Subgroups — C₁₃₉×#32893 #48027489

Order 35584.

3630 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#456×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#455×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#3007×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1793×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1792×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1789×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1785×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#585×C₁₃₉	—	2	8	no	—
11	#585×C₁₃₉	—	2	8	no	—
12	C₂×2₋¹⁺⁴×C₁₃₉	—	2	2	no	—
13	C₂×2₋¹⁺⁴×C₁₃₉	C₂²	1	2	yes	—
14	C₂×H(5,𝔽₂)×C₁₃₉	—	2	2	no	—
15	C₂×H(5,𝔽₂)×C₁₃₉	—	2	2	no	—
16	C₂×H(5,𝔽₂)×C₁₃₉	C₂²	1	2	yes	—
17	C₂²×#41×C₁₃₉	—	2	4	no	—
18	C₂²×#41×C₁₃₉	—	2	2	no	—
19	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#137×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	#456×C₁₃₉	—	2	8	no	—
26	#455×C₁₃₉	—	2	8	no	—
27	#452×C₁₃₉	—	2	4	no	—
28	#451×C₁₃₉	—	2	2	no	—
29	#450×C₁₃₉	—	2	2	no	—
30	C₂×#104×C₁₃₉	C₂²	1	4	yes	complemented
31	C₂×#104×C₁₃₉	C₂²	1	4	yes	complemented
32	#417×C₁₃₉	C₂²	1	4	yes	complemented
33	C₂×#101×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×#100×C₁₃₉	C₂²	1	2	yes	complemented
35	#407×C₁₃₉	C₂²	1	2	yes	complemented
36	#394×C₁₃₉	—	2	2	no	—
37	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	#385×C₁₃₉	—	2	2	no	—
40	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
41	2₋¹⁺⁴×C₁₃₉	—	2	32	no	—
42	2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
43	2₋¹⁺⁴×C₁₃₉	—	2	4	no	—
44	2₋¹⁺⁴×C₁₃₉	D₄	1	8	yes	—
45	H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
46	H(5,𝔽₂)×C₁₃₉	—	2	32	no	—
47	H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
48	H(5,𝔽₂)×C₁₃₉	—	2	8	no	—
49	H(5,𝔽₂)×C₁₃₉	—	2	4	no	—
50	H(5,𝔽₂)×C₁₃₉	D₄	1	8	yes	—
51	C₂×#41×C₁₃₉	—	2	4	no	—
52	C₂×#41×C₁₃₉	—	2	8	no	—
53	C₂×#41×C₁₃₉	—	2	4	no	—
54	C₂×#41×C₁₃₉	—	2	32	no	—
55	C₂×#41×C₁₃₉	—	2	32	no	—
56	C₂×#41×C₁₃₉	—	2	16	no	—
57	C₂×#41×C₁₃₉	—	2	16	no	—
58	C₂×#41×C₁₃₉	—	2	8	no	—
59	C₂×#41×C₁₃₉	—	2	8	no	—
60	C₂×#41×C₁₃₉	—	2	4	no	—
61	C₂×#41×C₁₃₉	—	2	4	no	—
62	C₂×#41×C₁₃₉	—	2	4	no	—
63	C₂×#41×C₁₃₉	—	2	4	no	—
64	C₂×#41×C₁₃₉	—	2	2	no	—
65	C₂×#41×C₁₃₉	—	2	2	no	—
66	C₂×#41×C₁₃₉	—	2	4	no	—
67	C₂×#41×C₁₃₉	—	2	2	no	—
68	C₂×#41×C₁₃₉	—	2	2	no	—
69	C₂×#41×C₁₃₉	D₄	1	4	yes	—
70	C₂×#41×C₁₃₉	C₂³	1	4	yes	—
71	C₂²×Q₈×C₁₃₉	—	2	2	no	—
72	C₂²×Q₈×C₁₃₉	—	2	4	no	—
73	C₂²×Q₈×C₁₃₉	D₄	1	2	yes	—
74	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃₉	—	2	8	no	—
77	C₂²×D₄×C₁₃₉	—	2	2	no	—
78	C₂²×D₄×C₁₃₉	—	2	4	no	—
79	C₂²×D₄×C₁₃₉	—	2	2	no	—
80	C₂²×D₄×C₁₃₉	—	2	4	no	—
81	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
82	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₉	—	2	4	no	—
85	C₂³×C₄×C₁₃₉	—	2	2	no	—
86	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	#137×C₁₃₉	—	2	8	no	—
89	#137×C₁₃₉	—	2	8	no	—
90	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
91	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
92	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
94	#124×C₁₃₉	—	2	4	no	—
95	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
96	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
104	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
106	#104×C₁₃₉	—	2	8	no	—
107	#104×C₁₃₉	—	2	8	no	—
108	#103×C₁₃₉	—	2	4	no	—
109	#102×C₁₃₉	—	2	4	no	—
110	#101×C₁₃₉	—	2	4	no	—
111	#100×C₁₃₉	—	2	4	no	—
112	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
113	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
114	#95×C₁₃₉	—	2	1	no	—
115	#95×C₁₃₉	—	2	2	no	—
116	C₂⁴×C₁₃₉	—	2	4	no	—
117	C₂⁴×C₁₃₉	—	2	2	no	—
118	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
119	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
120	#41×C₁₃₉	—	2	32	no	—
121	#41×C₁₃₉	—	2	8	no	—
122	#41×C₁₃₉	—	2	8	no	—
123	#41×C₁₃₉	—	2	16	no	—
124	#41×C₁₃₉	—	2	64	no	—
125	#41×C₁₃₉	—	2	32	no	—
126	#41×C₁₃₉	—	2	16	no	—
127	#41×C₁₃₉	—	2	16	no	—
128	#41×C₁₃₉	—	2	16	no	—
129	#41×C₁₃₉	—	2	16	no	—
130	#41×C₁₃₉	—	2	16	no	—
131	#41×C₁₃₉	—	2	8	no	—
132	#41×C₁₃₉	—	2	16	no	—
133	#41×C₁₃₉	—	2	8	no	—
134	#41×C₁₃₉	—	2	16	no	—
135	#41×C₁₃₉	—	2	16	no	—
136	#41×C₁₃₉	—	2	4	no	—
137	#41×C₁₃₉	—	2	4	no	—
138	#41×C₁₃₉	C₂×D₄	1	8	yes	—
139	#41×C₁₃₉	C₂×D₄	1	8	yes	—
140	C₂×Q₈×C₁₃₉	—	2	4	no	—
141	C₂×Q₈×C₁₃₉	—	2	16	no	—
142	C₂×Q₈×C₁₃₉	—	2	16	no	—
143	C₂×Q₈×C₁₃₉	—	2	16	no	—
144	C₂×Q₈×C₁₃₉	—	2	8	no	—
145	C₂×Q₈×C₁₃₉	—	2	2	no	—
146	C₂×Q₈×C₁₃₉	—	2	2	no	—
147	C₂×Q₈×C₁₃₉	—	2	2	no	—
148	C₂×Q₈×C₁₃₉	—	2	2	no	—
149	C₂×Q₈×C₁₃₉	—	2	2	no	—
150	C₂×Q₈×C₁₃₉	—	2	2	no	—
151	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
152	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
153	C₂×D₄×C₁₃₉	—	2	8	no	—
154	C₂×D₄×C₁₃₉	—	2	4	no	—
155	C₂×D₄×C₁₃₉	—	2	64	no	—
156	C₂×D₄×C₁₃₉	—	2	16	no	—
157	C₂×D₄×C₁₃₉	—	2	16	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	8	no	—
160	C₂×D₄×C₁₃₉	—	2	16	no	—
161	C₂×D₄×C₁₃₉	—	2	4	no	—
162	C₂×D₄×C₁₃₉	—	2	4	no	—
163	C₂×D₄×C₁₃₉	—	2	16	no	—
164	C₂×D₄×C₁₃₉	—	2	4	no	—
165	C₂×D₄×C₁₃₉	—	2	4	no	—
166	C₂×D₄×C₁₃₉	—	2	16	no	—
167	C₂×D₄×C₁₃₉	—	2	8	no	—
168	C₂×D₄×C₁₃₉	—	2	2	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	2	2	no	—
171	C₂×D₄×C₁₃₉	—	2	2	no	—
172	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
173	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃₉	—	2	4	no	—
175	C₂²×C₄×C₁₃₉	—	2	8	no	—
176	C₂²×C₄×C₁₃₉	—	2	32	no	—
177	C₂²×C₄×C₁₃₉	—	2	16	no	—
178	C₂²×C₄×C₁₃₉	—	2	2	no	—
179	C₂²×C₄×C₁₃₉	—	2	4	no	—
180	C₂²×C₄×C₁₃₉	—	2	4	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	2	2	no	—
183	C₂²×C₄×C₁₃₉	—	2	4	no	—
184	C₂²×C₄×C₁₃₉	—	2	4	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	1	no	—
188	C₂²×C₄×C₁₃₉	—	2	1	no	—
189	C₂²×C₄×C₁₃₉	—	2	1	no	—
190	C₂²×C₄×C₁₃₉	—	2	1	no	—
191	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	Q₁₆×C₁₃₉	—	4	8	no	—
197	SD₁₆×C₁₃₉	—	4	8	no	—
198	M₁₆×C₁₃₉	—	2	4	no	—
199	M₁₆×C₁₃₉	—	2	4	no	—
200	C₂×C₈×C₁₃₉	—	2	4	no	—
201	C₄⋊C₄×C₁₃₉	—	2	2	no	—
202	C₄⋊C₄×C₁₃₉	—	4	1	no	—
203	C₄⋊C₄×C₁₃₉	—	4	1	no	—
204	C₄⋊C₄×C₁₃₉	—	4	4	no	—
205	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
206	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
207	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
209	C₄²×C₁₃₉	—	2	2	no	—
210	C₄²×C₁₃₉	—	2	2	no	—
211	C₂³×C₁₃₉	—	2	8	no	—
212	C₂³×C₁₃₉	—	2	16	no	—
213	C₂³×C₁₃₉	—	2	2	no	—
214	C₂³×C₁₃₉	—	2	4	no	—
215	C₂³×C₁₃₉	—	2	1	no	—
216	C₂³×C₁₃₉	—	2	2	no	—
217	C₂³×C₁₃₉	—	2	1	no	—
218	C₂³×C₁₃₉	—	4	1	no	—
219	C₂³×C₁₃₉	—	4	1	no	—
220	C₂³×C₁₃₉	—	4	2	no	—
221	C₂³×C₁₃₉	—	4	2	no	—
222	C₂³×C₁₃₉	—	8	2	no	—
223	C₂³×C₁₃₉	—	8	2	no	—
224	C₂³×C₁₃₉	—	8	4	no	—
225	C₂³×C₁₃₉	—	8	4	no	—
226	C₂³×C₁₃₉	#120	1	2	yes	—
227	C₂³×C₁₃₉	#120	1	4	yes	—
228	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₁₃₉	—	2	16	no	—
230	Q₈×C₁₃₉	—	2	8	no	—
231	Q₈×C₁₃₉	—	2	4	no	—
232	Q₈×C₁₃₉	—	2	8	no	—
233	Q₈×C₁₃₉	—	4	4	no	—
234	Q₈×C₁₃₉	#120	1	8	yes	—
235	D₄×C₁₃₉	—	2	32	no	—
236	D₄×C₁₃₉	—	2	16	no	—
237	D₄×C₁₃₉	—	2	16	no	—
238	D₄×C₁₃₉	—	2	16	no	—
239	D₄×C₁₃₉	—	2	8	no	—
240	D₄×C₁₃₉	—	2	8	no	—
241	D₄×C₁₃₉	—	2	8	no	—
242	D₄×C₁₃₉	—	2	8	no	—
243	D₄×C₁₃₉	—	2	4	no	—
244	D₄×C₁₃₉	#120	1	8	yes	—
245	C₂×C₄×C₁₃₉	—	2	16	no	—
246	C₂×C₄×C₁₃₉	—	2	8	no	—
247	C₂×C₄×C₁₃₉	—	2	16	no	—
248	C₂×C₄×C₁₃₉	—	2	8	no	—
249	C₂×C₄×C₁₃₉	—	2	32	no	—
250	C₂×C₄×C₁₃₉	—	2	8	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	4	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	4	no	—
257	C₂×C₄×C₁₃₉	—	2	8	no	—
258	C₂×C₄×C₁₃₉	—	2	8	no	—
259	C₂×C₄×C₁₃₉	—	2	4	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	4	1	no	—
262	C₂×C₄×C₁₃₉	—	4	1	no	—
263	C₂×C₄×C₁₃₉	—	4	1	no	—
264	C₂×C₄×C₁₃₉	—	4	2	no	—
265	C₂×C₄×C₁₃₉	—	4	1	no	—
266	C₂×C₄×C₁₃₉	—	4	1	no	—
267	C₂×C₄×C₁₃₉	—	4	1	no	—
268	C₂×C₄×C₁₃₉	—	4	1	no	—
269	C₂×C₄×C₁₃₉	—	4	1	no	—
270	C₂×C₄×C₁₃₉	—	4	1	no	—
271	C₂×C₄×C₁₃₉	#120	1	4	yes	—
272	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
277	C₈×C₁₃₉	—	4	4	no	—
278	C₂²×C₁₃₉	—	2	1	no	—
279	C₂²×C₁₃₉	—	2	1	no	—
280	C₂²×C₁₃₉	—	2	2	no	—
281	C₂²×C₁₃₉	—	2	4	no	—
282	C₂²×C₁₃₉	—	2	8	no	—
283	C₂²×C₁₃₉	—	2	2	no	—
284	C₂²×C₁₃₉	—	2	2	no	—
285	C₂²×C₁₃₉	—	4	4	no	—
286	C₂²×C₁₃₉	—	4	2	no	—
287	C₂²×C₁₃₉	—	4	4	no	—
288	C₂²×C₁₃₉	—	4	2	no	—
289	C₂²×C₁₃₉	—	4	4	no	—
290	C₂²×C₁₃₉	—	8	1	no	—
291	C₂²×C₁₃₉	—	8	2	no	—
292	C₂²×C₁₃₉	—	8	1	no	—
293	C₂²×C₁₃₉	—	8	8	no	—
294	C₂²×C₁₃₉	—	8	16	no	—
295	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
296	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
297	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
298	C₄×C₁₃₉	—	2	1	no	—
299	C₄×C₁₃₉	—	2	8	no	—
300	C₄×C₁₃₉	—	2	4	no	—
301	C₄×C₁₃₉	—	2	1	no	—
302	C₄×C₁₃₉	—	4	2	no	—
303	C₄×C₁₃₉	—	8	1	no	—
304	C₄×C₁₃₉	—	8	1	no	—
305	C₄×C₁₃₉	—	8	1	no	—
306	C₄×C₁₃₉	C₂×#120	1	4	yes	—
307	C₂×C₁₃₉	—	2	1	no	—
308	C₂×C₁₃₉	—	2	1	no	—
309	C₂×C₁₃₉	—	4	2	no	—
310	C₂×C₁₃₉	—	4	4	no	—
311	C₂×C₁₃₉	—	4	8	no	—
312	C₂×C₁₃₉	#2846	1	1	yes	characteristic
313	C₂×C₁₃₉	#3018	1	1	yes	characteristic
314	C₂×C₁₃₉	#3022	1	1	yes	characteristic
315	#32893	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₁₃₉	#32893	1	1	yes	characteristic, direct product factor, Sylow
317	C₂×#585	C₂×C₁₃₉	1	1	yes	characteristic
318	C₂×#456	C₂×C₁₃₉	1	2	yes	complemented
319	C₂×#455	C₂×C₁₃₉	1	2	yes	complemented
320	#3007	C₂×C₁₃₉	1	2	yes	complemented
321	#2432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
322	#1793	C₂×C₁₃₉	1	2	yes	complemented
323	#1792	C₂×C₁₃₉	1	2	yes	complemented
324	#1789	C₂×C₁₃₉	1	2	yes	complemented
325	#1785	C₂×C₁₃₉	1	1	yes	characteristic, complemented
326	#585	—	2	8	no	—
327	#585	—	2	8	no	—
328	C₂×2₋¹⁺⁴	—	2	2	no	—
329	C₂×2₋¹⁺⁴	C₂²×C₁₃₉	1	2	yes	—
330	C₂×H(5,𝔽₂)	—	2	2	no	—
331	C₂×H(5,𝔽₂)	—	2	2	no	—
332	C₂×H(5,𝔽₂)	C₂²×C₁₃₉	1	2	yes	—
333	C₂²×#41	—	2	4	no	—
334	C₂²×#41	—	2	2	no	—
335	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
336	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
337	C₂×#137	C₂²×C₁₃₉	1	4	yes	complemented
338	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
339	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
340	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
341	#456	—	2	8	no	—
342	#455	—	2	8	no	—
343	#452	—	2	4	no	—
344	#451	—	2	2	no	—
345	#450	—	2	2	no	—
346	C₂×#104	C₂²×C₁₃₉	1	4	yes	complemented
347	C₂×#104	C₂²×C₁₃₉	1	4	yes	complemented
348	#417	C₂²×C₁₃₉	1	4	yes	complemented
349	C₂×#101	C₂²×C₁₃₉	1	2	yes	complemented
350	C₂×#100	C₂²×C₁₃₉	1	2	yes	complemented
351	#407	C₂²×C₁₃₉	1	2	yes	complemented
352	#394	—	2	2	no	—
353	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
354	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
355	#385	—	2	2	no	—
356	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
357	2₋¹⁺⁴	—	2	32	no	—
358	2₋¹⁺⁴	—	2	8	no	—
359	2₋¹⁺⁴	—	2	4	no	—
360	2₋¹⁺⁴	D₄×C₁₃₉	1	8	yes	—
361	H(5,𝔽₂)	—	2	16	no	—
362	H(5,𝔽₂)	—	2	32	no	—
363	H(5,𝔽₂)	—	2	16	no	—
364	H(5,𝔽₂)	—	2	8	no	—
365	H(5,𝔽₂)	—	2	4	no	—
366	H(5,𝔽₂)	D₄×C₁₃₉	1	8	yes	—
367	C₂×#41	—	2	4	no	—
368	C₂×#41	—	2	8	no	—
369	C₂×#41	—	2	4	no	—
370	C₂×#41	—	2	32	no	—
371	C₂×#41	—	2	32	no	—
372	C₂×#41	—	2	16	no	—
373	C₂×#41	—	2	16	no	—
374	C₂×#41	—	2	8	no	—
375	C₂×#41	—	2	8	no	—
376	C₂×#41	—	2	4	no	—
377	C₂×#41	—	2	4	no	—
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	4	no	—
380	C₂×#41	—	2	2	no	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	—	2	4	no	—
383	C₂×#41	—	2	2	no	—
384	C₂×#41	—	2	2	no	—
385	C₂×#41	D₄×C₁₃₉	1	4	yes	—
386	C₂×#41	C₂³×C₁₃₉	1	4	yes	—
387	C₂²×Q₈	—	2	2	no	—
388	C₂²×Q₈	—	2	4	no	—
389	C₂²×Q₈	D₄×C₁₃₉	1	2	yes	—
390	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂²×D₄	—	2	8	no	—
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	—	2	4	no	—
395	C₂²×D₄	—	2	2	no	—
396	C₂²×D₄	—	2	4	no	—
397	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
398	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
399	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂³×C₄	—	2	4	no	—
401	C₂³×C₄	—	2	2	no	—
402	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
403	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
404	#137	—	2	8	no	—
405	#137	—	2	8	no	—
406	C₂×Q₁₆	—	2	4	no	—
407	C₂×SD₁₆	—	2	4	no	—
408	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
409	C₄⋊Q₈	—	2	4	no	—
410	#124	—	2	4	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
422	#104	—	2	8	no	—
423	#104	—	2	8	no	—
424	#103	—	2	4	no	—
425	#102	—	2	4	no	—
426	#101	—	2	4	no	—
427	#100	—	2	4	no	—
428	C₂²⋊C₈	—	2	2	no	—
429	C₂²⋊C₈	—	2	2	no	—
430	#95	—	2	1	no	—
431	#95	—	2	2	no	—
432	C₂⁴	—	2	4	no	—
433	C₂⁴	—	2	2	no	—
434	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
435	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
436	#41	—	2	32	no	—
437	#41	—	2	8	no	—
438	#41	—	2	8	no	—
439	#41	—	2	16	no	—
440	#41	—	2	64	no	—
441	#41	—	2	32	no	—
442	#41	—	2	16	no	—
443	#41	—	2	16	no	—
444	#41	—	2	16	no	—
445	#41	—	2	16	no	—
446	#41	—	2	16	no	—
447	#41	—	2	8	no	—
448	#41	—	2	16	no	—
449	#41	—	2	8	no	—
450	#41	—	2	16	no	—
451	#41	—	2	16	no	—
452	#41	—	2	4	no	—
453	#41	—	2	4	no	—
454	#41	C₂×D₄×C₁₃₉	1	8	yes	—
455	#41	C₂×D₄×C₁₃₉	1	8	yes	—
456	C₂×Q₈	—	2	4	no	—
457	C₂×Q₈	—	2	16	no	—
458	C₂×Q₈	—	2	16	no	—
459	C₂×Q₈	—	2	16	no	—
460	C₂×Q₈	—	2	8	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
468	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	64	no	—
472	C₂×D₄	—	2	16	no	—
473	C₂×D₄	—	2	16	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	16	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	16	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	16	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
489	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	8	no	—
492	C₂²×C₄	—	2	32	no	—
493	C₂²×C₄	—	2	16	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
512	Q₁₆	—	4	8	no	—
513	SD₁₆	—	4	8	no	—
514	M₁₆	—	2	4	no	—
515	M₁₆	—	2	4	no	—
516	C₂×C₈	—	2	4	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	4	1	no	—
519	C₄⋊C₄	—	4	1	no	—
520	C₄⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	4	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	16	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	8	2	no	—
539	C₂³	—	8	2	no	—
540	C₂³	—	8	4	no	—
541	C₂³	—	8	4	no	—
542	C₂³	#120×C₁₃₉	1	2	yes	—
543	C₂³	#120×C₁₃₉	1	4	yes	—
544	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
545	Q₈	—	2	16	no	—
546	Q₈	—	2	8	no	—
547	Q₈	—	2	4	no	—
548	Q₈	—	2	8	no	—
549	Q₈	—	4	4	no	—
550	Q₈	#120×C₁₃₉	1	8	yes	—
551	D₄	—	2	32	no	—
552	D₄	—	2	16	no	—
553	D₄	—	2	16	no	—
554	D₄	—	2	16	no	—
555	D₄	—	2	8	no	—
556	D₄	—	2	8	no	—
557	D₄	—	2	8	no	—
558	D₄	—	2	8	no	—
559	D₄	—	2	4	no	—
560	D₄	#120×C₁₃₉	1	8	yes	—
561	C₂×C₄	—	2	16	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	16	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	32	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
588	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
589	C₂×C₄	#120×C₁₃₉	1	4	yes	—
590	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
593	C₈	—	4	4	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	2	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	8	no	—
610	C₂²	—	8	16	no	—
611	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
612	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
613	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	8	no	—
616	C₄	—	2	4	no	—
617	C₄	—	2	1	no	—
618	C₄	—	4	2	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	C₂×#120×C₁₃₉	1	4	yes	—
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	4	2	no	—
626	C₂	—	4	4	no	—
627	C₂	—	4	8	no	—
628	C₂	#2846×C₁₃₉	1	1	yes	characteristic
629	C₂	#3018×C₁₃₉	1	1	yes	characteristic
630	C₂	#3022×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#585×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#456×C₁₃₉	C₂	semidirect
3. C₂×#455×C₁₃₉	C₂	semidirect
4. #3007×C₁₃₉	C₂	semidirect
5. #2432×C₁₃₉	C₂	semidirect
6. #1793×C₁₃₉	C₂	semidirect
7. #1792×C₁₃₉	C₂	semidirect
8. #1789×C₁₃₉	C₂	semidirect
9. #1785×C₁₃₉	C₂	semidirect
21. C₂×#137×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
23. C₂×#124×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×#104×C₁₃₉	C₂²	semidirect
31. C₂×#104×C₁₃₉	C₂²	semidirect
32. #417×C₁₃₉	C₂²	semidirect
33. C₂×#101×C₁₃₉	C₂²	semidirect
34. C₂×#100×C₁₃₉	C₂²	semidirect
35. #407×C₁₃₉	C₂²	semidirect
37. #391×C₁₃₉	C₂²	semidirect
38. #390×C₁₃₉	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
315. #32893	C₁₃₉	direct (N × H)
316. C₁₃₉	#32893	direct (N × H)
318. C₂×#456	C₂×C₁₃₉	semidirect
319. C₂×#455	C₂×C₁₃₉	semidirect
320. #3007	C₂×C₁₃₉	semidirect
321. #2432	C₂×C₁₃₉	semidirect
322. #1793	C₂×C₁₃₉	semidirect
323. #1792	C₂×C₁₃₉	semidirect
324. #1789	C₂×C₁₃₉	semidirect
325. #1785	C₂×C₁₃₉	semidirect
337. C₂×#137	C₂²×C₁₃₉	semidirect
338. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
339. C₂×#124	C₂²×C₁₃₉	semidirect
340. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
346. C₂×#104	C₂²×C₁₃₉	semidirect
347. C₂×#104	C₂²×C₁₃₉	semidirect
348. #417	C₂²×C₁₃₉	semidirect
349. C₂×#101	C₂²×C₁₃₉	semidirect
350. C₂×#100	C₂²×C₁₃₉	semidirect
351. #407	C₂²×C₁₃₉	semidirect
353. #391	C₂²×C₁₃₉	semidirect
354. #390	C₂²×C₁₃₉	semidirect
356. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₁₃₉	2
C₂×#456×C₁₃₉	2
C₂×#455×C₁₃₉	2
#3007×C₁₃₉	2
#2432×C₁₃₉	2
#1793×C₁₃₉	2
#1792×C₁₃₉	2
#1789×C₁₃₉	2
#1785×C₁₃₉	2
#32893	139

Subgroups — C139×#32893 #48027489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#32893 #48027489