Subgroups — C₁₃₉×#36182 #48030778

Order 35584.

2582 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2566×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2512×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2504×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2422×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2416×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2361×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#553×C₁₃₉	—	2	16	no	—
17	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
34	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
36	#397×C₁₃₉	C₂²	1	8	yes	—
37	#396×C₁₃₉	C₂²	1	8	yes	—
38	#394×C₁₃₉	C₂²	1	8	yes	—
39	#390×C₁₃₉	C₂²	1	4	yes	—
40	#390×C₁₃₉	C₂²	1	4	yes	—
41	#390×C₁₃₉	C₂²	1	4	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#390×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	4	yes	—
46	#389×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	8	yes	—
48	#386×C₁₃₉	C₂²	1	8	yes	—
49	#385×C₁₃₉	C₂²	1	8	yes	—
50	#384×C₁₃₉	C₂²	1	4	yes	—
51	#384×C₁₃₉	C₂²	1	1	yes	characteristic
52	#384×C₁₃₉	C₂²	1	2	yes	—
53	#384×C₁₃₉	C₂²	1	1	yes	characteristic
54	#384×C₁₃₉	C₂²	1	1	yes	characteristic
55	#382×C₁₃₉	C₂²	1	2	yes	—
56	#382×C₁₃₉	C₂²	1	2	yes	—
57	#380×C₁₃₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
77	#127×C₁₃₉	—	2	4	no	—
78	#126×C₁₃₉	—	2	16	no	—
79	#125×C₁₃₉	—	2	8	no	—
80	#123×C₁₃₉	—	2	16	no	—
81	#121×C₁₃₉	—	2	16	no	—
82	#121×C₁₃₉	—	2	8	no	—
83	#121×C₁₃₉	—	2	8	no	—
84	#121×C₁₃₉	—	2	16	no	—
85	#121×C₁₃₉	—	4	8	no	—
86	C₄×D₄×C₁₃₉	—	2	8	no	—
87	C₄×D₄×C₁₃₉	—	2	16	no	—
88	C₄×D₄×C₁₃₉	—	2	8	no	—
89	C₄×D₄×C₁₃₉	—	4	8	no	—
90	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
91	#117×C₁₃₉	—	2	8	no	—
92	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
93	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃₉	—	2	4	no	—
118	C₂×C₄²×C₁₃₉	—	2	4	no	—
119	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
129	#95×C₁₃₉	C₂³	1	8	yes	—
130	#95×C₁₃₉	C₂³	1	2	yes	—
131	#95×C₁₃₉	C₂³	1	8	yes	—
132	#95×C₁₃₉	C₂³	1	2	yes	—
133	#95×C₁₃₉	C₂³	1	2	yes	—
134	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
136	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
137	C₂×D₄×C₁₃₉	—	2	4	no	—
138	C₂×D₄×C₁₃₉	—	2	8	no	—
139	C₂×D₄×C₁₃₉	—	2	16	no	—
140	C₂×D₄×C₁₃₉	—	2	8	no	—
141	C₂×D₄×C₁₃₉	—	2	4	no	—
142	C₂×D₄×C₁₃₉	—	2	8	no	—
143	C₂×D₄×C₁₃₉	—	2	4	no	—
144	C₂×D₄×C₁₃₉	—	2	8	no	—
145	C₂×D₄×C₁₃₉	—	2	8	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	4	8	no	—
148	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃₉	—	2	2	no	—
150	C₂²×C₄×C₁₃₉	—	2	2	no	—
151	C₂²×C₄×C₁₃₉	—	2	4	no	—
152	C₂²×C₄×C₁₃₉	—	2	4	no	—
153	C₂²×C₄×C₁₃₉	—	2	2	no	—
154	C₂²×C₄×C₁₃₉	—	2	2	no	—
155	C₂²×C₄×C₁₃₉	—	2	8	no	—
156	C₂²×C₄×C₁₃₉	—	2	4	no	—
157	C₂²×C₄×C₁₃₉	—	2	4	no	—
158	C₂²×C₄×C₁₃₉	—	2	4	no	—
159	C₂²×C₄×C₁₃₉	—	2	8	no	—
160	C₂²×C₄×C₁₃₉	—	4	8	no	—
161	C₂²×C₄×C₁₃₉	—	4	8	no	—
162	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
177	C₄⋊C₄×C₁₃₉	—	2	4	no	—
178	C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₄⋊C₄×C₁₃₉	—	2	8	no	—
180	C₄⋊C₄×C₁₃₉	—	2	4	no	—
181	C₄⋊C₄×C₁₃₉	—	2	8	no	—
182	C₄⋊C₄×C₁₃₉	—	2	8	no	—
183	C₄⋊C₄×C₁₃₉	—	2	4	no	—
184	C₄⋊C₄×C₁₃₉	—	2	8	no	—
185	C₄⋊C₄×C₁₃₉	—	2	8	no	—
186	C₄⋊C₄×C₁₃₉	—	2	8	no	—
187	C₄⋊C₄×C₁₃₉	—	4	8	no	—
188	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
189	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
191	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
192	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
196	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
197	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
198	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
199	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
200	C₄²×C₁₃₉	—	2	8	no	—
201	C₄²×C₁₃₉	—	2	2	no	—
202	C₄²×C₁₃₉	—	2	4	no	—
203	C₄²×C₁₃₉	—	2	4	no	—
204	C₄²×C₁₃₉	—	2	2	no	—
205	C₄²×C₁₃₉	—	2	4	no	—
206	C₄²×C₁₃₉	—	2	4	no	—
207	C₄²×C₁₃₉	—	2	2	no	—
208	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
209	C₄²×C₁₃₉	#41	1	4	yes	—
210	C₂³×C₁₃₉	—	2	1	no	—
211	C₂³×C₁₃₉	—	2	2	no	—
212	C₂³×C₁₃₉	—	2	1	no	—
213	C₂³×C₁₃₉	—	2	2	no	—
214	C₂³×C₁₃₉	—	2	1	no	—
215	C₂³×C₁₃₉	—	2	2	no	—
216	C₂³×C₁₃₉	—	2	1	no	—
217	C₂³×C₁₃₉	—	2	4	no	—
218	C₂³×C₁₃₉	—	2	8	no	—
219	C₂³×C₁₃₉	—	2	4	no	—
220	C₂³×C₁₃₉	—	2	8	no	—
221	C₂³×C₁₃₉	—	2	4	no	—
222	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
224	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
225	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
226	D₄×C₁₃₉	—	2	8	no	—
227	D₄×C₁₃₉	—	4	16	no	—
228	D₄×C₁₃₉	—	4	8	no	—
229	D₄×C₁₃₉	—	4	16	no	—
230	D₄×C₁₃₉	—	8	8	no	—
231	C₂×C₄×C₁₃₉	—	2	1	no	—
232	C₂×C₄×C₁₃₉	—	2	1	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	2	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	1	no	—
238	C₂×C₄×C₁₃₉	—	2	1	no	—
239	C₂×C₄×C₁₃₉	—	2	8	no	—
240	C₂×C₄×C₁₃₉	—	2	8	no	—
241	C₂×C₄×C₁₃₉	—	2	16	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	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	2	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	8	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	8	no	—
252	C₂×C₄×C₁₃₉	—	2	8	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	4	8	no	—
255	C₂×C₄×C₁₃₉	—	8	8	no	—
256	C₂×C₄×C₁₃₉	—	8	8	no	—
257	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
263	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
265	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
266	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
267	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
268	C₂²×C₁₃₉	—	2	2	no	—
269	C₂²×C₁₃₉	—	2	4	no	—
270	C₂²×C₁₃₉	—	2	2	no	—
271	C₂²×C₁₃₉	—	2	4	no	—
272	C₂²×C₁₃₉	—	2	2	no	—
273	C₂²×C₁₃₉	—	2	2	no	—
274	C₂²×C₁₃₉	—	2	2	no	—
275	C₂²×C₁₃₉	—	4	2	no	—
276	C₂²×C₁₃₉	—	4	2	no	—
277	C₂²×C₁₃₉	—	4	4	no	—
278	C₂²×C₁₃₉	—	4	4	no	—
279	C₂²×C₁₃₉	—	4	8	no	—
280	C₂²×C₁₃₉	—	4	4	no	—
281	C₂²×C₁₃₉	—	4	8	no	—
282	C₂²×C₁₃₉	#532	1	4	yes	—
283	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
284	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
285	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
286	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
288	C₄×C₁₃₉	—	2	2	no	—
289	C₄×C₁₃₉	—	2	2	no	—
290	C₄×C₁₃₉	—	2	2	no	—
291	C₄×C₁₃₉	—	2	4	no	—
292	C₄×C₁₃₉	—	2	2	no	—
293	C₄×C₁₃₉	—	4	4	no	—
294	C₄×C₁₃₉	—	4	2	no	—
295	C₄×C₁₃₉	—	4	4	no	—
296	C₄×C₁₃₉	—	4	4	no	—
297	C₄×C₁₃₉	—	4	2	no	—
298	C₄×C₁₃₉	#547	1	4	yes	—
299	C₄×C₁₃₉	#553	1	8	yes	complemented
300	C₂×C₁₃₉	—	2	4	no	—
301	C₂×C₁₃₉	—	4	2	no	—
302	C₂×C₁₃₉	—	8	4	no	—
303	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
304	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
305	C₂×C₁₃₉	C₂×#553	1	2	yes	—
306	C₂×C₁₃₉	#3498	1	1	yes	characteristic
307	C₂×C₁₃₉	#3511	1	2	yes	—
308	#36182	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₁₃₉	#36182	1	1	yes	characteristic, direct product factor, Sylow
310	C₂×#553	C₂×C₁₃₉	1	2	yes	complemented
311	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
312	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
313	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
314	#2566	C₂×C₁₃₉	1	2	yes	complemented
315	#2512	C₂×C₁₃₉	1	4	yes	complemented
316	#2504	C₂×C₁₃₉	1	2	yes	complemented
317	#2500	C₂×C₁₃₉	1	2	yes	complemented
318	#2422	C₂×C₁₃₉	1	4	yes	complemented
319	#2416	C₂×C₁₃₉	1	4	yes	complemented
320	#2361	C₂×C₁₃₉	1	4	yes	complemented
321	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
322	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
323	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic, complemented
324	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
325	#553	—	2	16	no	—
326	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
327	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
328	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
329	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
330	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
331	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
332	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
333	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
334	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
335	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
336	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
337	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
338	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
339	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
340	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
341	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
342	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
343	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
344	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
345	#397	C₂²×C₁₃₉	1	8	yes	—
346	#396	C₂²×C₁₃₉	1	8	yes	—
347	#394	C₂²×C₁₃₉	1	8	yes	—
348	#390	C₂²×C₁₃₉	1	4	yes	—
349	#390	C₂²×C₁₃₉	1	2	yes	—
350	#390	C₂²×C₁₃₉	1	2	yes	—
351	#390	C₂²×C₁₃₉	1	2	yes	—
352	#390	C₂²×C₁₃₉	1	4	yes	—
353	#390	C₂²×C₁₃₉	1	4	yes	—
354	#389	C₂²×C₁₃₉	1	4	yes	—
355	#389	C₂²×C₁₃₉	1	4	yes	—
356	#388	C₂²×C₁₃₉	1	8	yes	—
357	#386	C₂²×C₁₃₉	1	8	yes	—
358	#385	C₂²×C₁₃₉	1	8	yes	—
359	#384	C₂²×C₁₃₉	1	1	yes	characteristic
360	#384	C₂²×C₁₃₉	1	2	yes	—
361	#384	C₂²×C₁₃₉	1	1	yes	characteristic
362	#384	C₂²×C₁₃₉	1	1	yes	characteristic
363	#384	C₂²×C₁₃₉	1	4	yes	—
364	#382	C₂²×C₁₃₉	1	2	yes	—
365	#382	C₂²×C₁₃₉	1	2	yes	—
366	#380	C₂²×C₁₃₉	1	4	yes	—
367	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
373	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
374	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
376	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
377	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
378	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
380	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
386	#127	—	2	4	no	—
387	#126	—	2	16	no	—
388	#125	—	2	8	no	—
389	#123	—	2	16	no	—
390	#121	—	2	16	no	—
391	#121	—	2	8	no	—
392	#121	—	2	8	no	—
393	#121	—	2	16	no	—
394	#121	—	4	8	no	—
395	C₄×D₄	—	2	8	no	—
396	C₄×D₄	—	2	16	no	—
397	C₄×D₄	—	2	8	no	—
398	C₄×D₄	—	4	8	no	—
399	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
400	#117	—	2	8	no	—
401	C₂×C₄⋊C₄	—	2	8	no	—
402	C₂×C₄⋊C₄	—	4	8	no	—
403	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	—	2	4	no	—
428	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
429	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
435	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
438	#95	C₂³×C₁₃₉	1	2	yes	—
439	#95	C₂³×C₁₃₉	1	2	yes	—
440	#95	C₂³×C₁₃₉	1	2	yes	—
441	#95	C₂³×C₁₃₉	1	8	yes	—
442	#95	C₂³×C₁₃₉	1	8	yes	—
443	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
444	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
445	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	16	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	4	8	no	—
457	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	4	8	no	—
470	C₂²×C₄	—	4	8	no	—
471	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
472	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
473	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
474	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	8	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	8	no	—
494	C₄⋊C₄	—	2	8	no	—
495	C₄⋊C₄	—	2	8	no	—
496	C₄⋊C₄	—	4	8	no	—
497	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	16	no	—
505	C₂²⋊C₄	—	4	8	no	—
506	C₂²⋊C₄	—	4	8	no	—
507	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
508	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
509	C₄²	—	2	8	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	2	4	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	2	no	—
517	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
518	C₄²	#41×C₁₃₉	1	4	yes	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	8	no	—
530	C₂³	—	2	4	no	—
531	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
532	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
533	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
534	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
535	D₄	—	2	8	no	—
536	D₄	—	4	16	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	16	no	—
539	D₄	—	8	8	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	8	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	16	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	8	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	—	8	8	no	—
565	C₂×C₄	—	8	8	no	—
566	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
571	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
572	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
573	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
574	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
575	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
576	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	8	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	8	no	—
591	C₂²	#532×C₁₃₉	1	4	yes	—
592	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
593	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
594	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
595	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
596	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	4	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	2	no	—
607	C₄	#547×C₁₃₉	1	4	yes	—
608	C₄	#553×C₁₃₉	1	8	yes	complemented
609	C₂	—	2	4	no	—
610	C₂	—	4	2	no	—
611	C₂	—	8	4	no	—
612	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
613	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
614	C₂	C₂×#553×C₁₃₉	1	2	yes	—
615	C₂	#3498×C₁₃₉	1	1	yes	characteristic
616	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×#553×C₁₃₉	C₂	semidirect
2. #2859×C₁₃₉	C₂	semidirect
3. #2856×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2566×C₁₃₉	C₂	semidirect
6. #2512×C₁₃₉	C₂	semidirect
7. #2504×C₁₃₉	C₂	semidirect
8. #2500×C₁₃₉	C₂	semidirect
9. #2422×C₁₃₉	C₂	semidirect
10. #2416×C₁₃₉	C₂	semidirect
11. #2361×C₁₃₉	C₂	semidirect
12. C₄×#127×C₁₃₉	C₂	semidirect
13. #2285×C₁₃₉	C₂	semidirect
14. C₂×#384×C₁₃₉	C₂	semidirect
15. C₄²×D₄×C₁₃₉	C₂	semidirect
90. C₄×D₄×C₁₃₉	D₄	semidirect
299. C₄×C₁₃₉	#553	semidirect
308. #36182	C₁₃₉	direct (N × H)
309. C₁₃₉	#36182	direct (N × H)
310. C₂×#553	C₂×C₁₃₉	semidirect
311. #2859	C₂×C₁₃₉	semidirect
312. #2856	C₂×C₁₃₉	semidirect
313. #2856	C₂×C₁₃₉	semidirect
314. #2566	C₂×C₁₃₉	semidirect
315. #2512	C₂×C₁₃₉	semidirect
316. #2504	C₂×C₁₃₉	semidirect
317. #2500	C₂×C₁₃₉	semidirect
318. #2422	C₂×C₁₃₉	semidirect
319. #2416	C₂×C₁₃₉	semidirect
320. #2361	C₂×C₁₃₉	semidirect
321. C₄×#127	C₂×C₁₃₉	semidirect
322. #2285	C₂×C₁₃₉	semidirect
323. C₂×#384	C₂×C₁₃₉	semidirect
324. C₄²×D₄	C₂×C₁₃₉	semidirect
399. C₄×D₄	D₄×C₁₃₉	semidirect
608. C₄	#553×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
#2859×C₁₃₉	2
#2856×C₁₃₉	2
#2566×C₁₃₉	2
#2512×C₁₃₉	2
#2504×C₁₃₉	2
#2500×C₁₃₉	2
#2422×C₁₃₉	2
#2416×C₁₃₉	2
#2361×C₁₃₉	2
C₄×#127×C₁₃₉	2
#2285×C₁₃₉	2
C₂×#384×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36182	139

Subgroups — C139×#36182 #48030778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36182 #48030778