Subgroups — C₁₃₉×#36164 #48030760

Order 35584.

2458 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2568×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2504×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2503×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2489×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2488×C₁₃₉	C₂	1	8	yes	maximal, complemented
11	#2339×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#382×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	#554×C₁₃₉	—	2	8	no	—
17	#547×C₁₃₉	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	4	yes	—
36	#400×C₁₃₉	C₂²	1	8	yes	—
37	#397×C₁₃₉	C₂²	1	8	yes	—
38	#393×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	1	yes	characteristic
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	4	yes	—
43	#391×C₁₃₉	C₂²	1	4	yes	—
44	#390×C₁₃₉	C₂²	1	1	yes	characteristic
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	8	yes	—
48	#386×C₁₃₉	C₂²	1	8	yes	—
49	#386×C₁₃₉	C₂²	1	8	yes	—
50	#382×C₁₃₉	C₂²	1	1	yes	characteristic
51	#382×C₁₃₉	C₂²	1	2	yes	—
52	#382×C₁₃₉	C₂²	1	2	yes	—
53	#382×C₁₃₉	C₂²	1	2	yes	—
54	#382×C₁₃₉	C₂²	1	8	yes	—
55	#382×C₁₃₉	C₂²	1	2	yes	—
56	#381×C₁₃₉	C₂²	1	8	yes	—
57	#380×C₁₃₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
63	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂×#41×C₁₃₉	—	2	8	no	—
66	C₂×#41×C₁₃₉	—	2	16	no	—
67	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
79	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
80	#125×C₁₃₉	—	2	8	no	—
81	#124×C₁₃₉	—	2	4	no	—
82	#123×C₁₃₉	—	2	16	no	—
83	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
84	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
85	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
86	#121×C₁₃₉	—	2	8	no	—
87	C₄×Q₈×C₁₃₉	—	2	4	no	—
88	C₄×D₄×C₁₃₉	—	2	8	no	—
89	C₄×D₄×C₁₃₉	—	2	8	no	—
90	C₄×D₄×C₁₃₉	—	2	4	no	—
91	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
93	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃₉	—	2	8	no	—
115	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	8	yes	—
125	#95×C₁₃₉	C₂³	1	8	yes	—
126	#95×C₁₃₉	C₂³	1	2	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	8	yes	—
129	#95×C₁₃₉	C₂³	1	8	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	8	yes	—
132	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
133	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
134	#41×C₁₃₉	—	4	32	no	—
135	C₂×Q₈×C₁₃₉	—	2	2	no	—
136	C₂×Q₈×C₁₃₉	—	2	4	no	—
137	C₂×Q₈×C₁₃₉	—	2	4	no	—
138	C₂×Q₈×C₁₃₉	—	2	2	no	—
139	C₂×Q₈×C₁₃₉	—	2	8	no	—
140	C₂×Q₈×C₁₃₉	—	2	2	no	—
141	C₂×Q₈×C₁₃₉	—	4	4	no	—
142	C₂×D₄×C₁₃₉	—	2	8	no	—
143	C₂×D₄×C₁₃₉	—	2	16	no	—
144	C₂×D₄×C₁₃₉	—	2	2	no	—
145	C₂×D₄×C₁₃₉	—	2	2	no	—
146	C₂×D₄×C₁₃₉	—	2	2	no	—
147	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
148	C₂×D₄×C₁₃₉	#41	1	8	yes	—
149	C₂²×C₄×C₁₃₉	—	2	4	no	—
150	C₂²×C₄×C₁₃₉	—	2	4	no	—
151	C₂²×C₄×C₁₃₉	—	2	8	no	—
152	C₂²×C₄×C₁₃₉	—	2	8	no	—
153	C₂²×C₄×C₁₃₉	—	2	16	no	—
154	C₂²×C₄×C₁₃₉	—	2	8	no	—
155	C₂²×C₄×C₁₃₉	—	2	4	no	—
156	C₂²×C₄×C₁₃₉	—	2	8	no	—
157	C₂²×C₄×C₁₃₉	—	2	8	no	—
158	C₂²×C₄×C₁₃₉	—	4	4	no	—
159	C₂²×C₄×C₁₃₉	—	4	8	no	—
160	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
173	C₄⋊C₄×C₁₃₉	—	2	2	no	—
174	C₄⋊C₄×C₁₃₉	—	2	2	no	—
175	C₄⋊C₄×C₁₃₉	—	2	4	no	—
176	C₄⋊C₄×C₁₃₉	—	2	8	no	—
177	C₄⋊C₄×C₁₃₉	—	2	8	no	—
178	C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₄⋊C₄×C₁₃₉	—	2	4	no	—
180	C₄⋊C₄×C₁₃₉	—	2	4	no	—
181	C₄⋊C₄×C₁₃₉	—	2	8	no	—
182	C₄⋊C₄×C₁₃₉	—	2	4	no	—
183	C₄⋊C₄×C₁₃₉	—	2	4	no	—
184	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
185	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
187	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
191	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
192	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
193	C₄²×C₁₃₉	—	2	4	no	—
194	C₄²×C₁₃₉	—	2	8	no	—
195	C₄²×C₁₃₉	—	2	4	no	—
196	C₄²×C₁₃₉	—	2	4	no	—
197	C₄²×C₁₃₉	—	2	2	no	—
198	C₄²×C₁₃₉	—	4	2	no	—
199	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
200	C₄²×C₁₃₉	#41	1	4	yes	complemented
201	C₂³×C₁₃₉	—	2	2	no	—
202	C₂³×C₁₃₉	—	2	2	no	—
203	C₂³×C₁₃₉	—	2	4	no	—
204	C₂³×C₁₃₉	—	2	2	no	—
205	C₂³×C₁₃₉	—	2	2	no	—
206	C₂³×C₁₃₉	—	2	4	no	—
207	C₂³×C₁₃₉	—	2	2	no	—
208	C₂³×C₁₃₉	—	2	4	no	—
209	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
211	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃₉	—	4	8	no	—
213	Q₈×C₁₃₉	—	4	4	no	—
214	Q₈×C₁₃₉	—	8	4	no	—
215	D₄×C₁₃₉	—	4	16	no	—
216	D₄×C₁₃₉	—	4	4	no	—
217	D₄×C₁₃₉	#124	1	16	yes	complemented
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	16	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	2	4	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	8	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	4	no	—
240	C₂×C₄×C₁₃₉	—	2	8	no	—
241	C₂×C₄×C₁₃₉	—	4	16	no	—
242	C₂×C₄×C₁₃₉	—	4	16	no	—
243	C₂×C₄×C₁₃₉	—	4	8	no	—
244	C₂×C₄×C₁₃₉	—	8	8	no	—
245	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
251	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
252	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
253	C₂²×C₁₃₉	—	2	4	no	—
254	C₂²×C₁₃₉	—	2	8	no	—
255	C₂²×C₁₃₉	—	2	4	no	—
256	C₂²×C₁₃₉	—	2	8	no	—
257	C₂²×C₁₃₉	—	4	2	no	—
258	C₂²×C₁₃₉	—	4	2	no	—
259	C₂²×C₁₃₉	—	4	4	no	—
260	C₂²×C₁₃₉	—	4	2	no	—
261	C₂²×C₁₃₉	—	4	4	no	—
262	C₂²×C₁₃₉	C₂×#124	1	8	yes	—
263	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
264	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
265	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
266	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	C₂²×C₁₃₉	#585	1	2	yes	—
268	C₄×C₁₃₉	—	2	4	no	—
269	C₄×C₁₃₉	—	2	4	no	—
270	C₄×C₁₃₉	—	2	2	no	—
271	C₄×C₁₃₉	—	4	2	no	—
272	C₄×C₁₃₉	—	4	4	no	—
273	C₄×C₁₃₉	—	4	2	no	—
274	C₄×C₁₃₉	—	4	4	no	—
275	C₄×C₁₃₉	—	4	2	no	—
276	C₄×C₁₃₉	—	4	4	no	—
277	C₄×C₁₃₉	—	4	2	no	—
278	C₄×C₁₃₉	C₂×#124	1	4	yes	—
279	C₄×C₁₃₉	#547	1	4	yes	—
280	C₂×C₁₃₉	—	2	8	no	—
281	C₂×C₁₃₉	—	8	2	no	—
282	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
283	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
284	C₂×C₁₃₉	#3475	1	2	yes	—
285	C₂×C₁₃₉	#3500	1	1	yes	characteristic
286	C₂×C₁₃₉	#3515	1	2	yes	—
287	#36164	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₁₃₉	#36164	1	1	yes	characteristic, direct product factor, Sylow
289	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic
291	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
292	#2850	C₂×C₁₃₉	1	2	yes	complemented
293	#2568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
295	#2504	C₂×C₁₃₉	1	2	yes	complemented
296	#2503	C₂×C₁₃₉	1	2	yes	complemented
297	#2489	C₂×C₁₃₉	1	4	yes	complemented
298	#2488	C₂×C₁₃₉	1	8	yes	complemented
299	#2339	C₂×C₁₃₉	1	4	yes	complemented
300	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
301	C₂×#382	C₂×C₁₃₉	1	2	yes	complemented
302	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
303	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
304	#554	—	2	8	no	—
305	#547	—	2	8	no	—
306	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
307	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
308	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
309	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
310	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
311	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
312	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
313	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
314	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
315	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
319	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
322	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
323	#400	C₂²×C₁₃₉	1	4	yes	—
324	#400	C₂²×C₁₃₉	1	8	yes	—
325	#397	C₂²×C₁₃₉	1	8	yes	—
326	#393	C₂²×C₁₃₉	1	4	yes	—
327	#391	C₂²×C₁₃₉	1	2	yes	—
328	#391	C₂²×C₁₃₉	1	4	yes	—
329	#391	C₂²×C₁₃₉	1	4	yes	—
330	#391	C₂²×C₁₃₉	1	4	yes	—
331	#391	C₂²×C₁₃₉	1	1	yes	characteristic
332	#390	C₂²×C₁₃₉	1	2	yes	—
333	#390	C₂²×C₁₃₉	1	1	yes	characteristic
334	#388	C₂²×C₁₃₉	1	8	yes	—
335	#388	C₂²×C₁₃₉	1	4	yes	—
336	#386	C₂²×C₁₃₉	1	8	yes	—
337	#386	C₂²×C₁₃₉	1	8	yes	—
338	#382	C₂²×C₁₃₉	1	2	yes	—
339	#382	C₂²×C₁₃₉	1	2	yes	—
340	#382	C₂²×C₁₃₉	1	2	yes	—
341	#382	C₂²×C₁₃₉	1	2	yes	—
342	#382	C₂²×C₁₃₉	1	8	yes	—
343	#382	C₂²×C₁₃₉	1	1	yes	characteristic
344	#381	C₂²×C₁₃₉	1	8	yes	—
345	#380	C₂²×C₁₃₉	1	4	yes	—
346	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
351	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
352	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
353	C₂×#41	—	2	8	no	—
354	C₂×#41	—	2	16	no	—
355	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
356	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
357	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
358	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
360	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
366	C₄⋊Q₈	—	2	4	no	—
367	C₄⋊Q₈	—	2	4	no	—
368	#125	—	2	8	no	—
369	#124	—	2	4	no	—
370	#123	—	2	16	no	—
371	C₂²⋊Q₈	—	2	8	no	—
372	C₂²⋊Q₈	—	2	8	no	—
373	C₂²⋊Q₈	—	2	16	no	—
374	#121	—	2	8	no	—
375	C₄×Q₈	—	2	4	no	—
376	C₄×D₄	—	2	8	no	—
377	C₄×D₄	—	2	8	no	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
380	C₂×C₄⋊C₄	—	2	8	no	—
381	C₂×C₄⋊C₄	—	2	8	no	—
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
402	C₂×C₄²	—	2	8	no	—
403	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
411	#95	C₂³×C₁₃₉	1	4	yes	—
412	#95	C₂³×C₁₃₉	1	8	yes	—
413	#95	C₂³×C₁₃₉	1	8	yes	—
414	#95	C₂³×C₁₃₉	1	8	yes	—
415	#95	C₂³×C₁₃₉	1	2	yes	—
416	#95	C₂³×C₁₃₉	1	4	yes	—
417	#95	C₂³×C₁₃₉	1	4	yes	—
418	#95	C₂³×C₁₃₉	1	8	yes	—
419	#95	C₂³×C₁₃₉	1	8	yes	—
420	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
421	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
422	#41	—	4	32	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	8	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	4	4	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	16	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
436	C₂×D₄	#41×C₁₃₉	1	8	yes	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	16	no	—
442	C₂²×C₄	—	2	8	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	8	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	8	no	—
448	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
449	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	8	no	—
480	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
481	C₄²	—	2	4	no	—
482	C₄²	—	2	8	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	4	2	no	—
487	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
488	C₄²	#41×C₁₃₉	1	4	yes	complemented
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
498	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
499	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
500	Q₈	—	4	8	no	—
501	Q₈	—	4	4	no	—
502	Q₈	—	8	4	no	—
503	D₄	—	4	16	no	—
504	D₄	—	4	4	no	—
505	D₄	#124×C₁₃₉	1	16	yes	complemented
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	4	16	no	—
530	C₂×C₄	—	4	16	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	8	8	no	—
533	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
535	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
537	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
538	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
539	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
540	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	8	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	C₂×#124×C₁₃₉	1	8	yes	—
551	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
552	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
553	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
554	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
555	C₂²	#585×C₁₃₉	1	2	yes	—
556	C₄	—	2	4	no	—
557	C₄	—	2	4	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	2	no	—
566	C₄	C₂×#124×C₁₃₉	1	4	yes	—
567	C₄	#547×C₁₃₉	1	4	yes	—
568	C₂	—	2	8	no	—
569	C₂	—	8	2	no	—
570	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
571	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
572	C₂	#3475×C₁₃₉	1	2	yes	—
573	C₂	#3500×C₁₃₉	1	1	yes	characteristic
574	C₂	#3515×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#547×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₁₃₉	C₂	semidirect
3. #2862×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2568×C₁₃₉	C₂	semidirect
6. #2563×C₁₃₉	C₂	semidirect
7. #2504×C₁₃₉	C₂	semidirect
8. #2503×C₁₃₉	C₂	semidirect
9. #2489×C₁₃₉	C₂	semidirect
10. #2488×C₁₃₉	C₂	semidirect
11. #2339×C₁₃₉	C₂	semidirect
12. C₄×#124×C₁₃₉	C₂	semidirect
13. C₂×#382×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
200. C₄²×C₁₃₉	#41	semidirect
217. D₄×C₁₃₉	#124	semidirect
287. #36164	C₁₃₉	direct (N × H)
288. C₁₃₉	#36164	direct (N × H)
289. C₂×#554	C₂×C₁₃₉	semidirect
291. #2862	C₂×C₁₃₉	semidirect
292. #2850	C₂×C₁₃₉	semidirect
293. #2568	C₂×C₁₃₉	semidirect
294. #2563	C₂×C₁₃₉	semidirect
295. #2504	C₂×C₁₃₉	semidirect
296. #2503	C₂×C₁₃₉	semidirect
297. #2489	C₂×C₁₃₉	semidirect
298. #2488	C₂×C₁₃₉	semidirect
299. #2339	C₂×C₁₃₉	semidirect
300. C₄×#124	C₂×C₁₃₉	semidirect
301. C₂×#382	C₂×C₁₃₉	semidirect
302. C₄²×D₄	C₂×C₁₃₉	semidirect
488. C₄²	#41×C₁₃₉	semidirect
505. D₄	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂×#547×C₁₃₉	2
#2862×C₁₃₉	2
#2850×C₁₃₉	2
#2568×C₁₃₉	2
#2563×C₁₃₉	2
#2504×C₁₃₉	2
#2503×C₁₃₉	2
#2489×C₁₃₉	2
#2488×C₁₃₉	2
#2339×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₂×#382×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36164	139

Subgroups — C139×#36164 #48030760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36164 #48030760