Subgroups — C₁₃₉×#36127 #48030723

Order 35584.

3242 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2547×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2537×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2432×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2422×C₁₃₉	C₂	1	8	yes	maximal, complemented
9	D₄×C₄⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
13	#547×C₁₃₉	—	2	16	no	—
14	#532×C₁₃₉	—	2	16	no	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#123×C₁₃₉	C₂²	1	8	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	8	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
30	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
31	#397×C₁₃₉	C₂²	1	8	yes	—
32	#394×C₁₃₉	C₂²	1	16	yes	—
33	#391×C₁₃₉	C₂²	1	4	yes	—
34	#390×C₁₃₉	C₂²	1	4	yes	—
35	#390×C₁₃₉	C₂²	1	2	yes	—
36	#389×C₁₃₉	C₂²	1	8	yes	—
37	#385×C₁₃₉	C₂²	1	16	yes	—
38	#384×C₁₃₉	C₂²	1	4	yes	—
39	#384×C₁₃₉	C₂²	1	1	yes	characteristic
40	#384×C₁₃₉	C₂²	1	4	yes	—
41	#380×C₁₃₉	C₂²	1	8	yes	—
42	#380×C₁₃₉	C₂²	1	8	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
46	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
47	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×#41×C₁₃₉	—	2	16	no	—
49	C₂×#41×C₁₃₉	—	2	16	no	—
50	C₂×#41×C₁₃₉	—	4	8	no	—
51	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
53	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
59	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
61	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
62	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
63	#127×C₁₃₉	D₄	1	8	yes	complemented
64	#124×C₁₃₉	—	2	16	no	—
65	#123×C₁₃₉	—	2	32	no	—
66	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
67	#121×C₁₃₉	—	2	32	no	—
68	#121×C₁₃₉	—	2	16	no	—
69	C₄×D₄×C₁₃₉	—	2	32	no	—
70	C₄×D₄×C₁₃₉	—	2	8	no	—
71	C₄×D₄×C₁₃₉	—	2	8	no	—
72	C₄×D₄×C₁₃₉	—	2	16	no	—
73	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
74	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃₉	—	2	8	no	—
91	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
98	#95×C₁₃₉	C₂³	1	2	yes	—
99	#95×C₁₃₉	C₂³	1	16	yes	—
100	#95×C₁₃₉	C₂³	1	4	yes	—
101	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
102	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
103	#41×C₁₃₉	—	4	64	no	—
104	C₂×Q₈×C₁₃₉	—	2	8	no	—
105	C₂×Q₈×C₁₃₉	—	2	8	no	—
106	C₂×Q₈×C₁₃₉	—	2	8	no	—
107	C₂×D₄×C₁₃₉	—	2	16	no	—
108	C₂×D₄×C₁₃₉	—	2	16	no	—
109	C₂×D₄×C₁₃₉	—	2	4	no	—
110	C₂×D₄×C₁₃₉	—	2	4	no	—
111	C₂×D₄×C₁₃₉	—	2	8	no	—
112	C₂×D₄×C₁₃₉	—	2	4	no	—
113	C₂×D₄×C₁₃₉	—	2	8	no	—
114	C₂×D₄×C₁₃₉	—	4	8	no	—
115	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
116	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
117	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
118	C₂²×C₄×C₁₃₉	—	2	4	no	—
119	C₂²×C₄×C₁₃₉	—	2	4	no	—
120	C₂²×C₄×C₁₃₉	—	2	16	no	—
121	C₂²×C₄×C₁₃₉	—	2	8	no	—
122	C₂²×C₄×C₁₃₉	—	2	8	no	—
123	C₂²×C₄×C₁₃₉	—	2	16	no	—
124	C₂²×C₄×C₁₃₉	—	2	16	no	—
125	C₂²×C₄×C₁₃₉	—	2	8	no	—
126	C₂²×C₄×C₁₃₉	—	2	8	no	—
127	C₂²×C₄×C₁₃₉	—	4	8	no	—
128	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	C₄⋊C₄×C₁₃₉	—	2	8	no	—
139	C₄⋊C₄×C₁₃₉	—	2	16	no	—
140	C₄⋊C₄×C₁₃₉	—	2	16	no	—
141	C₄⋊C₄×C₁₃₉	—	2	4	no	—
142	C₄⋊C₄×C₁₃₉	—	2	8	no	—
143	C₄⋊C₄×C₁₃₉	—	2	4	no	—
144	C₄⋊C₄×C₁₃₉	—	2	8	no	—
145	C₄⋊C₄×C₁₃₉	—	4	8	no	—
146	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
147	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
148	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
149	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
152	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
153	C₄²×C₁₃₉	—	2	8	no	—
154	C₄²×C₁₃₉	—	2	4	no	—
155	C₄²×C₁₃₉	—	2	2	no	—
156	C₄²×C₁₃₉	—	2	4	no	—
157	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
158	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
159	C₄²×C₁₃₉	#41	1	8	yes	complemented
160	C₂³×C₁₃₉	—	2	4	no	—
161	C₂³×C₁₃₉	—	2	2	no	—
162	C₂³×C₁₃₉	—	2	4	no	—
163	C₂³×C₁₃₉	—	2	8	no	—
164	C₂³×C₁₃₉	—	2	2	no	—
165	C₂³×C₁₃₉	—	2	4	no	—
166	C₂³×C₁₃₉	—	2	4	no	—
167	C₂³×C₁₃₉	—	2	8	no	—
168	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
169	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
170	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
171	Q₈×C₁₃₉	—	4	16	no	—
172	D₄×C₁₃₉	—	2	8	no	—
173	D₄×C₁₃₉	—	2	16	no	—
174	D₄×C₁₃₉	—	2	32	no	—
175	D₄×C₁₃₉	—	4	32	no	—
176	C₂×C₄×C₁₃₉	—	2	2	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	16	no	—
182	C₂×C₄×C₁₃₉	—	2	4	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	8	no	—
185	C₂×C₄×C₁₃₉	—	2	8	no	—
186	C₂×C₄×C₁₃₉	—	2	8	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	2	8	no	—
189	C₂×C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₄×C₁₃₉	—	4	32	no	—
191	C₂×C₄×C₁₃₉	—	4	16	no	—
192	C₂×C₄×C₁₃₉	—	4	16	no	—
193	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
200	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
201	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
202	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
203	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
204	C₂²×C₁₃₉	—	2	4	no	—
205	C₂²×C₁₃₉	—	2	4	no	—
206	C₂²×C₁₃₉	—	2	8	no	—
207	C₂²×C₁₃₉	—	2	16	no	—
208	C₂²×C₁₃₉	—	2	4	no	—
209	C₂²×C₁₃₉	—	4	4	no	—
210	C₂²×C₁₃₉	—	4	4	no	—
211	C₂²×C₁₃₉	—	4	4	no	—
212	C₂²×C₁₃₉	—	4	4	no	—
213	C₂²×C₁₃₉	—	4	8	no	—
214	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
215	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
216	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
217	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
219	C₄×C₁₃₉	—	2	4	no	—
220	C₄×C₁₃₉	—	2	2	no	—
221	C₄×C₁₃₉	—	2	4	no	—
222	C₄×C₁₃₉	—	4	4	no	—
223	C₄×C₁₃₉	—	4	8	no	—
224	C₄×C₁₃₉	—	4	4	no	—
225	C₄×C₁₃₉	#532	1	4	yes	complemented
226	C₄×C₁₃₉	D₄²	1	4	yes	—
227	C₄×C₁₃₉	#547	1	8	yes	complemented
228	C₂×C₁₃₉	—	4	4	no	—
229	C₂×C₁₃₉	—	4	8	no	—
230	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
231	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
232	C₂×C₁₃₉	C₂×#547	1	2	yes	—
233	C₂×C₁₃₉	#3499	1	1	yes	characteristic
234	C₂×C₁₃₉	#3511	1	2	yes	—
235	#36127	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₁₃₉	#36127	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×#547	C₂×C₁₃₉	1	2	yes	complemented
238	C₂×#532	C₂×C₁₃₉	1	2	yes	complemented
239	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
240	#2857	C₂×C₁₃₉	1	2	yes	complemented
241	#2547	C₂×C₁₃₉	1	2	yes	complemented
242	#2537	C₂×C₁₃₉	1	4	yes	complemented
243	#2432	C₂×C₁₃₉	1	4	yes	complemented
244	#2422	C₂×C₁₃₉	1	8	yes	complemented
245	D₄×C₄⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
246	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
247	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
248	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
249	#547	—	2	16	no	—
250	#532	—	2	16	no	—
251	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
252	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
253	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
254	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
255	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
256	C₂×#123	C₂²×C₁₃₉	1	8	yes	—
257	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
258	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
259	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
260	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
261	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
262	C₂×C₄×D₄	C₂²×C₁₃₉	1	8	yes	—
263	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
264	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
266	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
267	#397	C₂²×C₁₃₉	1	8	yes	—
268	#394	C₂²×C₁₃₉	1	16	yes	—
269	#391	C₂²×C₁₃₉	1	4	yes	—
270	#390	C₂²×C₁₃₉	1	4	yes	—
271	#390	C₂²×C₁₃₉	1	2	yes	—
272	#389	C₂²×C₁₃₉	1	8	yes	—
273	#385	C₂²×C₁₃₉	1	16	yes	—
274	#384	C₂²×C₁₃₉	1	1	yes	characteristic
275	#384	C₂²×C₁₃₉	1	4	yes	—
276	#384	C₂²×C₁₃₉	1	4	yes	—
277	#380	C₂²×C₁₃₉	1	8	yes	—
278	#380	C₂²×C₁₃₉	1	8	yes	—
279	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
280	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
281	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
282	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
283	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
284	C₂×#41	—	2	16	no	—
285	C₂×#41	—	2	16	no	—
286	C₂×#41	—	4	8	no	—
287	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
288	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
289	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
291	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
293	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
294	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
295	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
296	C₄⋊Q₈	—	2	8	no	—
297	C₄⋊Q₈	—	2	8	no	—
298	C₄⋊Q₈	—	4	4	no	—
299	#127	D₄×C₁₃₉	1	8	yes	complemented
300	#124	—	2	16	no	—
301	#123	—	2	32	no	—
302	C₂²⋊Q₈	—	2	16	no	—
303	#121	—	2	32	no	—
304	#121	—	2	16	no	—
305	C₄×D₄	—	2	32	no	—
306	C₄×D₄	—	2	8	no	—
307	C₄×D₄	—	2	16	no	—
308	C₄×D₄	—	2	8	no	—
309	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
310	C₂×C₄⋊C₄	—	2	16	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
326	C₂×C₄²	—	2	8	no	—
327	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
328	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
329	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
334	#95	C₂³×C₁₃₉	1	4	yes	—
335	#95	C₂³×C₁₃₉	1	2	yes	—
336	#95	C₂³×C₁₃₉	1	16	yes	—
337	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
338	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
339	#41	—	4	64	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	16	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
352	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
353	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	16	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	16	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
365	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
368	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	16	no	—
376	C₄⋊C₄	—	2	16	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	4	8	no	—
382	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
383	C₂²⋊C₄	—	2	32	no	—
384	C₂²⋊C₄	—	2	16	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	16	no	—
388	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
389	C₄²	—	2	8	no	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	4	no	—
393	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
394	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
395	C₄²	#41×C₁₃₉	1	8	yes	complemented
396	C₂³	—	2	4	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	8	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	8	no	—
404	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
405	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
406	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
407	Q₈	—	4	16	no	—
408	D₄	—	2	8	no	—
409	D₄	—	2	16	no	—
410	D₄	—	2	32	no	—
411	D₄	—	4	32	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	16	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	32	no	—
427	C₂×C₄	—	4	16	no	—
428	C₂×C₄	—	4	16	no	—
429	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
433	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
435	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
436	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
437	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
438	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
439	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	16	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	8	no	—
450	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
451	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
452	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
453	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
454	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
455	C₄	—	2	4	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	4	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	8	no	—
460	C₄	—	4	4	no	—
461	C₄	#532×C₁₃₉	1	4	yes	complemented
462	C₄	D₄²×C₁₃₉	1	4	yes	—
463	C₄	#547×C₁₃₉	1	8	yes	complemented
464	C₂	—	4	4	no	—
465	C₂	—	4	8	no	—
466	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
467	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
468	C₂	C₂×#547×C₁₃₉	1	2	yes	—
469	C₂	#3499×C₁₃₉	1	1	yes	characteristic
470	C₂	#3511×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. C₂×#547×C₁₃₉	C₂	semidirect
2. C₂×#532×C₁₃₉	C₂	semidirect
3. #2868×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2547×C₁₃₉	C₂	semidirect
6. #2537×C₁₃₉	C₂	semidirect
7. #2432×C₁₃₉	C₂	semidirect
8. #2422×C₁₃₉	C₂	semidirect
9. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
10. C₄×#127×C₁₃₉	C₂	semidirect
11. C₄²×D₄×C₁₃₉	C₂	semidirect
63. #127×C₁₃₉	D₄	semidirect
73. C₄×D₄×C₁₃₉	D₄	semidirect
159. C₄²×C₁₃₉	#41	semidirect
225. C₄×C₁₃₉	#532	semidirect
227. C₄×C₁₃₉	#547	semidirect
235. #36127	C₁₃₉	direct (N × H)
236. C₁₃₉	#36127	direct (N × H)
237. C₂×#547	C₂×C₁₃₉	semidirect
238. C₂×#532	C₂×C₁₃₉	semidirect
239. #2868	C₂×C₁₃₉	semidirect
240. #2857	C₂×C₁₃₉	semidirect
241. #2547	C₂×C₁₃₉	semidirect
242. #2537	C₂×C₁₃₉	semidirect
243. #2432	C₂×C₁₃₉	semidirect
244. #2422	C₂×C₁₃₉	semidirect
245. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
246. C₄×#127	C₂×C₁₃₉	semidirect
247. C₄²×D₄	C₂×C₁₃₉	semidirect
299. #127	D₄×C₁₃₉	semidirect
309. C₄×D₄	D₄×C₁₃₉	semidirect
395. C₄²	#41×C₁₃₉	semidirect
461. C₄	#532×C₁₃₉	semidirect
463. C₄	#547×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂×#532×C₁₃₉	2
#2868×C₁₃₉	2
#2857×C₁₃₉	2
#2547×C₁₃₉	2
#2537×C₁₃₉	2
#2432×C₁₃₉	2
#2422×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36127	139

Subgroups — C139×#36127 #48030723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36127 #48030723