Subgroups — C₁₃₉×#36428 #48031024

Order 35584.

5378 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#548×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2848×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2435×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2432×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2408×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	#2407×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2341×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#120×C₁₃₉	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₁₃₉	—	2	16	no	—
13	C₂²×#41×C₁₃₉	—	2	8	no	—
14	C₂²×#41×C₁₃₉	C₂²	1	6	yes	—
15	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	3	yes	—
19	C₂⁴×C₄×C₁₃₉	C₂²	1	3	yes	—
20	D₄×Q₈×C₁₃₉	—	2	8	no	—
21	#548×C₁₃₉	—	2	16	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
23	C₂×#124×C₁₃₉	C₂²	1	6	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
27	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
28	C₂×#120×C₁₃₉	C₂²	1	3	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	complemented
33	#394×C₁₃₉	C₂²	1	12	yes	complemented
34	#394×C₁₃₉	C₂²	1	6	yes	complemented
35	#392×C₁₃₉	C₂²	1	6	yes	complemented
36	#391×C₁₃₉	C₂²	1	6	yes	complemented
37	#390×C₁₃₉	C₂²	1	6	yes	complemented
38	#390×C₁₃₉	C₂²	1	6	yes	complemented
39	#386×C₁₃₉	C₂²	1	1	yes	characteristic
40	#386×C₁₃₉	C₂²	1	6	yes	complemented
41	#385×C₁₃₉	C₂²	1	3	yes	—
42	#385×C₁₃₉	C₂²	1	6	yes	complemented
43	#385×C₁₃₉	C₂²	1	12	yes	complemented
44	#380×C₁₃₉	C₂²	1	3	yes	—
45	#380×C₁₃₉	C₂²	1	6	yes	complemented
46	#379×C₁₃₉	C₂²	1	3	yes	—
47	#379×C₁₃₉	C₂²	1	6	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
49	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
50	C₂⁵×C₁₃₉	C₂³	1	3	yes	—
51	C₂×#41×C₁₃₉	—	2	128	no	—
52	C₂×#41×C₁₃₉	—	2	24	no	—
53	C₂×#41×C₁₃₉	—	2	8	no	—
54	C₂×#41×C₁₃₉	—	2	8	no	—
55	C₂×#41×C₁₃₉	—	2	24	no	—
56	C₂×#41×C₁₃₉	—	2	24	no	—
57	C₂×#41×C₁₃₉	D₄	1	16	yes	complemented
58	C₂²×Q₈×C₁₃₉	—	2	8	no	—
59	C₂²×Q₈×C₁₃₉	—	2	8	no	—
60	C₂²×Q₈×C₁₃₉	—	2	4	no	—
61	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	complemented
62	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
63	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
64	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃₉	—	2	24	no	—
66	C₂²×D₄×C₁₃₉	—	2	12	no	—
67	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₉	—	2	12	no	—
72	C₂³×C₄×C₁₃₉	—	2	24	no	—
73	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
78	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
79	#124×C₁₃₉	—	2	24	no	—
80	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
82	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
83	#121×C₁₃₉	—	2	24	no	—
84	#120×C₁₃₉	—	2	12	no	—
85	C₄×Q₈×C₁₃₉	—	2	8	no	—
86	C₄×Q₈×C₁₃₉	—	2	4	no	—
87	C₄×D₄×C₁₃₉	—	2	12	no	—
88	C₄×D₄×C₁₃₉	—	2	24	no	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
104	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
105	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
106	#95×C₁₃₉	C₂³	1	6	yes	—
107	#95×C₁₃₉	C₂³	1	2	yes	—
108	#95×C₁₃₉	C₂³	1	6	yes	—
109	#95×C₁₃₉	C₂³	1	6	yes	—
110	C₂⁴×C₁₃₉	—	2	12	no	—
111	C₂⁴×C₁₃₉	—	2	6	no	—
112	C₂⁴×C₁₃₉	—	2	6	no	—
113	C₂⁴×C₁₃₉	—	2	6	no	—
114	C₂⁴×C₁₃₉	—	4	6	no	—
115	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
116	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	#41×C₁₃₉	—	2	192	no	—
119	#41×C₁₃₉	—	2	64	no	—
120	C₂×Q₈×C₁₃₉	—	2	32	no	—
121	C₂×Q₈×C₁₃₉	—	2	12	no	—
122	C₂×Q₈×C₁₃₉	—	2	12	no	—
123	C₂×Q₈×C₁₃₉	—	2	6	no	—
124	C₂×Q₈×C₁₃₉	—	4	16	no	—
125	C₂×Q₈×C₁₃₉	C₂×D₄	1	12	yes	—
126	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
127	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₁₃₉	—	2	96	no	—
129	C₂×D₄×C₁₃₉	—	2	2	no	—
130	C₂×D₄×C₁₃₉	—	2	24	no	—
131	C₂×D₄×C₁₃₉	—	2	2	no	—
132	C₂×D₄×C₁₃₉	—	2	12	no	—
133	C₂×D₄×C₁₃₉	—	2	12	no	—
134	C₂×D₄×C₁₃₉	—	2	12	no	—
135	C₂×D₄×C₁₃₉	—	2	12	no	—
136	C₂×D₄×C₁₃₉	—	2	12	no	—
137	C₂×D₄×C₁₃₉	—	4	6	no	—
138	C₂×D₄×C₁₃₉	C₂×D₄	1	24	yes	—
139	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
140	C₂²×C₄×C₁₃₉	—	2	96	no	—
141	C₂²×C₄×C₁₃₉	—	2	2	no	—
142	C₂²×C₄×C₁₃₉	—	2	12	no	—
143	C₂²×C₄×C₁₃₉	—	2	4	no	—
144	C₂²×C₄×C₁₃₉	—	2	12	no	—
145	C₂²×C₄×C₁₃₉	—	2	12	no	—
146	C₂²×C₄×C₁₃₉	—	2	12	no	—
147	C₂²×C₄×C₁₃₉	—	2	12	no	—
148	C₂²×C₄×C₁₃₉	—	2	12	no	—
149	C₂²×C₄×C₁₃₉	—	2	12	no	—
150	C₂²×C₄×C₁₃₉	—	2	6	no	—
151	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
152	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
161	C₄⋊C₄×C₁₃₉	—	2	12	no	—
162	C₄⋊C₄×C₁₃₉	—	2	6	no	—
163	C₄⋊C₄×C₁₃₉	—	2	12	no	—
164	C₄⋊C₄×C₁₃₉	—	2	6	no	—
165	C₄⋊C₄×C₁₃₉	—	2	12	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
168	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
169	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
170	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
174	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
175	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
176	C₄²×C₁₃₉	—	2	12	no	—
177	C₄²×C₁₃₉	—	2	6	no	—
178	C₂³×C₁₃₉	—	2	2	no	—
179	C₂³×C₁₃₉	—	2	2	no	—
180	C₂³×C₁₃₉	—	2	24	no	—
181	C₂³×C₁₃₉	—	2	1	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	6	no	—
184	C₂³×C₁₃₉	—	2	6	no	—
185	C₂³×C₁₃₉	—	2	6	no	—
186	C₂³×C₁₃₉	—	2	1	no	—
187	C₂³×C₁₃₉	—	2	6	no	—
188	C₂³×C₁₃₉	—	2	6	no	—
189	C₂³×C₁₃₉	—	2	6	no	—
190	C₂³×C₁₃₉	—	2	2	no	—
191	C₂³×C₁₃₉	—	4	24	no	—
192	C₂³×C₁₃₉	—	4	24	no	—
193	C₂³×C₁₃₉	—	4	12	no	—
194	C₂³×C₁₃₉	—	4	12	no	—
195	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
196	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
197	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
198	C₂³×C₁₃₉	C₂×#41	1	2	yes	complemented
199	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
200	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
201	Q₈×C₁₃₉	—	2	24	no	—
202	Q₈×C₁₃₉	—	4	12	no	—
203	Q₈×C₁₃₉	#120	1	16	yes	complemented
204	D₄×C₁₃₉	—	2	48	no	—
205	D₄×C₁₃₉	—	2	8	no	—
206	D₄×C₁₃₉	—	2	48	no	—
207	D₄×C₁₃₉	—	4	24	no	—
208	C₂×C₄×C₁₃₉	—	2	8	no	—
209	C₂×C₄×C₁₃₉	—	2	48	no	—
210	C₂×C₄×C₁₃₉	—	2	1	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	6	no	—
214	C₂×C₄×C₁₃₉	—	2	1	no	—
215	C₂×C₄×C₁₃₉	—	2	24	no	—
216	C₂×C₄×C₁₃₉	—	2	48	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	3	no	—
219	C₂×C₄×C₁₃₉	—	2	6	no	—
220	C₂×C₄×C₁₃₉	—	2	6	no	—
221	C₂×C₄×C₁₃₉	—	2	3	no	—
222	C₂×C₄×C₁₃₉	—	2	6	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	6	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	6	no	—
227	C₂×C₄×C₁₃₉	—	4	12	no	—
228	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
229	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
230	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
231	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
232	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	complemented
233	C₂²×C₁₃₉	—	2	2	no	—
234	C₂²×C₁₃₉	—	2	4	no	—
235	C₂²×C₁₃₉	—	2	2	no	—
236	C₂²×C₁₃₉	—	2	4	no	—
237	C₂²×C₁₃₉	—	2	12	no	—
238	C₂²×C₁₃₉	—	2	2	no	—
239	C₂²×C₁₃₉	—	2	4	no	—
240	C₂²×C₁₃₉	—	2	12	no	—
241	C₂²×C₁₃₉	—	2	12	no	—
242	C₂²×C₁₃₉	—	4	48	no	—
243	C₂²×C₁₃₉	—	4	1	no	—
244	C₂²×C₁₃₉	—	4	6	no	—
245	C₂²×C₁₃₉	—	4	6	no	—
246	C₂²×C₁₃₉	—	4	1	no	—
247	C₂²×C₁₃₉	—	4	6	no	—
248	C₂²×C₁₃₉	—	4	2	no	—
249	C₂²×C₁₃₉	—	4	6	no	—
250	C₂²×C₁₃₉	#548	1	4	yes	complemented
251	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
252	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
253	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
254	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
255	C₂²×C₁₃₉	#585	1	2	yes	—
256	C₄×C₁₃₉	—	2	4	no	—
257	C₄×C₁₃₉	—	2	6	no	—
258	C₄×C₁₃₉	—	2	2	no	—
259	C₄×C₁₃₉	—	4	3	no	—
260	C₄×C₁₃₉	—	4	6	no	—
261	C₄×C₁₃₉	—	4	3	no	—
262	C₄×C₁₃₉	—	4	2	no	—
263	C₄×C₁₃₉	C₂×#120	1	12	yes	—
264	C₂×C₁₃₉	—	2	4	no	—
265	C₂×C₁₃₉	—	4	2	no	—
266	C₂×C₁₃₉	—	4	12	no	—
267	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
268	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
269	C₂×C₁₃₉	D₄×#41	1	2	yes	—
270	C₂×C₁₃₉	#3487	1	1	yes	characteristic
271	C₂×C₁₃₉	#3489	1	2	yes	—
272	#36428	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₁₃₉	#36428	1	1	yes	characteristic, direct product factor, Sylow
274	C₂³×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
275	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	C₂×#548	C₂×C₁₃₉	1	2	yes	complemented
277	#2848	C₂×C₁₃₉	1	3	yes	complemented
278	#2435	C₂×C₁₃₉	1	3	yes	complemented
279	#2432	C₂×C₁₃₉	1	6	yes	complemented
280	#2408	C₂×C₁₃₉	1	3	yes	complemented
281	#2407	C₂×C₁₃₉	1	6	yes	complemented
282	#2341	C₂×C₁₃₉	1	2	yes	complemented
283	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
284	C₄×#120	C₂×C₁₃₉	1	3	yes	complemented
285	C₂²×#41	—	2	16	no	—
286	C₂²×#41	—	2	8	no	—
287	C₂²×#41	C₂²×C₁₃₉	1	6	yes	—
288	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
289	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
291	C₂³×D₄	C₂²×C₁₃₉	1	3	yes	—
292	C₂⁴×C₄	C₂²×C₁₃₉	1	3	yes	—
293	D₄×Q₈	—	2	8	no	—
294	#548	—	2	16	no	—
295	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	complemented
296	C₂×#124	C₂²×C₁₃₉	1	6	yes	complemented
297	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	complemented
299	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	complemented
300	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
301	C₂×#120	C₂²×C₁₃₉	1	3	yes	—
302	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
303	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
304	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
305	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	complemented
306	#394	C₂²×C₁₃₉	1	12	yes	complemented
307	#394	C₂²×C₁₃₉	1	6	yes	complemented
308	#392	C₂²×C₁₃₉	1	6	yes	complemented
309	#391	C₂²×C₁₃₉	1	6	yes	complemented
310	#390	C₂²×C₁₃₉	1	6	yes	complemented
311	#390	C₂²×C₁₃₉	1	6	yes	complemented
312	#386	C₂²×C₁₃₉	1	1	yes	characteristic
313	#386	C₂²×C₁₃₉	1	6	yes	complemented
314	#385	C₂²×C₁₃₉	1	3	yes	—
315	#385	C₂²×C₁₃₉	1	12	yes	complemented
316	#385	C₂²×C₁₃₉	1	6	yes	complemented
317	#380	C₂²×C₁₃₉	1	3	yes	—
318	#380	C₂²×C₁₃₉	1	6	yes	complemented
319	#379	C₂²×C₁₃₉	1	6	yes	—
320	#379	C₂²×C₁₃₉	1	3	yes	—
321	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
323	C₂⁵	C₂³×C₁₃₉	1	3	yes	—
324	C₂×#41	—	2	128	no	—
325	C₂×#41	—	2	24	no	—
326	C₂×#41	—	2	8	no	—
327	C₂×#41	—	2	8	no	—
328	C₂×#41	—	2	24	no	—
329	C₂×#41	—	2	24	no	—
330	C₂×#41	D₄×C₁₃₉	1	16	yes	complemented
331	C₂²×Q₈	—	2	8	no	—
332	C₂²×Q₈	—	2	8	no	—
333	C₂²×Q₈	—	2	4	no	—
334	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	complemented
335	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
336	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
337	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
338	C₂²×D₄	—	2	24	no	—
339	C₂²×D₄	—	2	12	no	—
340	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
341	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
342	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
343	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
344	C₂³×C₄	—	2	12	no	—
345	C₂³×C₄	—	2	24	no	—
346	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
347	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
349	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
350	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
351	C₄⋊Q₈	—	2	12	no	—
352	#124	—	2	24	no	—
353	C₂²⋊Q₈	—	2	12	no	—
354	C₂²⋊Q₈	—	2	12	no	—
355	C₂²⋊Q₈	—	2	24	no	—
356	#121	—	2	24	no	—
357	#120	—	2	12	no	—
358	C₄×Q₈	—	2	8	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×D₄	—	2	12	no	—
361	C₄×D₄	—	2	24	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
377	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
378	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
379	#95	C₂³×C₁₃₉	1	6	yes	—
380	#95	C₂³×C₁₃₉	1	2	yes	—
381	#95	C₂³×C₁₃₉	1	6	yes	—
382	#95	C₂³×C₁₃₉	1	6	yes	—
383	C₂⁴	—	2	12	no	—
384	C₂⁴	—	2	6	no	—
385	C₂⁴	—	2	6	no	—
386	C₂⁴	—	2	6	no	—
387	C₂⁴	—	4	6	no	—
388	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
389	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
390	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
391	#41	—	2	192	no	—
392	#41	—	2	64	no	—
393	C₂×Q₈	—	2	32	no	—
394	C₂×Q₈	—	2	12	no	—
395	C₂×Q₈	—	2	12	no	—
396	C₂×Q₈	—	2	6	no	—
397	C₂×Q₈	—	4	16	no	—
398	C₂×Q₈	C₂×D₄×C₁₃₉	1	12	yes	—
399	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
400	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
401	C₂×D₄	—	2	96	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	24	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	12	no	—
406	C₂×D₄	—	2	12	no	—
407	C₂×D₄	—	2	12	no	—
408	C₂×D₄	—	2	12	no	—
409	C₂×D₄	—	2	12	no	—
410	C₂×D₄	—	4	6	no	—
411	C₂×D₄	C₂×D₄×C₁₃₉	1	24	yes	—
412	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
413	C₂²×C₄	—	2	96	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	12	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	12	no	—
418	C₂²×C₄	—	2	12	no	—
419	C₂²×C₄	—	2	12	no	—
420	C₂²×C₄	—	2	12	no	—
421	C₂²×C₄	—	2	12	no	—
422	C₂²×C₄	—	2	12	no	—
423	C₂²×C₄	—	2	6	no	—
424	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
426	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
429	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
430	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
434	C₄⋊C₄	—	2	12	no	—
435	C₄⋊C₄	—	2	6	no	—
436	C₄⋊C₄	—	2	12	no	—
437	C₄⋊C₄	—	2	6	no	—
438	C₄⋊C₄	—	2	12	no	—
439	C₂²⋊C₄	—	2	6	no	—
440	C₂²⋊C₄	—	2	12	no	—
441	C₂²⋊C₄	—	2	24	no	—
442	C₂²⋊C₄	—	2	6	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	6	no	—
446	C₂²⋊C₄	—	2	12	no	—
447	C₂²⋊C₄	—	4	6	no	—
448	C₂²⋊C₄	—	4	12	no	—
449	C₄²	—	2	12	no	—
450	C₄²	—	2	6	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	24	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	6	no	—
457	C₂³	—	2	6	no	—
458	C₂³	—	2	6	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	6	no	—
461	C₂³	—	2	6	no	—
462	C₂³	—	2	6	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	4	24	no	—
465	C₂³	—	4	24	no	—
466	C₂³	—	4	12	no	—
467	C₂³	—	4	12	no	—
468	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
469	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
470	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
471	C₂³	C₂×#41×C₁₃₉	1	2	yes	complemented
472	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
473	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
474	Q₈	—	2	24	no	—
475	Q₈	—	4	12	no	—
476	Q₈	#120×C₁₃₉	1	16	yes	complemented
477	D₄	—	2	48	no	—
478	D₄	—	2	8	no	—
479	D₄	—	2	48	no	—
480	D₄	—	4	24	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	48	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	6	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	24	no	—
489	C₂×C₄	—	2	48	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	3	no	—
492	C₂×C₄	—	2	6	no	—
493	C₂×C₄	—	2	6	no	—
494	C₂×C₄	—	2	3	no	—
495	C₂×C₄	—	2	6	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	6	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	6	no	—
500	C₂×C₄	—	4	12	no	—
501	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
505	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	complemented
506	C₂²	—	2	2	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	12	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	12	no	—
514	C₂²	—	2	12	no	—
515	C₂²	—	4	48	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	6	no	—
518	C₂²	—	4	6	no	—
519	C₂²	—	4	6	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	6	no	—
522	C₂²	—	4	2	no	—
523	C₂²	#548×C₁₃₉	1	4	yes	complemented
524	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
525	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
526	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
527	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
528	C₂²	#585×C₁₃₉	1	2	yes	—
529	C₄	—	2	4	no	—
530	C₄	—	2	6	no	—
531	C₄	—	2	2	no	—
532	C₄	—	4	3	no	—
533	C₄	—	4	6	no	—
534	C₄	—	4	3	no	—
535	C₄	—	4	2	no	—
536	C₄	C₂×#120×C₁₃₉	1	12	yes	—
537	C₂	—	2	4	no	—
538	C₂	—	4	12	no	—
539	C₂	—	4	2	no	—
540	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
541	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
542	C₂	D₄×#41×C₁₃₉	1	2	yes	—
543	C₂	#3487×C₁₃₉	1	1	yes	characteristic
544	C₂	#3489×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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. C₂³×#41×C₁₃₉	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃₉	C₂	semidirect
3. C₂×#548×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2435×C₁₃₉	C₂	semidirect
6. #2432×C₁₃₉	C₂	semidirect
7. #2408×C₁₃₉	C₂	semidirect
8. #2407×C₁₃₉	C₂	semidirect
9. #2341×C₁₃₉	C₂	semidirect
10. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
11. C₄×#120×C₁₃₉	C₂	semidirect
17. C₂³×Q₈×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
23. C₂×#124×C₁₃₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
29. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
33. #394×C₁₃₉	C₂²	semidirect
34. #394×C₁₃₉	C₂²	semidirect
35. #392×C₁₃₉	C₂²	semidirect
36. #391×C₁₃₉	C₂²	semidirect
37. #390×C₁₃₉	C₂²	semidirect
38. #390×C₁₃₉	C₂²	semidirect
40. #386×C₁₃₉	C₂²	semidirect
42. #385×C₁₃₉	C₂²	semidirect
43. #385×C₁₃₉	C₂²	semidirect
45. #380×C₁₃₉	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
57. C₂×#41×C₁₃₉	D₄	semidirect
61. C₂²×Q₈×C₁₃₉	D₄	semidirect
139. C₂×D₄×C₁₃₉	#41	semidirect
198. C₂³×C₁₃₉	C₂×#41	semidirect
203. Q₈×C₁₃₉	#120	semidirect
232. C₂×C₄×C₁₃₉	C₂×#41	semidirect
250. C₂²×C₁₃₉	#548	semidirect
272. #36428	C₁₃₉	direct (N × H)
273. C₁₃₉	#36428	direct (N × H)
274. C₂³×#41	C₂×C₁₃₉	semidirect
275. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
276. C₂×#548	C₂×C₁₃₉	semidirect
277. #2848	C₂×C₁₃₉	semidirect
278. #2435	C₂×C₁₃₉	semidirect
279. #2432	C₂×C₁₃₉	semidirect
280. #2408	C₂×C₁₃₉	semidirect
281. #2407	C₂×C₁₃₉	semidirect
282. #2341	C₂×C₁₃₉	semidirect
283. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
284. C₄×#120	C₂×C₁₃₉	semidirect
290. C₂³×Q₈	C₂²×C₁₃₉	semidirect
295. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
296. C₂×#124	C₂²×C₁₃₉	semidirect
298. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
299. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
300. C₂×#121	C₂²×C₁₃₉	semidirect
302. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
303. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
305. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
306. #394	C₂²×C₁₃₉	semidirect
307. #394	C₂²×C₁₃₉	semidirect
308. #392	C₂²×C₁₃₉	semidirect
309. #391	C₂²×C₁₃₉	semidirect
310. #390	C₂²×C₁₃₉	semidirect
311. #390	C₂²×C₁₃₉	semidirect
313. #386	C₂²×C₁₃₉	semidirect
315. #385	C₂²×C₁₃₉	semidirect
316. #385	C₂²×C₁₃₉	semidirect
318. #380	C₂²×C₁₃₉	semidirect
322. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
330. C₂×#41	D₄×C₁₃₉	semidirect
334. C₂²×Q₈	D₄×C₁₃₉	semidirect
412. C₂×D₄	#41×C₁₃₉	semidirect
471. C₂³	C₂×#41×C₁₃₉	semidirect
476. Q₈	#120×C₁₃₉	semidirect
505. C₂×C₄	C₂×#41×C₁₃₉	semidirect
523. C₂²	#548×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₃₉	2
C₂×D₄×Q₈×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2848×C₁₃₉	2
#2435×C₁₃₉	2
#2432×C₁₃₉	2
#2408×C₁₃₉	2
#2407×C₁₃₉	2
#2341×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36428	139

Subgroups — C139×#36428 #48031024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36428 #48031024