Subgroups — C₁₃₉×#29598 #48024194

Order 35584.

1786 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#484×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#450×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2033×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2000×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1824×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1786×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1779×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃₉	—	2	1	no	—
11	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₉	C₂²	1	2	yes	complemented
14	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
16	C₂×#121×C₁₃₉	—	2	4	no	—
17	C₂×#121×C₁₃₉	—	2	2	no	—
18	C₂×#121×C₁₃₉	—	2	4	no	—
19	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
22	#484×C₁₃₉	—	2	4	no	—
23	#450×C₁₃₉	—	2	4	no	—
24	C₂×#107×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#103×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×#102×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#102×C₁₃₉	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	complemented
31	#385×C₁₃₉	—	2	2	no	—
32	#385×C₁₃₉	—	2	1	no	—
33	#380×C₁₃₉	C₂²	1	1	yes	characteristic
34	#380×C₁₃₉	C₂²	1	2	yes	complemented
35	#379×C₁₃₉	—	2	1	no	—
36	#340×C₁₃₉	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₃₉	—	2	1	no	—
38	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃₉	—	2	8	no	—
41	C₂²×D₄×C₁₃₉	—	2	4	no	—
42	C₂²×D₄×C₁₃₉	—	2	1	no	—
43	C₂²×D₄×C₁₃₉	—	2	2	no	—
44	C₂²×D₄×C₁₃₉	—	4	4	no	—
45	C₂²×D₄×C₁₃₉	—	4	8	no	—
46	C₂²×D₄×C₁₃₉	D₄	1	4	yes	—
47	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃₉	—	2	1	no	—
49	C₂³×C₄×C₁₃₉	—	2	2	no	—
50	C₂³×C₄×C₁₃₉	—	2	2	no	—
51	C₂³×C₄×C₁₃₉	—	4	4	no	—
52	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
54	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
57	C₂×SD₁₆×C₁₃₉	—	4	4	no	—
58	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
60	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
61	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
63	#121×C₁₃₉	—	2	16	no	—
64	#121×C₁₃₉	—	2	8	no	—
65	#121×C₁₃₉	—	2	8	no	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
80	#107×C₁₃₉	—	2	4	no	—
81	#103×C₁₃₉	—	2	4	no	—
82	#102×C₁₃₉	—	2	4	no	—
83	#102×C₁₃₉	—	4	4	no	—
84	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
85	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
86	C₂²⋊C₈×C₁₃₉	—	4	4	no	—
87	#95×C₁₃₉	—	2	1	no	—
88	#95×C₁₃₉	—	2	2	no	—
89	C₂⁴×C₁₃₉	—	2	2	no	—
90	C₂⁴×C₁₃₉	—	2	4	no	—
91	C₂⁴×C₁₃₉	—	2	4	no	—
92	C₂⁴×C₁₃₉	—	2	2	no	—
93	C₂⁴×C₁₃₉	—	2	2	no	—
94	C₂⁴×C₁₃₉	—	2	2	no	—
95	C₂⁴×C₁₃₉	—	4	2	no	—
96	C₂⁴×C₁₃₉	—	4	4	no	—
97	C₂⁴×C₁₃₉	—	4	4	no	—
98	C₂⁴×C₁₃₉	—	4	2	no	—
99	C₂⁴×C₁₃₉	—	4	2	no	—
100	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
101	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₃₉	—	2	1	no	—
103	C₂×Q₈×C₁₃₉	—	2	1	no	—
104	C₂×Q₈×C₁₃₉	—	2	4	no	—
105	C₂×D₄×C₁₃₉	—	2	16	no	—
106	C₂×D₄×C₁₃₉	—	2	4	no	—
107	C₂×D₄×C₁₃₉	—	2	2	no	—
108	C₂×D₄×C₁₃₉	—	2	4	no	—
109	C₂×D₄×C₁₃₉	—	2	4	no	—
110	C₂×D₄×C₁₃₉	—	4	8	no	—
111	C₂×D₄×C₁₃₉	—	4	4	no	—
112	C₂×D₄×C₁₃₉	—	4	8	no	—
113	C₂×D₄×C₁₃₉	—	4	32	no	—
114	C₂×D₄×C₁₃₉	—	4	8	no	—
115	C₂×D₄×C₁₃₉	—	4	8	no	—
116	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₃₉	—	2	4	no	—
118	C₂²×C₄×C₁₃₉	—	2	2	no	—
119	C₂²×C₄×C₁₃₉	—	2	4	no	—
120	C₂²×C₄×C₁₃₉	—	2	2	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	2	no	—
123	C₂²×C₄×C₁₃₉	—	2	2	no	—
124	C₂²×C₄×C₁₃₉	—	2	4	no	—
125	C₂²×C₄×C₁₃₉	—	2	4	no	—
126	C₂²×C₄×C₁₃₉	—	2	1	no	—
127	C₂²×C₄×C₁₃₉	—	2	2	no	—
128	C₂²×C₄×C₁₃₉	—	2	1	no	—
129	C₂²×C₄×C₁₃₉	—	4	2	no	—
130	C₂²×C₄×C₁₃₉	—	4	2	no	—
131	C₂²×C₄×C₁₃₉	—	4	2	no	—
132	C₂²×C₄×C₁₃₉	—	4	8	no	—
133	C₂²×C₄×C₁₃₉	—	4	8	no	—
134	C₂²×C₄×C₁₃₉	—	4	4	no	—
135	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₁₃₉	—	4	8	no	—
141	C₂×C₈×C₁₃₉	—	2	2	no	—
142	C₂×C₈×C₁₃₉	—	2	2	no	—
143	C₂×C₈×C₁₃₉	—	2	4	no	—
144	C₂×C₈×C₁₃₉	—	2	4	no	—
145	C₄⋊C₄×C₁₃₉	—	2	4	no	—
146	C₄⋊C₄×C₁₃₉	—	2	2	no	—
147	C₄⋊C₄×C₁₃₉	—	2	1	no	—
148	C₄⋊C₄×C₁₃₉	—	2	1	no	—
149	C₄⋊C₄×C₁₃₉	—	2	4	no	—
150	C₄⋊C₄×C₁₃₉	—	4	4	no	—
151	C₄⋊C₄×C₁₃₉	—	4	2	no	—
152	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
154	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
156	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
157	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	2	2	no	—
160	C₂³×C₁₃₉	—	2	8	no	—
161	C₂³×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	2	no	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	2	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	4	no	—
168	C₂³×C₁₃₉	—	4	8	no	—
169	C₂³×C₁₃₉	—	4	8	no	—
170	C₂³×C₁₃₉	—	4	4	no	—
171	C₂³×C₁₃₉	—	4	8	no	—
172	C₂³×C₁₃₉	—	4	8	no	—
173	C₂³×C₁₃₉	—	4	4	no	—
174	C₂³×C₁₃₉	—	4	4	no	—
175	C₂³×C₁₃₉	—	4	2	no	—
176	C₂³×C₁₃₉	—	4	4	no	—
177	C₂³×C₁₃₉	—	4	2	no	—
178	C₂³×C₁₃₉	—	4	8	no	—
179	C₂³×C₁₃₉	—	8	8	no	—
180	C₂³×C₁₃₉	—	8	8	no	—
181	C₂³×C₁₃₉	#120	1	2	yes	—
182	C₂³×C₁₃₉	#135	1	2	yes	—
183	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
184	C₂³×C₁₃₉	#137	1	2	yes	—
185	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃₉	—	4	2	no	—
187	Q₈×C₁₃₉	—	4	2	no	—
188	D₄×C₁₃₉	—	2	4	no	—
189	D₄×C₁₃₉	—	2	4	no	—
190	D₄×C₁₃₉	—	4	8	no	—
191	D₄×C₁₃₉	—	4	32	no	—
192	D₄×C₁₃₉	—	4	4	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	4	no	—
195	C₂×C₄×C₁₃₉	—	2	4	no	—
196	C₂×C₄×C₁₃₉	—	2	2	no	—
197	C₂×C₄×C₁₃₉	—	2	4	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	4	8	no	—
201	C₂×C₄×C₁₃₉	—	4	4	no	—
202	C₂×C₄×C₁₃₉	—	4	8	no	—
203	C₂×C₄×C₁₃₉	—	4	4	no	—
204	C₂×C₄×C₁₃₉	—	4	4	no	—
205	C₂×C₄×C₁₃₉	—	4	4	no	—
206	C₂×C₄×C₁₃₉	—	4	1	no	—
207	C₂×C₄×C₁₃₉	—	4	1	no	—
208	C₂×C₄×C₁₃₉	—	4	2	no	—
209	C₂×C₄×C₁₃₉	—	4	2	no	—
210	C₂×C₄×C₁₃₉	—	4	2	no	—
211	C₂×C₄×C₁₃₉	—	4	2	no	—
212	C₂×C₄×C₁₃₉	—	4	2	no	—
213	C₂×C₄×C₁₃₉	#120	1	2	yes	—
214	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
217	C₈×C₁₃₉	—	4	2	no	—
218	C₈×C₁₃₉	—	4	2	no	—
219	C₂²×C₁₃₉	—	2	2	no	—
220	C₂²×C₁₃₉	—	2	4	no	—
221	C₂²×C₁₃₉	—	2	4	no	—
222	C₂²×C₁₃₉	—	2	2	no	—
223	C₂²×C₁₃₉	—	2	4	no	—
224	C₂²×C₁₃₉	—	2	4	no	—
225	C₂²×C₁₃₉	—	2	4	no	—
226	C₂²×C₁₃₉	—	4	16	no	—
227	C₂²×C₁₃₉	—	4	2	no	—
228	C₂²×C₁₃₉	—	4	2	no	—
229	C₂²×C₁₃₉	—	4	2	no	—
230	C₂²×C₁₃₉	—	4	2	no	—
231	C₂²×C₁₃₉	—	4	4	no	—
232	C₂²×C₁₃₉	—	4	4	no	—
233	C₂²×C₁₃₉	—	4	4	no	—
234	C₂²×C₁₃₉	—	8	16	no	—
235	C₂²×C₁₃₉	—	8	4	no	—
236	C₂²×C₁₃₉	—	8	4	no	—
237	C₂²×C₁₃₉	#452	1	4	yes	—
238	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
239	C₂²×C₁₃₉	#534	1	2	yes	—
240	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
241	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
242	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
243	C₄×C₁₃₉	—	2	2	no	—
244	C₄×C₁₃₉	—	4	2	no	—
245	C₄×C₁₃₉	—	4	4	no	—
246	C₄×C₁₃₉	—	8	1	no	—
247	C₄×C₁₃₉	—	8	2	no	—
248	C₄×C₁₃₉	—	8	1	no	—
249	C₄×C₁₃₉	#534	1	2	yes	—
250	C₄×C₁₃₉	#535	1	2	yes	—
251	C₂×C₁₃₉	—	2	4	no	—
252	C₂×C₁₃₉	—	4	4	no	—
253	C₂×C₁₃₉	—	8	4	no	—
254	C₂×C₁₃₉	#2613	1	1	yes	characteristic
255	C₂×C₁₃₉	C₂×#452	1	1	yes	characteristic
256	C₂×C₁₃₉	#3003	1	1	yes	characteristic
257	C₂×C₁₃₉	#3188	1	2	yes	—
258	C₂×C₁₃₉	#3193	1	2	yes	—
259	#29598	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₁₃₉	#29598	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×#121	C₂×C₁₃₉	1	1	yes	characteristic
262	C₂×#484	C₂×C₁₃₉	1	1	yes	characteristic, complemented
263	C₂×#450	C₂×C₁₃₉	1	1	yes	characteristic, complemented
264	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
265	#2033	C₂×C₁₃₉	1	4	yes	complemented
266	#2000	C₂×C₁₃₉	1	4	yes	complemented
267	#1824	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	#1786	C₂×C₁₃₉	1	1	yes	characteristic, complemented
269	#1779	C₂×C₁₃₉	1	1	yes	characteristic, complemented
270	C₂³×D₄	—	2	1	no	—
271	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
273	C₂²×SD₁₆	C₂²×C₁₃₉	1	2	yes	complemented
274	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
275	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
276	C₂×#121	—	2	4	no	—
277	C₂×#121	—	2	2	no	—
278	C₂×#121	—	2	4	no	—
279	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	—	2	1	no	—
282	#484	—	2	4	no	—
283	#450	—	2	4	no	—
284	C₂×#107	C₂²×C₁₃₉	1	2	yes	complemented
285	C₂×#103	C₂²×C₁₃₉	1	2	yes	complemented
286	C₂×#102	C₂²×C₁₃₉	1	2	yes	complemented
287	C₂×#102	C₂²×C₁₃₉	1	4	yes	complemented
288	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
291	#385	—	2	2	no	—
292	#385	—	2	1	no	—
293	#380	C₂²×C₁₃₉	1	1	yes	characteristic
294	#380	C₂²×C₁₃₉	1	2	yes	complemented
295	#379	—	2	1	no	—
296	#340	C₂²×C₁₃₉	1	4	yes	complemented
297	C₂⁵	—	2	1	no	—
298	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
299	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	—	4	8	no	—
306	C₂²×D₄	D₄×C₁₃₉	1	4	yes	—
307	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	—	4	4	no	—
318	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
319	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	4	4	no	—
323	#121	—	2	16	no	—
324	#121	—	2	8	no	—
325	#121	—	2	8	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	#107	—	2	4	no	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#102	—	4	4	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	4	4	no	—
347	#95	—	2	1	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	4	2	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	—	4	4	no	—
358	C₂⁴	—	4	2	no	—
359	C₂⁴	—	4	2	no	—
360	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
361	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×D₄	—	2	16	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	—	4	32	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	8	no	—
376	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	8	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
400	SD₁₆	—	4	8	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
413	C₂²⋊C₄	—	2	16	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	8	no	—
435	C₂³	—	4	4	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	8	8	no	—
440	C₂³	—	8	8	no	—
441	C₂³	#120×C₁₃₉	1	2	yes	—
442	C₂³	#135×C₁₃₉	1	2	yes	—
443	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
444	C₂³	#137×C₁₃₉	1	2	yes	—
445	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	32	no	—
452	D₄	—	4	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	#120×C₁₃₉	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
476	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	16	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	8	16	no	—
495	C₂²	—	8	4	no	—
496	C₂²	—	8	4	no	—
497	C₂²	#452×C₁₃₉	1	4	yes	—
498	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
499	C₂²	#534×C₁₃₉	1	2	yes	—
500	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
501	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
502	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	1	no	—
509	C₄	#534×C₁₃₉	1	2	yes	—
510	C₄	#535×C₁₃₉	1	2	yes	—
511	C₂	—	2	4	no	—
512	C₂	—	4	4	no	—
513	C₂	—	8	4	no	—
514	C₂	#2613×C₁₃₉	1	1	yes	characteristic
515	C₂	C₂×#452×C₁₃₉	1	1	yes	characteristic
516	C₂	#3003×C₁₃₉	1	1	yes	characteristic
517	C₂	#3188×C₁₃₉	1	2	yes	—
518	C₂	#3193×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×#121×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#484×C₁₃₉	C₂	semidirect
3. C₂×#450×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2033×C₁₃₉	C₂	semidirect
6. #2000×C₁₃₉	C₂	semidirect
7. #1824×C₁₃₉	C₂	semidirect
8. #1786×C₁₃₉	C₂	semidirect
9. #1779×C₁₃₉	C₂	semidirect
13. C₂²×SD₁₆×C₁₃₉	C₂²	semidirect
15. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×#107×C₁₃₉	C₂²	semidirect
25. C₂×#103×C₁₃₉	C₂²	semidirect
26. C₂×#102×C₁₃₉	C₂²	semidirect
27. C₂×#102×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊C₈×C₁₃₉	C₂²	semidirect
34. #380×C₁₃₉	C₂²	semidirect
36. #340×C₁₃₉	C₂²	semidirect
259. #29598	C₁₃₉	direct (N × H)
260. C₁₃₉	#29598	direct (N × H)
262. C₂×#484	C₂×C₁₃₉	semidirect
263. C₂×#450	C₂×C₁₃₉	semidirect
264. #2848	C₂×C₁₃₉	semidirect
265. #2033	C₂×C₁₃₉	semidirect
266. #2000	C₂×C₁₃₉	semidirect
267. #1824	C₂×C₁₃₉	semidirect
268. #1786	C₂×C₁₃₉	semidirect
269. #1779	C₂×C₁₃₉	semidirect
273. C₂²×SD₁₆	C₂²×C₁₃₉	semidirect
275. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
284. C₂×#107	C₂²×C₁₃₉	semidirect
285. C₂×#103	C₂²×C₁₃₉	semidirect
286. C₂×#102	C₂²×C₁₃₉	semidirect
287. C₂×#102	C₂²×C₁₃₉	semidirect
290. C₂×C₂²⋊C₈	C₂²×C₁₃₉	semidirect
294. #380	C₂²×C₁₃₉	semidirect
296. #340	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₃₉	2
C₂×#484×C₁₃₉	2
C₂×#450×C₁₃₉	2
#2848×C₁₃₉	2
#2033×C₁₃₉	2
#2000×C₁₃₉	2
#1824×C₁₃₉	2
#1786×C₁₃₉	2
#1779×C₁₃₉	2
#29598	139

Subgroups — C139×#29598 #48024194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29598 #48024194