—	4	2	no	—
147	C₂²×C₄×C₁₃₉	—	4	1	no	—
148	C₂²×C₄×C₁₃₉	—	4	1	no	—
149	C₂²×C₄×C₁₃₉	—	4	1	no	—
150	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
151	Q₁₆×C₁₃₉	—	2	8	no	—
152	Q₁₆×C₁₃₉	—	2	1	no	—
153	Q₁₆×C₁₃₉	—	2	2	no	—
154	Q₁₆×C₁₃₉	—	2	2	no	—
155	Q₁₆×C₁₃₉	—	2	2	no	—
156	Q₁₆×C₁₃₉	—	2	2	no	—
157	Q₁₆×C₁₃₉	—	2	2	no	—
158	Q₁₆×C₁₃₉	—	4	4	no	—
159	Q₁₆×C₁₃₉	—	4	1	no	—
160	Q₁₆×C₁₃₉	—	4	1	no	—
161	Q₁₆×C₁₃₉	C₂×D₄	1	2	yes	—
162	Q₁₆×C₁₃₉	C₂×D₄	1	4	yes	—
163	SD₁₆×C₁₃₉	—	2	8	no	—
164	SD₁₆×C₁₃₉	—	2	2	no	—
165	SD₁₆×C₁₃₉	—	2	2	no	—
166	SD₁₆×C₁₃₉	—	4	4	no	—
167	D₈×C₁₃₉	—	2	1	no	—
168	D₈×C₁₃₉	C₂×D₄	1	2	yes	—
169	M₁₆×C₁₃₉	—	2	1	no	—
170	M₁₆×C₁₃₉	—	2	2	no	—
171	M₁₆×C₁₃₉	—	2	2	no	—
172	M₁₆×C₁₃₉	—	2	2	no	—
173	M₁₆×C₁₃₉	—	4	1	no	—
174	M₁₆×C₁₃₉	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₁₃₉	—	2	1	no	—
176	C₂×C₈×C₁₃₉	—	2	2	no	—
177	C₂×C₈×C₁₃₉	—	2	2	no	—
178	C₂×C₈×C₁₃₉	—	4	1	no	—
179	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
185	C₁₆×C₁₃₉	—	2	2	no	—
186	C₁₆×C₁₃₉	—	2	2	no	—
187	C₂³×C₁₃₉	—	2	1	no	—
188	C₂³×C₁₃₉	—	4	1	no	—
189	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
190	Q₈×C₁₃₉	—	2	1	no	—
191	Q₈×C₁₃₉	—	2	4	no	—
192	Q₈×C₁₃₉	—	2	2	no	—
193	Q₈×C₁₃₉	—	4	8	no	—
194	Q₈×C₁₃₉	—	4	2	no	—
195	Q₈×C₁₃₉	—	4	1	no	—
196	Q₈×C₁₃₉	—	4	2	no	—
197	Q₈×C₁₃₉	—	4	2	no	—
198	Q₈×C₁₃₉	—	4	2	no	—
199	Q₈×C₁₃₉	—	4	2	no	—
200	Q₈×C₁₃₉	—	8	1	no	—
201	Q₈×C₁₃₉	—	8	1	no	—
202	Q₈×C₁₃₉	C₂×D₈	1	2	yes	—
203	D₄×C₁₃₉	—	2	2	no	—
204	D₄×C₁₃₉	—	2	2	no	—
205	D₄×C₁₃₉	—	2	2	no	—
206	D₄×C₁₃₉	—	2	1	no	—
207	D₄×C₁₃₉	—	4	8	no	—
208	D₄×C₁₃₉	—	4	2	no	—
209	D₄×C₁₃₉	—	4	2	no	—
210	D₄×C₁₃₉	—	4	1	no	—
211	D₄×C₁₃₉	C₂×D₈	1	2	yes	—
212	C₂×C₄×C₁₃₉	—	2	1	no	—
213	C₂×C₄×C₁₃₉	—	2	2	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	4	8	no	—
216	C₂×C₄×C₁₃₉	—	4	8	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	1	no	—
221	C₂×C₄×C₁₃₉	—	4	2	no	—
222	C₂×C₄×C₁₃₉	—	4	2	no	—
223	C₂×C₄×C₁₃₉	—	4	2	no	—
224	C₂×C₄×C₁₃₉	—	8	1	no	—
225	C₂×C₄×C₁₃₉	—	8	1	no	—
226	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
229	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
230	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₁₃₉	—	2	2	no	—
233	C₈×C₁₃₉	—	4	2	no	—
234	C₈×C₁₃₉	#120	1	1	yes	characteristic
235	C₈×C₁₃₉	#120	1	1	yes	characteristic
236	C₈×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
238	C₂²×C₁₃₉	—	2	2	no	—
239	C₂²×C₁₃₉	—	2	2	no	—
240	C₂²×C₁₃₉	—	4	2	no	—
241	C₂²×C₁₃₉	—	4	2	no	—
242	C₂²×C₁₃₉	—	8	2	no	—
243	C₂²×C₁₃₉	#447	1	1	yes	characteristic
244	C₂²×C₁₃₉	#447	1	1	yes	characteristic
245	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₄×C₁₃₉	—	2	2	no	—
247	C₄×C₁₃₉	—	4	4	no	—
248	C₄×C₁₃₉	—	4	2	no	—
249	C₄×C₁₃₉	—	8	2	no	—
250	C₄×C₁₃₉	#447	1	1	yes	characteristic
251	C₄×C₁₃₉	#447	1	1	yes	characteristic
252	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
253	C₄×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
254	C₂×C₁₃₉	—	2	1	no	—
255	C₂×C₁₃₉	—	2	1	no	—
256	C₂×C₁₃₉	—	4	2	no	—
257	C₂×C₁₃₉	—	8	2	no	—
258	C₂×C₁₃₉	#2195	1	2	yes	direct product factor
259	C₂×C₁₃₉	C₂×#447	1	1	yes	characteristic
260	C₂×#2195	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₁₃₉	C₂×#2195	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×#578	C₂×C₁₃₉	1	1	yes	characteristic
263	C₂×#510	C₂×C₁₃₉	1	1	yes	characteristic, complemented
264	C₂²×Q₃₂	C₂×C₁₃₉	1	1	yes	characteristic, complemented
265	C₂×#473	C₂×C₁₃₉	1	1	yes	characteristic, complemented
266	#2195	C₂×C₁₃₉	1	8	yes	direct product factor
267	C₂×#362	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	C₂×#359	C₂×C₁₃₉	1	1	yes	characteristic, complemented
269	C₂×#350	C₂×C₁₃₉	1	1	yes	characteristic, complemented
270	C₂×2₋¹⁺⁴	—	2	1	no	—
271	#578	—	2	2	no	—
272	#578	—	2	2	no	—
273	#578	—	2	2	no	—
274	#578	C₂²×C₁₃₉	1	4	yes	—
275	C₂×#137	—	2	2	no	—
276	C₂×#137	—	2	1	no	—
277	C₂×#137	—	2	1	no	—
278	C₂×#135	—	2	1	no	—
279	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic
280	C₂²×Q₁₆	—	2	1	no	—
281	C₂²×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂²×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
283	C₂×#131	C₂²×C₁₃₉	1	1	yes	characteristic
284	#510	—	2	2	no	—
285	#510	C₂²×C₁₃₉	1	4	yes	complemented
286	C₂×Q₃₂	—	2	2	no	—
287	C₂×Q₃₂	—	2	2	no	—
288	C₂×Q₃₂	—	2	1	no	—
289	C₂×Q₃₂	C₂²×C₁₃₉	1	4	yes	complemented
290	C₂×SD₃₂	—	2	1	no	—
291	C₂×M₃₂	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂²×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
293	#473	—	2	2	no	—
294	#473	C₂²×C₁₃₉	1	4	yes	complemented
295	C₂×#108	C₂²×C₁₃₉	1	1	yes	characteristic
296	C₂×#101	—	2	1	no	—
297	#362	C₂²×C₁₃₉	1	4	yes	complemented
298	#359	C₂²×C₁₃₉	1	4	yes	complemented
299	#350	C₂²×C₁₃₉	1	4	yes	complemented
300	2₋¹⁺⁴	—	2	4	no	—
301	2₋¹⁺⁴	—	2	4	no	—
302	2₋¹⁺⁴	—	4	2	no	—
303	2₋¹⁺⁴	—	4	2	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	4	2	no	—
307	C₂×#41	—	4	1	no	—
308	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
309	C₂²×Q₈	—	2	2	no	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	4	1	no	—
313	#137	—	2	4	no	—
314	#137	—	2	8	no	—
315	#137	—	2	8	no	—
316	#137	—	2	4	no	—
317	#137	—	2	4	no	—
318	#137	—	4	2	no	—
319	#135	—	2	4	no	—
320	#135	—	2	4	no	—
321	#135	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	D₄×C₁₃₉	1	2	yes	—
324	#135	C₂³×C₁₃₉	1	2	yes	—
325	C₂×Q₁₆	—	2	2	no	—
326	C₂×Q₁₆	—	2	4	no	—
327	C₂×Q₁₆	—	2	4	no	—
328	C₂×Q₁₆	—	2	1	no	—
329	C₂×Q₁₆	—	2	1	no	—
330	C₂×Q₁₆	—	2	1	no	—
331	C₂×Q₁₆	—	2	1	no	—
332	C₂×Q₁₆	—	2	1	no	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×Q₁₆	—	2	1	no	—
336	C₂×Q₁₆	—	4	1	no	—
337	C₂×Q₁₆	D₄×C₁₃₉	1	1	yes	characteristic
338	C₂×Q₁₆	D₄×C₁₃₉	1	2	yes	—
339	C₂×Q₁₆	D₄×C₁₃₉	1	2	yes	—
340	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
341	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	4	1	no	—
345	C₂×D₈	D₄×C₁₃₉	1	1	yes	characteristic
346	#131	—	2	1	no	—
347	#131	—	2	1	no	—
348	#131	D₄×C₁₃₉	1	2	yes	—
349	#131	C₂³×C₁₃₉	1	2	yes	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	D₄×C₁₃₉	1	1	yes	characteristic
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
355	Q₃₂	—	2	8	no	—
356	Q₃₂	—	2	4	no	—
357	SD₃₂	—	2	4	no	—
358	M₃₂	—	2	1	no	—
359	M₃₂	C₂³×C₁₃₉	1	2	yes	—
360	C₂×C₁₆	—	2	1	no	—
361	C₂×C₁₆	—	2	1	no	—
362	C₂×C₁₆	—	2	1	no	—
363	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
364	#108	—	2	1	no	—
365	#108	C₂³×C₁₃₉	1	2	yes	—
366	#101	—	2	4	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	8	no	—
370	#41	—	2	2	no	—
371	#41	—	2	2	no	—
372	#41	—	4	4	no	—
373	#41	—	4	8	no	—
374	#41	—	4	8	no	—
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	1	no	—
378	#41	—	4	1	no	—
379	#41	D₈×C₁₃₉	1	2	yes	—
380	#41	C₂×D₄×C₁₃₉	1	2	yes	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	4	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂×Q₈	—	4	4	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	D₈×C₁₃₉	1	1	yes	characteristic
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	D₈×C₁₃₉	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
412	Q₁₆	—	2	8	no	—
413	Q₁₆	—	2	1	no	—
414	Q₁₆	—	2	2	no	—
415	Q₁₆	—	2	2	no	—
416	Q₁₆	—	2	2	no	—
417	Q₁₆	—	2	2	no	—
418	Q₁₆	—	2	2	no	—
419	Q₁₆	—	4	4	no	—
420	Q₁₆	—	4	1	no	—
421	Q₁₆	—	4	1	no	—
422	Q₁₆	C₂×D₄×C₁₃₉	1	2	yes	—
423	Q₁₆	C₂×D₄×C₁₃₉	1	4	yes	—
424	SD₁₆	—	2	8	no	—
425	SD₁₆	—	2	2	no	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	4	4	no	—
428	D₈	—	2	1	no	—
429	D₈	C₂×D₄×C₁₃₉	1	2	yes	—
430	M₁₆	—	2	1	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	4	1	no	—
435	M₁₆	C₂×D₄×C₁₃₉	1	2	yes	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	4	1	no	—
440	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
441	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
444	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
445	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
446	C₁₆	—	2	2	no	—
447	C₁₆	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
451	Q₈	—	2	1	no	—
452	Q₈	—	2	4	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	8	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	8	1	no	—
462	Q₈	—	8	1	no	—
463	Q₈	C₂×D₈×C₁₃₉	1	2	yes	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	C₂×D₈×C₁₃₉	1	2	yes	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	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	—	8	1	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
491	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	4	2	no	—
495	C₈	#120×C₁₃₉	1	1	yes	characteristic
496	C₈	#120×C₁₃₉	1	1	yes	characteristic
497	C₈	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
498	C₈	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	#447×C₁₃₉	1	1	yes	characteristic
505	C₂²	#447×C₁₃₉	1	1	yes	characteristic
506	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	2	no	—
510	C₄	—	8	2	no	—
511	C₄	#447×C₁₃₉	1	1	yes	characteristic
512	C₄	#447×C₁₃₉	1	1	yes	characteristic
513	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
514	C₄	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	2	no	—
519	C₂	#2195×C₁₃₉	1	2	yes	direct product factor
520	C₂	C₂×#447×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
prime radical	C₂×#578×C₁₃₉	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ C₂×#131×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#510×C₁₃₉	C₂	semidirect
3. C₂²×Q₃₂×C₁₃₉	C₂	semidirect
4. C₂×#473×C₁₃₉	C₂	semidirect
5. #2195×C₁₃₉	C₂	direct (N × H)
6. C₂×#362×C₁₃₉	C₂	semidirect
7. C₂×#359×C₁₃₉	C₂	semidirect
8. C₂×#350×C₁₃₉	C₂	semidirect
24. #510×C₁₃₉	C₂²	semidirect
28. C₂×Q₃₂×C₁₃₉	C₂²	semidirect
33. #473×C₁₃₉	C₂²	semidirect
36. #362×C₁₃₉	C₂²	semidirect
37. #359×C₁₃₉	C₂²	semidirect
38. #350×C₁₃₉	C₂²	semidirect
258. C₂×C₁₃₉	#2195	direct (N × H)
260. C₂×#2195	C₁₃₉	direct (N × H)
261. C₁₃₉	C₂×#2195	direct (N × H)
263. C₂×#510	C₂×C₁₃₉	semidirect
264. C₂²×Q₃₂	C₂×C₁₃₉	semidirect
265. C₂×#473	C₂×C₁₃₉	semidirect
266. #2195	C₂×C₁₃₉	direct (N × H)
267. C₂×#362	C₂×C₁₃₉	semidirect
268. C₂×#359	C₂×C₁₃₉	semidirect
269. C₂×#350	C₂×C₁₃₉	semidirect
285. #510	C₂²×C₁₃₉	semidirect
289. C₂×Q₃₂	C₂²×C₁₃₉	semidirect
294. #473	C₂²×C₁₃₉	semidirect
297. #362	C₂²×C₁₃₉	semidirect
298. #359	C₂²×C₁₃₉	semidirect
299. #350	C₂²×C₁₃₉	semidirect
519. C₂	#2195×C₁₃₉	direct (N × H)

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
C₂²×Q₃₂×C₁₃₉	2
C₂×#473×C₁₃₉	2
#2195×C₁₃₉	2
C₂×#362×C₁₃₉	2
C₂×#359×C₁₃₉	2
C₂×#350×C₁₃₉	2
C₂×#2195	139

Subgroups — C2×#2195×C139 #48028133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2195×C₁₃₉ #48028133