Subgroups — C₁₃₉×#36419 #48031015

Order 35584.

2574 conjugacy classes of subgroups.

The subgroup lattice has 600 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×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2858×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	#2559×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2544×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2432×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2367×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2297×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	#556×C₁₃₉	—	2	8	no	—
17	#550×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×#127×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	4	yes	—
38	#394×C₁₃₉	C₂²	1	8	yes	—
39	#394×C₁₃₉	C₂²	1	8	yes	—
40	#394×C₁₃₉	C₂²	1	4	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	1	yes	characteristic
43	#391×C₁₃₉	C₂²	1	2	yes	—
44	#391×C₁₃₉	C₂²	1	1	yes	characteristic
45	#390×C₁₃₉	C₂²	1	4	yes	—
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	4	yes	—
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	4	yes	—
51	#388×C₁₃₉	C₂²	1	8	yes	—
52	#388×C₁₃₉	C₂²	1	8	yes	—
53	#386×C₁₃₉	C₂²	1	8	yes	—
54	#386×C₁₃₉	C₂²	1	8	yes	—
55	#385×C₁₃₉	C₂²	1	8	yes	—
56	#384×C₁₃₉	C₂²	1	1	yes	characteristic
57	#382×C₁₃₉	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×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	8	no	—
67	C₂×#41×C₁₃₉	—	4	4	no	—
68	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
81	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
82	#127×C₁₃₉	—	2	8	no	—
83	#127×C₁₃₉	—	2	4	no	—
84	#126×C₁₃₉	—	2	16	no	—
85	#124×C₁₃₉	—	2	8	no	—
86	#124×C₁₃₉	—	2	16	no	—
87	#124×C₁₃₉	—	4	4	no	—
88	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
89	#121×C₁₃₉	—	2	8	no	—
90	#121×C₁₃₉	—	2	16	no	—
91	C₄×Q₈×C₁₃₉	—	2	8	no	—
92	C₄×Q₈×C₁₃₉	—	2	4	no	—
93	C₄×Q₈×C₁₃₉	—	2	4	no	—
94	C₄×D₄×C₁₃₉	—	2	8	no	—
95	C₄×D₄×C₁₃₉	—	2	8	no	—
96	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
97	#117×C₁₃₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃₉	—	4	4	no	—
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	#95×C₁₃₉	C₂³	1	2	yes	—
130	#95×C₁₃₉	C₂³	1	8	yes	—
131	#95×C₁₃₉	C₂³	1	8	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
136	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
137	#41×C₁₃₉	—	4	32	no	—
138	C₂×Q₈×C₁₃₉	—	2	2	no	—
139	C₂×Q₈×C₁₃₉	—	2	2	no	—
140	C₂×Q₈×C₁₃₉	—	2	4	no	—
141	C₂×Q₈×C₁₃₉	—	2	8	no	—
142	C₂×Q₈×C₁₃₉	—	2	2	no	—
143	C₂×Q₈×C₁₃₉	—	2	2	no	—
144	C₂×Q₈×C₁₃₉	—	2	2	no	—
145	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
146	C₂×D₄×C₁₃₉	—	2	8	no	—
147	C₂×D₄×C₁₃₉	—	2	8	no	—
148	C₂×D₄×C₁₃₉	—	2	4	no	—
149	C₂×D₄×C₁₃₉	—	2	4	no	—
150	C₂×D₄×C₁₃₉	—	2	4	no	—
151	C₂×D₄×C₁₃₉	—	2	4	no	—
152	C₂×D₄×C₁₃₉	—	2	8	no	—
153	C₂×D₄×C₁₃₉	—	2	8	no	—
154	C₂×D₄×C₁₃₉	—	2	4	no	—
155	C₂×D₄×C₁₃₉	—	2	4	no	—
156	C₂×D₄×C₁₃₉	—	4	4	no	—
157	C₂×D₄×C₁₃₉	—	4	4	no	—
158	C₂×D₄×C₁₃₉	—	4	8	no	—
159	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃₉	—	2	4	no	—
161	C₂²×C₄×C₁₃₉	—	2	4	no	—
162	C₂²×C₄×C₁₃₉	—	2	8	no	—
163	C₂²×C₄×C₁₃₉	—	2	8	no	—
164	C₂²×C₄×C₁₃₉	—	2	8	no	—
165	C₂²×C₄×C₁₃₉	—	4	4	no	—
166	C₂²×C₄×C₁₃₉	—	4	4	no	—
167	C₂²×C₄×C₁₃₉	—	4	4	no	—
168	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
169	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₁₃₉	—	2	2	no	—
182	C₄⋊C₄×C₁₃₉	—	2	4	no	—
183	C₄⋊C₄×C₁₃₉	—	2	4	no	—
184	C₄⋊C₄×C₁₃₉	—	2	2	no	—
185	C₄⋊C₄×C₁₃₉	—	2	8	no	—
186	C₄⋊C₄×C₁₃₉	—	2	4	no	—
187	C₄⋊C₄×C₁₃₉	—	2	4	no	—
188	C₄⋊C₄×C₁₃₉	—	2	4	no	—
189	C₄⋊C₄×C₁₃₉	—	2	8	no	—
190	C₄⋊C₄×C₁₃₉	—	4	4	no	—
191	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
192	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
197	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
198	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
199	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
200	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
201	C₄²×C₁₃₉	—	2	8	no	—
202	C₄²×C₁₃₉	—	2	4	no	—
203	C₄²×C₁₃₉	—	2	4	no	—
204	C₄²×C₁₃₉	—	2	2	no	—
205	C₄²×C₁₃₉	—	2	2	no	—
206	C₄²×C₁₃₉	—	2	4	no	—
207	C₄²×C₁₃₉	—	4	4	no	—
208	C₄²×C₁₃₉	—	4	2	no	—
209	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
210	C₄²×C₁₃₉	#41	1	8	yes	complemented
211	C₂³×C₁₃₉	—	2	4	no	—
212	C₂³×C₁₃₉	—	2	2	no	—
213	C₂³×C₁₃₉	—	2	2	no	—
214	C₂³×C₁₃₉	—	2	4	no	—
215	C₂³×C₁₃₉	—	2	4	no	—
216	C₂³×C₁₃₉	—	2	8	no	—
217	C₂³×C₁₃₉	—	2	4	no	—
218	C₂³×C₁₃₉	—	2	4	no	—
219	C₂³×C₁₃₉	—	2	8	no	—
220	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
221	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
222	Q₈×C₁₃₉	—	2	8	no	—
223	Q₈×C₁₃₉	—	4	8	no	—
224	Q₈×C₁₃₉	—	4	4	no	—
225	D₄×C₁₃₉	—	2	8	no	—
226	D₄×C₁₃₉	—	4	16	no	—
227	D₄×C₁₃₉	—	4	8	no	—
228	D₄×C₁₃₉	—	4	8	no	—
229	D₄×C₁₃₉	—	8	4	no	—
230	D₄×C₁₃₉	—	8	8	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	2	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
239	C₂×C₄×C₁₃₉	—	2	2	no	—
240	C₂×C₄×C₁₃₉	—	2	16	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	4	no	—
243	C₂×C₄×C₁₃₉	—	2	2	no	—
244	C₂×C₄×C₁₃₉	—	2	2	no	—
245	C₂×C₄×C₁₃₉	—	2	8	no	—
246	C₂×C₄×C₁₃₉	—	2	4	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	4	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	4	no	—
251	C₂×C₄×C₁₃₉	—	2	4	no	—
252	C₂×C₄×C₁₃₉	—	2	4	no	—
253	C₂×C₄×C₁₃₉	—	4	16	no	—
254	C₂×C₄×C₁₃₉	—	4	16	no	—
255	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
256	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
260	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
261	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
262	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
263	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
265	C₂²×C₁₃₉	—	2	4	no	—
266	C₂²×C₁₃₉	—	2	4	no	—
267	C₂²×C₁₃₉	—	2	4	no	—
268	C₂²×C₁₃₉	—	4	4	no	—
269	C₂²×C₁₃₉	—	4	4	no	—
270	C₂²×C₁₃₉	—	4	4	no	—
271	C₂²×C₁₃₉	—	4	4	no	—
272	C₂²×C₁₃₉	—	4	8	no	—
273	C₂²×C₁₃₉	—	4	4	no	—
274	C₂²×C₁₃₉	—	4	8	no	—
275	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
276	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
277	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
278	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂²×C₁₃₉	#585	1	2	yes	—
280	C₄×C₁₃₉	—	2	4	no	—
281	C₄×C₁₃₉	—	2	4	no	—
282	C₄×C₁₃₉	—	2	4	no	—
283	C₄×C₁₃₉	—	2	2	no	—
284	C₄×C₁₃₉	—	2	4	no	—
285	C₄×C₁₃₉	—	4	4	no	—
286	C₄×C₁₃₉	—	4	2	no	—
287	C₄×C₁₃₉	—	4	2	no	—
288	C₄×C₁₃₉	—	4	2	no	—
289	C₄×C₁₃₉	—	4	4	no	—
290	C₄×C₁₃₉	#532	1	4	yes	—
291	C₄×C₁₃₉	#546	1	4	yes	—
292	C₂×C₁₃₉	—	4	4	no	—
293	C₂×C₁₃₉	—	8	4	no	—
294	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
295	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
296	C₂×C₁₃₉	#3480	1	2	yes	—
297	C₂×C₁₃₉	#3500	1	1	yes	characteristic
298	C₂×C₁₃₉	#3506	1	2	yes	—
299	#36419	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₁₃₉	#36419	1	1	yes	characteristic, direct product factor, Sylow
301	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
302	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic
303	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
304	#2850	C₂×C₁₃₉	1	2	yes	complemented
305	#2568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
306	#2559	C₂×C₁₃₉	1	8	yes	complemented
307	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
308	#2544	C₂×C₁₃₉	1	4	yes	complemented
309	#2500	C₂×C₁₃₉	1	2	yes	complemented
310	#2432	C₂×C₁₃₉	1	2	yes	complemented
311	#2367	C₂×C₁₃₉	1	4	yes	complemented
312	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
313	#2297	C₂×C₁₃₉	1	2	yes	complemented
314	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
315	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
316	#556	—	2	8	no	—
317	#550	—	2	8	no	—
318	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
319	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
320	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
321	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
322	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
323	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
324	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
325	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
327	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
328	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
329	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
332	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
333	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
334	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
335	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
336	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
337	#400	C₂²×C₁₃₉	1	4	yes	—
338	#394	C₂²×C₁₃₉	1	8	yes	—
339	#394	C₂²×C₁₃₉	1	8	yes	—
340	#394	C₂²×C₁₃₉	1	4	yes	—
341	#391	C₂²×C₁₃₉	1	1	yes	characteristic
342	#391	C₂²×C₁₃₉	1	1	yes	characteristic
343	#391	C₂²×C₁₃₉	1	4	yes	—
344	#391	C₂²×C₁₃₉	1	2	yes	—
345	#390	C₂²×C₁₃₉	1	2	yes	—
346	#390	C₂²×C₁₃₉	1	2	yes	—
347	#390	C₂²×C₁₃₉	1	4	yes	—
348	#390	C₂²×C₁₃₉	1	4	yes	—
349	#390	C₂²×C₁₃₉	1	2	yes	—
350	#389	C₂²×C₁₃₉	1	4	yes	—
351	#388	C₂²×C₁₃₉	1	8	yes	—
352	#388	C₂²×C₁₃₉	1	8	yes	—
353	#386	C₂²×C₁₃₉	1	8	yes	—
354	#386	C₂²×C₁₃₉	1	8	yes	—
355	#385	C₂²×C₁₃₉	1	8	yes	—
356	#384	C₂²×C₁₃₉	1	1	yes	characteristic
357	#382	C₂²×C₁₃₉	1	2	yes	—
358	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
359	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
362	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
364	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
365	C₂×#41	—	2	8	no	—
366	C₂×#41	—	2	8	no	—
367	C₂×#41	—	4	4	no	—
368	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
370	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
371	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
372	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
373	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
374	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
376	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
377	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
378	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
379	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
380	C₄⋊Q₈	—	2	4	no	—
381	C₄⋊Q₈	—	2	4	no	—
382	#127	—	2	8	no	—
383	#127	—	2	4	no	—
384	#126	—	2	16	no	—
385	#124	—	2	8	no	—
386	#124	—	2	16	no	—
387	#124	—	4	4	no	—
388	C₂²⋊Q₈	—	2	8	no	—
389	#121	—	2	8	no	—
390	#121	—	2	16	no	—
391	C₄×Q₈	—	2	8	no	—
392	C₄×Q₈	—	2	4	no	—
393	C₄×Q₈	—	2	4	no	—
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	8	no	—
396	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
397	#117	—	2	8	no	—
398	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
418	C₂×C₄²	—	4	4	no	—
419	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
420	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
426	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
429	#95	C₂³×C₁₃₉	1	4	yes	—
430	#95	C₂³×C₁₃₉	1	4	yes	—
431	#95	C₂³×C₁₃₉	1	2	yes	—
432	#95	C₂³×C₁₃₉	1	8	yes	—
433	#95	C₂³×C₁₃₉	1	4	yes	—
434	#95	C₂³×C₁₃₉	1	8	yes	—
435	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
436	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
437	#41	—	4	32	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	8	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	—	4	4	no	—
468	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
469	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	4	4	no	—
491	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	2	8	no	—
496	C₂²⋊C₄	—	2	16	no	—
497	C₂²⋊C₄	—	2	16	no	—
498	C₂²⋊C₄	—	4	8	no	—
499	C₂²⋊C₄	—	4	8	no	—
500	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
501	C₄²	—	2	8	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	4	4	no	—
508	C₄²	—	4	2	no	—
509	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
510	C₄²	#41×C₁₃₉	1	8	yes	complemented
511	C₂³	—	2	4	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	8	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	8	no	—
520	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
521	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
522	Q₈	—	2	8	no	—
523	Q₈	—	4	8	no	—
524	Q₈	—	4	4	no	—
525	D₄	—	2	8	no	—
526	D₄	—	4	16	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	8	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	8	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	16	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	4	16	no	—
554	C₂×C₄	—	4	16	no	—
555	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
556	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
558	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
559	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
560	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
561	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
562	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
563	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
564	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
565	C₂²	—	2	4	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	8	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	8	no	—
575	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
576	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
577	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
578	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
579	C₂²	#585×C₁₃₉	1	2	yes	—
580	C₄	—	2	4	no	—
581	C₄	—	2	4	no	—
582	C₄	—	2	4	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	4	no	—
585	C₄	—	4	4	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	4	no	—
590	C₄	#532×C₁₃₉	1	4	yes	—
591	C₄	#546×C₁₃₉	1	4	yes	—
592	C₂	—	4	4	no	—
593	C₂	—	8	4	no	—
594	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
595	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
596	C₂	#3480×C₁₃₉	1	2	yes	—
597	C₂	#3500×C₁₃₉	1	1	yes	characteristic
598	C₂	#3506×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#550×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×#556×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2568×C₁₃₉	C₂	semidirect
6. #2559×C₁₃₉	C₂	semidirect
7. #2548×C₁₃₉	C₂	semidirect
8. #2544×C₁₃₉	C₂	semidirect
9. #2500×C₁₃₉	C₂	semidirect
10. #2432×C₁₃₉	C₂	semidirect
11. #2367×C₁₃₉	C₂	semidirect
12. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
13. #2297×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
210. C₄²×C₁₃₉	#41	semidirect
299. #36419	C₁₃₉	direct (N × H)
300. C₁₃₉	#36419	direct (N × H)
301. C₂×#556	C₂×C₁₃₉	semidirect
303. #2858	C₂×C₁₃₉	semidirect
304. #2850	C₂×C₁₃₉	semidirect
305. #2568	C₂×C₁₃₉	semidirect
306. #2559	C₂×C₁₃₉	semidirect
307. #2548	C₂×C₁₃₉	semidirect
308. #2544	C₂×C₁₃₉	semidirect
309. #2500	C₂×C₁₃₉	semidirect
310. #2432	C₂×C₁₃₉	semidirect
311. #2367	C₂×C₁₃₉	semidirect
312. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
313. #2297	C₂×C₁₃₉	semidirect
314. C₄²×D₄	C₂×C₁₃₉	semidirect
510. C₄²	#41×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×#550×C₁₃₉	2
#2858×C₁₃₉	2
#2850×C₁₃₉	2
#2568×C₁₃₉	2
#2559×C₁₃₉	2
#2548×C₁₃₉	2
#2544×C₁₃₉	2
#2500×C₁₃₉	2
#2432×C₁₃₉	2
#2367×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2297×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36419	139

Subgroups — C139×#36419 #48031015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36419 #48031015