Subgroups — C₁₃₉×#36151 #48030747

Order 35584.

2226 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2536×C₁₃₉	C₂	1	2	yes	maximal
5	#2489×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2453×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2421×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2415×C₁₃₉	C₂	1	4	yes	maximal
9	#2362×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2351×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#533×C₁₃₉	—	2	16	no	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
27	#400×C₁₃₉	C₂²	1	8	yes	—
28	#398×C₁₃₉	C₂²	1	4	yes	—
29	#397×C₁₃₉	C₂²	1	8	yes	—
30	#394×C₁₃₉	C₂²	1	4	yes	—
31	#391×C₁₃₉	C₂²	1	2	yes	—
32	#391×C₁₃₉	C₂²	1	4	yes	—
33	#391×C₁₃₉	C₂²	1	4	yes	—
34	#391×C₁₃₉	C₂²	1	4	yes	—
35	#389×C₁₃₉	C₂²	1	4	yes	—
36	#389×C₁₃₉	C₂²	1	4	yes	—
37	#389×C₁₃₉	C₂²	1	4	yes	—
38	#389×C₁₃₉	C₂²	1	8	yes	—
39	#388×C₁₃₉	C₂²	1	8	yes	—
40	#388×C₁₃₉	C₂²	1	8	yes	—
41	#387×C₁₃₉	C₂²	1	8	yes	—
42	#384×C₁₃₉	C₂²	1	1	yes	characteristic
43	#382×C₁₃₉	C₂²	1	2	yes	—
44	#382×C₁₃₉	C₂²	1	2	yes	—
45	#382×C₁₃₉	C₂²	1	4	yes	—
46	#380×C₁₃₉	C₂²	1	4	yes	—
47	#380×C₁₃₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
54	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
57	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
63	C₄⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
64	#125×C₁₃₉	—	2	16	no	—
65	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
66	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
67	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
68	C₄×Q₈×C₁₃₉	—	2	16	no	—
69	C₄×Q₈×C₁₃₉	—	2	16	no	—
70	C₄×Q₈×C₁₃₉	—	2	8	no	—
71	C₄×D₄×C₁₃₉	—	2	8	no	—
72	C₄×D₄×C₁₃₉	—	2	4	no	—
73	#117×C₁₃₉	—	2	16	no	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃₉	—	2	8	no	—
91	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
101	#95×C₁₃₉	C₂³	1	8	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	4	yes	—
106	#95×C₁₃₉	C₂³	1	2	yes	—
107	#95×C₁₃₉	C₂³	1	1	yes	characteristic
108	#95×C₁₃₉	C₂³	1	1	yes	characteristic
109	#95×C₁₃₉	C₂³	1	2	yes	—
110	#95×C₁₃₉	C₂³	1	4	yes	—
111	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
112	C₂×Q₈×C₁₃₉	—	2	8	no	—
113	C₂×Q₈×C₁₃₉	—	2	4	no	—
114	C₂×Q₈×C₁₃₉	—	2	8	no	—
115	C₂×Q₈×C₁₃₉	—	2	4	no	—
116	C₂×Q₈×C₁₃₉	—	2	8	no	—
117	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
118	C₂×D₄×C₁₃₉	—	2	4	no	—
119	C₂×D₄×C₁₃₉	—	2	2	no	—
120	C₂²×C₄×C₁₃₉	—	2	4	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	4	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	2	4	no	—
125	C₂²×C₄×C₁₃₉	—	2	4	no	—
126	C₂²×C₄×C₁₃₉	—	2	4	no	—
127	C₂²×C₄×C₁₃₉	—	2	4	no	—
128	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
140	C₄⋊C₄×C₁₃₉	—	2	8	no	—
141	C₄⋊C₄×C₁₃₉	—	2	16	no	—
142	C₄⋊C₄×C₁₃₉	—	2	16	no	—
143	C₄⋊C₄×C₁₃₉	—	2	8	no	—
144	C₄⋊C₄×C₁₃₉	—	2	4	no	—
145	C₄⋊C₄×C₁₃₉	—	2	2	no	—
146	C₄⋊C₄×C₁₃₉	—	2	8	no	—
147	C₄⋊C₄×C₁₃₉	—	2	4	no	—
148	C₄⋊C₄×C₁₃₉	—	2	8	no	—
149	C₄⋊C₄×C₁₃₉	—	2	16	no	—
150	C₄⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
151	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
156	C₄²×C₁₃₉	—	2	4	no	—
157	C₄²×C₁₃₉	—	2	4	no	—
158	C₄²×C₁₃₉	—	2	4	no	—
159	C₄²×C₁₃₉	—	2	16	no	—
160	C₄²×C₁₃₉	—	2	4	no	—
161	C₄²×C₁₃₉	—	2	8	no	—
162	C₄²×C₁₃₉	—	2	4	no	—
163	C₄²×C₁₃₉	—	2	2	no	—
164	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
165	C₄²×C₁₃₉	#41	1	4	yes	—
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	2	no	—
168	C₂³×C₁₃₉	—	2	2	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	2	no	—
171	C₂³×C₁₃₉	—	2	2	no	—
172	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
173	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
174	Q₈×C₁₃₉	—	2	16	no	—
175	Q₈×C₁₃₉	—	4	16	no	—
176	D₄×C₁₃₉	—	2	8	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	4	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	4	no	—
183	C₂×C₄×C₁₃₉	—	2	16	no	—
184	C₂×C₄×C₁₃₉	—	2	2	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	8	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	4	no	—
189	C₂×C₄×C₁₃₉	—	2	8	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	8	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	2	no	—
196	C₂×C₄×C₁₃₉	—	2	2	no	—
197	C₂×C₄×C₁₃₉	—	2	8	no	—
198	C₂×C₄×C₁₃₉	—	4	8	no	—
199	C₂×C₄×C₁₃₉	—	4	8	no	—
200	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
201	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
205	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
206	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
208	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
209	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
210	C₂²×C₁₃₉	—	2	4	no	—
211	C₂²×C₁₃₉	—	2	4	no	—
212	C₂²×C₁₃₉	—	2	4	no	—
213	C₂²×C₁₃₉	—	4	2	no	—
214	C₂²×C₁₃₉	—	4	2	no	—
215	C₂²×C₁₃₉	—	4	2	no	—
216	C₂²×C₁₃₉	—	4	2	no	—
217	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
218	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
219	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
220	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
222	C₄×C₁₃₉	—	2	2	no	—
223	C₄×C₁₃₉	—	2	8	no	—
224	C₄×C₁₃₉	—	2	4	no	—
225	C₄×C₁₃₉	—	2	2	no	—
226	C₄×C₁₃₉	—	4	4	no	—
227	C₄×C₁₃₉	—	4	2	no	—
228	C₄×C₁₃₉	—	4	2	no	—
229	C₄×C₁₃₉	—	4	8	no	—
230	C₄×C₁₃₉	—	4	2	no	—
231	C₄×C₁₃₉	#547	1	4	yes	—
232	C₄×C₁₃₉	#548	1	8	yes	—
233	C₂×C₁₃₉	—	4	4	no	—
234	C₂×C₁₃₉	#3444	1	1	yes	characteristic
235	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
236	C₂×C₁₃₉	C₂×#548	1	2	yes	—
237	C₂×C₁₃₉	#3509	1	1	yes	characteristic
238	C₂×C₁₃₉	#3509	1	2	yes	—
239	#36151	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₁₃₉	#36151	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×#533	C₂×C₁₃₉	1	2	yes	complemented
242	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	#2857	C₂×C₁₃₉	1	2	yes	complemented
244	#2536	C₂×C₁₃₉	1	2	yes	—
245	#2489	C₂×C₁₃₉	1	4	yes	complemented
246	#2453	C₂×C₁₃₉	1	4	yes	complemented
247	#2421	C₂×C₁₃₉	1	4	yes	complemented
248	#2415	C₂×C₁₃₉	1	4	yes	—
249	#2362	C₂×C₁₃₉	1	4	yes	complemented
250	#2351	C₂×C₁₃₉	1	2	yes	complemented
251	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
252	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
253	#533	—	2	16	no	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
257	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
258	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
259	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
260	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
262	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
263	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
264	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
266	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
267	#400	C₂²×C₁₃₉	1	8	yes	—
268	#398	C₂²×C₁₃₉	1	4	yes	—
269	#397	C₂²×C₁₃₉	1	8	yes	—
270	#394	C₂²×C₁₃₉	1	4	yes	—
271	#391	C₂²×C₁₃₉	1	2	yes	—
272	#391	C₂²×C₁₃₉	1	4	yes	—
273	#391	C₂²×C₁₃₉	1	4	yes	—
274	#391	C₂²×C₁₃₉	1	4	yes	—
275	#389	C₂²×C₁₃₉	1	4	yes	—
276	#389	C₂²×C₁₃₉	1	4	yes	—
277	#389	C₂²×C₁₃₉	1	4	yes	—
278	#389	C₂²×C₁₃₉	1	8	yes	—
279	#388	C₂²×C₁₃₉	1	8	yes	—
280	#388	C₂²×C₁₃₉	1	8	yes	—
281	#387	C₂²×C₁₃₉	1	8	yes	—
282	#384	C₂²×C₁₃₉	1	1	yes	characteristic
283	#382	C₂²×C₁₃₉	1	2	yes	—
284	#382	C₂²×C₁₃₉	1	2	yes	—
285	#382	C₂²×C₁₃₉	1	4	yes	—
286	#380	C₂²×C₁₃₉	1	4	yes	—
287	#380	C₂²×C₁₃₉	1	4	yes	—
288	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
289	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
291	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
292	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
294	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
295	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
296	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
297	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
298	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
302	C₄⋊Q₈	—	2	8	no	—
303	C₄⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
304	#125	—	2	16	no	—
305	C₂²⋊Q₈	—	2	16	no	—
306	C₂²⋊Q₈	—	2	16	no	—
307	C₂²⋊Q₈	—	2	16	no	—
308	C₄×Q₈	—	2	16	no	—
309	C₄×Q₈	—	2	16	no	—
310	C₄×Q₈	—	2	8	no	—
311	C₄×D₄	—	2	8	no	—
312	C₄×D₄	—	2	4	no	—
313	#117	—	2	16	no	—
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
330	C₂×C₄²	—	2	8	no	—
331	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
332	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
334	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
335	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
336	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
337	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
338	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
341	#95	C₂³×C₁₃₉	1	1	yes	characteristic
342	#95	C₂³×C₁₃₉	1	1	yes	characteristic
343	#95	C₂³×C₁₃₉	1	2	yes	—
344	#95	C₂³×C₁₃₉	1	2	yes	—
345	#95	C₂³×C₁₃₉	1	4	yes	—
346	#95	C₂³×C₁₃₉	1	8	yes	—
347	#95	C₂³×C₁₃₉	1	8	yes	—
348	#95	C₂³×C₁₃₉	1	8	yes	—
349	#95	C₂³×C₁₃₉	1	8	yes	—
350	#95	C₂³×C₁₃₉	1	4	yes	—
351	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
352	C₂×Q₈	—	2	8	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	8	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	2	8	no	—
357	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
369	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
374	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	16	no	—
382	C₄⋊C₄	—	2	16	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	16	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	16	no	—
393	C₂²⋊C₄	—	2	16	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	16	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
405	C₄²	#41×C₁₃₉	1	4	yes	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
413	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
414	Q₈	—	2	16	no	—
415	Q₈	—	4	16	no	—
416	D₄	—	2	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	16	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
441	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
443	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
444	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
445	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
446	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
447	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
448	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
449	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
458	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
459	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
460	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
461	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	8	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	8	no	—
470	C₄	—	4	2	no	—
471	C₄	#547×C₁₃₉	1	4	yes	—
472	C₄	#548×C₁₃₉	1	8	yes	—
473	C₂	—	4	4	no	—
474	C₂	#3444×C₁₃₉	1	1	yes	characteristic
475	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
476	C₂	C₂×#548×C₁₃₉	1	2	yes	—
477	C₂	#3509×C₁₃₉	1	1	yes	characteristic
478	C₂	#3509×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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×#533×C₁₃₉	C₂	semidirect
2. #2862×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
5. #2489×C₁₃₉	C₂	semidirect
6. #2453×C₁₃₉	C₂	semidirect
7. #2421×C₁₃₉	C₂	semidirect
9. #2362×C₁₃₉	C₂	semidirect
10. #2351×C₁₃₉	C₂	semidirect
11. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
63. C₄⋊Q₈×C₁₃₉	D₄	semidirect
239. #36151	C₁₃₉	direct (N × H)
240. C₁₃₉	#36151	direct (N × H)
241. C₂×#533	C₂×C₁₃₉	semidirect
242. #2862	C₂×C₁₃₉	semidirect
243. #2857	C₂×C₁₃₉	semidirect
245. #2489	C₂×C₁₃₉	semidirect
246. #2453	C₂×C₁₃₉	semidirect
247. #2421	C₂×C₁₃₉	semidirect
249. #2362	C₂×C₁₃₉	semidirect
250. #2351	C₂×C₁₃₉	semidirect
251. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
303. C₄⋊Q₈	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×#533×C₁₃₉	2
#2862×C₁₃₉	2
#2857×C₁₃₉	2
#2536×C₁₃₉	2
#2489×C₁₃₉	2
#2453×C₁₃₉	2
#2421×C₁₃₉	2
#2415×C₁₃₉	2
#2362×C₁₃₉	2
#2351×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36151	139

Subgroups — C139×#36151 #48030747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36151 #48030747