Subgroups — C₁₃₉×#20737 #48015333

Order 35584.

1402 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1825×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1803×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1802×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1788×C₁₃₉	C₂	1	2	yes	maximal
8	C₄×#103×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₄×#102×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₄×#41×C₁₃₉	—	2	4	no	—
12	C₄×#41×C₁₃₉	C₄	1	8	yes	complemented
13	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#117×C₁₃₉	—	2	1	no	—
20	C₂×#117×C₁₃₉	—	2	1	no	—
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃₉	—	2	1	no	—
23	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
24	#431×C₁₃₉	—	2	4	no	—
25	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#103×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
30	#384×C₁₃₉	C₂²	1	2	yes	—
31	#382×C₁₃₉	—	2	1	no	—
32	#380×C₁₃₉	—	2	1	no	—
33	#380×C₁₃₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
36	#340×C₁₃₉	C₂²	1	4	yes	—
37	#340×C₁₃₉	C₂²	1	4	yes	—
38	C₂×#41×C₁₃₉	—	2	4	no	—
39	C₂×#41×C₁₃₉	—	2	4	no	—
40	C₂×#41×C₁₃₉	—	2	2	no	—
41	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₉	—	2	1	no	—
44	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₉	—	2	1	no	—
46	C₂³×C₄×C₁₃₉	—	2	1	no	—
47	C₂³×C₄×C₁₃₉	—	2	1	no	—
48	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
52	C₄×Q₈×C₁₃₉	—	2	2	no	—
53	C₄×Q₈×C₁₃₉	—	2	2	no	—
54	C₄×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₁₃₉	—	2	8	no	—
57	C₄×D₄×C₁₃₉	—	2	8	no	—
58	C₄×D₄×C₁₃₉	—	2	2	no	—
59	C₄×D₄×C₁₃₉	—	2	2	no	—
60	C₄×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
61	C₄×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
62	#117×C₁₃₉	—	2	2	no	—
63	#117×C₁₃₉	—	2	8	no	—
64	#117×C₁₃₉	—	4	4	no	—
65	#117×C₁₃₉	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
77	C₂×C₄²×C₁₃₉	—	2	1	no	—
78	C₂×C₄²×C₁₃₉	—	2	1	no	—
79	C₂×C₄²×C₁₃₉	—	2	1	no	—
80	C₂×C₄²×C₁₃₉	—	2	8	no	—
81	C₂×C₄²×C₁₃₉	—	2	2	no	—
82	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
83	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
86	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₁₃₉	—	2	4	no	—
89	#103×C₁₃₉	—	2	8	no	—
90	#102×C₁₃₉	—	2	8	no	—
91	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
92	C₄×C₈×C₁₃₉	—	2	4	no	—
93	#95×C₁₃₉	—	2	2	no	—
94	#95×C₁₃₉	—	2	2	no	—
95	C₂⁴×C₁₃₉	—	2	1	no	—
96	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
97	#41×C₁₃₉	—	2	16	no	—
98	#41×C₁₃₉	—	2	8	no	—
99	#41×C₁₃₉	—	2	8	no	—
100	C₂×Q₈×C₁₃₉	—	2	1	no	—
101	C₂×Q₈×C₁₃₉	—	2	2	no	—
102	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
103	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
104	C₂×D₄×C₁₃₉	—	2	8	no	—
105	C₂×D₄×C₁₃₉	—	2	4	no	—
106	C₂×D₄×C₁₃₉	—	2	1	no	—
107	C₂×D₄×C₁₃₉	—	2	2	no	—
108	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₁₃₉	#41	1	4	yes	—
110	C₂²×C₄×C₁₃₉	—	2	8	no	—
111	C₂²×C₄×C₁₃₉	—	2	1	no	—
112	C₂²×C₄×C₁₃₉	—	2	4	no	—
113	C₂²×C₄×C₁₃₉	—	2	4	no	—
114	C₂²×C₄×C₁₃₉	—	2	2	no	—
115	C₂²×C₄×C₁₃₉	—	2	2	no	—
116	C₂²×C₄×C₁₃₉	—	2	2	no	—
117	C₂²×C₄×C₁₃₉	—	2	2	no	—
118	C₂²×C₄×C₁₃₉	—	2	1	no	—
119	C₂²×C₄×C₁₃₉	—	2	1	no	—
120	C₂²×C₄×C₁₃₉	—	2	4	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	4	no	—
123	C₂²×C₄×C₁₃₉	—	4	4	no	—
124	C₂²×C₄×C₁₃₉	—	4	2	no	—
125	C₂²×C₄×C₁₃₉	—	4	2	no	—
126	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
127	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
128	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₃₉	—	2	4	no	—
137	C₂×C₈×C₁₃₉	—	2	4	no	—
138	C₂×C₈×C₁₃₉	—	2	4	no	—
139	C₄⋊C₄×C₁₃₉	—	2	4	no	—
140	C₄⋊C₄×C₁₃₉	—	2	4	no	—
141	C₄⋊C₄×C₁₃₉	—	2	1	no	—
142	C₄⋊C₄×C₁₃₉	—	2	1	no	—
143	C₄⋊C₄×C₁₃₉	—	2	4	no	—
144	C₄⋊C₄×C₁₃₉	—	2	4	no	—
145	C₄⋊C₄×C₁₃₉	—	4	4	no	—
146	C₄⋊C₄×C₁₃₉	—	4	4	no	—
147	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
148	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
149	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
153	C₄²×C₁₃₉	—	2	4	no	—
154	C₄²×C₁₃₉	—	2	4	no	—
155	C₄²×C₁₃₉	—	2	4	no	—
156	C₄²×C₁₃₉	—	4	4	no	—
157	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
158	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
159	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
161	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
162	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	2	no	—
165	C₂³×C₁₃₉	—	2	4	no	—
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	1	no	—
168	C₂³×C₁₃₉	—	2	1	no	—
169	C₂³×C₁₃₉	—	4	2	no	—
170	C₂³×C₁₃₉	—	4	1	no	—
171	C₂³×C₁₃₉	—	4	1	no	—
172	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₃₉	—	2	2	no	—
175	Q₈×C₁₃₉	—	2	4	no	—
176	Q₈×C₁₃₉	#117	1	4	yes	complemented
177	D₄×C₁₃₉	—	2	16	no	—
178	D₄×C₁₃₉	—	2	2	no	—
179	D₄×C₁₃₉	—	2	4	no	—
180	D₄×C₁₃₉	#117	1	4	yes	complemented
181	C₂×C₄×C₁₃₉	—	2	16	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	2	2	no	—
184	C₂×C₄×C₁₃₉	—	2	4	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	1	no	—
187	C₂×C₄×C₁₃₉	—	2	1	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	2	no	—
190	C₂×C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₄×C₁₃₉	—	2	8	no	—
192	C₂×C₄×C₁₃₉	—	2	8	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	4	2	no	—
196	C₂×C₄×C₁₃₉	—	4	1	no	—
197	C₂×C₄×C₁₃₉	—	4	1	no	—
198	C₂×C₄×C₁₃₉	—	4	8	no	—
199	C₂×C₄×C₁₃₉	—	4	8	no	—
200	C₂×C₄×C₁₃₉	—	4	4	no	—
201	C₂×C₄×C₁₃₉	—	4	4	no	—
202	C₂×C₄×C₁₃₉	—	4	4	no	—
203	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₃₉	#135	1	4	yes	—
209	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
210	C₂×C₄×C₁₃₉	#137	1	2	yes	—
211	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
215	C₈×C₁₃₉	—	4	4	no	—
216	C₂²×C₁₃₉	—	2	2	no	—
217	C₂²×C₁₃₉	—	2	2	no	—
218	C₂²×C₁₃₉	—	2	2	no	—
219	C₂²×C₁₃₉	—	2	4	no	—
220	C₂²×C₁₃₉	—	4	2	no	—
221	C₂²×C₁₃₉	—	4	4	no	—
222	C₂²×C₁₃₉	—	4	2	no	—
223	C₂²×C₁₃₉	—	4	4	no	—
224	C₂²×C₁₃₉	—	4	2	no	—
225	C₂²×C₁₃₉	—	4	2	no	—
226	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₁₃₉	#525	1	2	yes	—
228	C₂²×C₁₃₉	C₂×#135	1	2	yes	—
229	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
231	C₄×C₁₃₉	—	2	2	no	—
232	C₄×C₁₃₉	—	2	2	no	—
233	C₄×C₁₃₉	—	2	2	no	—
234	C₄×C₁₃₉	—	2	4	no	—
235	C₄×C₁₃₉	—	4	2	no	—
236	C₄×C₁₃₉	—	4	2	no	—
237	C₄×C₁₃₉	—	8	4	no	—
238	C₄×C₁₃₉	#416	1	4	yes	—
239	C₄×C₁₃₉	#417	1	4	yes	—
240	C₄×C₁₃₉	C₂×#117	1	1	yes	characteristic
241	C₄×C₁₃₉	C₂×#117	1	1	yes	characteristic
242	C₄×C₁₃₉	#525	1	2	yes	—
243	C₂×C₁₃₉	—	4	2	no	—
244	C₂×C₁₃₉	—	4	4	no	—
245	C₂×C₁₃₉	#2280	1	1	yes	characteristic
246	C₂×C₁₃₉	C₂×#416	1	1	yes	characteristic
247	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
248	C₂×C₁₃₉	#3106	1	2	yes	—
249	C₂×C₁₃₉	#3107	1	2	yes	—
250	#20737	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₁₃₉	#20737	1	1	yes	characteristic, direct product factor, Sylow
252	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
253	C₂×#431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
254	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
255	#1825	C₂×C₁₃₉	1	2	yes	complemented
256	#1803	C₂×C₁₃₉	1	2	yes	complemented
257	#1802	C₂×C₁₃₉	1	2	yes	complemented
258	#1788	C₂×C₁₃₉	1	2	yes	—
259	C₄×#103	C₂×C₁₃₉	1	2	yes	complemented
260	C₄×#102	C₂×C₁₃₉	1	2	yes	complemented
261	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
262	C₄×#41	—	2	4	no	—
263	C₄×#41	C₄×C₁₃₉	1	8	yes	complemented
264	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
270	C₂×#117	—	2	1	no	—
271	C₂×#117	—	2	1	no	—
272	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
273	C₂²×C₄²	—	2	1	no	—
274	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
275	#431	—	2	4	no	—
276	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
277	C₂×#103	C₂²×C₁₃₉	1	4	yes	—
278	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
279	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
280	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
281	#384	C₂²×C₁₃₉	1	2	yes	—
282	#382	—	2	1	no	—
283	#380	—	2	1	no	—
284	#380	C₂²×C₁₃₉	1	2	yes	—
285	C₄×C₄⋊C₄	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
287	#340	C₂²×C₁₃₉	1	4	yes	—
288	#340	C₂²×C₁₃₉	1	4	yes	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	2	2	no	—
292	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
293	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
306	C₄×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
307	C₄×D₄	—	2	8	no	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
312	C₄×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
313	#117	—	2	2	no	—
314	#117	—	2	8	no	—
315	#117	—	4	4	no	—
316	#117	C₂×C₄×C₁₃₉	1	4	yes	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	8	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
334	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
336	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
337	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
339	C₄⋊C₈	—	2	4	no	—
340	#103	—	2	8	no	—
341	#102	—	2	8	no	—
342	C₂²⋊C₈	—	2	4	no	—
343	C₄×C₈	—	2	4	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
348	#41	—	2	16	no	—
349	#41	—	2	8	no	—
350	#41	—	2	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
354	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
360	C₂×D₄	#41×C₁₃₉	1	4	yes	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
378	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	4	4	no	—
397	C₄⋊C₄	—	4	4	no	—
398	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	4	4	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	4	4	no	—
408	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
409	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
410	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
411	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
412	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
413	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
424	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	4	no	—
427	Q₈	#117×C₁₃₉	1	4	yes	complemented
428	D₄	—	2	16	no	—
429	D₄	—	2	2	no	—
430	D₄	—	2	4	no	—
431	D₄	#117×C₁₃₉	1	4	yes	complemented
432	C₂×C₄	—	2	16	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
455	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
458	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
459	C₂×C₄	#135×C₁₃₉	1	4	yes	—
460	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
461	C₂×C₄	#137×C₁₃₉	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
465	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
466	C₈	—	4	4	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
478	C₂²	#525×C₁₃₉	1	2	yes	—
479	C₂²	C₂×#135×C₁₃₉	1	2	yes	—
480	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
481	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	4	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	4	no	—
489	C₄	#416×C₁₃₉	1	4	yes	—
490	C₄	#417×C₁₃₉	1	4	yes	—
491	C₄	C₂×#117×C₁₃₉	1	1	yes	characteristic
492	C₄	C₂×#117×C₁₃₉	1	1	yes	characteristic
493	C₄	#525×C₁₃₉	1	2	yes	—
494	C₂	—	4	2	no	—
495	C₂	—	4	4	no	—
496	C₂	#2280×C₁₃₉	1	1	yes	characteristic
497	C₂	C₂×#416×C₁₃₉	1	1	yes	characteristic
498	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
499	C₂	#3106×C₁₃₉	1	2	yes	—
500	C₂	#3107×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂³×C₁₃₉	C₂²×D₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₃₉	C₂	semidirect
3. #2285×C₁₃₉	C₂	semidirect
4. #1825×C₁₃₉	C₂	semidirect
5. #1803×C₁₃₉	C₂	semidirect
6. #1802×C₁₃₉	C₂	semidirect
8. C₄×#103×C₁₃₉	C₂	semidirect
9. C₄×#102×C₁₃₉	C₂	semidirect
12. C₄×#41×C₁₃₉	C₄	semidirect
176. Q₈×C₁₃₉	#117	semidirect
180. D₄×C₁₃₉	#117	semidirect
250. #20737	C₁₃₉	direct (N × H)
251. C₁₃₉	#20737	direct (N × H)
253. C₂×#431	C₂×C₁₃₉	semidirect
254. #2285	C₂×C₁₃₉	semidirect
255. #1825	C₂×C₁₃₉	semidirect
256. #1803	C₂×C₁₃₉	semidirect
257. #1802	C₂×C₁₃₉	semidirect
259. C₄×#103	C₂×C₁₃₉	semidirect
260. C₄×#102	C₂×C₁₃₉	semidirect
263. C₄×#41	C₄×C₁₃₉	semidirect
427. Q₈	#117×C₁₃₉	semidirect
431. D₄	#117×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₃₉	2
C₂×#431×C₁₃₉	2
#2285×C₁₃₉	2
#1825×C₁₃₉	2
#1803×C₁₃₉	2
#1802×C₁₃₉	2
#1788×C₁₃₉	2
C₄×#103×C₁₃₉	2
C₄×#102×C₁₃₉	2
#20737	139

Subgroups — C139×#20737 #48015333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20737 #48015333