Subgroups — C₁₃₉×#35673 #48030269

Order 35584.

2326 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2498×C₁₃₉	C₂	1	8	yes	maximal, complemented
4	#2448×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2446×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2423×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2421×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2311×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	#536×C₁₃₉	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
20	#519×C₁₃₉	—	2	8	no	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#400×C₁₃₉	C₂²	1	8	yes	—
30	#399×C₁₃₉	C₂²	1	8	yes	—
31	#398×C₁₃₉	C₂²	1	8	yes	—
32	#397×C₁₃₉	C₂²	1	8	yes	—
33	#391×C₁₃₉	C₂²	1	2	yes	—
34	#391×C₁₃₉	C₂²	1	2	yes	—
35	#391×C₁₃₉	C₂²	1	4	yes	—
36	#391×C₁₃₉	C₂²	1	2	yes	—
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#389×C₁₃₉	C₂²	1	4	yes	—
41	#389×C₁₃₉	C₂²	1	4	yes	—
42	#388×C₁₃₉	C₂²	1	8	yes	—
43	#388×C₁₃₉	C₂²	1	8	yes	—
44	#387×C₁₃₉	C₂²	1	8	yes	—
45	#387×C₁₃₉	C₂²	1	8	yes	—
46	#386×C₁₃₉	C₂²	1	4	yes	—
47	#386×C₁₃₉	C₂²	1	4	yes	—
48	#384×C₁₃₉	C₂²	1	2	yes	—
49	#382×C₁₃₉	C₂²	1	2	yes	—
50	#380×C₁₃₉	C₂²	1	4	yes	—
51	#380×C₁₃₉	C₂²	1	4	yes	—
52	#380×C₁₃₉	C₂²	1	4	yes	—
53	C₄×C₄⋊C₄×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×#95×C₁₃₉	C₂²	1	4	yes	—
57	C₂×#41×C₁₃₉	—	2	4	no	—
58	C₂×#41×C₁₃₉	—	2	4	no	—
59	C₂×#41×C₁₃₉	—	2	4	no	—
60	C₂²×Q₈×C₁₃₉	—	2	4	no	—
61	C₂²×Q₈×C₁₃₉	—	2	4	no	—
62	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	—
63	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₉	C₂³	1	2	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	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
74	#124×C₁₃₉	—	2	8	no	—
75	#123×C₁₃₉	—	2	16	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
77	C₄×Q₈×C₁₃₉	—	2	16	no	—
78	C₄×Q₈×C₁₃₉	—	2	16	no	—
79	#117×C₁₃₉	—	2	16	no	—
80	#117×C₁₃₉	—	2	4	no	—
81	#117×C₁₃₉	—	2	4	no	—
82	#117×C₁₃₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
101	C₂×C₄²×C₁₃₉	—	2	4	no	—
102	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
108	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
109	#95×C₁₃₉	C₂³	1	4	yes	—
110	#95×C₁₃₉	C₂³	1	8	yes	—
111	#95×C₁₃₉	C₂³	1	8	yes	—
112	#95×C₁₃₉	C₂³	1	4	yes	—
113	#95×C₁₃₉	C₂³	1	8	yes	—
114	#95×C₁₃₉	C₂³	1	8	yes	—
115	#95×C₁₃₉	C₂³	1	4	yes	—
116	#95×C₁₃₉	C₂³	1	4	yes	—
117	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
118	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
119	#41×C₁₃₉	—	4	16	no	—
120	C₂×Q₈×C₁₃₉	—	2	32	no	—
121	C₂×Q₈×C₁₃₉	—	2	2	no	—
122	C₂×Q₈×C₁₃₉	—	2	4	no	—
123	C₂×Q₈×C₁₃₉	—	2	4	no	—
124	C₂×Q₈×C₁₃₉	—	2	4	no	—
125	C₂×Q₈×C₁₃₉	—	2	4	no	—
126	C₂×Q₈×C₁₃₉	—	2	2	no	—
127	C₂×Q₈×C₁₃₉	—	2	2	no	—
128	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
129	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
130	C₂×D₄×C₁₃₉	—	2	4	no	—
131	C₂×D₄×C₁₃₉	—	2	4	no	—
132	C₂×D₄×C₁₃₉	—	2	4	no	—
133	C₂×D₄×C₁₃₉	—	2	2	no	—
134	C₂×D₄×C₁₃₉	—	2	2	no	—
135	C₂×D₄×C₁₃₉	—	2	2	no	—
136	C₂²×C₄×C₁₃₉	—	2	4	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	4	no	—
142	C₂²×C₄×C₁₃₉	—	2	4	no	—
143	C₂²×C₄×C₁₃₉	—	2	4	no	—
144	C₂²×C₄×C₁₃₉	—	4	2	no	—
145	C₂²×C₄×C₁₃₉	—	4	4	no	—
146	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
147	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
149	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
150	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₁₃₉	—	2	16	no	—
161	C₄⋊C₄×C₁₃₉	—	2	4	no	—
162	C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₄⋊C₄×C₁₃₉	—	2	4	no	—
164	C₄⋊C₄×C₁₃₉	—	2	16	no	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₄⋊C₄×C₁₃₉	—	2	8	no	—
168	C₄⋊C₄×C₁₃₉	—	4	4	no	—
169	C₄⋊C₄×C₁₃₉	—	4	8	no	—
170	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
174	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
176	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
177	C₄²×C₁₃₉	—	2	16	no	—
178	C₄²×C₁₃₉	—	2	4	no	—
179	C₄²×C₁₃₉	—	2	4	no	—
180	C₄²×C₁₃₉	—	2	4	no	—
181	C₄²×C₁₃₉	—	2	2	no	—
182	C₄²×C₁₃₉	—	2	4	no	—
183	C₄²×C₁₃₉	—	2	2	no	—
184	C₂³×C₁₃₉	—	2	2	no	—
185	C₂³×C₁₃₉	—	2	2	no	—
186	C₂³×C₁₃₉	—	2	2	no	—
187	C₂³×C₁₃₉	—	2	2	no	—
188	C₂³×C₁₃₉	—	2	2	no	—
189	C₂³×C₁₃₉	—	2	4	no	—
190	C₂³×C₁₃₉	—	2	4	no	—
191	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
192	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
193	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
194	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
195	Q₈×C₁₃₉	—	2	16	no	—
196	Q₈×C₁₃₉	—	2	16	no	—
197	Q₈×C₁₃₉	—	4	4	no	—
198	D₄×C₁₃₉	—	4	8	no	—
199	D₄×C₁₃₉	—	4	4	no	—
200	C₂×C₄×C₁₃₉	—	2	16	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	2	no	—
205	C₂×C₄×C₁₃₉	—	2	4	no	—
206	C₂×C₄×C₁₃₉	—	2	4	no	—
207	C₂×C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₄×C₁₃₉	—	2	2	no	—
209	C₂×C₄×C₁₃₉	—	2	2	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	2	4	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	4	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	4	no	—
220	C₂×C₄×C₁₃₉	—	2	8	no	—
221	C₂×C₄×C₁₃₉	—	2	4	no	—
222	C₂×C₄×C₁₃₉	—	4	8	no	—
223	C₂×C₄×C₁₃₉	—	4	8	no	—
224	C₂×C₄×C₁₃₉	—	8	4	no	—
225	C₂×C₄×C₁₃₉	#123	1	16	yes	—
226	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
227	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
230	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
231	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
232	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
233	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
234	C₂²×C₁₃₉	—	2	4	no	—
235	C₂²×C₁₃₉	—	2	4	no	—
236	C₂²×C₁₃₉	—	2	2	no	—
237	C₂²×C₁₃₉	—	2	2	no	—
238	C₂²×C₁₃₉	—	4	2	no	—
239	C₂²×C₁₃₉	—	4	4	no	—
240	C₂²×C₁₃₉	—	4	4	no	—
241	C₂²×C₁₃₉	—	4	2	no	—
242	C₂²×C₁₃₉	—	4	2	no	—
243	C₂²×C₁₃₉	C₂×#123	1	4	yes	—
244	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
245	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
246	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
247	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
248	C₂²×C₁₃₉	#585	1	2	yes	—
249	C₄×C₁₃₉	—	2	8	no	—
250	C₄×C₁₃₉	—	2	4	no	—
251	C₄×C₁₃₉	—	4	2	no	—
252	C₄×C₁₃₉	—	4	2	no	—
253	C₄×C₁₃₉	—	4	4	no	—
254	C₄×C₁₃₉	—	4	4	no	—
255	C₄×C₁₃₉	—	4	4	no	—
256	C₄×C₁₃₉	—	4	4	no	—
257	C₄×C₁₃₉	C₂×#123	1	4	yes	—
258	C₄×C₁₃₉	C₂×#123	1	4	yes	—
259	C₂×C₁₃₉	—	2	4	no	—
260	C₂×C₁₃₉	—	8	2	no	—
261	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
262	C₂×C₁₃₉	#3495	1	2	yes	—
263	C₂×C₁₃₉	#3497	1	2	yes	—
264	C₂×C₁₃₉	#3509	1	1	yes	characteristic
265	C₂×C₁₃₉	#3510	1	1	yes	characteristic
266	#35673	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₁₃₉	#35673	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic
269	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
270	#2498	C₂×C₁₃₉	1	8	yes	complemented
271	#2448	C₂×C₁₃₉	1	4	yes	complemented
272	#2446	C₂×C₁₃₉	1	4	yes	complemented
273	#2423	C₂×C₁₃₉	1	4	yes	complemented
274	#2421	C₂×C₁₃₉	1	4	yes	complemented
275	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	#2311	C₂×C₁₃₉	1	1	yes	characteristic
277	#2297	C₂×C₁₃₉	1	1	yes	characteristic
278	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
279	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
280	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
281	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
282	#536	—	2	8	no	—
283	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
284	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
285	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
286	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
287	#519	—	2	8	no	—
288	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
289	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
290	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
291	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
293	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
294	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
295	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
296	#400	C₂²×C₁₃₉	1	8	yes	—
297	#399	C₂²×C₁₃₉	1	8	yes	—
298	#398	C₂²×C₁₃₉	1	8	yes	—
299	#397	C₂²×C₁₃₉	1	8	yes	—
300	#391	C₂²×C₁₃₉	1	2	yes	—
301	#391	C₂²×C₁₃₉	1	2	yes	—
302	#391	C₂²×C₁₃₉	1	2	yes	—
303	#391	C₂²×C₁₃₉	1	2	yes	—
304	#391	C₂²×C₁₃₉	1	4	yes	—
305	#390	C₂²×C₁₃₉	1	2	yes	—
306	#390	C₂²×C₁₃₉	1	2	yes	—
307	#389	C₂²×C₁₃₉	1	4	yes	—
308	#389	C₂²×C₁₃₉	1	4	yes	—
309	#388	C₂²×C₁₃₉	1	8	yes	—
310	#388	C₂²×C₁₃₉	1	8	yes	—
311	#387	C₂²×C₁₃₉	1	8	yes	—
312	#387	C₂²×C₁₃₉	1	8	yes	—
313	#386	C₂²×C₁₃₉	1	4	yes	—
314	#386	C₂²×C₁₃₉	1	4	yes	—
315	#384	C₂²×C₁₃₉	1	2	yes	—
316	#382	C₂²×C₁₃₉	1	2	yes	—
317	#380	C₂²×C₁₃₉	1	4	yes	—
318	#380	C₂²×C₁₃₉	1	4	yes	—
319	#380	C₂²×C₁₃₉	1	4	yes	—
320	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
321	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
323	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
324	C₂×#41	—	2	4	no	—
325	C₂×#41	—	2	4	no	—
326	C₂×#41	—	2	4	no	—
327	C₂²×Q₈	—	2	4	no	—
328	C₂²×Q₈	—	2	4	no	—
329	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	—
330	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
331	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
332	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
334	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
336	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
340	C₄⋊Q₈	—	2	8	no	—
341	#124	—	2	8	no	—
342	#123	—	2	16	no	—
343	C₂²⋊Q₈	—	2	16	no	—
344	C₄×Q₈	—	2	16	no	—
345	C₄×Q₈	—	2	16	no	—
346	#117	—	2	16	no	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	#117	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
368	C₂×C₄²	—	2	4	no	—
369	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
370	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
371	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
372	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
373	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
376	#95	C₂³×C₁₃₉	1	8	yes	—
377	#95	C₂³×C₁₃₉	1	8	yes	—
378	#95	C₂³×C₁₃₉	1	4	yes	—
379	#95	C₂³×C₁₃₉	1	4	yes	—
380	#95	C₂³×C₁₃₉	1	4	yes	—
381	#95	C₂³×C₁₃₉	1	4	yes	—
382	#95	C₂³×C₁₃₉	1	8	yes	—
383	#95	C₂³×C₁₃₉	1	8	yes	—
384	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
385	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
386	#41	—	4	16	no	—
387	C₂×Q₈	—	2	32	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
396	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
415	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
416	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
427	C₄⋊C₄	—	2	16	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	16	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	4	4	no	—
436	C₄⋊C₄	—	4	8	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	16	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	4	8	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₄²	—	2	16	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
459	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
460	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
461	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
462	Q₈	—	2	16	no	—
463	Q₈	—	2	16	no	—
464	Q₈	—	4	4	no	—
465	D₄	—	4	8	no	—
466	D₄	—	4	4	no	—
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	#123×C₁₃₉	1	16	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
496	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
497	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
498	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
499	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
500	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	C₂×#123×C₁₃₉	1	4	yes	—
511	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
512	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
513	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
514	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
515	C₂²	#585×C₁₃₉	1	2	yes	—
516	C₄	—	2	8	no	—
517	C₄	—	2	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	C₂×#123×C₁₃₉	1	4	yes	—
525	C₄	C₂×#123×C₁₃₉	1	4	yes	—
526	C₂	—	2	4	no	—
527	C₂	—	8	2	no	—
528	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
529	C₂	#3495×C₁₃₉	1	2	yes	—
530	C₂	#3497×C₁₃₉	1	2	yes	—
531	C₂	#3509×C₁₃₉	1	1	yes	characteristic
532	C₂	#3510×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×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
2. C₂×#519×C₁₃₉	C₂	semidirect
3. #2498×C₁₃₉	C₂	semidirect
4. #2448×C₁₃₉	C₂	semidirect
5. #2446×C₁₃₉	C₂	semidirect
6. #2423×C₁₃₉	C₂	semidirect
7. #2421×C₁₃₉	C₂	semidirect
8. #2316×C₁₃₉	C₂	semidirect
11. C₂×#391×C₁₃₉	C₂	semidirect
12. #2285×C₁₃₉	C₂	semidirect
266. #35673	C₁₃₉	direct (N × H)
267. C₁₃₉	#35673	direct (N × H)
269. C₂×#519	C₂×C₁₃₉	semidirect
270. #2498	C₂×C₁₃₉	semidirect
271. #2448	C₂×C₁₃₉	semidirect
272. #2446	C₂×C₁₃₉	semidirect
273. #2423	C₂×C₁₃₉	semidirect
274. #2421	C₂×C₁₃₉	semidirect
275. #2316	C₂×C₁₃₉	semidirect
278. C₂×#391	C₂×C₁₃₉	semidirect
279. #2285	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2498×C₁₃₉	2
#2448×C₁₃₉	2
#2446×C₁₃₉	2
#2423×C₁₃₉	2
#2421×C₁₃₉	2
#2316×C₁₃₉	2
#2311×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#391×C₁₃₉	2
#2285×C₁₃₉	2
#35673	139

Subgroups — C139×#35673 #48030269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35673 #48030269