Subgroups — C₁₃₉×#36152 #48030748

Order 35584.

7616 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	3	yes	maximal, complemented
3	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2846×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2435×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2410×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2408×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	#2405×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	3	yes	maximal, complemented
10	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#379×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂⁶×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₃₉	—	2	24	no	—
15	C₂³×D₄×C₁₃₉	C₂²	1	6	yes	—
16	C₂³×D₄×C₁₃₉	C₂²	1	3	yes	—
17	C₂³×D₄×C₁₃₉	C₂²	1	3	yes	—
18	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	#546×C₁₃₉	—	2	24	no	—
20	C₂×#124×C₁₃₉	C₂²	1	3	yes	complemented
21	C₂×#123×C₁₃₉	C₂²	1	6	yes	complemented
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
23	C₂×#121×C₁₃₉	C₂²	1	3	yes	complemented
24	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
25	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#120×C₁₃₉	C₂²	1	6	yes	complemented
27	C₂×#120×C₁₃₉	C₂²	1	6	yes	complemented
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	complemented
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	complemented
30	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
31	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
32	#394×C₁₃₉	C₂²	1	6	yes	complemented
33	#394×C₁₃₉	C₂²	1	12	yes	complemented
34	#392×C₁₃₉	C₂²	1	6	yes	complemented
35	#390×C₁₃₉	C₂²	1	6	yes	complemented
36	#386×C₁₃₉	C₂²	1	3	yes	complemented
37	#386×C₁₃₉	C₂²	1	12	yes	complemented
38	#385×C₁₃₉	C₂²	1	3	yes	complemented
39	#385×C₁₃₉	C₂²	1	6	yes	complemented
40	#380×C₁₃₉	C₂²	1	3	yes	complemented
41	#379×C₁₃₉	C₂²	1	1	yes	characteristic
42	#379×C₁₃₉	C₂²	1	2	yes	—
43	#379×C₁₃₉	C₂²	1	6	yes	complemented
44	#379×C₁₃₉	C₂²	1	6	yes	complemented
45	#379×C₁₃₉	C₂²	1	6	yes	complemented
46	#379×C₁₃₉	C₂²	1	6	yes	complemented
47	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
48	C₂⁵×C₁₃₉	—	2	24	no	—
49	C₂⁵×C₁₃₉	—	2	8	no	—
50	C₂⁵×C₁₃₉	—	4	12	no	—
51	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃₉	C₂³	1	6	yes	—
53	C₂⁵×C₁₃₉	C₂³	1	6	yes	—
54	C₂×#41×C₁₃₉	—	2	12	no	—
55	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic, complemented
56	C₂²×D₄×C₁₃₉	—	2	128	no	—
57	C₂²×D₄×C₁₃₉	—	2	24	no	—
58	C₂²×D₄×C₁₃₉	—	2	48	no	—
59	C₂²×D₄×C₁₃₉	—	2	24	no	—
60	C₂²×D₄×C₁₃₉	—	2	24	no	—
61	C₂²×D₄×C₁₃₉	—	2	12	no	—
62	C₂²×D₄×C₁₃₉	D₄	1	24	yes	complemented
63	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
64	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
65	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	complemented
69	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	complemented
70	C₂³×C₄×C₁₃₉	—	2	12	no	—
71	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	complemented
74	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic, complemented
75	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	complemented
76	#124×C₁₃₉	—	2	12	no	—
77	#123×C₁₃₉	—	2	24	no	—
78	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
79	#121×C₁₃₉	—	2	12	no	—
80	#121×C₁₃₉	—	2	24	no	—
81	#120×C₁₃₉	—	2	24	no	—
82	#120×C₁₃₉	—	2	4	no	—
83	#120×C₁₃₉	—	4	12	no	—
84	C₄×D₄×C₁₃₉	—	2	12	no	—
85	C₄×D₄×C₁₃₉	—	2	12	no	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	complemented
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	complemented
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	complemented
89	C₂×C₂²⋊C₄×C₁₃₉	—	2	24	no	—
90	C₂×C₂²⋊C₄×C₁₃₉	—	4	12	no	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	complemented
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	complemented
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	complemented
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	complemented
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	complemented
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	complemented
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	complemented
103	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	complemented
104	#95×C₁₃₉	C₂³	1	6	yes	complemented
105	#95×C₁₃₉	C₂³	1	6	yes	complemented
106	C₂⁴×C₁₃₉	—	2	6	no	—
107	C₂⁴×C₁₃₉	—	2	6	no	—
108	C₂⁴×C₁₃₉	—	2	64	no	—
109	C₂⁴×C₁₃₉	—	2	24	no	—
110	C₂⁴×C₁₃₉	—	2	24	no	—
111	C₂⁴×C₁₃₉	—	2	12	no	—
112	C₂⁴×C₁₃₉	—	2	12	no	—
113	C₂⁴×C₁₃₉	—	2	12	no	—
114	C₂⁴×C₁₃₉	—	2	12	no	—
115	C₂⁴×C₁₃₉	—	2	12	no	—
116	C₂⁴×C₁₃₉	—	4	12	no	—
117	C₂⁴×C₁₃₉	—	4	12	no	—
118	C₂⁴×C₁₃₉	—	4	96	no	—
119	C₂⁴×C₁₃₉	—	4	96	no	—
120	C₂⁴×C₁₃₉	C₂×D₄	1	24	yes	—
121	C₂⁴×C₁₃₉	#41	1	4	yes	complemented
122	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
123	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
124	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
125	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
126	#41×C₁₃₉	—	4	16	no	—
127	C₂×Q₈×C₁₃₉	—	2	6	no	—
128	C₂×D₄×C₁₃₉	—	2	192	no	—
129	C₂×D₄×C₁₃₉	—	2	96	no	—
130	C₂×D₄×C₁₃₉	—	2	24	no	—
131	C₂×D₄×C₁₃₉	—	2	24	no	—
132	C₂×D₄×C₁₃₉	—	2	96	no	—
133	C₂×D₄×C₁₃₉	—	2	6	no	—
134	C₂×D₄×C₁₃₉	—	2	12	no	—
135	C₂×D₄×C₁₃₉	—	2	6	no	—
136	C₂×D₄×C₁₃₉	—	2	6	no	—
137	C₂×D₄×C₁₃₉	—	2	12	no	—
138	C₂×D₄×C₁₃₉	—	2	12	no	—
139	C₂×D₄×C₁₃₉	—	2	12	no	—
140	C₂×D₄×C₁₃₉	—	4	12	no	—
141	C₂×D₄×C₁₃₉	C₂×D₄	1	24	yes	—
142	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
143	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
144	C₂²×C₄×C₁₃₉	—	2	32	no	—
145	C₂²×C₄×C₁₃₉	—	2	6	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	—	4	12	no	—
152	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₁₃₉	—	2	6	no	—
161	C₄⋊C₄×C₁₃₉	—	2	6	no	—
162	C₄⋊C₄×C₁₃₉	—	2	12	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
167	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
168	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
169	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
170	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
173	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
174	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
175	C₄²×C₁₃₉	—	2	6	no	—
176	C₂³×C₁₃₉	—	2	8	no	—
177	C₂³×C₁₃₉	—	2	24	no	—
178	C₂³×C₁₃₉	—	2	24	no	—
179	C₂³×C₁₃₉	—	2	6	no	—
180	C₂³×C₁₃₉	—	2	2	no	—
181	C₂³×C₁₃₉	—	2	6	no	—
182	C₂³×C₁₃₉	—	2	6	no	—
183	C₂³×C₁₃₉	—	2	48	no	—
184	C₂³×C₁₃₉	—	2	48	no	—
185	C₂³×C₁₃₉	—	2	48	no	—
186	C₂³×C₁₃₉	—	2	12	no	—
187	C₂³×C₁₃₉	—	2	6	no	—
188	C₂³×C₁₃₉	—	2	6	no	—
189	C₂³×C₁₃₉	—	2	12	no	—
190	C₂³×C₁₃₉	—	2	3	no	—
191	C₂³×C₁₃₉	—	2	1	no	—
192	C₂³×C₁₃₉	—	2	3	no	—
193	C₂³×C₁₃₉	—	4	24	no	—
194	C₂³×C₁₃₉	—	4	48	no	—
195	C₂³×C₁₃₉	—	4	48	no	—
196	C₂³×C₁₃₉	—	4	48	no	—
197	C₂³×C₁₃₉	—	4	48	no	—
198	C₂³×C₁₃₉	—	4	256	no	—
199	C₂³×C₁₃₉	—	4	24	no	—
200	C₂³×C₁₃₉	—	4	24	no	—
201	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
202	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
203	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
204	C₂³×C₁₃₉	C₂×#41	1	6	yes	—
205	C₂³×C₁₃₉	H(5,𝔽₂)	1	6	yes	—
206	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
207	Q₈×C₁₃₉	—	4	4	no	—
208	D₄×C₁₃₉	—	2	48	no	—
209	D₄×C₁₃₉	—	2	48	no	—
210	D₄×C₁₃₉	—	2	24	no	—
211	D₄×C₁₃₉	—	4	8	no	—
212	D₄×C₁₃₉	—	4	12	no	—
213	D₄×C₁₃₉	—	8	12	no	—
214	D₄×C₁₃₉	#120	1	16	yes	complemented
215	C₂×C₄×C₁₃₉	—	2	24	no	—
216	C₂×C₄×C₁₃₉	—	2	6	no	—
217	C₂×C₄×C₁₃₉	—	2	24	no	—
218	C₂×C₄×C₁₃₉	—	2	3	no	—
219	C₂×C₄×C₁₃₉	—	2	3	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	3	no	—
224	C₂×C₄×C₁₃₉	—	2	6	no	—
225	C₂×C₄×C₁₃₉	—	2	12	no	—
226	C₂×C₄×C₁₃₉	—	2	3	no	—
227	C₂×C₄×C₁₃₉	—	4	8	no	—
228	C₂×C₄×C₁₃₉	—	4	4	no	—
229	C₂×C₄×C₁₃₉	—	8	12	no	—
230	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
231	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
232	C₂²×C₁₃₉	—	2	32	no	—
233	C₂²×C₁₃₉	—	2	6	no	—
234	C₂²×C₁₃₉	—	2	12	no	—
235	C₂²×C₁₃₉	—	2	12	no	—
236	C₂²×C₁₃₉	—	2	12	no	—
237	C₂²×C₁₃₉	—	2	6	no	—
238	C₂²×C₁₃₉	—	2	12	no	—
239	C₂²×C₁₃₉	—	2	12	no	—
240	C₂²×C₁₃₉	—	2	12	no	—
241	C₂²×C₁₃₉	—	2	12	no	—
242	C₂²×C₁₃₉	—	4	96	no	—
243	C₂²×C₁₃₉	—	4	96	no	—
244	C₂²×C₁₃₉	—	4	12	no	—
245	C₂²×C₁₃₉	—	4	12	no	—
246	C₂²×C₁₃₉	—	4	1	no	—
247	C₂²×C₁₃₉	—	4	3	no	—
248	C₂²×C₁₃₉	—	4	3	no	—
249	C₂²×C₁₃₉	C₂×#120	1	8	yes	—
250	C₂²×C₁₃₉	#546	1	12	yes	complemented
251	C₂²×C₁₃₉	C₂³×D₄	1	3	yes	—
252	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
253	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	3	yes	—
254	C₄×C₁₃₉	—	2	6	no	—
255	C₄×C₁₃₉	—	4	1	no	—
256	C₄×C₁₃₉	—	4	2	no	—
257	C₄×C₁₃₉	—	4	3	no	—
258	C₄×C₁₃₉	—	4	3	no	—
259	C₄×C₁₃₉	—	4	6	no	—
260	C₄×C₁₃₉	C₂×#120	1	4	yes	—
261	C₂×C₁₃₉	—	2	12	no	—
262	C₂×C₁₃₉	—	2	8	no	—
263	C₂×C₁₃₉	—	4	12	no	—
264	C₂×C₁₃₉	—	8	1	no	—
265	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
266	C₂×C₁₃₉	C₂×#546	1	3	yes	—
267	C₂×C₁₃₉	#3484	1	3	yes	—
268	#36152	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₁₃₉	#36152	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
271	C₂×#546	C₂×C₁₃₉	1	3	yes	complemented
272	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
273	#2846	C₂×C₁₃₉	1	2	yes	complemented
274	#2435	C₂×C₁₃₉	1	3	yes	complemented
275	#2410	C₂×C₁₃₉	1	6	yes	complemented
276	#2408	C₂×C₁₃₉	1	3	yes	complemented
277	#2405	C₂×C₁₃₉	1	6	yes	complemented
278	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	3	yes	complemented
279	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic, complemented
280	C₂×#379	C₂×C₁₃₉	1	2	yes	complemented
281	C₂⁶	C₂²×C₁₃₉	1	2	yes	—
282	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
283	C₂³×D₄	—	2	24	no	—
284	C₂³×D₄	C₂²×C₁₃₉	1	6	yes	—
285	C₂³×D₄	C₂²×C₁₃₉	1	3	yes	—
286	C₂³×D₄	C₂²×C₁₃₉	1	3	yes	—
287	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
288	#546	—	2	24	no	—
289	C₂×#124	C₂²×C₁₃₉	1	3	yes	complemented
290	C₂×#123	C₂²×C₁₃₉	1	6	yes	complemented
291	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	complemented
292	C₂×#121	C₂²×C₁₃₉	1	3	yes	complemented
293	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
294	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
295	C₂×#120	C₂²×C₁₃₉	1	6	yes	complemented
296	C₂×#120	C₂²×C₁₃₉	1	6	yes	complemented
297	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	complemented
298	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	complemented
299	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
300	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
301	#394	C₂²×C₁₃₉	1	6	yes	complemented
302	#394	C₂²×C₁₃₉	1	12	yes	complemented
303	#392	C₂²×C₁₃₉	1	6	yes	complemented
304	#390	C₂²×C₁₃₉	1	6	yes	complemented
305	#386	C₂²×C₁₃₉	1	3	yes	complemented
306	#386	C₂²×C₁₃₉	1	12	yes	complemented
307	#385	C₂²×C₁₃₉	1	6	yes	complemented
308	#385	C₂²×C₁₃₉	1	3	yes	complemented
309	#380	C₂²×C₁₃₉	1	3	yes	complemented
310	#379	C₂²×C₁₃₉	1	2	yes	—
311	#379	C₂²×C₁₃₉	1	1	yes	characteristic
312	#379	C₂²×C₁₃₉	1	6	yes	complemented
313	#379	C₂²×C₁₃₉	1	6	yes	complemented
314	#379	C₂²×C₁₃₉	1	6	yes	complemented
315	#379	C₂²×C₁₃₉	1	6	yes	complemented
316	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
317	C₂⁵	—	2	24	no	—
318	C₂⁵	—	2	8	no	—
319	C₂⁵	—	4	12	no	—
320	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
321	C₂⁵	C₂³×C₁₃₉	1	6	yes	—
322	C₂⁵	C₂³×C₁₃₉	1	6	yes	—
323	C₂×#41	—	2	12	no	—
324	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic, complemented
325	C₂²×D₄	—	2	128	no	—
326	C₂²×D₄	—	2	24	no	—
327	C₂²×D₄	—	2	48	no	—
328	C₂²×D₄	—	2	24	no	—
329	C₂²×D₄	—	2	24	no	—
330	C₂²×D₄	—	2	12	no	—
331	C₂²×D₄	D₄×C₁₃₉	1	24	yes	complemented
332	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
333	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
334	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
335	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
336	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	complemented
338	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	complemented
339	C₂³×C₄	—	2	12	no	—
340	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
341	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
342	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	complemented
343	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic, complemented
344	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	complemented
345	#124	—	2	12	no	—
346	#123	—	2	24	no	—
347	C₂²⋊Q₈	—	2	12	no	—
348	#121	—	2	12	no	—
349	#121	—	2	24	no	—
350	#120	—	2	24	no	—
351	#120	—	2	4	no	—
352	#120	—	4	12	no	—
353	C₄×D₄	—	2	12	no	—
354	C₄×D₄	—	2	12	no	—
355	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	complemented
356	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	complemented
357	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	complemented
358	C₂×C₂²⋊C₄	—	2	24	no	—
359	C₂×C₂²⋊C₄	—	4	12	no	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	complemented
366	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	complemented
367	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	complemented
368	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	complemented
369	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	complemented
370	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	complemented
371	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	complemented
372	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	complemented
373	#95	C₂³×C₁₃₉	1	6	yes	complemented
374	#95	C₂³×C₁₃₉	1	6	yes	complemented
375	C₂⁴	—	2	6	no	—
376	C₂⁴	—	2	6	no	—
377	C₂⁴	—	2	64	no	—
378	C₂⁴	—	2	24	no	—
379	C₂⁴	—	2	24	no	—
380	C₂⁴	—	2	12	no	—
381	C₂⁴	—	2	12	no	—
382	C₂⁴	—	2	12	no	—
383	C₂⁴	—	2	12	no	—
384	C₂⁴	—	2	12	no	—
385	C₂⁴	—	4	12	no	—
386	C₂⁴	—	4	12	no	—
387	C₂⁴	—	4	96	no	—
388	C₂⁴	—	4	96	no	—
389	C₂⁴	C₂×D₄×C₁₃₉	1	24	yes	—
390	C₂⁴	#41×C₁₃₉	1	4	yes	complemented
391	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
392	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
393	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
394	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
395	#41	—	4	16	no	—
396	C₂×Q₈	—	2	6	no	—
397	C₂×D₄	—	2	192	no	—
398	C₂×D₄	—	2	96	no	—
399	C₂×D₄	—	2	24	no	—
400	C₂×D₄	—	2	24	no	—
401	C₂×D₄	—	2	96	no	—
402	C₂×D₄	—	2	6	no	—
403	C₂×D₄	—	2	12	no	—
404	C₂×D₄	—	2	6	no	—
405	C₂×D₄	—	2	6	no	—
406	C₂×D₄	—	2	12	no	—
407	C₂×D₄	—	2	12	no	—
408	C₂×D₄	—	2	12	no	—
409	C₂×D₄	—	4	12	no	—
410	C₂×D₄	C₂×D₄×C₁₃₉	1	24	yes	—
411	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
412	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
413	C₂²×C₄	—	2	32	no	—
414	C₂²×C₄	—	2	6	no	—
415	C₂²×C₄	—	2	12	no	—
416	C₂²×C₄	—	2	12	no	—
417	C₂²×C₄	—	2	12	no	—
418	C₂²×C₄	—	2	12	no	—
419	C₂²×C₄	—	2	6	no	—
420	C₂²×C₄	—	4	12	no	—
421	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
422	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
423	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
424	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
425	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
429	C₄⋊C₄	—	2	6	no	—
430	C₄⋊C₄	—	2	6	no	—
431	C₄⋊C₄	—	2	12	no	—
432	C₂²⋊C₄	—	2	6	no	—
433	C₂²⋊C₄	—	2	12	no	—
434	C₂²⋊C₄	—	2	12	no	—
435	C₂²⋊C₄	—	2	12	no	—
436	C₂²⋊C₄	—	2	12	no	—
437	C₂²⋊C₄	—	2	12	no	—
438	C₂²⋊C₄	—	2	6	no	—
439	C₂²⋊C₄	—	2	6	no	—
440	C₂²⋊C₄	—	2	12	no	—
441	C₂²⋊C₄	—	2	6	no	—
442	C₂²⋊C₄	—	4	12	no	—
443	C₂²⋊C₄	—	4	12	no	—
444	C₄²	—	2	6	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	24	no	—
447	C₂³	—	2	24	no	—
448	C₂³	—	2	6	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	6	no	—
451	C₂³	—	2	6	no	—
452	C₂³	—	2	48	no	—
453	C₂³	—	2	48	no	—
454	C₂³	—	2	48	no	—
455	C₂³	—	2	12	no	—
456	C₂³	—	2	6	no	—
457	C₂³	—	2	6	no	—
458	C₂³	—	2	12	no	—
459	C₂³	—	2	3	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	3	no	—
462	C₂³	—	4	24	no	—
463	C₂³	—	4	48	no	—
464	C₂³	—	4	48	no	—
465	C₂³	—	4	48	no	—
466	C₂³	—	4	48	no	—
467	C₂³	—	4	256	no	—
468	C₂³	—	4	24	no	—
469	C₂³	—	4	24	no	—
470	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
471	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
472	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
473	C₂³	C₂×#41×C₁₃₉	1	6	yes	—
474	C₂³	H(5,𝔽₂)×C₁₃₉	1	6	yes	—
475	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
476	Q₈	—	4	4	no	—
477	D₄	—	2	48	no	—
478	D₄	—	2	48	no	—
479	D₄	—	2	24	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	12	no	—
482	D₄	—	8	12	no	—
483	D₄	#120×C₁₃₉	1	16	yes	complemented
484	C₂×C₄	—	2	24	no	—
485	C₂×C₄	—	2	6	no	—
486	C₂×C₄	—	2	24	no	—
487	C₂×C₄	—	2	3	no	—
488	C₂×C₄	—	2	3	no	—
489	C₂×C₄	—	2	6	no	—
490	C₂×C₄	—	2	3	no	—
491	C₂×C₄	—	2	6	no	—
492	C₂×C₄	—	2	3	no	—
493	C₂×C₄	—	2	6	no	—
494	C₂×C₄	—	2	12	no	—
495	C₂×C₄	—	2	3	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	8	12	no	—
499	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
501	C₂²	—	2	32	no	—
502	C₂²	—	2	6	no	—
503	C₂²	—	2	12	no	—
504	C₂²	—	2	12	no	—
505	C₂²	—	2	12	no	—
506	C₂²	—	2	6	no	—
507	C₂²	—	2	12	no	—
508	C₂²	—	2	12	no	—
509	C₂²	—	2	12	no	—
510	C₂²	—	2	12	no	—
511	C₂²	—	4	96	no	—
512	C₂²	—	4	96	no	—
513	C₂²	—	4	12	no	—
514	C₂²	—	4	12	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	3	no	—
517	C₂²	—	4	3	no	—
518	C₂²	C₂×#120×C₁₃₉	1	8	yes	—
519	C₂²	#546×C₁₃₉	1	12	yes	complemented
520	C₂²	C₂³×D₄×C₁₃₉	1	3	yes	—
521	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
522	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	3	yes	—
523	C₄	—	2	6	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	3	no	—
527	C₄	—	4	3	no	—
528	C₄	—	4	6	no	—
529	C₄	C₂×#120×C₁₃₉	1	4	yes	—
530	C₂	—	2	12	no	—
531	C₂	—	2	8	no	—
532	C₂	—	4	12	no	—
533	C₂	—	8	1	no	—
534	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
535	C₂	C₂×#546×C₁₃₉	1	3	yes	—
536	C₂	#3484×C₁₃₉	1	3	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. C₂⁴×D₄×C₁₃₉	C₂	semidirect
2. C₂×#546×C₁₃₉	C₂	semidirect
3. #2848×C₁₃₉	C₂	semidirect
4. #2846×C₁₃₉	C₂	semidirect
5. #2435×C₁₃₉	C₂	semidirect
6. #2410×C₁₃₉	C₂	semidirect
7. #2408×C₁₃₉	C₂	semidirect
8. #2405×C₁₃₉	C₂	semidirect
9. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
10. C₄×#120×C₁₃₉	C₂	semidirect
11. C₂×#379×C₁₃₉	C₂	semidirect
13. C₂²×#41×C₁₃₉	C₂²	semidirect
20. C₂×#124×C₁₃₉	C₂²	semidirect
21. C₂×#123×C₁₃₉	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
23. C₂×#121×C₁₃₉	C₂²	semidirect
24. C₂×#121×C₁₃₉	C₂²	semidirect
26. C₂×#120×C₁₃₉	C₂²	semidirect
27. C₂×#120×C₁₃₉	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
30. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
31. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
32. #394×C₁₃₉	C₂²	semidirect
33. #394×C₁₃₉	C₂²	semidirect
34. #392×C₁₃₉	C₂²	semidirect
35. #390×C₁₃₉	C₂²	semidirect
36. #386×C₁₃₉	C₂²	semidirect
37. #386×C₁₃₉	C₂²	semidirect
38. #385×C₁₃₉	C₂²	semidirect
39. #385×C₁₃₉	C₂²	semidirect
40. #380×C₁₃₉	C₂²	semidirect
43. #379×C₁₃₉	C₂²	semidirect
44. #379×C₁₃₉	C₂²	semidirect
45. #379×C₁₃₉	C₂²	semidirect
46. #379×C₁₃₉	C₂²	semidirect
47. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
55. C₂²×Q₈×C₁₃₉	C₂³	semidirect
62. C₂²×D₄×C₁₃₉	D₄	semidirect
68. C₂²×D₄×C₁₃₉	C₂³	semidirect
69. C₂²×D₄×C₁₃₉	C₂³	semidirect
73. C₂³×C₄×C₁₃₉	C₂³	semidirect
74. C₂³×C₄×C₁₃₉	C₂³	semidirect
75. C₂³×C₄×C₁₃₉	C₂³	semidirect
86. C₂×C₄⋊C₄×C₁₃₉	C₂³	semidirect
87. C₂×C₄⋊C₄×C₁₃₉	C₂³	semidirect
88. C₂×C₄⋊C₄×C₁₃₉	C₂³	semidirect
96. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
97. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
98. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
99. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
100. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
101. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
102. C₂×C₂²⋊C₄×C₁₃₉	C₂³	semidirect
103. C₂×C₄²×C₁₃₉	C₂³	semidirect
104. #95×C₁₃₉	C₂³	semidirect
105. #95×C₁₃₉	C₂³	semidirect
121. C₂⁴×C₁₃₉	#41	semidirect
214. D₄×C₁₃₉	#120	semidirect
250. C₂²×C₁₃₉	#546	semidirect
268. #36152	C₁₃₉	direct (N × H)
269. C₁₃₉	#36152	direct (N × H)
270. C₂⁴×D₄	C₂×C₁₃₉	semidirect
271. C₂×#546	C₂×C₁₃₉	semidirect
272. #2848	C₂×C₁₃₉	semidirect
273. #2846	C₂×C₁₃₉	semidirect
274. #2435	C₂×C₁₃₉	semidirect
275. #2410	C₂×C₁₃₉	semidirect
276. #2408	C₂×C₁₃₉	semidirect
277. #2405	C₂×C₁₃₉	semidirect
278. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
279. C₄×#120	C₂×C₁₃₉	semidirect
280. C₂×#379	C₂×C₁₃₉	semidirect
282. C₂²×#41	C₂²×C₁₃₉	semidirect
289. C₂×#124	C₂²×C₁₃₉	semidirect
290. C₂×#123	C₂²×C₁₃₉	semidirect
291. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
292. C₂×#121	C₂²×C₁₃₉	semidirect
293. C₂×#121	C₂²×C₁₃₉	semidirect
295. C₂×#120	C₂²×C₁₃₉	semidirect
296. C₂×#120	C₂²×C₁₃₉	semidirect
297. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
298. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
299. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
300. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
301. #394	C₂²×C₁₃₉	semidirect
302. #394	C₂²×C₁₃₉	semidirect
303. #392	C₂²×C₁₃₉	semidirect
304. #390	C₂²×C₁₃₉	semidirect
305. #386	C₂²×C₁₃₉	semidirect
306. #386	C₂²×C₁₃₉	semidirect
307. #385	C₂²×C₁₃₉	semidirect
308. #385	C₂²×C₁₃₉	semidirect
309. #380	C₂²×C₁₃₉	semidirect
312. #379	C₂²×C₁₃₉	semidirect
313. #379	C₂²×C₁₃₉	semidirect
314. #379	C₂²×C₁₃₉	semidirect
315. #379	C₂²×C₁₃₉	semidirect
316. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
324. C₂²×Q₈	C₂³×C₁₃₉	semidirect
331. C₂²×D₄	D₄×C₁₃₉	semidirect
337. C₂²×D₄	C₂³×C₁₃₉	semidirect
338. C₂²×D₄	C₂³×C₁₃₉	semidirect
342. C₂³×C₄	C₂³×C₁₃₉	semidirect
343. C₂³×C₄	C₂³×C₁₃₉	semidirect
344. C₂³×C₄	C₂³×C₁₃₉	semidirect
355. C₂×C₄⋊C₄	C₂³×C₁₃₉	semidirect
356. C₂×C₄⋊C₄	C₂³×C₁₃₉	semidirect
357. C₂×C₄⋊C₄	C₂³×C₁₃₉	semidirect
365. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
366. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
367. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
368. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
369. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
370. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
371. C₂×C₂²⋊C₄	C₂³×C₁₃₉	semidirect
372. C₂×C₄²	C₂³×C₁₃₉	semidirect
373. #95	C₂³×C₁₃₉	semidirect
374. #95	C₂³×C₁₃₉	semidirect
390. C₂⁴	#41×C₁₃₉	semidirect
483. D₄	#120×C₁₃₉	semidirect
519. C₂²	#546×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2848×C₁₃₉	2
#2846×C₁₃₉	2
#2435×C₁₃₉	2
#2410×C₁₃₉	2
#2408×C₁₃₉	2
#2405×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#120×C₁₃₉	2
C₂×#379×C₁₃₉	2
#36152	139

Subgroups — C139×#36152 #48030748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36152 #48030748