Subgroups — C₁₃₉×#35004 #48029600

Order 35584.

2322 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2659×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2656×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2618×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2556×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2554×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2519×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2461×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2325×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#539×C₁₃₉	—	2	16	no	—
15	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#399×C₁₃₉	C₂²	1	4	yes	—
33	#398×C₁₃₉	C₂²	1	4	yes	—
34	#398×C₁₃₉	C₂²	1	4	yes	—
35	#396×C₁₃₉	C₂²	1	4	yes	—
36	#396×C₁₃₉	C₂²	1	4	yes	—
37	#395×C₁₃₉	C₂²	1	4	yes	—
38	#394×C₁₃₉	C₂²	1	4	yes	—
39	#392×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	2	yes	—
47	#389×C₁₃₉	C₂²	1	2	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	4	yes	—
57	#386×C₁₃₉	C₂²	1	4	yes	—
58	#385×C₁₃₉	C₂²	1	4	yes	—
59	#382×C₁₃₉	C₂²	1	2	yes	—
60	#380×C₁₃₉	C₂²	1	2	yes	—
61	#380×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
64	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
66	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
81	#126×C₁₃₉	—	2	16	no	—
82	#125×C₁₃₉	—	2	16	no	—
83	#124×C₁₃₉	—	4	4	no	—
84	#123×C₁₃₉	—	2	16	no	—
85	#123×C₁₃₉	—	2	16	no	—
86	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
87	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
88	#121×C₁₃₉	—	2	8	no	—
89	#121×C₁₃₉	—	2	8	no	—
90	#121×C₁₃₉	—	2	8	no	—
91	C₄×D₄×C₁₃₉	—	2	16	no	—
92	C₄×D₄×C₁₃₉	—	4	4	no	—
93	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
94	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃₉	—	2	4	no	—
121	C₂×C₄²×C₁₃₉	—	4	2	no	—
122	C₂×C₄²×C₁₃₉	—	4	2	no	—
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	4	yes	—
136	#95×C₁₃₉	C₂³	1	4	yes	—
137	#95×C₁₃₉	C₂³	1	4	yes	—
138	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
139	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
140	C₂×Q₈×C₁₃₉	—	2	4	no	—
141	C₂×Q₈×C₁₃₉	—	4	2	no	—
142	C₂×Q₈×C₁₃₉	—	4	2	no	—
143	C₂×D₄×C₁₃₉	—	2	8	no	—
144	C₂×D₄×C₁₃₉	—	2	8	no	—
145	C₂×D₄×C₁₃₉	—	2	8	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	2	4	no	—
148	C₂×D₄×C₁₃₉	—	2	4	no	—
149	C₂×D₄×C₁₃₉	—	4	2	no	—
150	C₂×D₄×C₁₃₉	—	4	2	no	—
151	C₂×D₄×C₁₃₉	—	4	2	no	—
152	C₂×D₄×C₁₃₉	—	4	2	no	—
153	C₂×D₄×C₁₃₉	—	4	2	no	—
154	C₂×D₄×C₁₃₉	—	4	2	no	—
155	C₂²×C₄×C₁₃₉	—	2	2	no	—
156	C₂²×C₄×C₁₃₉	—	2	2	no	—
157	C₂²×C₄×C₁₃₉	—	2	2	no	—
158	C₂²×C₄×C₁₃₉	—	2	2	no	—
159	C₂²×C₄×C₁₃₉	—	2	2	no	—
160	C₂²×C₄×C₁₃₉	—	2	2	no	—
161	C₂²×C₄×C₁₃₉	—	2	8	no	—
162	C₂²×C₄×C₁₃₉	—	4	1	no	—
163	C₂²×C₄×C₁₃₉	—	4	1	no	—
164	C₂²×C₄×C₁₃₉	—	4	1	no	—
165	C₂²×C₄×C₁₃₉	—	4	1	no	—
166	C₂²×C₄×C₁₃₉	—	4	1	no	—
167	C₂²×C₄×C₁₃₉	—	4	1	no	—
168	C₂²×C₄×C₁₃₉	—	4	1	no	—
169	C₂²×C₄×C₁₃₉	—	4	1	no	—
170	C₂²×C₄×C₁₃₉	—	4	1	no	—
171	C₂²×C₄×C₁₃₉	—	4	1	no	—
172	C₂²×C₄×C₁₃₉	—	4	4	no	—
173	C₂²×C₄×C₁₃₉	—	4	4	no	—
174	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
178	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₄⋊C₄×C₁₃₉	—	2	8	no	—
191	C₄⋊C₄×C₁₃₉	—	2	4	no	—
192	C₄⋊C₄×C₁₃₉	—	2	8	no	—
193	C₄⋊C₄×C₁₃₉	—	2	8	no	—
194	C₄⋊C₄×C₁₃₉	—	2	4	no	—
195	C₄⋊C₄×C₁₃₉	—	2	8	no	—
196	C₄⋊C₄×C₁₃₉	—	2	8	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	—	2	4	no	—
199	C₄⋊C₄×C₁₃₉	—	4	2	no	—
200	C₄⋊C₄×C₁₃₉	—	4	2	no	—
201	C₄⋊C₄×C₁₃₉	—	4	2	no	—
202	C₄⋊C₄×C₁₃₉	—	4	2	no	—
203	C₄⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
204	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
205	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
206	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
207	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
208	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
209	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
210	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
213	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
214	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
215	C₄²×C₁₃₉	—	2	8	no	—
216	C₄²×C₁₃₉	—	2	4	no	—
217	C₄²×C₁₃₉	—	2	4	no	—
218	C₄²×C₁₃₉	—	2	4	no	—
219	C₄²×C₁₃₉	—	2	4	no	—
220	C₄²×C₁₃₉	—	4	2	no	—
221	C₄²×C₁₃₉	—	4	2	no	—
222	C₂³×C₁₃₉	—	2	1	no	—
223	C₂³×C₁₃₉	—	2	1	no	—
224	C₂³×C₁₃₉	—	2	1	no	—
225	C₂³×C₁₃₉	—	2	1	no	—
226	C₂³×C₁₃₉	—	2	4	no	—
227	C₂³×C₁₃₉	—	2	4	no	—
228	C₂³×C₁₃₉	—	2	4	no	—
229	C₂³×C₁₃₉	—	2	4	no	—
230	C₂³×C₁₃₉	—	2	4	no	—
231	C₂³×C₁₃₉	—	2	4	no	—
232	C₂³×C₁₃₉	—	2	4	no	—
233	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
234	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
235	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
236	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
237	Q₈×C₁₃₉	—	8	4	no	—
238	D₄×C₁₃₉	—	4	8	no	—
239	D₄×C₁₃₉	—	4	16	no	—
240	D₄×C₁₃₉	—	8	4	no	—
241	D₄×C₁₃₉	—	8	4	no	—
242	C₂×C₄×C₁₃₉	—	2	8	no	—
243	C₂×C₄×C₁₃₉	—	2	8	no	—
244	C₂×C₄×C₁₃₉	—	2	2	no	—
245	C₂×C₄×C₁₃₉	—	2	1	no	—
246	C₂×C₄×C₁₃₉	—	2	1	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	1	no	—
252	C₂×C₄×C₁₃₉	—	2	1	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	4	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	4	no	—
262	C₂×C₄×C₁₃₉	—	2	4	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	4	no	—
266	C₂×C₄×C₁₃₉	—	2	4	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	4	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	4	4	no	—
271	C₂×C₄×C₁₃₉	—	4	4	no	—
272	C₂×C₄×C₁₃₉	—	4	4	no	—
273	C₂×C₄×C₁₃₉	—	4	4	no	—
274	C₂×C₄×C₁₃₉	—	4	4	no	—
275	C₂×C₄×C₁₃₉	—	8	8	no	—
276	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
277	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
280	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
281	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
282	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
283	C₂²×C₁₃₉	—	2	2	no	—
284	C₂²×C₁₃₉	—	2	2	no	—
285	C₂²×C₁₃₉	—	2	2	no	—
286	C₂²×C₁₃₉	—	2	2	no	—
287	C₂²×C₁₃₉	—	2	2	no	—
288	C₂²×C₁₃₉	—	2	2	no	—
289	C₂²×C₁₃₉	—	4	4	no	—
290	C₂²×C₁₃₉	—	4	4	no	—
291	C₂²×C₁₃₉	—	4	4	no	—
292	C₂²×C₁₃₉	—	4	4	no	—
293	C₂²×C₁₃₉	—	4	4	no	—
294	C₂²×C₁₃₉	—	4	4	no	—
295	C₂²×C₁₃₉	—	4	4	no	—
296	C₂²×C₁₃₉	#532	1	4	yes	—
297	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
298	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
299	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₂²×C₁₃₉	#585	1	1	yes	characteristic
303	C₂²×C₁₃₉	#585	1	1	yes	characteristic
304	C₄×C₁₃₉	—	2	4	no	—
305	C₄×C₁₃₉	—	2	4	no	—
306	C₄×C₁₃₉	—	2	4	no	—
307	C₄×C₁₃₉	—	2	2	no	—
308	C₄×C₁₃₉	—	2	2	no	—
309	C₄×C₁₃₉	—	2	4	no	—
310	C₄×C₁₃₉	—	2	4	no	—
311	C₄×C₁₃₉	—	4	4	no	—
312	C₄×C₁₃₉	—	4	2	no	—
313	C₄×C₁₃₉	—	4	4	no	—
314	C₄×C₁₃₉	—	4	4	no	—
315	C₂×C₁₃₉	—	2	4	no	—
316	C₂×C₁₃₉	—	8	4	no	—
317	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
318	C₂×C₁₃₉	#3459	1	1	yes	characteristic
319	C₂×C₁₃₉	#3461	1	1	yes	characteristic
320	C₂×C₁₃₉	#3491	1	1	yes	characteristic
321	C₂×C₁₃₉	#3492	1	1	yes	characteristic
322	C₂×C₁₃₉	#3496	1	1	yes	characteristic
323	C₂×C₁₃₉	#3497	1	1	yes	characteristic
324	#35004	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₁₃₉	#35004	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×#539	C₂×C₁₃₉	1	2	yes	complemented
327	#2854	C₂×C₁₃₉	1	2	yes	complemented
328	#2850	C₂×C₁₃₉	1	2	yes	complemented
329	#2659	C₂×C₁₃₉	1	1	yes	characteristic, complemented
330	#2656	C₂×C₁₃₉	1	1	yes	characteristic
331	#2618	C₂×C₁₃₉	1	2	yes	complemented
332	#2556	C₂×C₁₃₉	1	4	yes	complemented
333	#2554	C₂×C₁₃₉	1	4	yes	complemented
334	#2519	C₂×C₁₃₉	1	4	yes	complemented
335	#2461	C₂×C₁₃₉	1	4	yes	complemented
336	#2325	C₂×C₁₃₉	1	2	yes	complemented
337	C₄×#121	C₂×C₁₃₉	1	2	yes	complemented
338	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
339	#539	—	2	16	no	—
340	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
341	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
342	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
343	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
344	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
345	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
346	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
347	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
348	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
349	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
350	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
351	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
352	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
353	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
354	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
355	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
356	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
357	#399	C₂²×C₁₃₉	1	4	yes	—
358	#398	C₂²×C₁₃₉	1	4	yes	—
359	#398	C₂²×C₁₃₉	1	4	yes	—
360	#396	C₂²×C₁₃₉	1	4	yes	—
361	#396	C₂²×C₁₃₉	1	4	yes	—
362	#395	C₂²×C₁₃₉	1	4	yes	—
363	#394	C₂²×C₁₃₉	1	4	yes	—
364	#392	C₂²×C₁₃₉	1	4	yes	—
365	#391	C₂²×C₁₃₉	1	2	yes	—
366	#390	C₂²×C₁₃₉	1	2	yes	—
367	#390	C₂²×C₁₃₉	1	2	yes	—
368	#390	C₂²×C₁₃₉	1	2	yes	—
369	#390	C₂²×C₁₃₉	1	2	yes	—
370	#389	C₂²×C₁₃₉	1	2	yes	—
371	#389	C₂²×C₁₃₉	1	2	yes	—
372	#389	C₂²×C₁₃₉	1	2	yes	—
373	#388	C₂²×C₁₃₉	1	4	yes	—
374	#388	C₂²×C₁₃₉	1	4	yes	—
375	#388	C₂²×C₁₃₉	1	4	yes	—
376	#388	C₂²×C₁₃₉	1	4	yes	—
377	#388	C₂²×C₁₃₉	1	4	yes	—
378	#388	C₂²×C₁₃₉	1	4	yes	—
379	#387	C₂²×C₁₃₉	1	4	yes	—
380	#386	C₂²×C₁₃₉	1	4	yes	—
381	#386	C₂²×C₁₃₉	1	4	yes	—
382	#386	C₂²×C₁₃₉	1	4	yes	—
383	#385	C₂²×C₁₃₉	1	4	yes	—
384	#382	C₂²×C₁₃₉	1	2	yes	—
385	#380	C₂²×C₁₃₉	1	2	yes	—
386	#380	C₂²×C₁₃₉	1	2	yes	—
387	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
388	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
389	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
390	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
391	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
393	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
394	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
397	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
402	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
406	#126	—	2	16	no	—
407	#125	—	2	16	no	—
408	#124	—	4	4	no	—
409	#123	—	2	16	no	—
410	#123	—	2	16	no	—
411	C₂²⋊Q₈	—	2	8	no	—
412	C₂²⋊Q₈	—	2	16	no	—
413	#121	—	2	8	no	—
414	#121	—	2	8	no	—
415	#121	—	2	8	no	—
416	C₄×D₄	—	2	16	no	—
417	C₄×D₄	—	4	4	no	—
418	C₂×C₄⋊C₄	—	2	4	no	—
419	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
420	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
445	C₂×C₄²	—	2	4	no	—
446	C₂×C₄²	—	4	2	no	—
447	C₂×C₄²	—	4	2	no	—
448	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
449	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
451	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
454	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
455	#95	C₂³×C₁₃₉	1	4	yes	—
456	#95	C₂³×C₁₃₉	1	4	yes	—
457	#95	C₂³×C₁₃₉	1	4	yes	—
458	#95	C₂³×C₁₃₉	1	4	yes	—
459	#95	C₂³×C₁₃₉	1	4	yes	—
460	#95	C₂³×C₁₃₉	1	4	yes	—
461	#95	C₂³×C₁₃₉	1	4	yes	—
462	#95	C₂³×C₁₃₉	1	4	yes	—
463	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
464	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	4	2	no	—
467	C₂×Q₈	—	4	2	no	—
468	C₂×D₄	—	2	8	no	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	4	4	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
501	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
502	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
503	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
508	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
515	C₄⋊C₄	—	2	8	no	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	8	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	8	no	—
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
529	C₂²⋊C₄	—	2	8	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	8	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	8	no	—
538	C₂²⋊C₄	—	4	4	no	—
539	C₂²⋊C₄	—	4	4	no	—
540	C₄²	—	2	8	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	2	4	no	—
543	C₄²	—	2	4	no	—
544	C₄²	—	2	4	no	—
545	C₄²	—	4	2	no	—
546	C₄²	—	4	2	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
559	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
560	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
561	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
562	Q₈	—	8	4	no	—
563	D₄	—	4	8	no	—
564	D₄	—	4	16	no	—
565	D₄	—	8	4	no	—
566	D₄	—	8	4	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	8	8	no	—
601	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
602	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
603	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
604	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
605	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
606	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
607	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	4	no	—
621	C₂²	#532×C₁₃₉	1	4	yes	—
622	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
623	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
624	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
625	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
626	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
627	C₂²	#585×C₁₃₉	1	1	yes	characteristic
628	C₂²	#585×C₁₃₉	1	1	yes	characteristic
629	C₄	—	2	4	no	—
630	C₄	—	2	4	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	4	no	—
635	C₄	—	2	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	4	no	—
639	C₄	—	4	4	no	—
640	C₂	—	2	4	no	—
641	C₂	—	8	4	no	—
642	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
643	C₂	#3459×C₁₃₉	1	1	yes	characteristic
644	C₂	#3461×C₁₃₉	1	1	yes	characteristic
645	C₂	#3491×C₁₃₉	1	1	yes	characteristic
646	C₂	#3492×C₁₃₉	1	1	yes	characteristic
647	C₂	#3496×C₁₃₉	1	1	yes	characteristic
648	C₂	#3497×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2656×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×#539×C₁₃₉	C₂	semidirect
2. #2854×C₁₃₉	C₂	semidirect
3. #2850×C₁₃₉	C₂	semidirect
4. #2659×C₁₃₉	C₂	semidirect
6. #2618×C₁₃₉	C₂	semidirect
7. #2556×C₁₃₉	C₂	semidirect
8. #2554×C₁₃₉	C₂	semidirect
9. #2519×C₁₃₉	C₂	semidirect
10. #2461×C₁₃₉	C₂	semidirect
11. #2325×C₁₃₉	C₂	semidirect
12. C₄×#121×C₁₃₉	C₂	semidirect
13. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
94. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
324. #35004	C₁₃₉	direct (N × H)
325. C₁₃₉	#35004	direct (N × H)
326. C₂×#539	C₂×C₁₃₉	semidirect
327. #2854	C₂×C₁₃₉	semidirect
328. #2850	C₂×C₁₃₉	semidirect
329. #2659	C₂×C₁₃₉	semidirect
331. #2618	C₂×C₁₃₉	semidirect
332. #2556	C₂×C₁₃₉	semidirect
333. #2554	C₂×C₁₃₉	semidirect
334. #2519	C₂×C₁₃₉	semidirect
335. #2461	C₂×C₁₃₉	semidirect
336. #2325	C₂×C₁₃₉	semidirect
337. C₄×#121	C₂×C₁₃₉	semidirect
338. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
419. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₁₃₉	2
#2854×C₁₃₉	2
#2850×C₁₃₉	2
#2659×C₁₃₉	2
#2656×C₁₃₉	2
#2618×C₁₃₉	2
#2556×C₁₃₉	2
#2554×C₁₃₉	2
#2519×C₁₃₉	2
#2461×C₁₃₉	2
#2325×C₁₃₉	2
C₄×#121×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#35004	139

Subgroups — C139×#35004 #48029600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35004 #48029600