Subgroups — C₁₃₉×#37302 #48031898

Order 35584.

2974 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2867×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2673×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2669×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2657×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2641×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2544×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2541×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2433×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	#540×C₁₃₉	—	2	8	no	—
17	#535×C₁₃₉	—	2	8	no	—
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#127×C₁₃₉	C₂²	1	8	yes	complemented
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	8	yes	complemented
34	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
35	C₂×#120×C₁₃₉	C₂²	1	8	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
37	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
38	#394×C₁₃₉	C₂²	1	8	yes	complemented
39	#394×C₁₃₉	C₂²	1	8	yes	complemented
40	#392×C₁₃₉	C₂²	1	8	yes	—
41	#392×C₁₃₉	C₂²	1	8	yes	—
42	#392×C₁₃₉	C₂²	1	8	yes	complemented
43	#392×C₁₃₉	C₂²	1	8	yes	complemented
44	#391×C₁₃₉	C₂²	1	2	yes	complemented
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	2	yes	complemented
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#388×C₁₃₉	C₂²	1	8	yes	complemented
50	#387×C₁₃₉	C₂²	1	4	yes	complemented
51	#386×C₁₃₉	C₂²	1	8	yes	complemented
52	#386×C₁₃₉	C₂²	1	8	yes	complemented
53	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
58	C₂×#41×C₁₃₉	—	2	4	no	—
59	C₂×#41×C₁₃₉	—	4	4	no	—
60	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃₉	—	2	4	no	—
62	C₂²×D₄×C₁₃₉	—	4	4	no	—
63	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	#127×C₁₃₉	—	2	4	no	—
80	#127×C₁₃₉	—	2	4	no	—
81	#127×C₁₃₉	—	2	4	no	—
82	#127×C₁₃₉	—	4	4	no	—
83	#127×C₁₃₉	—	4	4	no	—
84	#127×C₁₃₉	—	4	4	no	—
85	#127×C₁₃₉	—	4	16	no	—
86	#125×C₁₃₉	—	2	4	no	—
87	#124×C₁₃₉	—	2	4	no	—
88	#124×C₁₃₉	—	2	4	no	—
89	#124×C₁₃₉	—	4	4	no	—
90	#123×C₁₃₉	—	2	16	no	—
91	#121×C₁₃₉	—	2	8	no	—
92	#121×C₁₃₉	—	2	16	no	—
93	#121×C₁₃₉	—	2	16	no	—
94	#121×C₁₃₉	—	4	16	no	—
95	#120×C₁₃₉	—	2	16	no	—
96	#120×C₁₃₉	—	4	16	no	—
97	C₄×D₄×C₁₃₉	—	2	8	no	—
98	#117×C₁₃₉	D₄	1	8	yes	complemented
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
118	#95×C₁₃₉	C₂³	1	4	yes	—
119	#95×C₁₃₉	C₂³	1	4	yes	—
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	8	yes	—
122	C₂⁴×C₁₃₉	—	2	4	no	—
123	C₂⁴×C₁₃₉	—	4	4	no	—
124	C₂⁴×C₁₃₉	—	4	8	no	—
125	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
126	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
127	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
128	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
129	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
130	#41×C₁₃₉	—	4	16	no	—
131	C₂×Q₈×C₁₃₉	—	2	2	no	—
132	C₂×Q₈×C₁₃₉	—	2	4	no	—
133	C₂×D₄×C₁₃₉	—	2	4	no	—
134	C₂×D₄×C₁₃₉	—	2	8	no	—
135	C₂×D₄×C₁₃₉	—	2	4	no	—
136	C₂×D₄×C₁₃₉	—	2	4	no	—
137	C₂×D₄×C₁₃₉	—	2	2	no	—
138	C₂×D₄×C₁₃₉	—	2	2	no	—
139	C₂×D₄×C₁₃₉	—	2	2	no	—
140	C₂×D₄×C₁₃₉	—	2	8	no	—
141	C₂×D₄×C₁₃₉	—	2	8	no	—
142	C₂×D₄×C₁₃₉	—	2	8	no	—
143	C₂×D₄×C₁₃₉	—	2	4	no	—
144	C₂×D₄×C₁₃₉	—	2	4	no	—
145	C₂×D₄×C₁₃₉	—	2	4	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	2	4	no	—
148	C₂×D₄×C₁₃₉	—	2	16	no	—
149	C₂×D₄×C₁₃₉	—	2	16	no	—
150	C₂×D₄×C₁₃₉	—	4	4	no	—
151	C₂×D₄×C₁₃₉	—	4	4	no	—
152	C₂×D₄×C₁₃₉	—	4	16	no	—
153	C₂×D₄×C₁₃₉	—	4	8	no	—
154	C₂×D₄×C₁₃₉	—	4	8	no	—
155	C₂×D₄×C₁₃₉	—	4	8	no	—
156	C₂×D₄×C₁₃₉	—	4	8	no	—
157	C₂×D₄×C₁₃₉	—	4	8	no	—
158	C₂×D₄×C₁₃₉	—	4	8	no	—
159	C₂×D₄×C₁₃₉	—	4	8	no	—
160	C₂×D₄×C₁₃₉	—	4	8	no	—
161	C₂×D₄×C₁₃₉	—	4	8	no	—
162	C₂×D₄×C₁₃₉	—	4	8	no	—
163	C₂×D₄×C₁₃₉	—	4	8	no	—
164	C₂²×C₄×C₁₃₉	—	2	4	no	—
165	C₂²×C₄×C₁₃₉	—	2	4	no	—
166	C₂²×C₄×C₁₃₉	—	2	8	no	—
167	C₂²×C₄×C₁₃₉	—	4	4	no	—
168	C₂²×C₄×C₁₃₉	—	4	8	no	—
169	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₄⋊C₄×C₁₃₉	—	2	8	no	—
180	C₄⋊C₄×C₁₃₉	—	2	8	no	—
181	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
182	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
187	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
188	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
191	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
192	C₄²×C₁₃₉	—	2	4	no	—
193	C₄²×C₁₃₉	—	2	8	no	—
194	C₄²×C₁₃₉	—	2	4	no	—
195	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
196	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
197	C₂³×C₁₃₉	—	2	4	no	—
198	C₂³×C₁₃₉	—	2	2	no	—
199	C₂³×C₁₃₉	—	2	4	no	—
200	C₂³×C₁₃₉	—	2	2	no	—
201	C₂³×C₁₃₉	—	2	2	no	—
202	C₂³×C₁₃₉	—	2	2	no	—
203	C₂³×C₁₃₉	—	2	8	no	—
204	C₂³×C₁₃₉	—	2	4	no	—
205	C₂³×C₁₃₉	—	2	8	no	—
206	C₂³×C₁₃₉	—	2	8	no	—
207	C₂³×C₁₃₉	—	2	4	no	—
208	C₂³×C₁₃₉	—	2	8	no	—
209	C₂³×C₁₃₉	—	2	4	no	—
210	C₂³×C₁₃₉	—	2	8	no	—
211	C₂³×C₁₃₉	—	2	4	no	—
212	C₂³×C₁₃₉	—	2	4	no	—
213	C₂³×C₁₃₉	—	4	8	no	—
214	C₂³×C₁₃₉	—	8	8	no	—
215	C₂³×C₁₃₉	—	8	16	no	—
216	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
217	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
218	Q₈×C₁₃₉	—	4	4	no	—
219	D₄×C₁₃₉	—	4	8	no	—
220	D₄×C₁₃₉	—	4	8	no	—
221	D₄×C₁₃₉	—	4	8	no	—
222	D₄×C₁₃₉	—	4	4	no	—
223	D₄×C₁₃₉	—	4	4	no	—
224	D₄×C₁₃₉	—	4	4	no	—
225	D₄×C₁₃₉	—	8	8	no	—
226	D₄×C₁₃₉	—	8	8	no	—
227	D₄×C₁₃₉	—	8	8	no	—
228	D₄×C₁₃₉	—	8	16	no	—
229	D₄×C₁₃₉	—	8	16	no	—
230	D₄×C₁₃₉	—	8	8	no	—
231	D₄×C₁₃₉	—	8	16	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	4	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	8	no	—
238	C₂×C₄×C₁₃₉	—	2	2	no	—
239	C₂×C₄×C₁₃₉	—	2	4	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	8	no	—
242	C₂×C₄×C₁₃₉	—	2	4	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	4	8	no	—
246	C₂×C₄×C₁₃₉	—	8	8	no	—
247	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	8	yes	—
252	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
253	C₂²×C₁₃₉	—	2	2	no	—
254	C₂²×C₁₃₉	—	2	4	no	—
255	C₂²×C₁₃₉	—	4	4	no	—
256	C₂²×C₁₃₉	—	4	2	no	—
257	C₂²×C₁₃₉	—	4	2	no	—
258	C₂²×C₁₃₉	—	4	2	no	—
259	C₂²×C₁₃₉	—	4	4	no	—
260	C₂²×C₁₃₉	—	4	4	no	—
261	C₂²×C₁₃₉	—	4	4	no	—
262	C₂²×C₁₃₉	—	4	4	no	—
263	C₂²×C₁₃₉	—	4	4	no	—
264	C₂²×C₁₃₉	—	4	4	no	—
265	C₂²×C₁₃₉	—	4	8	no	—
266	C₂²×C₁₃₉	—	4	8	no	—
267	C₂²×C₁₃₉	—	4	8	no	—
268	C₂²×C₁₃₉	—	4	8	no	—
269	C₂²×C₁₃₉	—	4	8	no	—
270	C₂²×C₁₃₉	—	8	16	no	—
271	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
272	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
273	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	4	yes	—
274	C₄×C₁₃₉	—	2	2	no	—
275	C₄×C₁₃₉	—	2	4	no	—
276	C₄×C₁₃₉	—	2	4	no	—
277	C₄×C₁₃₉	—	2	8	no	—
278	C₄×C₁₃₉	—	4	2	no	—
279	C₄×C₁₃₉	—	4	4	no	—
280	C₄×C₁₃₉	—	4	4	no	—
281	C₄×C₁₃₉	#535	1	4	yes	—
282	C₂×C₁₃₉	—	4	2	no	—
283	C₂×C₁₃₉	—	8	2	no	—
284	C₂×C₁₃₉	—	8	4	no	—
285	C₂×C₁₃₉	—	8	2	no	—
286	C₂×C₁₃₉	—	8	2	no	—
287	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
288	C₂×C₁₃₉	#3498	1	2	yes	—
289	C₂×C₁₃₉	#3543	1	4	yes	—
290	#37302	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₁₃₉	#37302	1	1	yes	characteristic, direct product factor, Sylow
292	C₂×#540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
293	C₂×#535	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	#2867	C₂×C₁₃₉	1	1	yes	characteristic, complemented
295	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
296	#2673	C₂×C₁₃₉	1	8	yes	complemented
297	#2669	C₂×C₁₃₉	1	8	yes	complemented
298	#2657	C₂×C₁₃₉	1	1	yes	characteristic, complemented
299	#2641	C₂×C₁₃₉	1	1	yes	characteristic, complemented
300	#2544	C₂×C₁₃₉	1	2	yes	complemented
301	#2541	C₂×C₁₃₉	1	2	yes	complemented
302	#2433	C₂×C₁₃₉	1	2	yes	complemented
303	#2431	C₂×C₁₃₉	1	2	yes	complemented
304	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
305	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
306	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
307	#540	—	2	8	no	—
308	#535	—	2	8	no	—
309	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
310	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
311	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
312	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
313	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
314	C₂×#127	C₂²×C₁₃₉	1	8	yes	complemented
315	C₂×#127	C₂²×C₁₃₉	1	2	yes	complemented
316	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
317	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
318	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
319	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
320	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
321	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
322	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
323	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
324	C₂×#121	C₂²×C₁₃₉	1	8	yes	complemented
325	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
326	C₂×#120	C₂²×C₁₃₉	1	8	yes	—
327	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
328	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
329	#394	C₂²×C₁₃₉	1	8	yes	complemented
330	#394	C₂²×C₁₃₉	1	8	yes	complemented
331	#392	C₂²×C₁₃₉	1	8	yes	—
332	#392	C₂²×C₁₃₉	1	8	yes	—
333	#392	C₂²×C₁₃₉	1	8	yes	complemented
334	#392	C₂²×C₁₃₉	1	8	yes	complemented
335	#391	C₂²×C₁₃₉	1	2	yes	complemented
336	#390	C₂²×C₁₃₉	1	2	yes	—
337	#390	C₂²×C₁₃₉	1	2	yes	—
338	#390	C₂²×C₁₃₉	1	2	yes	complemented
339	#388	C₂²×C₁₃₉	1	4	yes	—
340	#388	C₂²×C₁₃₉	1	8	yes	complemented
341	#387	C₂²×C₁₃₉	1	4	yes	complemented
342	#386	C₂²×C₁₃₉	1	8	yes	complemented
343	#386	C₂²×C₁₃₉	1	8	yes	complemented
344	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
345	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
346	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
347	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
348	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
349	C₂×#41	—	2	4	no	—
350	C₂×#41	—	4	4	no	—
351	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
352	C₂²×D₄	—	2	4	no	—
353	C₂²×D₄	—	4	4	no	—
354	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
355	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
359	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
361	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
363	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
364	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
365	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
366	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
367	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
369	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
370	#127	—	2	4	no	—
371	#127	—	2	4	no	—
372	#127	—	2	4	no	—
373	#127	—	4	4	no	—
374	#127	—	4	4	no	—
375	#127	—	4	4	no	—
376	#127	—	4	16	no	—
377	#125	—	2	4	no	—
378	#124	—	2	4	no	—
379	#124	—	2	4	no	—
380	#124	—	4	4	no	—
381	#123	—	2	16	no	—
382	#121	—	2	8	no	—
383	#121	—	2	16	no	—
384	#121	—	2	16	no	—
385	#121	—	4	16	no	—
386	#120	—	2	16	no	—
387	#120	—	4	16	no	—
388	C₄×D₄	—	2	8	no	—
389	#117	D₄×C₁₃₉	1	8	yes	complemented
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
406	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
409	#95	C₂³×C₁₃₉	1	4	yes	—
410	#95	C₂³×C₁₃₉	1	4	yes	—
411	#95	C₂³×C₁₃₉	1	4	yes	—
412	#95	C₂³×C₁₃₉	1	8	yes	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	4	4	no	—
415	C₂⁴	—	4	8	no	—
416	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
417	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
418	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
419	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
420	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
421	#41	—	4	16	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	8	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	16	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	—	4	16	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	4	8	no	—
447	C₂×D₄	—	4	8	no	—
448	C₂×D₄	—	4	8	no	—
449	C₂×D₄	—	4	8	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	8	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	4	8	no	—
460	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	16	no	—
479	C₂²⋊C₄	—	4	8	no	—
480	C₂²⋊C₄	—	4	8	no	—
481	C₂²⋊C₄	—	4	8	no	—
482	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	8	no	—
485	C₄²	—	2	4	no	—
486	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
487	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	8	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	8	no	—
498	C₂³	—	2	8	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	4	8	no	—
505	C₂³	—	8	8	no	—
506	C₂³	—	8	16	no	—
507	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
508	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
509	Q₈	—	4	4	no	—
510	D₄	—	4	8	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	8	no	—
516	D₄	—	8	16	no	—
517	D₄	—	8	16	no	—
518	D₄	—	8	8	no	—
519	D₄	—	8	8	no	—
520	D₄	—	8	8	no	—
521	D₄	—	8	8	no	—
522	D₄	—	8	16	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	8	8	no	—
538	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
542	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	8	yes	—
543	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	8	no	—
548	C₂²	—	4	8	no	—
549	C₂²	—	4	8	no	—
550	C₂²	—	4	8	no	—
551	C₂²	—	4	8	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	8	16	no	—
562	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
563	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
564	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	4	yes	—
565	C₄	—	2	8	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	4	no	—
569	C₄	—	4	4	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	#535×C₁₃₉	1	4	yes	—
573	C₂	—	4	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	2	no	—
576	C₂	—	8	4	no	—
577	C₂	—	8	2	no	—
578	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
579	C₂	#3498×C₁₃₉	1	2	yes	—
580	C₂	#3543×C₁₃₉	1	4	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. C₂×#540×C₁₃₉	C₂	semidirect
2. C₂×#535×C₁₃₉	C₂	semidirect
3. #2867×C₁₃₉	C₂	semidirect
4. #2861×C₁₃₉	C₂	semidirect
5. #2673×C₁₃₉	C₂	semidirect
6. #2669×C₁₃₉	C₂	semidirect
7. #2657×C₁₃₉	C₂	semidirect
8. #2641×C₁₃₉	C₂	semidirect
9. #2544×C₁₃₉	C₂	semidirect
10. #2541×C₁₃₉	C₂	semidirect
11. #2433×C₁₃₉	C₂	semidirect
12. #2431×C₁₃₉	C₂	semidirect
13. #2298×C₁₃₉	C₂	semidirect
22. C₂×#127×C₁₃₉	C₂²	semidirect
23. C₂×#127×C₁₃₉	C₂²	semidirect
24. C₂×#127×C₁₃₉	C₂²	semidirect
25. C₂×#125×C₁₃₉	C₂²	semidirect
28. C₂×#124×C₁₃₉	C₂²	semidirect
29. C₂×#123×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
38. #394×C₁₃₉	C₂²	semidirect
39. #394×C₁₃₉	C₂²	semidirect
42. #392×C₁₃₉	C₂²	semidirect
43. #392×C₁₃₉	C₂²	semidirect
44. #391×C₁₃₉	C₂²	semidirect
47. #390×C₁₃₉	C₂²	semidirect
49. #388×C₁₃₉	C₂²	semidirect
50. #387×C₁₃₉	C₂²	semidirect
51. #386×C₁₃₉	C₂²	semidirect
52. #386×C₁₃₉	C₂²	semidirect
53. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
55. #376×C₁₃₉	C₂²	semidirect
56. C₄³×C₁₃₉	C₂²	semidirect
98. #117×C₁₃₉	D₄	semidirect
290. #37302	C₁₃₉	direct (N × H)
291. C₁₃₉	#37302	direct (N × H)
292. C₂×#540	C₂×C₁₃₉	semidirect
293. C₂×#535	C₂×C₁₃₉	semidirect
294. #2867	C₂×C₁₃₉	semidirect
295. #2861	C₂×C₁₃₉	semidirect
296. #2673	C₂×C₁₃₉	semidirect
297. #2669	C₂×C₁₃₉	semidirect
298. #2657	C₂×C₁₃₉	semidirect
299. #2641	C₂×C₁₃₉	semidirect
300. #2544	C₂×C₁₃₉	semidirect
301. #2541	C₂×C₁₃₉	semidirect
302. #2433	C₂×C₁₃₉	semidirect
303. #2431	C₂×C₁₃₉	semidirect
304. #2298	C₂×C₁₃₉	semidirect
313. C₂×#127	C₂²×C₁₃₉	semidirect
314. C₂×#127	C₂²×C₁₃₉	semidirect
315. C₂×#127	C₂²×C₁₃₉	semidirect
316. C₂×#125	C₂²×C₁₃₉	semidirect
319. C₂×#124	C₂²×C₁₃₉	semidirect
320. C₂×#123	C₂²×C₁₃₉	semidirect
324. C₂×#121	C₂²×C₁₃₉	semidirect
327. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
329. #394	C₂²×C₁₃₉	semidirect
330. #394	C₂²×C₁₃₉	semidirect
333. #392	C₂²×C₁₃₉	semidirect
334. #392	C₂²×C₁₃₉	semidirect
335. #391	C₂²×C₁₃₉	semidirect
338. #390	C₂²×C₁₃₉	semidirect
340. #388	C₂²×C₁₃₉	semidirect
341. #387	C₂²×C₁₃₉	semidirect
342. #386	C₂²×C₁₃₉	semidirect
343. #386	C₂²×C₁₃₉	semidirect
344. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
346. #376	C₂²×C₁₃₉	semidirect
347. C₄³	C₂²×C₁₃₉	semidirect
389. #117	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×#540×C₁₃₉	2
C₂×#535×C₁₃₉	2
#2867×C₁₃₉	2
#2861×C₁₃₉	2
#2673×C₁₃₉	2
#2669×C₁₃₉	2
#2657×C₁₃₉	2
#2641×C₁₃₉	2
#2544×C₁₃₉	2
#2541×C₁₃₉	2
#2433×C₁₃₉	2
#2431×C₁₃₉	2
#2298×C₁₃₉	2
#37302	139

Subgroups — C139×#37302 #48031898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37302 #48031898