Subgroups — C₂×#2636×C₁₃₉ #48029182

Order 35584.

3218 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	C₂²×#126×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2636×C₁₃₉	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#396×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	C₂×#394×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#394×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×#392×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#386×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₂×#385×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#126×C₁₃₉	—	2	8	no	—
17	C₂×#126×C₁₃₉	C₂²	1	8	yes	complemented
18	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	8	yes	complemented
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
35	#400×C₁₃₉	C₂²	1	8	yes	complemented
36	#399×C₁₃₉	C₂²	1	8	yes	complemented
37	#396×C₁₃₉	C₂²	1	16	yes	complemented
38	#394×C₁₃₉	C₂²	1	8	yes	complemented
39	#394×C₁₃₉	C₂²	1	16	yes	complemented
40	#392×C₁₃₉	C₂²	1	8	yes	—
41	#386×C₁₃₉	C₂²	1	16	yes	complemented
42	#385×C₁₃₉	C₂²	1	16	yes	complemented
43	#382×C₁₃₉	C₂²	1	8	yes	complemented
44	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
45	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
48	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
49	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
50	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃₉	—	2	8	no	—
52	C₂²×D₄×C₁₃₉	—	2	8	no	—
53	C₂²×D₄×C₁₃₉	—	2	4	no	—
54	C₂²×D₄×C₁₃₉	—	4	4	no	—
55	C₂²×D₄×C₁₃₉	—	4	4	no	—
56	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
58	C₂³×C₄×C₁₃₉	—	2	8	no	—
59	C₂³×C₄×C₁₃₉	—	4	4	no	—
60	C₂³×C₄×C₁₃₉	—	4	4	no	—
61	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
70	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
71	#126×C₁₃₉	—	2	32	no	—
72	C₄×D₄×C₁₃₉	—	2	32	no	—
73	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
78	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
91	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
92	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
101	C₂×C₄²×C₁₃₉	D₄	1	8	yes	complemented
102	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	4	yes	—
105	#95×C₁₃₉	C₂³	1	4	yes	—
106	#95×C₁₃₉	C₂³	1	8	yes	—
107	#95×C₁₃₉	C₂³	1	8	yes	—
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	2	no	—
115	C₂⁴×C₁₃₉	—	2	4	no	—
116	C₂⁴×C₁₃₉	—	2	4	no	—
117	C₂⁴×C₁₃₉	—	2	2	no	—
118	C₂⁴×C₁₃₉	—	2	2	no	—
119	C₂⁴×C₁₃₉	#41	1	8	yes	—
120	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
121	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
122	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
123	C₂×D₄×C₁₃₉	—	2	32	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	—	4	8	no	—
128	C₂×D₄×C₁₃₉	—	4	8	no	—
129	C₂×D₄×C₁₃₉	—	4	32	no	—
130	C₂²×C₄×C₁₃₉	—	2	4	no	—
131	C₂²×C₄×C₁₃₉	—	2	2	no	—
132	C₂²×C₄×C₁₃₉	—	2	4	no	—
133	C₂²×C₄×C₁₃₉	—	2	2	no	—
134	C₂²×C₄×C₁₃₉	—	2	2	no	—
135	C₂²×C₄×C₁₃₉	—	2	2	no	—
136	C₂²×C₄×C₁₃₉	—	2	2	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	4	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	2	no	—
150	C₂²×C₄×C₁₃₉	—	2	16	no	—
151	C₂²×C₄×C₁₃₉	—	4	8	no	—
152	C₂²×C₄×C₁₃₉	—	4	8	no	—
153	C₂²×C₄×C₁₃₉	—	4	32	no	—
154	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
166	C₄⋊C₄×C₁₃₉	—	2	8	no	—
167	C₄⋊C₄×C₁₃₉	—	2	8	no	—
168	C₄⋊C₄×C₁₃₉	—	2	8	no	—
169	C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₄⋊C₄×C₁₃₉	—	4	8	no	—
171	C₄⋊C₄×C₁₃₉	—	4	8	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
174	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
176	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
178	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
179	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
180	C₄²×C₁₃₉	C₂×D₄	1	16	yes	complemented
181	C₂³×C₁₃₉	—	2	16	no	—
182	C₂³×C₁₃₉	—	2	16	no	—
183	C₂³×C₁₃₉	—	2	16	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	2	no	—
191	C₂³×C₁₃₉	—	2	4	no	—
192	C₂³×C₁₃₉	—	2	4	no	—
193	C₂³×C₁₃₉	—	2	2	no	—
194	C₂³×C₁₃₉	—	2	2	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	4	no	—
200	C₂³×C₁₃₉	—	4	4	no	—
201	C₂³×C₁₃₉	—	4	4	no	—
202	C₂³×C₁₃₉	—	4	8	no	—
203	C₂³×C₁₃₉	—	4	8	no	—
204	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
205	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
206	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
207	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
208	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
209	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
210	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
211	D₄×C₁₃₉	—	2	32	no	—
212	D₄×C₁₃₉	—	4	32	no	—
213	C₂×C₄×C₁₃₉	—	2	8	no	—
214	C₂×C₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	2	8	no	—
216	C₂×C₄×C₁₃₉	—	2	4	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	4	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	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	4	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	4	32	no	—
237	C₂×C₄×C₁₃₉	—	4	4	no	—
238	C₂×C₄×C₁₃₉	—	4	4	no	—
239	C₂×C₄×C₁₃₉	—	4	8	no	—
240	C₂×C₄×C₁₃₉	—	4	4	no	—
241	C₂×C₄×C₁₃₉	—	4	8	no	—
242	C₂×C₄×C₁₃₉	—	4	8	no	—
243	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
246	C₂²×C₁₃₉	—	2	8	no	—
247	C₂²×C₁₃₉	—	2	8	no	—
248	C₂²×C₁₃₉	—	2	8	no	—
249	C₂²×C₁₃₉	—	4	32	no	—
250	C₂²×C₁₃₉	—	4	4	no	—
251	C₂²×C₁₃₉	—	4	4	no	—
252	C₂²×C₁₃₉	—	4	4	no	—
253	C₂²×C₁₃₉	—	4	4	no	—
254	C₂²×C₁₃₉	—	4	2	no	—
255	C₂²×C₁₃₉	—	4	2	no	—
256	C₂²×C₁₃₉	—	4	2	no	—
257	C₂²×C₁₃₉	—	4	4	no	—
258	C₂²×C₁₃₉	—	4	4	no	—
259	C₂²×C₁₃₉	—	8	8	no	—
260	C₂²×C₁₃₉	#525	1	4	yes	—
261	C₂²×C₁₃₉	#535	1	4	yes	—
262	C₂²×C₁₃₉	#537	1	4	yes	—
263	C₂²×C₁₃₉	#538	1	8	yes	—
264	C₂²×C₁₃₉	#539	1	8	yes	—
265	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
266	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
267	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
268	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
269	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
270	C₄×C₁₃₉	—	2	4	no	—
271	C₄×C₁₃₉	—	2	4	no	—
272	C₄×C₁₃₉	—	2	4	no	—
273	C₄×C₁₃₉	—	4	2	no	—
274	C₄×C₁₃₉	—	4	2	no	—
275	C₄×C₁₃₉	—	4	4	no	—
276	C₄×C₁₃₉	—	4	2	no	—
277	C₄×C₁₃₉	—	4	4	no	—
278	C₄×C₁₃₉	—	4	4	no	—
279	C₂×C₁₃₉	—	4	8	no	—
280	C₂×C₁₃₉	—	8	2	no	—
281	C₂×C₁₃₉	#2636	1	8	yes	direct product factor
282	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
283	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
284	C₂×C₁₃₉	C₂×#537	1	1	yes	characteristic
285	C₂×C₁₃₉	C₂×#538	1	2	yes	—
286	C₂×C₁₃₉	C₂×#539	1	2	yes	—
287	C₂×#2636	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₁₃₉	C₂×#2636	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×#126	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
291	#2636	C₂×C₁₃₉	1	16	yes	direct product factor
292	C₂×#400	C₂×C₁₃₉	1	1	yes	characteristic, complemented
293	C₂×#399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	C₂×#396	C₂×C₁₃₉	1	2	yes	complemented
295	C₂×#394	C₂×C₁₃₉	1	2	yes	complemented
296	C₂×#394	C₂×C₁₃₉	1	1	yes	characteristic, complemented
297	C₂×#392	C₂×C₁₃₉	1	1	yes	characteristic
298	C₂×#386	C₂×C₁₃₉	1	2	yes	complemented
299	C₂×#385	C₂×C₁₃₉	1	2	yes	complemented
300	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
301	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
302	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
303	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
304	C₂×#126	—	2	8	no	—
305	C₂×#126	C₂²×C₁₃₉	1	8	yes	complemented
306	C₂×C₄×D₄	—	2	8	no	—
307	C₂×C₄×D₄	C₂²×C₁₃₉	1	8	yes	complemented
308	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
312	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
313	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
317	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
318	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
322	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
323	#400	C₂²×C₁₃₉	1	8	yes	complemented
324	#399	C₂²×C₁₃₉	1	8	yes	complemented
325	#396	C₂²×C₁₃₉	1	16	yes	complemented
326	#394	C₂²×C₁₃₉	1	8	yes	complemented
327	#394	C₂²×C₁₃₉	1	16	yes	complemented
328	#392	C₂²×C₁₃₉	1	8	yes	—
329	#386	C₂²×C₁₃₉	1	16	yes	complemented
330	#385	C₂²×C₁₃₉	1	16	yes	complemented
331	#382	C₂²×C₁₃₉	1	8	yes	complemented
332	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
333	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
334	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
335	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
336	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
337	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
338	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
339	C₂²×D₄	—	2	8	no	—
340	C₂²×D₄	—	2	8	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	—	4	4	no	—
343	C₂²×D₄	—	4	4	no	—
344	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
345	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
346	C₂³×C₄	—	2	8	no	—
347	C₂³×C₄	—	4	4	no	—
348	C₂³×C₄	—	4	4	no	—
349	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
359	#126	—	2	32	no	—
360	C₄×D₄	—	2	32	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	—	2	4	no	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	4	4	no	—
366	C₂×C₄⋊C₄	—	4	4	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	4	4	no	—
379	C₂×C₂²⋊C₄	—	4	4	no	—
380	C₂×C₂²⋊C₄	—	4	4	no	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
389	C₂×C₄²	D₄×C₁₃₉	1	8	yes	complemented
390	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
391	#95	C₂³×C₁₃₉	1	8	yes	—
392	#95	C₂³×C₁₃₉	1	4	yes	—
393	#95	C₂³×C₁₃₉	1	4	yes	—
394	#95	C₂³×C₁₃₉	1	8	yes	—
395	#95	C₂³×C₁₃₉	1	8	yes	—
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	—	2	4	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	#41×C₁₃₉	1	8	yes	—
408	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
409	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
410	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
411	C₂×D₄	—	2	32	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	32	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	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	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	16	no	—
439	C₂²×C₄	—	4	8	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	—	4	32	no	—
442	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
444	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	4	8	no	—
459	C₄⋊C₄	—	4	8	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	—	2	16	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	4	8	no	—
466	C₂²⋊C₄	—	4	8	no	—
467	C₂²⋊C₄	—	4	8	no	—
468	C₄²	C₂×D₄×C₁₃₉	1	16	yes	complemented
469	C₂³	—	2	16	no	—
470	C₂³	—	2	16	no	—
471	C₂³	—	2	16	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	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	4	8	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	8	no	—
492	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
493	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
494	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
495	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
496	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
497	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
498	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
499	D₄	—	2	32	no	—
500	D₄	—	4	32	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	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	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	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	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	32	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
532	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
533	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	4	32	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	8	8	no	—
548	C₂²	#525×C₁₃₉	1	4	yes	—
549	C₂²	#535×C₁₃₉	1	4	yes	—
550	C₂²	#537×C₁₃₉	1	4	yes	—
551	C₂²	#538×C₁₃₉	1	8	yes	—
552	C₂²	#539×C₁₃₉	1	8	yes	—
553	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
554	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
555	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
556	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
557	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
558	C₄	—	2	4	no	—
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	4	no	—
567	C₂	—	4	8	no	—
568	C₂	—	8	2	no	—
569	C₂	#2636×C₁₃₉	1	8	yes	direct product factor
570	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
571	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
572	C₂	C₂×#537×C₁₃₉	1	1	yes	characteristic
573	C₂	C₂×#538×C₁₃₉	1	2	yes	—
574	C₂	C₂×#539×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#392×C₁₃₉	C₂
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×#126×C₁₃₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
3. #2636×C₁₃₉	C₂	direct (N × H)
4. C₂×#400×C₁₃₉	C₂	semidirect
5. C₂×#399×C₁₃₉	C₂	semidirect
6. C₂×#396×C₁₃₉	C₂	semidirect
7. C₂×#394×C₁₃₉	C₂	semidirect
8. C₂×#394×C₁₃₉	C₂	semidirect
10. C₂×#386×C₁₃₉	C₂	semidirect
11. C₂×#385×C₁₃₉	C₂	semidirect
12. C₂×#382×C₁₃₉	C₂	semidirect
17. C₂×#126×C₁₃₉	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
35. #400×C₁₃₉	C₂²	semidirect
36. #399×C₁₃₉	C₂²	semidirect
37. #396×C₁₃₉	C₂²	semidirect
38. #394×C₁₃₉	C₂²	semidirect
39. #394×C₁₃₉	C₂²	semidirect
41. #386×C₁₃₉	C₂²	semidirect
42. #385×C₁₃₉	C₂²	semidirect
43. #382×C₁₃₉	C₂²	semidirect
101. C₂×C₄²×C₁₃₉	D₄	semidirect
180. C₄²×C₁₃₉	C₂×D₄	semidirect
281. C₂×C₁₃₉	#2636	direct (N × H)
287. C₂×#2636	C₁₃₉	direct (N × H)
288. C₁₃₉	C₂×#2636	direct (N × H)
289. C₂²×#126	C₂×C₁₃₉	semidirect
290. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
291. #2636	C₂×C₁₃₉	direct (N × H)
292. C₂×#400	C₂×C₁₃₉	semidirect
293. C₂×#399	C₂×C₁₃₉	semidirect
294. C₂×#396	C₂×C₁₃₉	semidirect
295. C₂×#394	C₂×C₁₃₉	semidirect
296. C₂×#394	C₂×C₁₃₉	semidirect
298. C₂×#386	C₂×C₁₃₉	semidirect
299. C₂×#385	C₂×C₁₃₉	semidirect
300. C₂×#382	C₂×C₁₃₉	semidirect
305. C₂×#126	C₂²×C₁₃₉	semidirect
307. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
323. #400	C₂²×C₁₃₉	semidirect
324. #399	C₂²×C₁₃₉	semidirect
325. #396	C₂²×C₁₃₉	semidirect
326. #394	C₂²×C₁₃₉	semidirect
327. #394	C₂²×C₁₃₉	semidirect
329. #386	C₂²×C₁₃₉	semidirect
330. #385	C₂²×C₁₃₉	semidirect
331. #382	C₂²×C₁₃₉	semidirect
389. C₂×C₄²	D₄×C₁₃₉	semidirect
468. C₄²	C₂×D₄×C₁₃₉	semidirect
569. C₂	#2636×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×#126×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2636×C₁₃₉	2
C₂×#400×C₁₃₉	2
C₂×#399×C₁₃₉	2
C₂×#396×C₁₃₉	2
C₂×#394×C₁₃₉	2
C₂×#392×C₁₃₉	2
C₂×#386×C₁₃₉	2
C₂×#385×C₁₃₉	2
C₂×#382×C₁₃₉	2
C₂×#2636	139

Subgroups — C2×#2636×C139 #48029182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2636×C₁₃₉ #48029182