Subgroups — C₁₃₉×#35667 #48030263

Order 35584.

2866 conjugacy classes of subgroups.

The subgroup lattice has 510 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×#536×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2546×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2545×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2429×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2413×C₁₃₉	C₂	1	8	yes	maximal, complemented
9	#2310×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	#536×C₁₃₉	—	2	8	no	—
16	#536×C₁₃₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
28	#519×C₁₃₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
36	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
37	#398×C₁₃₉	C₂²	1	16	yes	—
38	#396×C₁₃₉	C₂²	1	16	yes	—
39	#391×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	16	yes	—
44	#389×C₁₃₉	C₂²	1	4	yes	—
45	#388×C₁₃₉	C₂²	1	16	yes	—
46	#386×C₁₃₉	C₂²	1	4	yes	—
47	#385×C₁₃₉	C₂²	1	4	yes	—
48	#381×C₁₃₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
50	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
51	C₂×#41×C₁₃₉	—	2	4	no	—
52	C₂×#41×C₁₃₉	—	2	4	no	—
53	C₂×#41×C₁₃₉	—	2	4	no	—
54	C₂²×Q₈×C₁₃₉	—	2	4	no	—
55	C₂²×Q₈×C₁₃₉	—	2	4	no	—
56	C₂²×Q₈×C₁₃₉	—	2	4	no	—
57	C₂²×Q₈×C₁₃₉	—	2	4	no	—
58	C₂²×Q₈×C₁₃₉	—	2	4	no	—
59	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	—
60	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
61	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
64	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
72	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
73	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
74	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
75	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
76	#124×C₁₃₉	—	2	8	no	—
77	#124×C₁₃₉	—	2	8	no	—
78	#123×C₁₃₉	—	2	16	no	—
79	#123×C₁₃₉	—	2	16	no	—
80	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
82	C₄×Q₈×C₁₃₉	—	2	16	no	—
83	C₄×Q₈×C₁₃₉	—	2	16	no	—
84	#117×C₁₃₉	—	2	4	no	—
85	#117×C₁₃₉	—	2	4	no	—
86	#117×C₁₃₉	—	2	16	no	—
87	#117×C₁₃₉	D₄	1	8	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	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	2	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	2	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃₉	—	2	4	no	—
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	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
110	#95×C₁₃₉	C₂³	1	16	yes	—
111	#95×C₁₃₉	C₂³	1	8	yes	—
112	#95×C₁₃₉	C₂³	1	8	yes	—
113	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
114	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
115	#41×C₁₃₉	—	4	16	no	—
116	C₂×Q₈×C₁₃₉	—	2	32	no	—
117	C₂×Q₈×C₁₃₉	—	2	4	no	—
118	C₂×Q₈×C₁₃₉	—	2	4	no	—
119	C₂×Q₈×C₁₃₉	—	2	4	no	—
120	C₂×Q₈×C₁₃₉	—	2	4	no	—
121	C₂×Q₈×C₁₃₉	—	2	4	no	—
122	C₂×Q₈×C₁₃₉	—	2	4	no	—
123	C₂×Q₈×C₁₃₉	—	2	2	no	—
124	C₂×Q₈×C₁₃₉	—	2	2	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	—	2	4	no	—
129	C₂×Q₈×C₁₃₉	—	2	2	no	—
130	C₂×Q₈×C₁₃₉	—	4	16	no	—
131	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
132	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
133	C₂×D₄×C₁₃₉	—	2	4	no	—
134	C₂×D₄×C₁₃₉	—	2	4	no	—
135	C₂×D₄×C₁₃₉	—	2	4	no	—
136	C₂×D₄×C₁₃₉	—	2	2	no	—
137	C₂×D₄×C₁₃₉	—	2	2	no	—
138	C₂×D₄×C₁₃₉	—	2	2	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	8	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	C₂×D₄	1	8	yes	—
150	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₃₉	#41	1	4	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	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
162	C₄⋊C₄×C₁₃₉	—	2	32	no	—
163	C₄⋊C₄×C₁₃₉	—	2	16	no	—
164	C₄⋊C₄×C₁₃₉	—	2	4	no	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	16	no	—
167	C₄⋊C₄×C₁₃₉	—	2	16	no	—
168	C₄⋊C₄×C₁₃₉	—	2	16	no	—
169	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
170	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
174	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
175	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
176	C₄²×C₁₃₉	—	2	4	no	—
177	C₄²×C₁₃₉	—	2	4	no	—
178	C₄²×C₁₃₉	—	2	16	no	—
179	C₄²×C₁₃₉	—	2	4	no	—
180	C₄²×C₁₃₉	—	2	4	no	—
181	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
182	C₂³×C₁₃₉	—	2	4	no	—
183	C₂³×C₁₃₉	—	2	2	no	—
184	C₂³×C₁₃₉	—	2	2	no	—
185	C₂³×C₁₃₉	—	2	2	no	—
186	C₂³×C₁₃₉	—	2	8	no	—
187	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
188	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
189	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
190	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
191	Q₈×C₁₃₉	—	2	16	no	—
192	Q₈×C₁₃₉	—	2	16	no	—
193	Q₈×C₁₃₉	—	4	8	no	—
194	Q₈×C₁₃₉	—	4	8	no	—
195	Q₈×C₁₃₉	—	4	4	no	—
196	D₄×C₁₃₉	—	4	8	no	—
197	D₄×C₁₃₉	—	4	4	no	—
198	C₂×C₄×C₁₃₉	—	2	16	no	—
199	C₂×C₄×C₁₃₉	—	2	16	no	—
200	C₂×C₄×C₁₃₉	—	2	4	no	—
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	8	no	—
204	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
213	C₂×C₄×C₁₃₉	—	2	8	no	—
214	C₂×C₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	4	8	no	—
216	C₂×C₄×C₁₃₉	—	4	8	no	—
217	C₂×C₄×C₁₃₉	#121	1	16	yes	—
218	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
219	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
220	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	8	yes	—
227	C₂²×C₁₃₉	—	2	4	no	—
228	C₂²×C₁₃₉	—	2	4	no	—
229	C₂²×C₁₃₉	—	2	4	no	—
230	C₂²×C₁₃₉	—	4	2	no	—
231	C₂²×C₁₃₉	—	4	4	no	—
232	C₂²×C₁₃₉	—	4	4	no	—
233	C₂²×C₁₃₉	—	4	4	no	—
234	C₂²×C₁₃₉	C₂×#121	1	4	yes	—
235	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
236	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
237	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
238	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	4	yes	—
239	C₄×C₁₃₉	—	2	8	no	—
240	C₄×C₁₃₉	—	2	8	no	—
241	C₄×C₁₃₉	—	2	8	no	—
242	C₄×C₁₃₉	—	4	2	no	—
243	C₄×C₁₃₉	—	4	4	no	—
244	C₄×C₁₃₉	—	4	4	no	—
245	C₄×C₁₃₉	—	4	4	no	—
246	C₄×C₁₃₉	C₂×#121	1	4	yes	—
247	C₄×C₁₃₉	C₂×#121	1	4	yes	—
248	C₂×C₁₃₉	—	2	4	no	—
249	C₂×C₁₃₉	—	8	2	no	—
250	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
251	C₂×C₁₃₉	#3486	1	2	yes	—
252	C₂×C₁₃₉	#3499	1	2	yes	—
253	C₂×C₁₃₉	#3509	1	2	yes	—
254	#35667	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₁₃₉	#35667	1	1	yes	characteristic, direct product factor, Sylow
256	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic
257	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic
258	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
259	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
260	#2546	C₂×C₁₃₉	1	4	yes	complemented
261	#2545	C₂×C₁₃₉	1	4	yes	complemented
262	#2429	C₂×C₁₃₉	1	8	yes	complemented
263	#2413	C₂×C₁₃₉	1	8	yes	complemented
264	#2310	C₂×C₁₃₉	1	1	yes	characteristic, complemented
265	#2297	C₂×C₁₃₉	1	1	yes	characteristic
266	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
267	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
268	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
270	#536	—	2	8	no	—
271	#536	—	2	8	no	—
272	C₂×C₄⋊Q₈	—	2	8	no	—
273	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
274	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
277	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
278	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
279	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
280	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
281	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
282	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
283	#519	—	2	8	no	—
284	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
285	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
286	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
289	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
291	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
292	#398	C₂²×C₁₃₉	1	16	yes	—
293	#396	C₂²×C₁₃₉	1	16	yes	—
294	#391	C₂²×C₁₃₉	1	4	yes	—
295	#391	C₂²×C₁₃₉	1	4	yes	—
296	#391	C₂²×C₁₃₉	1	2	yes	—
297	#390	C₂²×C₁₃₉	1	2	yes	—
298	#389	C₂²×C₁₃₉	1	16	yes	—
299	#389	C₂²×C₁₃₉	1	4	yes	—
300	#388	C₂²×C₁₃₉	1	16	yes	—
301	#386	C₂²×C₁₃₉	1	4	yes	—
302	#385	C₂²×C₁₃₉	1	4	yes	—
303	#381	C₂²×C₁₃₉	1	4	yes	—
304	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
305	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
306	C₂×#41	—	2	4	no	—
307	C₂×#41	—	2	4	no	—
308	C₂×#41	—	2	4	no	—
309	C₂²×Q₈	—	2	4	no	—
310	C₂²×Q₈	—	2	4	no	—
311	C₂²×Q₈	—	2	4	no	—
312	C₂²×Q₈	—	2	4	no	—
313	C₂²×Q₈	—	2	4	no	—
314	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	—
315	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
317	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
318	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
319	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
320	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
321	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	16	no	—
328	C₄⋊Q₈	—	2	16	no	—
329	C₄⋊Q₈	—	2	8	no	—
330	C₄⋊Q₈	—	2	8	no	—
331	#124	—	2	8	no	—
332	#124	—	2	8	no	—
333	#123	—	2	16	no	—
334	#123	—	2	16	no	—
335	C₂²⋊Q₈	—	2	16	no	—
336	C₂²⋊Q₈	—	2	16	no	—
337	C₄×Q₈	—	2	16	no	—
338	C₄×Q₈	—	2	16	no	—
339	#117	—	2	4	no	—
340	#117	—	2	4	no	—
341	#117	—	2	16	no	—
342	#117	D₄×C₁₃₉	1	8	yes	—
343	C₂×C₄⋊C₄	—	2	16	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
358	C₂×C₄²	—	2	4	no	—
359	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
360	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
361	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
362	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
363	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
365	#95	C₂³×C₁₃₉	1	8	yes	—
366	#95	C₂³×C₁₃₉	1	8	yes	—
367	#95	C₂³×C₁₃₉	1	16	yes	—
368	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
369	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
370	#41	—	4	16	no	—
371	C₂×Q₈	—	2	32	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	4	16	no	—
386	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
387	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	4	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
407	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
417	C₄⋊C₄	—	2	32	no	—
418	C₄⋊C₄	—	2	16	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	16	no	—
422	C₄⋊C₄	—	2	16	no	—
423	C₄⋊C₄	—	2	16	no	—
424	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	16	no	—
428	C₂²⋊C₄	—	2	16	no	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	16	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	8	no	—
442	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
443	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
444	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
445	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
446	Q₈	—	2	16	no	—
447	Q₈	—	2	16	no	—
448	Q₈	—	4	8	no	—
449	Q₈	—	4	8	no	—
450	Q₈	—	4	4	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	4	no	—
453	C₂×C₄	—	2	16	no	—
454	C₂×C₄	—	2	16	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	#121×C₁₃₉	1	16	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
479	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
480	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
481	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	8	yes	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	C₂×#121×C₁₃₉	1	4	yes	—
490	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
491	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
492	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
493	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	4	yes	—
494	C₄	—	2	8	no	—
495	C₄	—	2	8	no	—
496	C₄	—	2	8	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	C₂×#121×C₁₃₉	1	4	yes	—
502	C₄	C₂×#121×C₁₃₉	1	4	yes	—
503	C₂	—	2	4	no	—
504	C₂	—	8	2	no	—
505	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
506	C₂	#3486×C₁₃₉	1	2	yes	—
507	C₂	#3499×C₁₃₉	1	2	yes	—
508	C₂	#3509×C₁₃₉	1	2	yes	—

	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
3. C₂²×C₄⋊Q₈×C₁₃₉	C₂	semidirect
4. C₂×#519×C₁₃₉	C₂	semidirect
5. #2546×C₁₃₉	C₂	semidirect
6. #2545×C₁₃₉	C₂	semidirect
7. #2429×C₁₃₉	C₂	semidirect
8. #2413×C₁₃₉	C₂	semidirect
9. #2310×C₁₃₉	C₂	semidirect
11. #2296×C₁₃₉	C₂	semidirect
254. #35667	C₁₃₉	direct (N × H)
255. C₁₃₉	#35667	direct (N × H)
258. C₂²×C₄⋊Q₈	C₂×C₁₃₉	semidirect
259. C₂×#519	C₂×C₁₃₉	semidirect
260. #2546	C₂×C₁₃₉	semidirect
261. #2545	C₂×C₁₃₉	semidirect
262. #2429	C₂×C₁₃₉	semidirect
263. #2413	C₂×C₁₃₉	semidirect
264. #2310	C₂×C₁₃₉	semidirect
266. #2296	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
C₂²×C₄⋊Q₈×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2546×C₁₃₉	2
#2545×C₁₃₉	2
#2429×C₁₃₉	2
#2413×C₁₃₉	2
#2310×C₁₃₉	2
#2297×C₁₃₉	2
#2296×C₁₃₉	2
#35667	139

Subgroups — C139×#35667 #48030263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35667 #48030263