Subgroups — C₁₃₉×#37296 #48031892

Order 35584.

2626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2732×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2682×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2671×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2620×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2502×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2501×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2432×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
15	#537×C₁₃₉	—	2	16	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#123×C₁₃₉	C₂²	1	8	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#399×C₁₃₉	C₂²	1	8	yes	—
33	#398×C₁₃₉	C₂²	1	8	yes	—
34	#396×C₁₃₉	C₂²	1	8	yes	—
35	#394×C₁₃₉	C₂²	1	8	yes	—
36	#394×C₁₃₉	C₂²	1	8	yes	—
37	#392×C₁₃₉	C₂²	1	8	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#391×C₁₃₉	C₂²	1	2	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#390×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	4	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	4	yes	—
46	#386×C₁₃₉	C₂²	1	4	yes	—
47	#386×C₁₃₉	C₂²	1	8	yes	—
48	#385×C₁₃₉	C₂²	1	8	yes	—
49	#385×C₁₃₉	C₂²	1	8	yes	—
50	#384×C₁₃₉	C₂²	1	1	yes	characteristic
51	#384×C₁₃₉	C₂²	1	1	yes	characteristic
52	#384×C₁₃₉	C₂²	1	2	yes	—
53	#380×C₁₃₉	C₂²	1	4	yes	—
54	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
56	C₂×#41×C₁₃₉	—	2	8	no	—
57	C₂×#41×C₁₃₉	—	4	2	no	—
58	C₂×#41×C₁₃₉	—	4	2	no	—
59	C₂×#41×C₁₃₉	—	4	4	no	—
60	C₂×#41×C₁₃₉	—	4	4	no	—
61	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
62	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
63	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
77	#127×C₁₃₉	—	4	2	no	—
78	#124×C₁₃₉	—	4	4	no	—
79	#123×C₁₃₉	—	4	16	no	—
80	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
82	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
83	#121×C₁₃₉	—	2	16	no	—
84	#121×C₁₃₉	—	2	16	no	—
85	#121×C₁₃₉	—	2	16	no	—
86	#121×C₁₃₉	—	2	8	no	—
87	#121×C₁₃₉	—	2	8	no	—
88	#121×C₁₃₉	—	4	8	no	—
89	#117×C₁₃₉	—	4	2	no	—
90	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃₉	—	4	2	no	—
112	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	#95×C₁₃₉	C₂³	1	8	yes	—
117	#95×C₁₃₉	C₂³	1	4	yes	—
118	#95×C₁₃₉	C₂³	1	8	yes	—
119	#95×C₁₃₉	C₂³	1	4	yes	—
120	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
121	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
122	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
123	#41×C₁₃₉	—	4	16	no	—
124	#41×C₁₃₉	—	4	32	no	—
125	C₂×Q₈×C₁₃₉	—	2	4	no	—
126	C₂×Q₈×C₁₃₉	—	2	4	no	—
127	C₂×Q₈×C₁₃₉	—	2	4	no	—
128	C₂×Q₈×C₁₃₉	—	4	1	no	—
129	C₂×Q₈×C₁₃₉	—	4	1	no	—
130	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
131	C₂×D₄×C₁₃₉	—	2	8	no	—
132	C₂×D₄×C₁₃₉	—	2	8	no	—
133	C₂×D₄×C₁₃₉	—	2	8	no	—
134	C₂×D₄×C₁₃₉	—	2	4	no	—
135	C₂×D₄×C₁₃₉	—	2	4	no	—
136	C₂×D₄×C₁₃₉	—	2	4	no	—
137	C₂×D₄×C₁₃₉	—	2	8	no	—
138	C₂×D₄×C₁₃₉	—	4	1	no	—
139	C₂×D₄×C₁₃₉	—	4	1	no	—
140	C₂×D₄×C₁₃₉	—	4	2	no	—
141	C₂×D₄×C₁₃₉	—	4	2	no	—
142	C₂×D₄×C₁₃₉	—	4	4	no	—
143	C₂×D₄×C₁₃₉	—	4	4	no	—
144	C₂×D₄×C₁₃₉	—	4	4	no	—
145	C₂×D₄×C₁₃₉	—	4	8	no	—
146	C₂×D₄×C₁₃₉	—	4	8	no	—
147	C₂×D₄×C₁₃₉	—	4	4	no	—
148	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
149	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
150	C₂²×C₄×C₁₃₉	—	2	2	no	—
151	C₂²×C₄×C₁₃₉	—	2	2	no	—
152	C₂²×C₄×C₁₃₉	—	2	4	no	—
153	C₂²×C₄×C₁₃₉	—	2	4	no	—
154	C₂²×C₄×C₁₃₉	—	2	8	no	—
155	C₂²×C₄×C₁₃₉	—	2	8	no	—
156	C₂²×C₄×C₁₃₉	—	2	4	no	—
157	C₂²×C₄×C₁₃₉	—	2	4	no	—
158	C₂²×C₄×C₁₃₉	—	4	2	no	—
159	C₂²×C₄×C₁₃₉	—	4	4	no	—
160	C₂²×C₄×C₁₃₉	—	4	4	no	—
161	C₂²×C₄×C₁₃₉	—	4	8	no	—
162	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
163	C₂²×C₄×C₁₃₉	C₂×D₄	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	4	yes	—
167	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
173	C₄⋊C₄×C₁₃₉	—	2	8	no	—
174	C₄⋊C₄×C₁₃₉	—	2	4	no	—
175	C₄⋊C₄×C₁₃₉	—	2	4	no	—
176	C₄⋊C₄×C₁₃₉	—	2	8	no	—
177	C₄⋊C₄×C₁₃₉	—	2	8	no	—
178	C₄⋊C₄×C₁₃₉	—	2	8	no	—
179	C₄⋊C₄×C₁₃₉	—	4	2	no	—
180	C₄⋊C₄×C₁₃₉	—	4	4	no	—
181	C₄⋊C₄×C₁₃₉	—	4	8	no	—
182	C₄⋊C₄×C₁₃₉	—	4	4	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
187	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
188	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
191	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
192	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
193	C₄²×C₁₃₉	—	2	2	no	—
194	C₄²×C₁₃₉	—	2	2	no	—
195	C₄²×C₁₃₉	—	2	4	no	—
196	C₄²×C₁₃₉	—	4	2	no	—
197	C₂³×C₁₃₉	—	2	4	no	—
198	C₂³×C₁₃₉	—	2	1	no	—
199	C₂³×C₁₃₉	—	2	1	no	—
200	C₂³×C₁₃₉	—	2	2	no	—
201	C₂³×C₁₃₉	—	2	2	no	—
202	C₂³×C₁₃₉	—	2	2	no	—
203	C₂³×C₁₃₉	—	2	4	no	—
204	C₂³×C₁₃₉	—	2	2	no	—
205	C₂³×C₁₃₉	—	2	4	no	—
206	C₂³×C₁₃₉	—	2	8	no	—
207	C₂³×C₁₃₉	—	2	4	no	—
208	C₂³×C₁₃₉	—	2	4	no	—
209	C₂³×C₁₃₉	—	2	8	no	—
210	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
212	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
213	Q₈×C₁₃₉	—	4	4	no	—
214	Q₈×C₁₃₉	—	4	8	no	—
215	D₄×C₁₃₉	—	4	8	no	—
216	D₄×C₁₃₉	—	4	4	no	—
217	D₄×C₁₃₉	—	4	16	no	—
218	D₄×C₁₃₉	—	4	8	no	—
219	D₄×C₁₃₉	—	8	8	no	—
220	D₄×C₁₃₉	—	8	8	no	—
221	D₄×C₁₃₉	—	8	8	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	1	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	1	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	8	no	—
231	C₂×C₄×C₁₃₉	—	2	16	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	4	no	—
236	C₂×C₄×C₁₃₉	—	2	4	no	—
237	C₂×C₄×C₁₃₉	—	2	8	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	8	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	4	no	—
242	C₂×C₄×C₁₃₉	—	4	8	no	—
243	C₂×C₄×C₁₃₉	—	4	16	no	—
244	C₂×C₄×C₁₃₉	—	8	8	no	—
245	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
249	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
250	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
252	C₂²×C₁₃₉	—	2	4	no	—
253	C₂²×C₁₃₉	—	2	2	no	—
254	C₂²×C₁₃₉	—	2	4	no	—
255	C₂²×C₁₃₉	—	2	2	no	—
256	C₂²×C₁₃₉	—	2	4	no	—
257	C₂²×C₁₃₉	—	2	2	no	—
258	C₂²×C₁₃₉	—	4	2	no	—
259	C₂²×C₁₃₉	—	4	4	no	—
260	C₂²×C₁₃₉	—	4	4	no	—
261	C₂²×C₁₃₉	—	4	2	no	—
262	C₂²×C₁₃₉	—	4	4	no	—
263	C₂²×C₁₃₉	—	4	4	no	—
264	C₂²×C₁₃₉	—	4	4	no	—
265	C₂²×C₁₃₉	—	4	8	no	—
266	C₂²×C₁₃₉	—	4	8	no	—
267	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
268	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
269	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
270	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
271	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
272	C₄×C₁₃₉	—	2	4	no	—
273	C₄×C₁₃₉	—	2	2	no	—
274	C₄×C₁₃₉	—	2	4	no	—
275	C₄×C₁₃₉	—	2	4	no	—
276	C₄×C₁₃₉	—	4	4	no	—
277	C₄×C₁₃₉	—	4	4	no	—
278	C₄×C₁₃₉	—	4	4	no	—
279	C₄×C₁₃₉	—	4	4	no	—
280	C₄×C₁₃₉	#534	1	4	yes	—
281	C₂×C₁₃₉	—	4	4	no	—
282	C₂×C₁₃₉	—	4	2	no	—
283	C₂×C₁₃₉	—	8	4	no	—
284	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
285	C₂×C₁₃₉	#3498	1	1	yes	characteristic
286	C₂×C₁₃₉	#3499	1	1	yes	characteristic
287	C₂×C₁₃₉	#3536	1	2	yes	—
288	C₂×C₁₃₉	#3548	1	2	yes	—
289	#37296	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₁₃₉	#37296	1	1	yes	characteristic, direct product factor, Sylow
291	C₂×#537	C₂×C₁₃₉	1	2	yes	complemented
292	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
293	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	#2732	C₂×C₁₃₉	1	4	yes	complemented
295	#2682	C₂×C₁₃₉	1	4	yes	complemented
296	#2671	C₂×C₁₃₉	1	8	yes	complemented
297	#2620	C₂×C₁₃₉	1	2	yes	complemented
298	#2502	C₂×C₁₃₉	1	2	yes	complemented
299	#2501	C₂×C₁₃₉	1	2	yes	complemented
300	#2432	C₂×C₁₃₉	1	2	yes	complemented
301	#2431	C₂×C₁₃₉	1	2	yes	complemented
302	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
303	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
304	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
305	#537	—	2	16	no	—
306	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
307	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
308	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
309	C₂×#123	C₂²×C₁₃₉	1	8	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
311	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
312	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
313	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
314	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
315	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
316	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
317	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
318	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
319	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
321	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
322	#399	C₂²×C₁₃₉	1	8	yes	—
323	#398	C₂²×C₁₃₉	1	8	yes	—
324	#396	C₂²×C₁₃₉	1	8	yes	—
325	#394	C₂²×C₁₃₉	1	8	yes	—
326	#394	C₂²×C₁₃₉	1	8	yes	—
327	#392	C₂²×C₁₃₉	1	8	yes	—
328	#391	C₂²×C₁₃₉	1	2	yes	—
329	#391	C₂²×C₁₃₉	1	2	yes	—
330	#391	C₂²×C₁₃₉	1	2	yes	—
331	#390	C₂²×C₁₃₉	1	4	yes	—
332	#390	C₂²×C₁₃₉	1	2	yes	—
333	#390	C₂²×C₁₃₉	1	2	yes	—
334	#390	C₂²×C₁₃₉	1	2	yes	—
335	#389	C₂²×C₁₃₉	1	4	yes	—
336	#386	C₂²×C₁₃₉	1	4	yes	—
337	#386	C₂²×C₁₃₉	1	8	yes	—
338	#385	C₂²×C₁₃₉	1	8	yes	—
339	#385	C₂²×C₁₃₉	1	8	yes	—
340	#384	C₂²×C₁₃₉	1	1	yes	characteristic
341	#384	C₂²×C₁₃₉	1	1	yes	characteristic
342	#384	C₂²×C₁₃₉	1	2	yes	—
343	#380	C₂²×C₁₃₉	1	4	yes	—
344	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
346	C₂×#41	—	2	8	no	—
347	C₂×#41	—	4	2	no	—
348	C₂×#41	—	4	2	no	—
349	C₂×#41	—	4	4	no	—
350	C₂×#41	—	4	4	no	—
351	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
352	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
353	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
354	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
355	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
356	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
357	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
358	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
359	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
365	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
366	C₄⋊Q₈	—	4	2	no	—
367	#127	—	4	2	no	—
368	#124	—	4	4	no	—
369	#123	—	4	16	no	—
370	C₂²⋊Q₈	—	2	16	no	—
371	C₂²⋊Q₈	—	2	8	no	—
372	C₂²⋊Q₈	—	2	8	no	—
373	#121	—	2	16	no	—
374	#121	—	2	16	no	—
375	#121	—	2	16	no	—
376	#121	—	2	8	no	—
377	#121	—	2	8	no	—
378	#121	—	4	8	no	—
379	#117	—	4	2	no	—
380	C₂×C₄⋊C₄	—	2	8	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
401	C₂×C₄²	—	4	2	no	—
402	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
406	#95	C₂³×C₁₃₉	1	4	yes	—
407	#95	C₂³×C₁₃₉	1	4	yes	—
408	#95	C₂³×C₁₃₉	1	8	yes	—
409	#95	C₂³×C₁₃₉	1	8	yes	—
410	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
411	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
412	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
413	#41	—	4	16	no	—
414	#41	—	4	32	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	4	1	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
439	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	8	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	8	no	—
452	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	8	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	4	4	no	—
471	C₄⋊C₄	—	4	8	no	—
472	C₄⋊C₄	—	4	4	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	16	no	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	—	4	8	no	—
482	C₂²⋊C₄	—	4	8	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	4	no	—
486	C₄²	—	4	2	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	8	no	—
500	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
501	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
502	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
503	Q₈	—	4	4	no	—
504	Q₈	—	4	8	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	16	no	—
508	D₄	—	4	8	no	—
509	D₄	—	8	8	no	—
510	D₄	—	8	8	no	—
511	D₄	—	8	8	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	16	no	—
534	C₂×C₄	—	8	8	no	—
535	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
537	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
538	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
539	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
540	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
541	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	8	no	—
553	C₂²	—	4	8	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
558	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
559	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
560	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
561	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
562	C₄	—	2	4	no	—
563	C₄	—	2	4	no	—
564	C₄	—	2	4	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	4	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	4	no	—
570	C₄	#534×C₁₃₉	1	4	yes	—
571	C₂	—	4	4	no	—
572	C₂	—	4	2	no	—
573	C₂	—	8	4	no	—
574	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
575	C₂	#3498×C₁₃₉	1	1	yes	characteristic
576	C₂	#3499×C₁₃₉	1	1	yes	characteristic
577	C₂	#3536×C₁₃₉	1	2	yes	—
578	C₂	#3548×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#537×C₁₃₉	C₂	semidirect
2. #2857×C₁₃₉	C₂	semidirect
3. #2856×C₁₃₉	C₂	semidirect
4. #2732×C₁₃₉	C₂	semidirect
5. #2682×C₁₃₉	C₂	semidirect
6. #2671×C₁₃₉	C₂	semidirect
7. #2620×C₁₃₉	C₂	semidirect
8. #2502×C₁₃₉	C₂	semidirect
9. #2501×C₁₃₉	C₂	semidirect
10. #2432×C₁₃₉	C₂	semidirect
11. #2431×C₁₃₉	C₂	semidirect
12. #2297×C₁₃₉	C₂	semidirect
61. C₂×#41×C₁₃₉	D₄	semidirect
289. #37296	C₁₃₉	direct (N × H)
290. C₁₃₉	#37296	direct (N × H)
291. C₂×#537	C₂×C₁₃₉	semidirect
292. #2857	C₂×C₁₃₉	semidirect
293. #2856	C₂×C₁₃₉	semidirect
294. #2732	C₂×C₁₃₉	semidirect
295. #2682	C₂×C₁₃₉	semidirect
296. #2671	C₂×C₁₃₉	semidirect
297. #2620	C₂×C₁₃₉	semidirect
298. #2502	C₂×C₁₃₉	semidirect
299. #2501	C₂×C₁₃₉	semidirect
300. #2432	C₂×C₁₃₉	semidirect
301. #2431	C₂×C₁₃₉	semidirect
302. #2297	C₂×C₁₃₉	semidirect
351. C₂×#41	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×#537×C₁₃₉	2
#2857×C₁₃₉	2
#2856×C₁₃₉	2
#2732×C₁₃₉	2
#2682×C₁₃₉	2
#2671×C₁₃₉	2
#2620×C₁₃₉	2
#2502×C₁₃₉	2
#2501×C₁₃₉	2
#2432×C₁₃₉	2
#2431×C₁₃₉	2
#2297×C₁₃₉	2
#37296	139

Subgroups — C139×#37296 #48031892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37296 #48031892