Subgroups — C₂×#2555×C₁₃₉ #48029418

Order 35584.

4110 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂²×#121×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2555×C₁₃₉	C₂	1	16	yes	maximal, direct product factor
4	C₂×#395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#394×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#392×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂×#390×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#388×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×#386×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#124×C₁₃₉	—	2	16	no	—
18	C₂×#124×C₁₃₉	C₂²	1	16	yes	complemented
19	C₂×#121×C₁₃₉	—	2	16	no	—
20	C₂×#121×C₁₃₉	C₂²	1	16	yes	complemented
21	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#395×C₁₃₉	C₂²	1	8	yes	complemented
33	#394×C₁₃₉	C₂²	1	8	yes	complemented
34	#392×C₁₃₉	C₂²	1	16	yes	complemented
35	#390×C₁₃₉	C₂²	1	8	yes	complemented
36	#388×C₁₃₉	C₂²	1	16	yes	complemented
37	#386×C₁₃₉	C₂²	1	16	yes	complemented
38	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	16	yes	complemented
39	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
40	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
41	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
44	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₃₉	—	2	8	no	—
46	C₂²×Q₈×C₁₃₉	—	4	2	no	—
47	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
48	C₂²×D₄×C₁₃₉	—	2	8	no	—
49	C₂²×D₄×C₁₃₉	—	2	8	no	—
50	C₂²×D₄×C₁₃₉	—	2	8	no	—
51	C₂²×D₄×C₁₃₉	—	2	8	no	—
52	C₂²×D₄×C₁₃₉	—	2	4	no	—
53	C₂²×D₄×C₁₃₉	—	2	8	no	—
54	C₂²×D₄×C₁₃₉	—	4	2	no	—
55	C₂²×D₄×C₁₃₉	—	4	2	no	—
56	C₂²×D₄×C₁₃₉	—	4	4	no	—
57	C₂²×D₄×C₁₃₉	—	4	4	no	—
58	C₂²×D₄×C₁₃₉	—	4	2	no	—
59	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
61	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
62	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃₉	—	2	8	no	—
64	C₂³×C₄×C₁₃₉	—	2	8	no	—
65	C₂³×C₄×C₁₃₉	—	4	4	no	—
66	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
70	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
74	#124×C₁₃₉	—	2	64	no	—
75	#121×C₁₃₉	—	2	64	no	—
76	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
77	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	16	yes	complemented
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
94	C₂×C₄²×C₁₃₉	—	2	8	no	—
95	C₂×C₄²×C₁₃₉	—	4	2	no	—
96	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
97	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
98	#95×C₁₃₉	C₂³	1	8	yes	—
99	#95×C₁₃₉	C₂³	1	4	yes	—
100	#95×C₁₃₉	C₂³	1	8	yes	—
101	#95×C₁₃₉	C₂³	1	4	yes	—
102	C₂⁴×C₁₃₉	—	2	4	no	—
103	C₂⁴×C₁₃₉	—	2	4	no	—
104	C₂⁴×C₁₃₉	—	2	4	no	—
105	C₂⁴×C₁₃₉	—	2	4	no	—
106	C₂⁴×C₁₃₉	—	2	4	no	—
107	C₂⁴×C₁₃₉	—	2	4	no	—
108	C₂⁴×C₁₃₉	—	2	4	no	—
109	C₂⁴×C₁₃₉	—	2	4	no	—
110	C₂⁴×C₁₃₉	—	2	4	no	—
111	C₂⁴×C₁₃₉	—	2	4	no	—
112	C₂⁴×C₁₃₉	—	2	4	no	—
113	C₂⁴×C₁₃₉	—	2	4	no	—
114	C₂⁴×C₁₃₉	—	2	4	no	—
115	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
116	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
117	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₁₃₉	—	2	16	no	—
120	C₂×Q₈×C₁₃₉	—	4	4	no	—
121	C₂×Q₈×C₁₃₉	—	4	16	no	—
122	C₂×D₄×C₁₃₉	—	2	16	no	—
123	C₂×D₄×C₁₃₉	—	2	16	no	—
124	C₂×D₄×C₁₃₉	—	2	16	no	—
125	C₂×D₄×C₁₃₉	—	2	16	no	—
126	C₂×D₄×C₁₃₉	—	2	8	no	—
127	C₂×D₄×C₁₃₉	—	2	16	no	—
128	C₂×D₄×C₁₃₉	—	4	4	no	—
129	C₂×D₄×C₁₃₉	—	4	4	no	—
130	C₂×D₄×C₁₃₉	—	4	8	no	—
131	C₂×D₄×C₁₃₉	—	4	8	no	—
132	C₂×D₄×C₁₃₉	—	4	4	no	—
133	C₂×D₄×C₁₃₉	—	4	32	no	—
134	C₂×D₄×C₁₃₉	—	4	32	no	—
135	C₂×D₄×C₁₃₉	—	4	16	no	—
136	C₂×D₄×C₁₃₉	—	4	16	no	—
137	C₂²×C₄×C₁₃₉	—	2	4	no	—
138	C₂²×C₄×C₁₃₉	—	2	4	no	—
139	C₂²×C₄×C₁₃₉	—	2	4	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	—	2	2	no	—
142	C₂²×C₄×C₁₃₉	—	2	2	no	—
143	C₂²×C₄×C₁₃₉	—	2	4	no	—
144	C₂²×C₄×C₁₃₉	—	2	4	no	—
145	C₂²×C₄×C₁₃₉	—	2	4	no	—
146	C₂²×C₄×C₁₃₉	—	2	4	no	—
147	C₂²×C₄×C₁₃₉	—	2	4	no	—
148	C₂²×C₄×C₁₃₉	—	2	4	no	—
149	C₂²×C₄×C₁₃₉	—	2	4	no	—
150	C₂²×C₄×C₁₃₉	—	2	2	no	—
151	C₂²×C₄×C₁₃₉	—	2	2	no	—
152	C₂²×C₄×C₁₃₉	—	2	16	no	—
153	C₂²×C₄×C₁₃₉	—	2	16	no	—
154	C₂²×C₄×C₁₃₉	—	4	8	no	—
155	C₂²×C₄×C₁₃₉	—	4	32	no	—
156	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
157	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
158	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
159	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₁₃₉	—	2	16	no	—
168	C₄⋊C₄×C₁₃₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
170	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
174	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
175	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	32	yes	complemented
176	C₄²×C₁₃₉	—	2	16	no	—
177	C₄²×C₁₃₉	—	4	4	no	—
178	C₂³×C₁₃₉	—	2	16	no	—
179	C₂³×C₁₃₉	—	2	16	no	—
180	C₂³×C₁₃₉	—	2	16	no	—
181	C₂³×C₁₃₉	—	2	4	no	—
182	C₂³×C₁₃₉	—	2	4	no	—
183	C₂³×C₁₃₉	—	2	4	no	—
184	C₂³×C₁₃₉	—	2	4	no	—
185	C₂³×C₁₃₉	—	2	4	no	—
186	C₂³×C₁₃₉	—	2	4	no	—
187	C₂³×C₁₃₉	—	2	4	no	—
188	C₂³×C₁₃₉	—	2	4	no	—
189	C₂³×C₁₃₉	—	2	4	no	—
190	C₂³×C₁₃₉	—	2	4	no	—
191	C₂³×C₁₃₉	—	2	4	no	—
192	C₂³×C₁₃₉	—	2	4	no	—
193	C₂³×C₁₃₉	—	2	4	no	—
194	C₂³×C₁₃₉	—	4	8	no	—
195	C₂³×C₁₃₉	—	4	8	no	—
196	C₂³×C₁₃₉	—	4	8	no	—
197	C₂³×C₁₃₉	—	4	8	no	—
198	C₂³×C₁₃₉	—	4	8	no	—
199	C₂³×C₁₃₉	—	4	8	no	—
200	C₂³×C₁₃₉	—	4	8	no	—
201	C₂³×C₁₃₉	—	4	8	no	—
202	C₂³×C₁₃₉	—	4	8	no	—
203	C₂³×C₁₃₉	—	4	8	no	—
204	C₂³×C₁₃₉	—	4	8	no	—
205	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
206	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
207	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
208	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
209	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
210	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
211	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃₉	—	4	16	no	—
213	D₄×C₁₃₉	—	4	32	no	—
214	D₄×C₁₃₉	—	4	32	no	—
215	D₄×C₁₃₉	—	4	16	no	—
216	D₄×C₁₃₉	—	4	16	no	—
217	C₂×C₄×C₁₃₉	—	2	8	no	—
218	C₂×C₄×C₁₃₉	—	2	16	no	—
219	C₂×C₄×C₁₃₉	—	2	16	no	—
220	C₂×C₄×C₁₃₉	—	2	16	no	—
221	C₂×C₄×C₁₃₉	—	2	4	no	—
222	C₂×C₄×C₁₃₉	—	2	4	no	—
223	C₂×C₄×C₁₃₉	—	2	4	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	4	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	2	4	no	—
230	C₂×C₄×C₁₃₉	—	2	4	no	—
231	C₂×C₄×C₁₃₉	—	2	4	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	2	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	4	32	no	—
237	C₂×C₄×C₁₃₉	—	4	8	no	—
238	C₂×C₄×C₁₃₉	—	4	4	no	—
239	C₂×C₄×C₁₃₉	—	4	4	no	—
240	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
241	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
242	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
243	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
244	C₂²×C₁₃₉	—	2	8	no	—
245	C₂²×C₁₃₉	—	2	8	no	—
246	C₂²×C₁₃₉	—	2	8	no	—
247	C₂²×C₁₃₉	—	4	4	no	—
248	C₂²×C₁₃₉	—	4	4	no	—
249	C₂²×C₁₃₉	—	4	4	no	—
250	C₂²×C₁₃₉	—	4	4	no	—
251	C₂²×C₁₃₉	—	4	32	no	—
252	C₂²×C₁₃₉	—	4	4	no	—
253	C₂²×C₁₃₉	—	4	4	no	—
254	C₂²×C₁₃₉	—	4	4	no	—
255	C₂²×C₁₃₉	—	4	4	no	—
256	C₂²×C₁₃₉	—	4	4	no	—
257	C₂²×C₁₃₉	—	4	4	no	—
258	C₂²×C₁₃₉	—	4	4	no	—
259	C₂²×C₁₃₉	—	8	16	no	—
260	C₂²×C₁₃₉	#532	1	8	yes	—
261	C₂²×C₁₃₉	#538	1	4	yes	—
262	C₂²×C₁₃₉	D₄²	1	4	yes	—
263	C₂²×C₁₃₉	#546	1	8	yes	—
264	C₂²×C₁₃₉	#555	1	4	yes	—
265	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
266	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
267	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
268	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
269	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
270	C₄×C₁₃₉	—	2	4	no	—
271	C₄×C₁₃₉	—	2	8	no	—
272	C₄×C₁₃₉	—	2	8	no	—
273	C₄×C₁₃₉	—	2	8	no	—
274	C₄×C₁₃₉	—	4	4	no	—
275	C₄×C₁₃₉	—	4	2	no	—
276	C₄×C₁₃₉	—	4	2	no	—
277	C₂×C₁₃₉	—	4	8	no	—
278	C₂×C₁₃₉	—	8	4	no	—
279	C₂×C₁₃₉	#2555	1	8	yes	direct product factor
280	C₂×C₁₃₉	C₂×#532	1	2	yes	—
281	C₂×C₁₃₉	C₂×#538	1	1	yes	characteristic
282	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
283	C₂×C₁₃₉	C₂×#546	1	2	yes	—
284	C₂×C₁₃₉	C₂×#555	1	1	yes	characteristic
285	C₂×#2555	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₁₃₉	C₂×#2555	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×#124	C₂×C₁₃₉	1	2	yes	complemented
288	C₂²×#121	C₂×C₁₃₉	1	2	yes	complemented
289	#2555	C₂×C₁₃₉	1	16	yes	direct product factor
290	C₂×#395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
291	C₂×#394	C₂×C₁₃₉	1	1	yes	characteristic, complemented
292	C₂×#392	C₂×C₁₃₉	1	2	yes	complemented
293	C₂×#390	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	C₂×#388	C₂×C₁₃₉	1	2	yes	complemented
295	C₂×#386	C₂×C₁₃₉	1	2	yes	complemented
296	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
297	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
299	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
300	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
302	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
303	C₂×#124	—	2	16	no	—
304	C₂×#124	C₂²×C₁₃₉	1	16	yes	complemented
305	C₂×#121	—	2	16	no	—
306	C₂×#121	C₂²×C₁₃₉	1	16	yes	complemented
307	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
310	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
316	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
317	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
318	#395	C₂²×C₁₃₉	1	8	yes	complemented
319	#394	C₂²×C₁₃₉	1	8	yes	complemented
320	#392	C₂²×C₁₃₉	1	16	yes	complemented
321	#390	C₂²×C₁₃₉	1	8	yes	complemented
322	#388	C₂²×C₁₃₉	1	16	yes	complemented
323	#386	C₂²×C₁₃₉	1	16	yes	complemented
324	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	16	yes	complemented
325	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
326	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
327	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
328	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
329	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
330	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
331	C₂²×Q₈	—	2	8	no	—
332	C₂²×Q₈	—	4	2	no	—
333	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
334	C₂²×D₄	—	2	8	no	—
335	C₂²×D₄	—	2	8	no	—
336	C₂²×D₄	—	2	8	no	—
337	C₂²×D₄	—	2	8	no	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	—	2	8	no	—
340	C₂²×D₄	—	4	2	no	—
341	C₂²×D₄	—	4	2	no	—
342	C₂²×D₄	—	4	4	no	—
343	C₂²×D₄	—	4	4	no	—
344	C₂²×D₄	—	4	2	no	—
345	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
346	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
347	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
348	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
349	C₂³×C₄	—	2	8	no	—
350	C₂³×C₄	—	2	8	no	—
351	C₂³×C₄	—	4	4	no	—
352	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
356	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
360	#124	—	2	64	no	—
361	#121	—	2	64	no	—
362	C₂×C₄⋊C₄	—	2	8	no	—
363	C₂×C₄⋊C₄	—	4	2	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
366	C₂×C₂²⋊C₄	—	2	8	no	—
367	C₂×C₂²⋊C₄	—	2	8	no	—
368	C₂×C₂²⋊C₄	—	2	8	no	—
369	C₂×C₂²⋊C₄	—	2	8	no	—
370	C₂×C₂²⋊C₄	—	2	8	no	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	16	yes	complemented
373	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
380	C₂×C₄²	—	2	8	no	—
381	C₂×C₄²	—	4	2	no	—
382	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
383	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
384	#95	C₂³×C₁₃₉	1	8	yes	—
385	#95	C₂³×C₁₃₉	1	8	yes	—
386	#95	C₂³×C₁₃₉	1	4	yes	—
387	#95	C₂³×C₁₃₉	1	4	yes	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	4	no	—
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	4	no	—
394	C₂⁴	—	2	4	no	—
395	C₂⁴	—	2	4	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
402	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
403	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
404	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
405	C₂×Q₈	—	2	16	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	16	no	—
408	C₂×D₄	—	2	16	no	—
409	C₂×D₄	—	2	16	no	—
410	C₂×D₄	—	2	16	no	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	32	no	—
420	C₂×D₄	—	4	32	no	—
421	C₂×D₄	—	4	16	no	—
422	C₂×D₄	—	4	16	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	16	no	—
439	C₂²×C₄	—	2	16	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	—	4	32	no	—
442	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
444	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
445	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
446	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
453	C₄⋊C₄	—	2	16	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₂²⋊C₄	—	2	16	no	—
457	C₂²⋊C₄	—	2	16	no	—
458	C₂²⋊C₄	—	2	16	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	32	yes	complemented
462	C₄²	—	2	16	no	—
463	C₄²	—	4	4	no	—
464	C₂³	—	2	16	no	—
465	C₂³	—	2	16	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	4	8	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	8	no	—
491	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
492	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
493	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
494	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
495	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
496	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
497	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
498	Q₈	—	4	16	no	—
499	D₄	—	4	32	no	—
500	D₄	—	4	32	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	16	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	16	no	—
505	C₂×C₄	—	2	16	no	—
506	C₂×C₄	—	2	16	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	32	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
527	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
528	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
529	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
530	C₂²	—	2	8	no	—
531	C₂²	—	2	8	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	4	32	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	8	16	no	—
546	C₂²	#532×C₁₃₉	1	8	yes	—
547	C₂²	#538×C₁₃₉	1	4	yes	—
548	C₂²	D₄²×C₁₃₉	1	4	yes	—
549	C₂²	#546×C₁₃₉	1	8	yes	—
550	C₂²	#555×C₁₃₉	1	4	yes	—
551	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
552	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
553	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
554	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
555	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
556	C₄	—	2	4	no	—
557	C₄	—	2	8	no	—
558	C₄	—	2	8	no	—
559	C₄	—	2	8	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₂	—	4	8	no	—
564	C₂	—	8	4	no	—
565	C₂	#2555×C₁₃₉	1	8	yes	direct product factor
566	C₂	C₂×#532×C₁₃₉	1	2	yes	—
567	C₂	C₂×#538×C₁₃₉	1	1	yes	characteristic
568	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
569	C₂	C₂×#546×C₁₃₉	1	2	yes	—
570	C₂	C₂×#555×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#124×C₁₃₉	C₂	semidirect
2. C₂²×#121×C₁₃₉	C₂	semidirect
3. #2555×C₁₃₉	C₂	direct (N × H)
4. C₂×#395×C₁₃₉	C₂	semidirect
5. C₂×#394×C₁₃₉	C₂	semidirect
6. C₂×#392×C₁₃₉	C₂	semidirect
7. C₂×#390×C₁₃₉	C₂	semidirect
8. C₂×#388×C₁₃₉	C₂	semidirect
9. C₂×#386×C₁₃₉	C₂	semidirect
10. C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
18. C₂×#124×C₁₃₉	C₂²	semidirect
20. C₂×#121×C₁₃₉	C₂²	semidirect
32. #395×C₁₃₉	C₂²	semidirect
33. #394×C₁₃₉	C₂²	semidirect
34. #392×C₁₃₉	C₂²	semidirect
35. #390×C₁₃₉	C₂²	semidirect
36. #388×C₁₃₉	C₂²	semidirect
37. #386×C₁₃₉	C₂²	semidirect
38. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
86. C₂×C₂²⋊C₄×C₁₃₉	D₄	semidirect
175. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
279. C₂×C₁₃₉	#2555	direct (N × H)
285. C₂×#2555	C₁₃₉	direct (N × H)
286. C₁₃₉	C₂×#2555	direct (N × H)
287. C₂²×#124	C₂×C₁₃₉	semidirect
288. C₂²×#121	C₂×C₁₃₉	semidirect
289. #2555	C₂×C₁₃₉	direct (N × H)
290. C₂×#395	C₂×C₁₃₉	semidirect
291. C₂×#394	C₂×C₁₃₉	semidirect
292. C₂×#392	C₂×C₁₃₉	semidirect
293. C₂×#390	C₂×C₁₃₉	semidirect
294. C₂×#388	C₂×C₁₃₉	semidirect
295. C₂×#386	C₂×C₁₃₉	semidirect
296. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
304. C₂×#124	C₂²×C₁₃₉	semidirect
306. C₂×#121	C₂²×C₁₃₉	semidirect
318. #395	C₂²×C₁₃₉	semidirect
319. #394	C₂²×C₁₃₉	semidirect
320. #392	C₂²×C₁₃₉	semidirect
321. #390	C₂²×C₁₃₉	semidirect
322. #388	C₂²×C₁₃₉	semidirect
323. #386	C₂²×C₁₃₉	semidirect
324. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
372. C₂×C₂²⋊C₄	D₄×C₁₃₉	semidirect
461. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
565. C₂	#2555×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₁₃₉	2
C₂²×#121×C₁₃₉	2
#2555×C₁₃₉	2
C₂×#395×C₁₃₉	2
C₂×#394×C₁₃₉	2
C₂×#392×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₂×#388×C₁₃₉	2
C₂×#386×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
C₂×#2555	139

Subgroups — C2×#2555×C139 #48029418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2555×C₁₃₉ #48029418