Subgroups — C₁₃₉×#21856 #48016452

Order 35584.

1200 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3444×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1994×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1962×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1871×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1806×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
9	#533×C₁₃₉	C₄	1	1	yes	characteristic, complemented
10	#533×C₁₃₉	C₄	1	1	yes	characteristic, complemented
11	#533×C₁₃₉	C₂²	1	1	yes	characteristic
12	#532×C₁₃₉	C₄	1	1	yes	characteristic, complemented
13	#532×C₁₃₉	C₄	1	1	yes	characteristic, complemented
14	#532×C₁₃₉	C₂²	1	1	yes	characteristic
15	#529×C₁₃₉	—	2	1	no	—
16	#529×C₁₃₉	—	2	1	no	—
17	#529×C₁₃₉	—	2	1	no	—
18	#529×C₁₃₉	—	2	1	no	—
19	#529×C₁₃₉	C₄	1	2	yes	complemented
20	#529×C₁₃₉	C₄	1	2	yes	complemented
21	#525×C₁₃₉	—	2	1	no	—
22	#525×C₁₃₉	—	2	1	no	—
23	#525×C₁₃₉	C₂²	1	2	yes	—
24	C₄×#41×C₁₃₉	—	2	1	no	—
25	C₄×#41×C₁₃₉	—	2	1	no	—
26	C₄×#41×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#117×C₁₃₉	—	2	1	no	—
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#423×C₁₃₉	—	2	1	no	—
30	#423×C₁₃₉	—	2	1	no	—
31	#423×C₁₃₉	C₂²	1	2	yes	—
32	#423×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
34	C₂×C₄⋊C₈×C₁₃₉	—	2	1	no	—
35	C₂×#104×C₁₃₉	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
39	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	#376×C₁₃₉	—	2	1	no	—
41	C₄³×C₁₃₉	C₂²	1	2	yes	—
42	#339×C₁₃₉	C₂²	1	8	yes	—
43	C₂×#41×C₁₃₉	—	2	1	no	—
44	C₂×#41×C₁₃₉	—	2	1	no	—
45	C₂×#41×C₁₃₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₃₉	—	2	2	no	—
50	C₂×M₁₆×C₁₃₉	—	4	4	no	—
51	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
52	C₂²×C₈×C₁₃₉	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
56	#127×C₁₃₉	C₂×C₄	1	1	yes	characteristic
57	#126×C₁₃₉	—	2	2	no	—
58	#126×C₁₃₉	—	2	2	no	—
59	#125×C₁₃₉	—	2	1	no	—
60	#125×C₁₃₉	—	2	1	no	—
61	#125×C₁₃₉	C₂×C₄	1	2	yes	—
62	#124×C₁₃₉	—	2	1	no	—
63	#124×C₁₃₉	—	2	1	no	—
64	#124×C₁₃₉	C₂×C₄	1	2	yes	—
65	#123×C₁₃₉	—	2	2	no	—
66	#123×C₁₃₉	—	2	2	no	—
67	#123×C₁₃₉	—	2	2	no	—
68	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
69	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
70	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
71	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
72	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
73	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
74	#121×C₁₃₉	—	2	1	no	—
75	#121×C₁₃₉	—	2	1	no	—
76	#121×C₁₃₉	—	2	1	no	—
77	#121×C₁₃₉	—	2	1	no	—
78	#121×C₁₃₉	C₂×C₄	1	2	yes	—
79	#121×C₁₃₉	C₂×C₄	1	2	yes	—
80	#120×C₁₃₉	—	2	2	no	—
81	C₄×Q₈×C₁₃₉	—	2	1	no	—
82	C₄×Q₈×C₁₃₉	—	2	1	no	—
83	C₄×Q₈×C₁₃₉	—	2	1	no	—
84	C₄×Q₈×C₁₃₉	—	2	1	no	—
85	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
86	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
87	C₄×D₄×C₁₃₉	—	2	2	no	—
88	C₄×D₄×C₁₃₉	—	2	2	no	—
89	C₄×D₄×C₁₃₉	—	2	2	no	—
90	C₄×D₄×C₁₃₉	—	2	2	no	—
91	C₄×D₄×C₁₃₉	—	2	2	no	—
92	C₄×D₄×C₁₃₉	—	2	2	no	—
93	C₄×D₄×C₁₃₉	—	2	1	no	—
94	C₄×D₄×C₁₃₉	—	2	1	no	—
95	C₄×D₄×C₁₃₉	—	2	1	no	—
96	C₄×D₄×C₁₃₉	—	2	1	no	—
97	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
99	#117×C₁₃₉	—	2	8	no	—
100	#117×C₁₃₉	—	2	1	no	—
101	#117×C₁₃₉	—	2	1	no	—
102	#117×C₁₃₉	—	2	2	no	—
103	#117×C₁₃₉	—	2	2	no	—
104	#117×C₁₃₉	—	2	2	no	—
105	#117×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
108	C₂×C₄²×C₁₃₉	—	2	2	no	—
109	C₂×C₄²×C₁₃₉	—	2	2	no	—
110	C₂×C₄²×C₁₃₉	—	2	2	no	—
111	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₁₃₉	—	2	2	no	—
125	C₄⋊C₈×C₁₃₉	—	2	2	no	—
126	C₄⋊C₈×C₁₃₉	—	2	2	no	—
127	C₄⋊C₈×C₁₃₉	—	2	2	no	—
128	#104×C₁₃₉	—	4	8	no	—
129	#95×C₁₃₉	—	2	2	no	—
130	#95×C₁₃₉	—	2	2	no	—
131	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
132	#41×C₁₃₉	—	2	4	no	—
133	#41×C₁₃₉	—	2	4	no	—
134	#41×C₁₃₉	—	4	4	no	—
135	#41×C₁₃₉	—	4	4	no	—
136	C₂×Q₈×C₁₃₉	—	2	1	no	—
137	C₂×Q₈×C₁₃₉	—	2	1	no	—
138	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₁₃₉	—	2	2	no	—
140	C₂×D₄×C₁₃₉	—	2	2	no	—
141	C₂×D₄×C₁₃₉	—	2	2	no	—
142	C₂×D₄×C₁₃₉	—	2	1	no	—
143	C₂×D₄×C₁₃₉	—	2	1	no	—
144	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₁₃₉	—	2	4	no	—
146	C₂²×C₄×C₁₃₉	—	2	2	no	—
147	C₂²×C₄×C₁₃₉	—	2	2	no	—
148	C₂²×C₄×C₁₃₉	—	2	4	no	—
149	C₂²×C₄×C₁₃₉	—	2	2	no	—
150	C₂²×C₄×C₁₃₉	—	2	2	no	—
151	C₂²×C₄×C₁₃₉	—	2	2	no	—
152	C₂²×C₄×C₁₃₉	—	4	2	no	—
153	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₁₃₉	—	2	8	no	—
172	M₁₆×C₁₃₉	—	4	4	no	—
173	C₂×C₈×C₁₃₉	—	2	4	no	—
174	C₂×C₈×C₁₃₉	—	4	4	no	—
175	C₄⋊C₄×C₁₃₉	—	2	8	no	—
176	C₄⋊C₄×C₁₃₉	—	2	1	no	—
177	C₄⋊C₄×C₁₃₉	—	2	1	no	—
178	C₄⋊C₄×C₁₃₉	—	2	1	no	—
179	C₄⋊C₄×C₁₃₉	—	2	1	no	—
180	C₄⋊C₄×C₁₃₉	—	2	2	no	—
181	C₄⋊C₄×C₁₃₉	—	2	2	no	—
182	C₄⋊C₄×C₁₃₉	—	2	2	no	—
183	C₄⋊C₄×C₁₃₉	—	2	2	no	—
184	C₄⋊C₄×C₁₃₉	—	2	2	no	—
185	C₄⋊C₄×C₁₃₉	—	2	2	no	—
186	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
188	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
198	C₄²×C₁₃₉	—	2	8	no	—
199	C₄²×C₁₃₉	—	2	2	no	—
200	C₄²×C₁₃₉	—	2	2	no	—
201	C₄²×C₁₃₉	—	2	2	no	—
202	C₄²×C₁₃₉	—	2	4	no	—
203	C₄²×C₁₃₉	—	2	4	no	—
204	C₄²×C₁₃₉	—	4	4	no	—
205	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₁₃₉	—	2	2	no	—
222	C₂³×C₁₃₉	—	2	2	no	—
223	C₂³×C₁₃₉	—	2	2	no	—
224	C₂³×C₁₃₉	—	4	1	no	—
225	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₁₃₉	—	2	4	no	—
229	Q₈×C₁₃₉	—	4	2	no	—
230	Q₈×C₁₃₉	—	4	2	no	—
231	D₄×C₁₃₉	—	2	4	no	—
232	D₄×C₁₃₉	—	4	4	no	—
233	D₄×C₁₃₉	—	4	4	no	—
234	D₄×C₁₃₉	—	4	4	no	—
235	D₄×C₁₃₉	—	4	2	no	—
236	D₄×C₁₃₉	—	4	2	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	2	no	—
239	C₂×C₄×C₁₃₉	—	2	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	1	no	—
242	C₂×C₄×C₁₃₉	—	2	1	no	—
243	C₂×C₄×C₁₃₉	—	2	1	no	—
244	C₂×C₄×C₁₃₉	—	2	1	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	2	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	8	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	4	1	no	—
257	C₂×C₄×C₁₃₉	—	4	1	no	—
258	C₂×C₄×C₁₃₉	—	4	1	no	—
259	C₂×C₄×C₁₃₉	—	4	4	no	—
260	C₂×C₄×C₁₃₉	—	4	4	no	—
261	C₂×C₄×C₁₃₉	—	4	4	no	—
262	C₂×C₄×C₁₃₉	—	4	2	no	—
263	C₂×C₄×C₁₃₉	—	4	2	no	—
264	C₂×C₄×C₁₃₉	—	4	4	no	—
265	C₂×C₄×C₁₃₉	#104	1	4	yes	complemented
266	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
279	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
280	C₈×C₁₃₉	—	4	4	no	—
281	C₂²×C₁₃₉	—	2	1	no	—
282	C₂²×C₁₃₉	—	2	1	no	—
283	C₂²×C₁₃₉	—	2	1	no	—
284	C₂²×C₁₃₉	—	2	1	no	—
285	C₂²×C₁₃₉	—	2	1	no	—
286	C₂²×C₁₃₉	—	2	1	no	—
287	C₂²×C₁₃₉	—	2	1	no	—
288	C₂²×C₁₃₉	—	4	4	no	—
289	C₂²×C₁₃₉	—	4	2	no	—
290	C₂²×C₁₃₉	—	4	2	no	—
291	C₂²×C₁₃₉	—	4	2	no	—
292	C₂²×C₁₃₉	C₂×#104	1	2	yes	—
293	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₁₃₉	#537	1	2	yes	—
295	C₄×C₁₃₉	—	2	1	no	—
296	C₄×C₁₃₉	—	2	1	no	—
297	C₄×C₁₃₉	—	2	1	no	—
298	C₄×C₁₃₉	—	2	1	no	—
299	C₄×C₁₃₉	—	2	1	no	—
300	C₄×C₁₃₉	—	2	1	no	—
301	C₄×C₁₃₉	—	2	1	no	—
302	C₄×C₁₃₉	—	4	8	no	—
303	C₄×C₁₃₉	—	4	2	no	—
304	C₄×C₁₃₉	—	4	2	no	—
305	C₄×C₁₃₉	—	4	2	no	—
306	C₄×C₁₃₉	C₂×#104	1	2	yes	—
307	C₄×C₁₃₉	C₂×#104	1	2	yes	—
308	C₄×C₁₃₉	#421	1	2	yes	—
309	C₄×C₁₃₉	#520	1	2	yes	—
310	C₄×C₁₃₉	#535	1	1	yes	characteristic
311	C₄×C₁₃₉	#536	1	1	yes	characteristic
312	C₂×C₁₃₉	—	2	2	no	—
313	C₂×C₁₃₉	—	2	2	no	—
314	C₂×C₁₃₉	—	4	1	no	—
315	C₂×C₁₃₉	—	8	2	no	—
316	C₂×C₁₃₉	#2311	1	1	yes	characteristic
317	C₂×C₁₃₉	C₂²×#104	1	1	yes	characteristic
318	C₂×C₁₃₉	C₂×#421	1	1	yes	characteristic
319	#21856	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₁₃₉	#21856	1	1	yes	characteristic, direct product factor, Sylow
321	#3444	C₂×C₁₃₉	1	1	yes	characteristic
322	C₂×#423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
323	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
324	#1994	C₂×C₁₃₉	1	2	yes	complemented
325	#1962	C₂×C₁₃₉	1	2	yes	complemented
326	#1871	C₂×C₁₃₉	1	4	yes	complemented
327	#1806	C₂×C₁₃₉	1	4	yes	complemented
328	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
329	#533	C₄×C₁₃₉	1	1	yes	characteristic, complemented
330	#533	C₄×C₁₃₉	1	1	yes	characteristic, complemented
331	#533	C₂²×C₁₃₉	1	1	yes	characteristic
332	#532	C₄×C₁₃₉	1	1	yes	characteristic, complemented
333	#532	C₄×C₁₃₉	1	1	yes	characteristic, complemented
334	#532	C₂²×C₁₃₉	1	1	yes	characteristic
335	#529	—	2	1	no	—
336	#529	—	2	1	no	—
337	#529	—	2	1	no	—
338	#529	—	2	1	no	—
339	#529	C₄×C₁₃₉	1	2	yes	complemented
340	#529	C₄×C₁₃₉	1	2	yes	complemented
341	#525	—	2	1	no	—
342	#525	—	2	1	no	—
343	#525	C₂²×C₁₃₉	1	2	yes	—
344	C₄×#41	—	2	1	no	—
345	C₄×#41	—	2	1	no	—
346	C₄×#41	C₂²×C₁₃₉	1	2	yes	—
347	C₂×#117	—	2	1	no	—
348	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
349	#423	—	2	1	no	—
350	#423	—	2	1	no	—
351	#423	C₂²×C₁₃₉	1	2	yes	—
352	#423	C₂²×C₁₃₉	1	2	yes	—
353	C₂×C₄⋊C₈	—	2	1	no	—
354	C₂×C₄⋊C₈	—	2	1	no	—
355	C₂×#104	C₂²×C₁₃₉	1	8	yes	—
356	C₄×C₄⋊C₄	—	2	1	no	—
357	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
358	C₄×C₂²⋊C₄	—	2	1	no	—
359	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
360	#376	—	2	1	no	—
361	C₄³	C₂²×C₁₃₉	1	2	yes	—
362	#339	C₂²×C₁₃₉	1	8	yes	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	C₂³×C₁₃₉	1	2	yes	—
366	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
367	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	4	4	no	—
371	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
372	C₂²×C₈	—	2	2	no	—
373	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
374	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
375	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
376	#127	C₂×C₄×C₁₃₉	1	1	yes	characteristic
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#125	C₂×C₄×C₁₃₉	1	2	yes	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	C₂×C₄×C₁₃₉	1	2	yes	—
385	#123	—	2	2	no	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
393	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	C₂×C₄×C₁₃₉	1	2	yes	—
399	#121	C₂×C₄×C₁₃₉	1	2	yes	—
400	#120	—	2	2	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
406	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
418	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
419	#117	—	2	8	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	2	2	no	—
425	#117	C₂³×C₁₃₉	1	2	yes	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₂²⋊C₄	—	2	2	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
435	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
436	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
437	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
442	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	#104	—	4	8	no	—
449	#95	—	2	2	no	—
450	#95	—	2	2	no	—
451	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
452	#41	—	2	4	no	—
453	#41	—	2	4	no	—
454	#41	—	4	4	no	—
455	#41	—	4	4	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
478	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
479	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
480	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
491	M₁₆	—	2	8	no	—
492	M₁₆	—	4	4	no	—
493	C₂×C₈	—	2	4	no	—
494	C₂×C₈	—	4	4	no	—
495	C₄⋊C₄	—	2	8	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₄²	—	2	8	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	4	4	no	—
525	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
526	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
527	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
528	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
529	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
530	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
531	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
532	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
533	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
534	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
535	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
536	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
539	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
540	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	4	1	no	—
545	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
546	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
547	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
548	Q₈	—	2	4	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	4	2	no	—
551	D₄	—	2	4	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	4	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	#104×C₁₃₉	1	4	yes	complemented
586	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
587	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
588	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
599	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
600	C₈	—	4	4	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	C₂×#104×C₁₃₉	1	2	yes	—
613	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
614	C₂²	#537×C₁₃₉	1	2	yes	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	4	8	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	C₂×#104×C₁₃₉	1	2	yes	—
627	C₄	C₂×#104×C₁₃₉	1	2	yes	—
628	C₄	#421×C₁₃₉	1	2	yes	—
629	C₄	#520×C₁₃₉	1	2	yes	—
630	C₄	#535×C₁₃₉	1	1	yes	characteristic
631	C₄	#536×C₁₃₉	1	1	yes	characteristic
632	C₂	—	2	2	no	—
633	C₂	—	2	2	no	—
634	C₂	—	4	1	no	—
635	C₂	—	8	2	no	—
636	C₂	#2311×C₁₃₉	1	1	yes	characteristic
637	C₂	C₂²×#104×C₁₃₉	1	1	yes	characteristic
638	C₂	C₂×#421×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
prime radical	#3444×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#423×C₁₃₉	C₂	semidirect
3. C₄×#117×C₁₃₉	C₂	semidirect
4. #1994×C₁₃₉	C₂	semidirect
5. #1962×C₁₃₉	C₂	semidirect
6. #1871×C₁₃₉	C₂	semidirect
7. #1806×C₁₃₉	C₂	semidirect
9. #533×C₁₃₉	C₄	semidirect
10. #533×C₁₃₉	C₄	semidirect
12. #532×C₁₃₉	C₄	semidirect
13. #532×C₁₃₉	C₄	semidirect
19. #529×C₁₃₉	C₄	semidirect
20. #529×C₁₃₉	C₄	semidirect
265. C₂×C₄×C₁₃₉	#104	semidirect
319. #21856	C₁₃₉	direct (N × H)
320. C₁₃₉	#21856	direct (N × H)
322. C₂×#423	C₂×C₁₃₉	semidirect
323. C₄×#117	C₂×C₁₃₉	semidirect
324. #1994	C₂×C₁₃₉	semidirect
325. #1962	C₂×C₁₃₉	semidirect
326. #1871	C₂×C₁₃₉	semidirect
327. #1806	C₂×C₁₃₉	semidirect
329. #533	C₄×C₁₃₉	semidirect
330. #533	C₄×C₁₃₉	semidirect
332. #532	C₄×C₁₃₉	semidirect
333. #532	C₄×C₁₃₉	semidirect
339. #529	C₄×C₁₃₉	semidirect
340. #529	C₄×C₁₃₉	semidirect
585. C₂×C₄	#104×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3444×C₁₃₉	2
C₂×#423×C₁₃₉	2
C₄×#117×C₁₃₉	2
#1994×C₁₃₉	2
#1962×C₁₃₉	2
#1871×C₁₃₉	2
#1806×C₁₃₉	2
#21856	139

Subgroups — C139×#21856 #48016452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21856 #48016452