Subgroups — C₁₃₉×#37134 #48031730

Order 35584.

2066 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2855×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2804×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2784×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2780×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2748×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2732×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2692×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2683×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2627×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2437×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2437×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2308×C₁₃₉	C₂	1	2	yes	maximal
13	C₂×#390×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
19	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
21	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
24	#400×C₁₃₉	C₂²	1	2	yes	complemented
25	#400×C₁₃₉	C₂²	1	2	yes	complemented
26	#399×C₁₃₉	C₂²	1	4	yes	complemented
27	#399×C₁₃₉	C₂²	1	4	yes	complemented
28	#398×C₁₃₉	C₂²	1	4	yes	complemented
29	#398×C₁₃₉	C₂²	1	4	yes	complemented
30	#396×C₁₃₉	C₂²	1	4	yes	complemented
31	#396×C₁₃₉	C₂²	1	4	yes	complemented
32	#396×C₁₃₉	C₂²	1	4	yes	complemented
33	#396×C₁₃₉	C₂²	1	4	yes	complemented
34	#395×C₁₃₉	C₂²	1	2	yes	complemented
35	#395×C₁₃₉	C₂²	1	2	yes	complemented
36	#393×C₁₃₉	C₂²	1	4	yes	complemented
37	#393×C₁₃₉	C₂²	1	4	yes	complemented
38	#391×C₁₃₉	C₂²	1	2	yes	complemented
39	#391×C₁₃₉	C₂²	1	2	yes	complemented
40	#390×C₁₃₉	C₂²	1	4	yes	—
41	#390×C₁₃₉	C₂²	1	1	yes	characteristic
42	#390×C₁₃₉	C₂²	1	1	yes	characteristic
43	#390×C₁₃₉	C₂²	1	1	yes	characteristic
44	#390×C₁₃₉	C₂²	1	1	yes	characteristic
45	#389×C₁₃₉	C₂²	1	2	yes	complemented
46	#389×C₁₃₉	C₂²	1	2	yes	complemented
47	#387×C₁₃₉	C₂²	1	4	yes	complemented
48	#387×C₁₃₉	C₂²	1	4	yes	complemented
49	#386×C₁₃₉	C₂²	1	2	yes	—
50	#386×C₁₃₉	C₂²	1	4	yes	—
51	#386×C₁₃₉	C₂²	1	4	yes	—
52	#386×C₁₃₉	C₂²	1	2	yes	—
53	#386×C₁₃₉	C₂²	1	2	yes	—
54	#386×C₁₃₉	C₂²	1	2	yes	—
55	#385×C₁₃₉	C₂²	1	4	yes	—
56	#385×C₁₃₉	C₂²	1	4	yes	—
57	#385×C₁₃₉	C₂²	1	4	yes	complemented
58	#385×C₁₃₉	C₂²	1	4	yes	complemented
59	#385×C₁₃₉	C₂²	1	4	yes	complemented
60	#385×C₁₃₉	C₂²	1	4	yes	complemented
61	#381×C₁₃₉	C₂²	1	4	yes	—
62	#380×C₁₃₉	C₂²	1	2	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	#380×C₁₃₉	C₂²	1	4	yes	complemented
65	#380×C₁₃₉	C₂²	1	4	yes	complemented
66	#379×C₁₃₉	C₂²	1	4	yes	—
67	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	—	4	2	no	—
71	C₂²×D₄×C₁₃₉	—	4	2	no	—
72	C₂²×D₄×C₁₃₉	Q₈	1	8	yes	complemented
73	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
83	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
84	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
85	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
86	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
102	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
103	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
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	2	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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×C₄²×C₁₃₉	—	4	2	no	—
118	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	#95×C₁₃₉	C₂³	1	2	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	2	yes	—
125	#95×C₁₃₉	C₂³	1	4	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	C₂⁴×C₁₃₉	—	2	4	no	—
133	C₂⁴×C₁₃₉	—	2	4	no	—
134	C₂⁴×C₁₃₉	—	4	4	no	—
135	C₂⁴×C₁₃₉	—	4	4	no	—
136	C₂⁴×C₁₃₉	C₂×Q₈	1	8	yes	—
137	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₃₉	C₂⁴	1	2	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×Q₈×C₁₃₉	—	4	4	no	—
144	C₂×Q₈×C₁₃₉	—	4	2	no	—
145	C₂×D₄×C₁₃₉	—	4	16	no	—
146	C₂×D₄×C₁₃₉	—	4	1	no	—
147	C₂×D₄×C₁₃₉	—	4	2	no	—
148	C₂×D₄×C₁₃₉	—	4	1	no	—
149	C₂×D₄×C₁₃₉	—	4	1	no	—
150	C₂×D₄×C₁₃₉	—	4	2	no	—
151	C₂×D₄×C₁₃₉	—	4	1	no	—
152	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
153	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
154	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₁₃₉	—	2	2	no	—
156	C₂²×C₄×C₁₃₉	—	2	2	no	—
157	C₂²×C₄×C₁₃₉	—	2	4	no	—
158	C₂²×C₄×C₁₃₉	—	2	4	no	—
159	C₂²×C₄×C₁₃₉	—	2	4	no	—
160	C₂²×C₄×C₁₃₉	—	4	2	no	—
161	C₂²×C₄×C₁₃₉	—	4	2	no	—
162	C₂²×C₄×C₁₃₉	—	4	4	no	—
163	C₂²×C₄×C₁₃₉	—	4	4	no	—
164	C₂²×C₄×C₁₃₉	—	4	2	no	—
165	C₂²×C₄×C₁₃₉	—	4	4	no	—
166	C₂²×C₄×C₁₃₉	—	4	4	no	—
167	C₂²×C₄×C₁₃₉	—	4	4	no	—
168	C₂²×C₄×C₁₃₉	—	4	4	no	—
169	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₄⋊C₄×C₁₃₉	—	2	8	no	—
181	C₄⋊C₄×C₁₃₉	—	2	4	no	—
182	C₄⋊C₄×C₁₃₉	—	4	1	no	—
183	C₄⋊C₄×C₁₃₉	—	4	2	no	—
184	C₄⋊C₄×C₁₃₉	—	4	1	no	—
185	C₄⋊C₄×C₁₃₉	—	4	2	no	—
186	C₄⋊C₄×C₁₃₉	—	4	4	no	—
187	C₄⋊C₄×C₁₃₉	—	4	2	no	—
188	C₄⋊C₄×C₁₃₉	—	4	4	no	—
189	C₄⋊C₄×C₁₃₉	—	4	2	no	—
190	C₄⋊C₄×C₁₃₉	—	4	4	no	—
191	C₄⋊C₄×C₁₃₉	—	4	4	no	—
192	C₄⋊C₄×C₁₃₉	—	4	4	no	—
193	C₄⋊C₄×C₁₃₉	—	4	4	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
197	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
198	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
200	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
201	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
202	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
203	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
204	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
205	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
206	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
207	C₄²×C₁₃₉	—	4	1	no	—
208	C₄²×C₁₃₉	—	4	2	no	—
209	C₄²×C₁₃₉	—	4	1	no	—
210	C₂³×C₁₃₉	—	2	2	no	—
211	C₂³×C₁₃₉	—	2	2	no	—
212	C₂³×C₁₃₉	—	2	4	no	—
213	C₂³×C₁₃₉	—	2	4	no	—
214	C₂³×C₁₃₉	—	2	2	no	—
215	C₂³×C₁₃₉	—	2	2	no	—
216	C₂³×C₁₃₉	—	2	2	no	—
217	C₂³×C₁₃₉	—	2	2	no	—
218	C₂³×C₁₃₉	—	2	4	no	—
219	C₂³×C₁₃₉	—	2	4	no	—
220	C₂³×C₁₃₉	—	2	16	no	—
221	C₂³×C₁₃₉	—	4	16	no	—
222	C₂³×C₁₃₉	—	8	8	no	—
223	C₂³×C₁₃₉	—	8	4	no	—
224	C₂³×C₁₃₉	—	8	4	no	—
225	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
226	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
227	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
228	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
229	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
230	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
231	Q₈×C₁₃₉	—	8	4	no	—
232	Q₈×C₁₃₉	—	8	4	no	—
233	D₄×C₁₃₉	—	4	4	no	—
234	D₄×C₁₃₉	—	4	8	no	—
235	D₄×C₁₃₉	—	4	4	no	—
236	C₂×C₄×C₁₃₉	—	2	8	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	1	no	—
239	C₂×C₄×C₁₃₉	—	2	1	no	—
240	C₂×C₄×C₁₃₉	—	2	1	no	—
241	C₂×C₄×C₁₃₉	—	2	1	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	2	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	2	4	no	—
246	C₂×C₄×C₁₃₉	—	2	4	no	—
247	C₂×C₄×C₁₃₉	—	2	4	no	—
248	C₂×C₄×C₁₃₉	—	2	4	no	—
249	C₂×C₄×C₁₃₉	—	2	4	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	4	no	—
252	C₂×C₄×C₁₃₉	—	2	4	no	—
253	C₂×C₄×C₁₃₉	—	2	4	no	—
254	C₂×C₄×C₁₃₉	—	2	4	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
262	C₂×C₄×C₁₃₉	—	4	8	no	—
263	C₂×C₄×C₁₃₉	—	8	4	no	—
264	C₂×C₄×C₁₃₉	—	8	8	no	—
265	C₂×C₄×C₁₃₉	—	8	4	no	—
266	C₂×C₄×C₁₃₉	—	8	4	no	—
267	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
268	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
269	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
270	C₂²×C₁₃₉	—	2	4	no	—
271	C₂²×C₁₃₉	—	2	4	no	—
272	C₂²×C₁₃₉	—	2	2	no	—
273	C₂²×C₁₃₉	—	2	2	no	—
274	C₂²×C₁₃₉	—	2	4	no	—
275	C₂²×C₁₃₉	—	2	4	no	—
276	C₂²×C₁₃₉	—	2	8	no	—
277	C₂²×C₁₃₉	—	2	8	no	—
278	C₂²×C₁₃₉	—	4	4	no	—
279	C₂²×C₁₃₉	—	4	4	no	—
280	C₂²×C₁₃₉	—	4	2	no	—
281	C₂²×C₁₃₉	—	4	2	no	—
282	C₂²×C₁₃₉	—	4	2	no	—
283	C₂²×C₁₃₉	—	4	2	no	—
284	C₂²×C₁₃₉	—	8	16	no	—
285	C₂²×C₁₃₉	#543	1	4	yes	—
286	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
287	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
290	C₂²×C₁₃₉	#585	1	2	yes	—
291	C₄×C₁₃₉	—	2	2	no	—
292	C₄×C₁₃₉	—	2	2	no	—
293	C₄×C₁₃₉	—	2	4	no	—
294	C₄×C₁₃₉	—	4	2	no	—
295	C₄×C₁₃₉	—	4	4	no	—
296	C₄×C₁₃₉	—	4	4	no	—
297	C₄×C₁₃₉	—	4	2	no	—
298	C₄×C₁₃₉	—	4	2	no	—
299	C₄×C₁₃₉	—	4	4	no	—
300	C₄×C₁₃₉	—	4	4	no	—
301	C₂×C₁₃₉	—	2	4	no	—
302	C₂×C₁₃₉	—	4	4	no	—
303	C₂×C₁₃₉	—	4	4	no	—
304	C₂×C₁₃₉	C₂×#543	1	1	yes	characteristic
305	C₂×C₁₃₉	#3501	1	2	yes	—
306	C₂×C₁₃₉	#3534	1	2	yes	—
307	C₂×C₁₃₉	#3543	1	1	yes	characteristic
308	C₂×C₁₃₉	#3545	1	1	yes	characteristic
309	#37134	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₁₃₉	#37134	1	1	yes	characteristic, direct product factor, Sylow
311	#2855	C₂×C₁₃₉	1	2	yes	complemented
312	#2804	C₂×C₁₃₉	1	1	yes	characteristic, complemented
313	#2784	C₂×C₁₃₉	1	2	yes	complemented
314	#2780	C₂×C₁₃₉	1	4	yes	complemented
315	#2748	C₂×C₁₃₉	1	2	yes	complemented
316	#2732	C₂×C₁₃₉	1	2	yes	complemented
317	#2692	C₂×C₁₃₉	1	4	yes	complemented
318	#2683	C₂×C₁₃₉	1	1	yes	characteristic, complemented
319	#2627	C₂×C₁₃₉	1	2	yes	complemented
320	#2437	C₂×C₁₃₉	1	4	yes	complemented
321	#2437	C₂×C₁₃₉	1	4	yes	complemented
322	#2308	C₂×C₁₃₉	1	2	yes	—
323	C₂×#390	C₂×C₁₃₉	1	1	yes	characteristic
324	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
325	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
327	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
328	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
329	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
333	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
334	#400	C₂²×C₁₃₉	1	2	yes	complemented
335	#400	C₂²×C₁₃₉	1	2	yes	complemented
336	#399	C₂²×C₁₃₉	1	4	yes	complemented
337	#399	C₂²×C₁₃₉	1	4	yes	complemented
338	#398	C₂²×C₁₃₉	1	4	yes	complemented
339	#398	C₂²×C₁₃₉	1	4	yes	complemented
340	#396	C₂²×C₁₃₉	1	4	yes	complemented
341	#396	C₂²×C₁₃₉	1	4	yes	complemented
342	#396	C₂²×C₁₃₉	1	4	yes	complemented
343	#396	C₂²×C₁₃₉	1	4	yes	complemented
344	#395	C₂²×C₁₃₉	1	2	yes	complemented
345	#395	C₂²×C₁₃₉	1	2	yes	complemented
346	#393	C₂²×C₁₃₉	1	4	yes	complemented
347	#393	C₂²×C₁₃₉	1	4	yes	complemented
348	#391	C₂²×C₁₃₉	1	2	yes	complemented
349	#391	C₂²×C₁₃₉	1	2	yes	complemented
350	#390	C₂²×C₁₃₉	1	1	yes	characteristic
351	#390	C₂²×C₁₃₉	1	4	yes	—
352	#390	C₂²×C₁₃₉	1	1	yes	characteristic
353	#390	C₂²×C₁₃₉	1	1	yes	characteristic
354	#390	C₂²×C₁₃₉	1	1	yes	characteristic
355	#389	C₂²×C₁₃₉	1	2	yes	complemented
356	#389	C₂²×C₁₃₉	1	2	yes	complemented
357	#387	C₂²×C₁₃₉	1	4	yes	complemented
358	#387	C₂²×C₁₃₉	1	4	yes	complemented
359	#386	C₂²×C₁₃₉	1	2	yes	—
360	#386	C₂²×C₁₃₉	1	2	yes	—
361	#386	C₂²×C₁₃₉	1	4	yes	—
362	#386	C₂²×C₁₃₉	1	4	yes	—
363	#386	C₂²×C₁₃₉	1	2	yes	—
364	#386	C₂²×C₁₃₉	1	2	yes	—
365	#385	C₂²×C₁₃₉	1	4	yes	—
366	#385	C₂²×C₁₃₉	1	4	yes	—
367	#385	C₂²×C₁₃₉	1	4	yes	complemented
368	#385	C₂²×C₁₃₉	1	4	yes	complemented
369	#385	C₂²×C₁₃₉	1	4	yes	complemented
370	#385	C₂²×C₁₃₉	1	4	yes	complemented
371	#381	C₂²×C₁₃₉	1	4	yes	—
372	#380	C₂²×C₁₃₉	1	2	yes	—
373	#380	C₂²×C₁₃₉	1	2	yes	—
374	#380	C₂²×C₁₃₉	1	4	yes	complemented
375	#380	C₂²×C₁₃₉	1	4	yes	complemented
376	#379	C₂²×C₁₃₉	1	4	yes	—
377	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
378	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
379	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
380	C₂²×D₄	—	4	2	no	—
381	C₂²×D₄	—	4	2	no	—
382	C₂²×D₄	Q₈×C₁₃₉	1	8	yes	complemented
383	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
385	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
389	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
390	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂²⋊Q₈	—	4	4	no	—
393	C₂²⋊Q₈	—	4	4	no	—
394	C₂²⋊Q₈	—	4	8	no	—
395	C₂²⋊Q₈	—	4	8	no	—
396	C₂×C₄⋊C₄	—	4	2	no	—
397	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
411	C₂×C₂²⋊C₄	—	4	8	no	—
412	C₂×C₂²⋊C₄	—	4	4	no	—
413	C₂×C₂²⋊C₄	—	4	4	no	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₄²	—	4	2	no	—
428	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
431	#95	C₂³×C₁₃₉	1	2	yes	—
432	#95	C₂³×C₁₃₉	1	4	yes	—
433	#95	C₂³×C₁₃₉	1	2	yes	—
434	#95	C₂³×C₁₃₉	1	4	yes	—
435	#95	C₂³×C₁₃₉	1	4	yes	—
436	#95	C₂³×C₁₃₉	1	4	yes	—
437	#95	C₂³×C₁₃₉	1	4	yes	—
438	#95	C₂³×C₁₃₉	1	4	yes	—
439	#95	C₂³×C₁₃₉	1	4	yes	—
440	#95	C₂³×C₁₃₉	1	4	yes	—
441	#95	C₂³×C₁₃₉	1	4	yes	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	4	4	no	—
445	C₂⁴	—	4	4	no	—
446	C₂⁴	C₂×Q₈×C₁₃₉	1	8	yes	—
447	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
448	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
449	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	4	2	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×D₄	—	4	16	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
463	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
464	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	4	4	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	4	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	4	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	4	no	—
513	C₂²⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	—	4	4	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₄²	—	4	1	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	1	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	16	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	8	8	no	—
533	C₂³	—	8	4	no	—
534	C₂³	—	8	4	no	—
535	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
536	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
537	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
538	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
539	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
540	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
541	Q₈	—	8	4	no	—
542	Q₈	—	8	4	no	—
543	D₄	—	4	4	no	—
544	D₄	—	4	8	no	—
545	D₄	—	4	4	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	8	4	no	—
574	C₂×C₄	—	8	8	no	—
575	C₂×C₄	—	8	4	no	—
576	C₂×C₄	—	8	4	no	—
577	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
578	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
579	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	4	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	8	16	no	—
595	C₂²	#543×C₁₃₉	1	4	yes	—
596	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
597	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
598	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
599	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
600	C₂²	#585×C₁₃₉	1	2	yes	—
601	C₄	—	2	4	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	4	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	4	no	—
611	C₂	—	2	4	no	—
612	C₂	—	4	4	no	—
613	C₂	—	4	4	no	—
614	C₂	C₂×#543×C₁₃₉	1	1	yes	characteristic
615	C₂	#3501×C₁₃₉	1	2	yes	—
616	C₂	#3534×C₁₃₉	1	2	yes	—
617	C₂	#3543×C₁₃₉	1	1	yes	characteristic
618	C₂	#3545×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
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. #2855×C₁₃₉	C₂	semidirect
2. #2804×C₁₃₉	C₂	semidirect
3. #2784×C₁₃₉	C₂	semidirect
4. #2780×C₁₃₉	C₂	semidirect
5. #2748×C₁₃₉	C₂	semidirect
6. #2732×C₁₃₉	C₂	semidirect
7. #2692×C₁₃₉	C₂	semidirect
8. #2683×C₁₃₉	C₂	semidirect
9. #2627×C₁₃₉	C₂	semidirect
10. #2437×C₁₃₉	C₂	semidirect
11. #2437×C₁₃₉	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
18. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
24. #400×C₁₃₉	C₂²	semidirect
25. #400×C₁₃₉	C₂²	semidirect
26. #399×C₁₃₉	C₂²	semidirect
27. #399×C₁₃₉	C₂²	semidirect
28. #398×C₁₃₉	C₂²	semidirect
29. #398×C₁₃₉	C₂²	semidirect
30. #396×C₁₃₉	C₂²	semidirect
31. #396×C₁₃₉	C₂²	semidirect
32. #396×C₁₃₉	C₂²	semidirect
33. #396×C₁₃₉	C₂²	semidirect
34. #395×C₁₃₉	C₂²	semidirect
35. #395×C₁₃₉	C₂²	semidirect
36. #393×C₁₃₉	C₂²	semidirect
37. #393×C₁₃₉	C₂²	semidirect
38. #391×C₁₃₉	C₂²	semidirect
39. #391×C₁₃₉	C₂²	semidirect
45. #389×C₁₃₉	C₂²	semidirect
46. #389×C₁₃₉	C₂²	semidirect
47. #387×C₁₃₉	C₂²	semidirect
48. #387×C₁₃₉	C₂²	semidirect
57. #385×C₁₃₉	C₂²	semidirect
58. #385×C₁₃₉	C₂²	semidirect
59. #385×C₁₃₉	C₂²	semidirect
60. #385×C₁₃₉	C₂²	semidirect
64. #380×C₁₃₉	C₂²	semidirect
65. #380×C₁₃₉	C₂²	semidirect
72. C₂²×D₄×C₁₃₉	Q₈	semidirect
309. #37134	C₁₃₉	direct (N × H)
310. C₁₃₉	#37134	direct (N × H)
311. #2855	C₂×C₁₃₉	semidirect
312. #2804	C₂×C₁₃₉	semidirect
313. #2784	C₂×C₁₃₉	semidirect
314. #2780	C₂×C₁₃₉	semidirect
315. #2748	C₂×C₁₃₉	semidirect
316. #2732	C₂×C₁₃₉	semidirect
317. #2692	C₂×C₁₃₉	semidirect
318. #2683	C₂×C₁₃₉	semidirect
319. #2627	C₂×C₁₃₉	semidirect
320. #2437	C₂×C₁₃₉	semidirect
321. #2437	C₂×C₁₃₉	semidirect
327. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
328. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
334. #400	C₂²×C₁₃₉	semidirect
335. #400	C₂²×C₁₃₉	semidirect
336. #399	C₂²×C₁₃₉	semidirect
337. #399	C₂²×C₁₃₉	semidirect
338. #398	C₂²×C₁₃₉	semidirect
339. #398	C₂²×C₁₃₉	semidirect
340. #396	C₂²×C₁₃₉	semidirect
341. #396	C₂²×C₁₃₉	semidirect
342. #396	C₂²×C₁₃₉	semidirect
343. #396	C₂²×C₁₃₉	semidirect
344. #395	C₂²×C₁₃₉	semidirect
345. #395	C₂²×C₁₃₉	semidirect
346. #393	C₂²×C₁₃₉	semidirect
347. #393	C₂²×C₁₃₉	semidirect
348. #391	C₂²×C₁₃₉	semidirect
349. #391	C₂²×C₁₃₉	semidirect
355. #389	C₂²×C₁₃₉	semidirect
356. #389	C₂²×C₁₃₉	semidirect
357. #387	C₂²×C₁₃₉	semidirect
358. #387	C₂²×C₁₃₉	semidirect
367. #385	C₂²×C₁₃₉	semidirect
368. #385	C₂²×C₁₃₉	semidirect
369. #385	C₂²×C₁₃₉	semidirect
370. #385	C₂²×C₁₃₉	semidirect
374. #380	C₂²×C₁₃₉	semidirect
375. #380	C₂²×C₁₃₉	semidirect
382. C₂²×D₄	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2855×C₁₃₉	2
#2804×C₁₃₉	2
#2784×C₁₃₉	2
#2780×C₁₃₉	2
#2748×C₁₃₉	2
#2732×C₁₃₉	2
#2692×C₁₃₉	2
#2683×C₁₃₉	2
#2627×C₁₃₉	2
#2437×C₁₃₉	2
#2308×C₁₃₉	2
C₂×#390×C₁₃₉	2
#37134	139

Subgroups — C139×#37134 #48031730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37134 #48031730