Subgroups — C₁₃₉×#24197 #48018793

Order 35584.

1116 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#461×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#442×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2580×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2042×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2012×C₁₃₉	C₂	1	2	yes	maximal
7	#1985×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1960×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1880×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1865×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#1804×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	#556×C₁₃₉	—	2	4	no	—
15	#556×C₁₃₉	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#126×C₁₃₉	—	2	2	no	—
18	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₃₉	—	2	1	no	—
25	#461×C₁₃₉	—	2	4	no	—
26	#442×C₁₃₉	—	2	4	no	—
27	C₂×#106×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
36	#399×C₁₃₉	—	2	1	no	—
37	#393×C₁₃₉	—	2	1	no	—
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#389×C₁₃₉	C₂²	1	2	yes	—
40	#385×C₁₃₉	—	2	2	no	—
41	#382×C₁₃₉	C₂²	1	1	yes	characteristic
42	#340×C₁₃₉	C₂²	1	2	yes	—
43	#336×C₁₃₉	C₂²	1	2	yes	—
44	#336×C₁₃₉	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₉	—	2	1	no	—
50	C₂³×C₄×C₁₃₉	—	2	1	no	—
51	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
52	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
53	C₂×SD₁₆×C₁₃₉	—	4	2	no	—
54	C₂×D₈×C₁₃₉	—	2	2	no	—
55	C₂×D₈×C₁₃₉	—	2	2	no	—
56	C₂×D₈×C₁₃₉	—	2	2	no	—
57	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
61	C₄⋊Q₈×C₁₃₉	D₄	1	4	yes	—
62	#126×C₁₃₉	—	2	16	no	—
63	#124×C₁₃₉	—	2	4	no	—
64	#124×C₁₃₉	—	2	4	no	—
65	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
66	C₄×Q₈×C₁₃₉	—	2	4	no	—
67	C₄×Q₈×C₁₃₉	—	2	4	no	—
68	C₄×Q₈×C₁₃₉	—	2	2	no	—
69	C₄×Q₈×C₁₃₉	—	2	2	no	—
70	C₄×D₄×C₁₃₉	—	2	2	no	—
71	C₄×D₄×C₁₃₉	—	2	2	no	—
72	C₄×D₄×C₁₃₉	—	2	2	no	—
73	C₄×D₄×C₁₃₉	D₄	1	4	yes	—
74	#117×C₁₃₉	—	2	8	no	—
75	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
90	C₂×C₄²×C₁₃₉	—	2	2	no	—
91	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
93	#106×C₁₃₉	—	2	2	no	—
94	C₄⋊C₈×C₁₃₉	—	2	2	no	—
95	#103×C₁₃₉	—	2	4	no	—
96	#103×C₁₃₉	—	2	4	no	—
97	#103×C₁₃₉	—	4	2	no	—
98	#102×C₁₃₉	—	2	2	no	—
99	#102×C₁₃₉	—	2	2	no	—
100	#102×C₁₃₉	—	4	2	no	—
101	#97×C₁₃₉	—	2	2	no	—
102	#95×C₁₃₉	—	2	1	no	—
103	#95×C₁₃₉	—	2	1	no	—
104	#95×C₁₃₉	—	2	2	no	—
105	C₂⁴×C₁₃₉	—	2	1	no	—
106	C₂⁴×C₁₃₉	—	2	1	no	—
107	C₂×Q₈×C₁₃₉	—	2	2	no	—
108	C₂×Q₈×C₁₃₉	—	2	2	no	—
109	C₂×Q₈×C₁₃₉	—	2	2	no	—
110	C₂×Q₈×C₁₃₉	—	2	2	no	—
111	C₂×Q₈×C₁₃₉	—	2	2	no	—
112	C₂×Q₈×C₁₃₉	—	2	2	no	—
113	C₂×Q₈×C₁₃₉	—	4	2	no	—
114	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₁₃₉	—	2	1	no	—
116	C₂×D₄×C₁₃₉	—	2	1	no	—
117	C₂×D₄×C₁₃₉	—	2	1	no	—
118	C₂×D₄×C₁₃₉	—	2	1	no	—
119	C₂×D₄×C₁₃₉	—	2	1	no	—
120	C₂×D₄×C₁₃₉	—	2	1	no	—
121	C₂×D₄×C₁₃₉	—	2	1	no	—
122	C₂×D₄×C₁₃₉	—	2	1	no	—
123	C₂×D₄×C₁₃₉	—	2	1	no	—
124	C₂×D₄×C₁₃₉	—	2	1	no	—
125	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₁₃₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₃₉	—	2	1	no	—
128	C₂²×C₄×C₁₃₉	—	2	2	no	—
129	C₂²×C₄×C₁₃₉	—	2	4	no	—
130	C₂²×C₄×C₁₃₉	—	2	2	no	—
131	C₂²×C₄×C₁₃₉	—	2	1	no	—
132	C₂²×C₄×C₁₃₉	—	4	4	no	—
133	C₂²×C₄×C₁₃₉	—	4	2	no	—
134	C₂²×C₄×C₁₃₉	—	8	2	no	—
135	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₁₃₉	—	4	8	no	—
141	D₈×C₁₃₉	—	2	8	no	—
142	C₂×C₈×C₁₃₉	—	2	1	no	—
143	C₂×C₈×C₁₃₉	—	2	1	no	—
144	C₂×C₈×C₁₃₉	—	2	1	no	—
145	C₂×C₈×C₁₃₉	—	2	2	no	—
146	C₂×C₈×C₁₃₉	—	2	2	no	—
147	C₂×C₈×C₁₃₉	—	2	2	no	—
148	C₂×C₈×C₁₃₉	—	2	1	no	—
149	C₂×C₈×C₁₃₉	—	2	1	no	—
150	C₂×C₈×C₁₃₉	#41	1	2	yes	—
151	C₄⋊C₄×C₁₃₉	—	2	8	no	—
152	C₄⋊C₄×C₁₃₉	—	2	4	no	—
153	C₄⋊C₄×C₁₃₉	—	2	4	no	—
154	C₄⋊C₄×C₁₃₉	—	2	2	no	—
155	C₄⋊C₄×C₁₃₉	—	2	4	no	—
156	C₄⋊C₄×C₁₃₉	—	2	1	no	—
157	C₄⋊C₄×C₁₃₉	—	2	1	no	—
158	C₄⋊C₄×C₁₃₉	—	2	1	no	—
159	C₄⋊C₄×C₁₃₉	—	2	2	no	—
160	C₄⋊C₄×C₁₃₉	—	2	2	no	—
161	C₄⋊C₄×C₁₃₉	—	8	2	no	—
162	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
163	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
167	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
169	C₄²×C₁₃₉	—	2	8	no	—
170	C₄²×C₁₃₉	—	2	2	no	—
171	C₄²×C₁₃₉	—	2	2	no	—
172	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
174	C₂³×C₁₃₉	—	2	2	no	—
175	C₂³×C₁₃₉	—	2	2	no	—
176	C₂³×C₁₃₉	—	4	1	no	—
177	C₂³×C₁₃₉	—	4	1	no	—
178	C₂³×C₁₃₉	—	4	1	no	—
179	C₂³×C₁₃₉	—	4	1	no	—
180	C₂³×C₁₃₉	—	4	2	no	—
181	C₂³×C₁₃₉	—	4	2	no	—
182	C₂³×C₁₃₉	—	4	2	no	—
183	C₂³×C₁₃₉	—	4	2	no	—
184	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃₉	—	2	4	no	—
186	Q₈×C₁₃₉	—	2	4	no	—
187	Q₈×C₁₃₉	—	4	4	no	—
188	Q₈×C₁₃₉	—	4	2	no	—
189	Q₈×C₁₃₉	—	4	2	no	—
190	D₄×C₁₃₉	—	2	2	no	—
191	D₄×C₁₃₉	—	2	2	no	—
192	D₄×C₁₃₉	—	2	2	no	—
193	D₄×C₁₃₉	—	2	2	no	—
194	D₄×C₁₃₉	—	4	1	no	—
195	D₄×C₁₃₉	—	4	1	no	—
196	D₄×C₁₃₉	—	4	1	no	—
197	D₄×C₁₃₉	—	4	1	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	2	2	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	2	no	—
204	C₂×C₄×C₁₃₉	—	2	2	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	4	8	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	1	no	—
213	C₂×C₄×C₁₃₉	—	4	2	no	—
214	C₂×C₄×C₁₃₉	—	4	2	no	—
215	C₂×C₄×C₁₃₉	—	4	2	no	—
216	C₂×C₄×C₁₃₉	—	4	2	no	—
217	C₂×C₄×C₁₃₉	—	8	4	no	—
218	C₂×C₄×C₁₃₉	#120	1	2	yes	—
219	C₂×C₄×C₁₃₉	#120	1	2	yes	—
220	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
226	C₈×C₁₃₉	—	2	2	no	—
227	C₈×C₁₃₉	—	4	1	no	—
228	C₈×C₁₃₉	—	4	2	no	—
229	C₂²×C₁₃₉	—	4	4	no	—
230	C₂²×C₁₃₉	—	4	2	no	—
231	C₂²×C₁₃₉	—	4	2	no	—
232	C₂²×C₁₃₉	—	4	2	no	—
233	C₂²×C₁₃₉	—	4	2	no	—
234	C₂²×C₁₃₉	—	8	2	no	—
235	C₂²×C₁₃₉	—	8	2	no	—
236	C₂²×C₁₃₉	—	8	2	no	—
237	C₂²×C₁₃₉	—	8	1	no	—
238	C₂²×C₁₃₉	—	8	1	no	—
239	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
240	C₂²×C₁₃₉	#548	1	1	yes	characteristic
241	C₂²×C₁₃₉	#550	1	1	yes	characteristic
242	C₂²×C₁₃₉	#575	1	2	yes	—
243	C₂²×C₁₃₉	#577	1	2	yes	—
244	C₄×C₁₃₉	—	2	2	no	—
245	C₄×C₁₃₉	—	2	2	no	—
246	C₄×C₁₃₉	—	4	4	no	—
247	C₄×C₁₃₉	—	4	2	no	—
248	C₄×C₁₃₉	—	4	2	no	—
249	C₄×C₁₃₉	—	4	2	no	—
250	C₄×C₁₃₉	—	8	2	no	—
251	C₄×C₁₃₉	—	8	1	no	—
252	C₄×C₁₃₉	#525	1	1	yes	characteristic
253	C₄×C₁₃₉	#537	1	1	yes	characteristic
254	C₄×C₁₃₉	#546	1	1	yes	characteristic
255	C₄×C₁₃₉	#547	1	1	yes	characteristic
256	C₂×C₁₃₉	—	8	2	no	—
257	C₂×C₁₃₉	—	8	2	no	—
258	C₂×C₁₃₉	#2407	1	1	yes	characteristic
259	C₂×C₁₃₉	#3005	1	1	yes	characteristic
260	C₂×C₁₃₉	#3010	1	1	yes	characteristic
261	C₂×C₁₃₉	#3376	1	2	yes	—
262	C₂×C₁₃₉	#3401	1	2	yes	—
263	#24197	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₁₃₉	#24197	1	1	yes	characteristic, direct product factor, Sylow
265	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
266	C₂×#461	C₂×C₁₃₉	1	1	yes	characteristic, complemented
267	C₂×#442	C₂×C₁₃₉	1	1	yes	characteristic
268	#2580	C₂×C₁₃₉	1	1	yes	characteristic, complemented
269	#2042	C₂×C₁₃₉	1	2	yes	complemented
270	#2012	C₂×C₁₃₉	1	2	yes	—
271	#1985	C₂×C₁₃₉	1	1	yes	characteristic, complemented
272	#1960	C₂×C₁₃₉	1	1	yes	characteristic, complemented
273	#1880	C₂×C₁₃₉	1	2	yes	complemented
274	#1865	C₂×C₁₃₉	1	2	yes	complemented
275	#1804	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	C₂²×SD₁₆	C₂²×C₁₃₉	1	2	yes	—
277	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
278	#556	—	2	4	no	—
279	#556	—	2	4	no	—
280	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
281	C₂×#126	—	2	2	no	—
282	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
283	C₂×C₂²⋊Q₈	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
288	C₂×#117	—	2	1	no	—
289	#461	—	2	4	no	—
290	#442	—	2	4	no	—
291	C₂×#106	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
293	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
294	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
295	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
296	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
297	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
299	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
300	#399	—	2	1	no	—
301	#393	—	2	1	no	—
302	#390	C₂²×C₁₃₉	1	2	yes	—
303	#389	C₂²×C₁₃₉	1	2	yes	—
304	#385	—	2	2	no	—
305	#382	C₂²×C₁₃₉	1	1	yes	characteristic
306	#340	C₂²×C₁₃₉	1	2	yes	—
307	#336	C₂²×C₁₃₉	1	2	yes	—
308	#336	C₂²×C₁₃₉	1	2	yes	—
309	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
311	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂×SD₁₆	—	2	4	no	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	—	4	2	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
322	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	D₄×C₁₃₉	1	4	yes	—
326	#126	—	2	16	no	—
327	#124	—	2	4	no	—
328	#124	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₄×Q₈	—	2	4	no	—
331	C₄×Q₈	—	2	4	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	D₄×C₁₃₉	1	4	yes	—
338	#117	—	2	8	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
357	#106	—	2	2	no	—
358	C₄⋊C₈	—	2	2	no	—
359	#103	—	2	4	no	—
360	#103	—	2	4	no	—
361	#103	—	4	2	no	—
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	4	2	no	—
365	#97	—	2	2	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	2	no	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
390	C₂×D₄	#41×C₁₃₉	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	8	2	no	—
399	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
404	SD₁₆	—	4	8	no	—
405	D₈	—	2	8	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	#41×C₁₃₉	1	2	yes	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	8	2	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	8	2	no	—
433	C₄²	—	2	8	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
437	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
449	Q₈	—	2	4	no	—
450	Q₈	—	2	4	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	4	1	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	8	4	no	—
482	C₂×C₄	#120×C₁₃₉	1	2	yes	—
483	C₂×C₄	#120×C₁₃₉	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	4	1	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
504	C₂²	#548×C₁₃₉	1	1	yes	characteristic
505	C₂²	#550×C₁₃₉	1	1	yes	characteristic
506	C₂²	#575×C₁₃₉	1	2	yes	—
507	C₂²	#577×C₁₃₉	1	2	yes	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	2	no	—
515	C₄	—	8	1	no	—
516	C₄	#525×C₁₃₉	1	1	yes	characteristic
517	C₄	#537×C₁₃₉	1	1	yes	characteristic
518	C₄	#546×C₁₃₉	1	1	yes	characteristic
519	C₄	#547×C₁₃₉	1	1	yes	characteristic
520	C₂	—	8	2	no	—
521	C₂	—	8	2	no	—
522	C₂	#2407×C₁₃₉	1	1	yes	characteristic
523	C₂	#3005×C₁₃₉	1	1	yes	characteristic
524	C₂	#3010×C₁₃₉	1	1	yes	characteristic
525	C₂	#3376×C₁₃₉	1	2	yes	—
526	C₂	#3401×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×D₈×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×C₄×Q₈×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#556×C₁₃₉	C₂	semidirect
2. C₂×#461×C₁₃₉	C₂	semidirect
4. #2580×C₁₃₉	C₂	semidirect
5. #2042×C₁₃₉	C₂	semidirect
7. #1985×C₁₃₉	C₂	semidirect
8. #1960×C₁₃₉	C₂	semidirect
9. #1880×C₁₃₉	C₂	semidirect
10. #1865×C₁₃₉	C₂	semidirect
11. #1804×C₁₃₉	C₂	semidirect
263. #24197	C₁₃₉	direct (N × H)
264. C₁₃₉	#24197	direct (N × H)
265. C₂×#556	C₂×C₁₃₉	semidirect
266. C₂×#461	C₂×C₁₃₉	semidirect
268. #2580	C₂×C₁₃₉	semidirect
269. #2042	C₂×C₁₃₉	semidirect
271. #1985	C₂×C₁₃₉	semidirect
272. #1960	C₂×C₁₃₉	semidirect
273. #1880	C₂×C₁₃₉	semidirect
274. #1865	C₂×C₁₃₉	semidirect
275. #1804	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₉	2
C₂×#461×C₁₃₉	2
C₂×#442×C₁₃₉	2
#2580×C₁₃₉	2
#2042×C₁₃₉	2
#2012×C₁₃₉	2
#1985×C₁₃₉	2
#1960×C₁₃₉	2
#1880×C₁₃₉	2
#1865×C₁₃₉	2
#1804×C₁₃₉	2
#24197	139

Subgroups — C139×#24197 #48018793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#24197 #48018793