Subgroups — C₁₃₉×#23095 #48017691

Order 35584.

966 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×#460×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2366×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2355×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1968×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1957×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#1948×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1926×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1877×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#103×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂²×SD₁₆×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#127×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	C₂²	1	2	yes	—
17	#460×C₁₃₉	C₄	1	8	yes	complemented
18	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#103×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#103×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
27	#391×C₁₃₉	C₂²	1	2	yes	—
28	#390×C₁₃₉	—	2	1	no	—
29	#390×C₁₃₉	C₂²	1	2	yes	—
30	#387×C₁₃₉	—	2	2	no	—
31	#386×C₁₃₉	—	2	2	no	—
32	#384×C₁₃₉	C₂²	1	1	yes	characteristic
33	#382×C₁₃₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	#340×C₁₃₉	C₂²	1	1	yes	characteristic
39	#340×C₁₃₉	C₂²	1	2	yes	—
40	#340×C₁₃₉	C₂²	1	1	yes	characteristic
41	#336×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₉	—	2	1	no	—
44	C₂²×D₄×C₁₃₉	—	2	1	no	—
45	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃₉	—	2	2	no	—
47	C₂×SD₁₆×C₁₃₉	—	4	2	no	—
48	C₂×SD₁₆×C₁₃₉	—	4	2	no	—
49	C₂×SD₁₆×C₁₃₉	C₂×C₄	1	8	yes	complemented
50	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
53	#127×C₁₃₉	—	2	2	no	—
54	#127×C₁₃₉	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₁₃₉	—	2	2	no	—
56	C₄×Q₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
57	C₄×D₄×C₁₃₉	—	2	4	no	—
58	C₄×D₄×C₁₃₉	—	4	2	no	—
59	C₄×D₄×C₁₃₉	—	4	4	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
72	C₂×C₄²×C₁₃₉	—	2	1	no	—
73	C₂×C₄²×C₁₃₉	—	2	1	no	—
74	C₂×C₄²×C₁₃₉	—	2	2	no	—
75	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
77	#106×C₁₃₉	—	4	2	no	—
78	C₄⋊C₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
79	#103×C₁₃₉	—	2	2	no	—
80	#103×C₁₃₉	—	2	2	no	—
81	#102×C₁₃₉	—	2	4	no	—
82	#102×C₁₃₉	—	4	2	no	—
83	#102×C₁₃₉	C₂×C₄	1	8	yes	complemented
84	C₄×C₈×C₁₃₉	—	2	2	no	—
85	C₄×C₈×C₁₃₉	—	4	2	no	—
86	#95×C₁₃₉	—	2	2	no	—
87	#95×C₁₃₉	—	2	2	no	—
88	#95×C₁₃₉	—	2	1	no	—
89	#95×C₁₃₉	—	2	2	no	—
90	#95×C₁₃₉	D₄	1	2	yes	—
91	C₂⁴×C₁₃₉	—	2	2	no	—
92	C₂×Q₈×C₁₃₉	—	2	1	no	—
93	C₂×Q₈×C₁₃₉	—	2	1	no	—
94	C₂×Q₈×C₁₃₉	—	2	1	no	—
95	C₂×Q₈×C₁₃₉	—	2	1	no	—
96	C₂×Q₈×C₁₃₉	—	2	1	no	—
97	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₁₃₉	—	2	4	no	—
99	C₂×D₄×C₁₃₉	—	2	4	no	—
100	C₂×D₄×C₁₃₉	—	2	2	no	—
101	C₂×D₄×C₁₃₉	—	2	2	no	—
102	C₂×D₄×C₁₃₉	—	2	2	no	—
103	C₂×D₄×C₁₃₉	—	2	2	no	—
104	C₂×D₄×C₁₃₉	—	2	2	no	—
105	C₂×D₄×C₁₃₉	—	4	2	no	—
106	C₂×D₄×C₁₃₉	—	4	2	no	—
107	C₂×D₄×C₁₃₉	—	8	1	no	—
108	C₂×D₄×C₁₃₉	—	8	1	no	—
109	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₁₃₉	—	2	1	no	—
111	C₂²×C₄×C₁₃₉	—	2	1	no	—
112	C₂²×C₄×C₁₃₉	—	2	1	no	—
113	C₂²×C₄×C₁₃₉	—	2	2	no	—
114	C₂²×C₄×C₁₃₉	—	2	1	no	—
115	C₂²×C₄×C₁₃₉	—	4	4	no	—
116	C₂²×C₄×C₁₃₉	—	4	4	no	—
117	C₂²×C₄×C₁₃₉	—	8	2	no	—
118	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
123	SD₁₆×C₁₃₉	—	4	8	no	—
124	C₂×C₈×C₁₃₉	—	2	1	no	—
125	C₂×C₈×C₁₃₉	—	2	1	no	—
126	C₂×C₈×C₁₃₉	—	2	2	no	—
127	C₂×C₈×C₁₃₉	—	2	2	no	—
128	C₂×C₈×C₁₃₉	—	2	1	no	—
129	C₂×C₈×C₁₃₉	—	2	1	no	—
130	C₂×C₈×C₁₃₉	—	2	1	no	—
131	C₂×C₈×C₁₃₉	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₁₃₉	#41	1	2	yes	—
133	C₄⋊C₄×C₁₃₉	—	2	4	no	—
134	C₄⋊C₄×C₁₃₉	—	2	2	no	—
135	C₄⋊C₄×C₁₃₉	—	2	1	no	—
136	C₄⋊C₄×C₁₃₉	—	2	1	no	—
137	C₄⋊C₄×C₁₃₉	—	2	2	no	—
138	C₄⋊C₄×C₁₃₉	—	2	1	no	—
139	C₄⋊C₄×C₁₃₉	—	2	2	no	—
140	C₄⋊C₄×C₁₃₉	—	2	1	no	—
141	C₄⋊C₄×C₁₃₉	—	4	2	no	—
142	C₄⋊C₄×C₁₃₉	—	8	1	no	—
143	C₄⋊C₄×C₁₃₉	SD₁₆	1	4	yes	complemented
144	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₁₃₉	#41	1	2	yes	—
146	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
147	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
149	C₄²×C₁₃₉	—	2	4	no	—
150	C₄²×C₁₃₉	—	2	2	no	—
151	C₄²×C₁₃₉	—	2	2	no	—
152	C₄²×C₁₃₉	—	4	2	no	—
153	C₄²×C₁₃₉	—	8	2	no	—
154	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
155	C₄²×C₁₃₉	#41	1	2	yes	—
156	C₂³×C₁₃₉	—	2	4	no	—
157	C₂³×C₁₃₉	—	4	2	no	—
158	C₂³×C₁₃₉	—	4	2	no	—
159	C₂³×C₁₃₉	—	4	2	no	—
160	C₂³×C₁₃₉	—	4	2	no	—
161	C₂³×C₁₃₉	—	4	2	no	—
162	C₂³×C₁₃₉	—	4	2	no	—
163	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃₉	—	2	2	no	—
165	Q₈×C₁₃₉	—	2	2	no	—
166	Q₈×C₁₃₉	—	4	1	no	—
167	Q₈×C₁₃₉	—	4	1	no	—
168	D₄×C₁₃₉	—	2	4	no	—
169	D₄×C₁₃₉	—	2	4	no	—
170	D₄×C₁₃₉	—	4	2	no	—
171	D₄×C₁₃₉	—	4	2	no	—
172	D₄×C₁₃₉	—	4	8	no	—
173	D₄×C₁₃₉	—	8	4	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	2	2	no	—
176	C₂×C₄×C₁₃₉	—	2	1	no	—
177	C₂×C₄×C₁₃₉	—	2	1	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	2	2	no	—
184	C₂×C₄×C₁₃₉	—	4	1	no	—
185	C₂×C₄×C₁₃₉	—	4	1	no	—
186	C₂×C₄×C₁₃₉	—	4	1	no	—
187	C₂×C₄×C₁₃₉	—	4	1	no	—
188	C₂×C₄×C₁₃₉	—	4	1	no	—
189	C₂×C₄×C₁₃₉	—	4	1	no	—
190	C₂×C₄×C₁₃₉	—	4	1	no	—
191	C₂×C₄×C₁₃₉	—	4	2	no	—
192	C₂×C₄×C₁₃₉	—	4	1	no	—
193	C₂×C₄×C₁₃₉	—	4	2	no	—
194	C₂×C₄×C₁₃₉	—	4	2	no	—
195	C₂×C₄×C₁₃₉	—	4	1	no	—
196	C₂×C₄×C₁₃₉	—	8	8	no	—
197	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	4	yes	—
200	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₁₃₉	#135	1	2	yes	—
202	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₈×C₁₃₉	—	2	4	no	—
209	C₈×C₁₃₉	—	2	2	no	—
210	C₈×C₁₃₉	—	4	1	no	—
211	C₂²×C₁₃₉	—	4	4	no	—
212	C₂²×C₁₃₉	—	4	4	no	—
213	C₂²×C₁₃₉	—	4	4	no	—
214	C₂²×C₁₃₉	—	8	2	no	—
215	C₂²×C₁₃₉	—	8	2	no	—
216	C₂²×C₁₃₉	—	8	2	no	—
217	C₂²×C₁₃₉	—	8	2	no	—
218	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₁₃₉	#546	1	1	yes	characteristic
220	C₂²×C₁₃₉	#550	1	1	yes	characteristic
221	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
222	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
223	C₂²×C₁₃₉	#576	1	1	yes	characteristic
224	C₂²×C₁₃₉	#577	1	1	yes	characteristic
225	C₄×C₁₃₉	—	2	2	no	—
226	C₄×C₁₃₉	—	2	4	no	—
227	C₄×C₁₃₉	—	4	2	no	—
228	C₄×C₁₃₉	—	4	2	no	—
229	C₄×C₁₃₉	—	4	2	no	—
230	C₄×C₁₃₉	—	4	2	no	—
231	C₄×C₁₃₉	—	8	1	no	—
232	C₄×C₁₃₉	—	8	2	no	—
233	C₄×C₁₃₉	C₄×SD₁₆	1	4	yes	—
234	C₄×C₁₃₉	C₄×#41	1	1	yes	characteristic
235	C₄×C₁₃₉	#518	1	1	yes	characteristic
236	C₄×C₁₃₉	#553	1	1	yes	characteristic
237	C₄×C₁₃₉	#555	1	1	yes	characteristic
238	C₂×C₁₃₉	—	8	4	no	—
239	C₂×C₁₃₉	#2363	1	1	yes	characteristic
240	C₂×C₁₃₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
241	C₂×C₁₃₉	#2946	1	1	yes	characteristic
242	C₂×C₁₃₉	#3295	1	1	yes	characteristic
243	C₂×C₁₃₉	#3304	1	1	yes	characteristic
244	C₂×C₁₃₉	#3392	1	1	yes	characteristic
245	C₂×C₁₃₉	#3396	1	1	yes	characteristic
246	#23095	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₁₃₉	#23095	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×#460	C₂×C₁₃₉	1	1	yes	characteristic
249	#2366	C₂×C₁₃₉	1	1	yes	characteristic
250	#2355	C₂×C₁₃₉	1	1	yes	characteristic, complemented
251	#1968	C₂×C₁₃₉	1	2	yes	complemented
252	#1957	C₂×C₁₃₉	1	1	yes	characteristic
253	#1948	C₂×C₁₃₉	1	1	yes	characteristic, complemented
254	#1926	C₂×C₁₃₉	1	2	yes	complemented
255	#1877	C₂×C₁₃₉	1	2	yes	complemented
256	C₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
257	C₄×#103	C₂×C₁₃₉	1	1	yes	characteristic, complemented
258	C₄×#102	C₂×C₁₃₉	1	2	yes	complemented
259	C₂²×SD₁₆	C₂²×C₁₃₉	1	2	yes	—
260	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
264	#460	C₄×C₁₃₉	1	8	yes	complemented
265	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
267	C₂×#103	C₂²×C₁₃₉	1	1	yes	characteristic
268	C₂×#103	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
270	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
271	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
272	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
274	#391	C₂²×C₁₃₉	1	2	yes	—
275	#390	—	2	1	no	—
276	#390	C₂²×C₁₃₉	1	2	yes	—
277	#387	—	2	2	no	—
278	#386	—	2	2	no	—
279	#384	C₂²×C₁₃₉	1	1	yes	characteristic
280	#382	—	2	1	no	—
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
283	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
285	#340	C₂²×C₁₃₉	1	2	yes	—
286	#340	C₂²×C₁₃₉	1	1	yes	characteristic
287	#340	C₂²×C₁₃₉	1	1	yes	characteristic
288	#336	C₂²×C₁₃₉	1	2	yes	—
289	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
293	C₂³×C₄	—	2	2	no	—
294	C₂×SD₁₆	—	4	2	no	—
295	C₂×SD₁₆	—	4	2	no	—
296	C₂×SD₁₆	C₂×C₄×C₁₃₉	1	8	yes	complemented
297	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
299	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
300	#127	—	2	2	no	—
301	#127	C₂×C₄×C₁₃₉	1	4	yes	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	4	2	no	—
306	C₄×D₄	—	4	4	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
324	#106	—	4	2	no	—
325	C₄⋊C₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
326	#103	—	2	2	no	—
327	#103	—	2	2	no	—
328	#102	—	2	4	no	—
329	#102	—	4	2	no	—
330	#102	C₂×C₄×C₁₃₉	1	8	yes	complemented
331	C₄×C₈	—	2	2	no	—
332	C₄×C₈	—	4	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	2	no	—
337	#95	D₄×C₁₃₉	1	2	yes	—
338	C₂⁴	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	8	1	no	—
355	C₂×D₄	—	8	1	no	—
356	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	8	2	no	—
365	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
370	SD₁₆	—	4	8	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	C₂²×C₄×C₁₃₉	1	4	yes	—
379	C₂×C₈	#41×C₁₃₉	1	2	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	8	1	no	—
390	C₄⋊C₄	SD₁₆×C₁₃₉	1	4	yes	complemented
391	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
392	C₄⋊C₄	#41×C₁₃₉	1	2	yes	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	8	2	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	8	2	no	—
401	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
402	C₄²	#41×C₁₃₉	1	2	yes	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	D₄	—	2	4	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	8	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
445	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
446	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	4	yes	—
447	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
448	C₂×C₄	#135×C₁₃₉	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
453	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	2	2	no	—
457	C₈	—	4	1	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
466	C₂²	#546×C₁₃₉	1	1	yes	characteristic
467	C₂²	#550×C₁₃₉	1	1	yes	characteristic
468	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
469	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
470	C₂²	#576×C₁₃₉	1	1	yes	characteristic
471	C₂²	#577×C₁₃₉	1	1	yes	characteristic
472	C₄	—	2	4	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	C₄×SD₁₆×C₁₃₉	1	4	yes	—
481	C₄	C₄×#41×C₁₃₉	1	1	yes	characteristic
482	C₄	#518×C₁₃₉	1	1	yes	characteristic
483	C₄	#553×C₁₃₉	1	1	yes	characteristic
484	C₄	#555×C₁₃₉	1	1	yes	characteristic
485	C₂	—	8	4	no	—
486	C₂	#2363×C₁₃₉	1	1	yes	characteristic
487	C₂	C₂×C₄×SD₁₆×C₁₃₉	1	1	yes	characteristic
488	C₂	#2946×C₁₃₉	1	1	yes	characteristic
489	C₂	#3295×C₁₃₉	1	1	yes	characteristic
490	C₂	#3304×C₁₃₉	1	1	yes	characteristic
491	C₂	#3392×C₁₃₉	1	1	yes	characteristic
492	C₂	#3396×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₄×C₄⋊C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #2355×C₁₃₉	C₂	semidirect
4. #1968×C₁₃₉	C₂	semidirect
6. #1948×C₁₃₉	C₂	semidirect
7. #1926×C₁₃₉	C₂	semidirect
8. #1877×C₁₃₉	C₂	semidirect
9. C₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
10. C₄×#103×C₁₃₉	C₂	semidirect
11. C₄×#102×C₁₃₉	C₂	semidirect
17. #460×C₁₃₉	C₄	semidirect
49. C₂×SD₁₆×C₁₃₉	C₂×C₄	semidirect
56. C₄×Q₈×C₁₃₉	C₂×C₄	semidirect
78. C₄⋊C₈×C₁₃₉	C₂×C₄	semidirect
83. #102×C₁₃₉	C₂×C₄	semidirect
143. C₄⋊C₄×C₁₃₉	SD₁₆	semidirect
246. #23095	C₁₃₉	direct (N × H)
247. C₁₃₉	#23095	direct (N × H)
250. #2355	C₂×C₁₃₉	semidirect
251. #1968	C₂×C₁₃₉	semidirect
253. #1948	C₂×C₁₃₉	semidirect
254. #1926	C₂×C₁₃₉	semidirect
255. #1877	C₂×C₁₃₉	semidirect
256. C₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
257. C₄×#103	C₂×C₁₃₉	semidirect
258. C₄×#102	C₂×C₁₃₉	semidirect
264. #460	C₄×C₁₃₉	semidirect
296. C₂×SD₁₆	C₂×C₄×C₁₃₉	semidirect
303. C₄×Q₈	C₂×C₄×C₁₃₉	semidirect
325. C₄⋊C₈	C₂×C₄×C₁₃₉	semidirect
330. #102	C₂×C₄×C₁₃₉	semidirect
390. C₄⋊C₄	SD₁₆×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#460×C₁₃₉	2
#2366×C₁₃₉	2
#2355×C₁₃₉	2
#1968×C₁₃₉	2
#1957×C₁₃₉	2
#1948×C₁₃₉	2
#1926×C₁₃₉	2
#1877×C₁₃₉	2
C₈×C₄⋊C₄×C₁₃₉	2
C₄×#103×C₁₃₉	2
C₄×#102×C₁₃₉	2
#23095	139

Subgroups — C139×#23095 #48017691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#23095 #48017691