Subgroups — C₁₃₉×#36211 #48030807

Order 35584.

2146 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2535×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2513×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2490×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2420×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2414×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2363×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2357×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2285×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
16	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
23	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
24	#397×C₁₃₉	C₂²	1	4	yes	—
25	#397×C₁₃₉	C₂²	1	8	yes	—
26	#394×C₁₃₉	C₂²	1	8	yes	—
27	#392×C₁₃₉	C₂²	1	4	yes	—
28	#390×C₁₃₉	C₂²	1	4	yes	—
29	#390×C₁₃₉	C₂²	1	4	yes	—
30	#390×C₁₃₉	C₂²	1	4	yes	—
31	#390×C₁₃₉	C₂²	1	2	yes	—
32	#390×C₁₃₉	C₂²	1	4	yes	—
33	#390×C₁₃₉	C₂²	1	8	yes	—
34	#389×C₁₃₉	C₂²	1	4	yes	—
35	#389×C₁₃₉	C₂²	1	4	yes	—
36	#388×C₁₃₉	C₂²	1	8	yes	—
37	#388×C₁₃₉	C₂²	1	8	yes	—
38	#386×C₁₃₉	C₂²	1	8	yes	—
39	#384×C₁₃₉	C₂²	1	1	yes	characteristic
40	#384×C₁₃₉	C₂²	1	2	yes	—
41	#382×C₁₃₉	C₂²	1	4	yes	—
42	#382×C₁₃₉	C₂²	1	2	yes	—
43	#381×C₁₃₉	C₂²	1	4	yes	—
44	#380×C₁₃₉	C₂²	1	4	yes	—
45	#380×C₁₃₉	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
50	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
54	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
59	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
63	#127×C₁₃₉	—	2	4	no	—
64	#125×C₁₃₉	—	4	4	no	—
65	#121×C₁₃₉	—	2	16	no	—
66	#121×C₁₃₉	—	4	8	no	—
67	#121×C₁₃₉	—	4	8	no	—
68	C₄×D₄×C₁₃₉	—	2	8	no	—
69	C₄×D₄×C₁₃₉	—	2	4	no	—
70	C₄×D₄×C₁₃₉	—	2	8	no	—
71	C₄×D₄×C₁₃₉	—	4	8	no	—
72	#117×C₁₃₉	—	4	8	no	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	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	8	yes	—
90	C₂×C₄²×C₁₃₉	—	2	8	no	—
91	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
100	#95×C₁₃₉	C₂³	1	2	yes	—
101	#95×C₁₃₉	C₂³	1	8	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	4	yes	—
104	#95×C₁₃₉	C₂³	1	1	yes	characteristic
105	#95×C₁₃₉	C₂³	1	1	yes	characteristic
106	#95×C₁₃₉	C₂³	1	2	yes	—
107	#95×C₁₃₉	C₂³	1	4	yes	—
108	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
109	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
110	C₂×D₄×C₁₃₉	—	2	4	no	—
111	C₂×D₄×C₁₃₉	—	2	16	no	—
112	C₂×D₄×C₁₃₉	—	2	2	no	—
113	C₂×D₄×C₁₃₉	—	2	4	no	—
114	C₂×D₄×C₁₃₉	—	2	8	no	—
115	C₂×D₄×C₁₃₉	—	2	8	no	—
116	C₂×D₄×C₁₃₉	—	2	4	no	—
117	C₂×D₄×C₁₃₉	—	2	8	no	—
118	C₂×D₄×C₁₃₉	—	2	4	no	—
119	C₂×D₄×C₁₃₉	—	4	8	no	—
120	C₂×D₄×C₁₃₉	—	4	8	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	4	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	2	4	no	—
125	C₂²×C₄×C₁₃₉	—	2	4	no	—
126	C₂²×C₄×C₁₃₉	—	2	4	no	—
127	C₂²×C₄×C₁₃₉	—	2	4	no	—
128	C₂²×C₄×C₁₃₉	—	2	4	no	—
129	C₂²×C₄×C₁₃₉	—	2	8	no	—
130	C₂²×C₄×C₁₃₉	—	4	8	no	—
131	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
136	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
142	C₄⋊C₄×C₁₃₉	—	2	4	no	—
143	C₄⋊C₄×C₁₃₉	—	2	2	no	—
144	C₄⋊C₄×C₁₃₉	—	2	4	no	—
145	C₄⋊C₄×C₁₃₉	—	2	8	no	—
146	C₄⋊C₄×C₁₃₉	—	2	8	no	—
147	C₄⋊C₄×C₁₃₉	—	2	8	no	—
148	C₄⋊C₄×C₁₃₉	—	2	8	no	—
149	C₄⋊C₄×C₁₃₉	—	4	8	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
155	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
156	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
157	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
158	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
159	C₄²×C₁₃₉	—	2	4	no	—
160	C₄²×C₁₃₉	—	2	4	no	—
161	C₄²×C₁₃₉	—	2	4	no	—
162	C₄²×C₁₃₉	—	2	4	no	—
163	C₄²×C₁₃₉	—	2	4	no	—
164	C₄²×C₁₃₉	—	2	2	no	—
165	C₄²×C₁₃₉	—	4	8	no	—
166	C₄²×C₁₃₉	#41	1	4	yes	—
167	C₄²×C₁₃₉	#41	1	4	yes	—
168	C₂³×C₁₃₉	—	2	2	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	2	no	—
171	C₂³×C₁₃₉	—	2	2	no	—
172	C₂³×C₁₃₉	—	2	2	no	—
173	C₂³×C₁₃₉	—	2	2	no	—
174	C₂³×C₁₃₉	—	2	4	no	—
175	C₂³×C₁₃₉	—	2	8	no	—
176	C₂³×C₁₃₉	—	2	4	no	—
177	C₂³×C₁₃₉	—	2	8	no	—
178	C₂³×C₁₃₉	—	2	4	no	—
179	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
180	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
181	D₄×C₁₃₉	—	2	8	no	—
182	D₄×C₁₃₉	—	4	16	no	—
183	D₄×C₁₃₉	—	4	8	no	—
184	D₄×C₁₃₉	—	8	16	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	16	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	2	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	4	no	—
196	C₂×C₄×C₁₃₉	—	2	8	no	—
197	C₂×C₄×C₁₃₉	—	2	2	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	8	no	—
200	C₂×C₄×C₁₃₉	—	2	8	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	8	no	—
204	C₂×C₄×C₁₃₉	—	4	8	no	—
205	C₂×C₄×C₁₃₉	—	4	8	no	—
206	C₂×C₄×C₁₃₉	—	8	8	no	—
207	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
209	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
210	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
211	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
212	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
213	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
215	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
216	C₂²×C₁₃₉	—	2	4	no	—
217	C₂²×C₁₃₉	—	2	4	no	—
218	C₂²×C₁₃₉	—	2	4	no	—
219	C₂²×C₁₃₉	—	4	2	no	—
220	C₂²×C₁₃₉	—	4	2	no	—
221	C₂²×C₁₃₉	—	4	2	no	—
222	C₂²×C₁₃₉	—	4	2	no	—
223	C₂²×C₁₃₉	—	4	4	no	—
224	C₂²×C₁₃₉	—	4	8	no	—
225	C₂²×C₁₃₉	—	4	4	no	—
226	C₂²×C₁₃₉	—	4	4	no	—
227	C₂²×C₁₃₉	—	4	8	no	—
228	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
229	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
230	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
231	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
232	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
233	C₄×C₁₃₉	—	2	2	no	—
234	C₄×C₁₃₉	—	2	4	no	—
235	C₄×C₁₃₉	—	2	2	no	—
236	C₄×C₁₃₉	—	4	2	no	—
237	C₄×C₁₃₉	—	4	2	no	—
238	C₄×C₁₃₉	—	4	2	no	—
239	C₄×C₁₃₉	—	4	4	no	—
240	C₄×C₁₃₉	—	4	8	no	—
241	C₄×C₁₃₉	#553	1	8	yes	—
242	C₄×C₁₃₉	#555	1	4	yes	—
243	C₂×C₁₃₉	—	4	4	no	—
244	C₂×C₁₃₉	—	8	4	no	—
245	C₂×C₁₃₉	#3444	1	1	yes	characteristic
246	C₂×C₁₃₉	C₂×#553	1	2	yes	—
247	C₂×C₁₃₉	C₂×#555	1	1	yes	characteristic
248	C₂×C₁₃₉	#3508	1	1	yes	characteristic
249	C₂×C₁₃₉	#3508	1	2	yes	—
250	#36211	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₁₃₉	#36211	1	1	yes	characteristic, direct product factor, Sylow
252	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
253	#2856	C₂×C₁₃₉	1	2	yes	complemented
254	#2535	C₂×C₁₃₉	1	2	yes	complemented
255	#2513	C₂×C₁₃₉	1	4	yes	complemented
256	#2490	C₂×C₁₃₉	1	4	yes	complemented
257	#2420	C₂×C₁₃₉	1	4	yes	complemented
258	#2414	C₂×C₁₃₉	1	4	yes	complemented
259	#2363	C₂×C₁₃₉	1	4	yes	complemented
260	#2357	C₂×C₁₃₉	1	2	yes	complemented
261	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
262	#2285	C₂×C₁₃₉	1	2	yes	complemented
263	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
264	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
266	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
267	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
268	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
269	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
273	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
274	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
275	#397	C₂²×C₁₃₉	1	8	yes	—
276	#397	C₂²×C₁₃₉	1	4	yes	—
277	#394	C₂²×C₁₃₉	1	8	yes	—
278	#392	C₂²×C₁₃₉	1	4	yes	—
279	#390	C₂²×C₁₃₉	1	4	yes	—
280	#390	C₂²×C₁₃₉	1	2	yes	—
281	#390	C₂²×C₁₃₉	1	4	yes	—
282	#390	C₂²×C₁₃₉	1	4	yes	—
283	#390	C₂²×C₁₃₉	1	4	yes	—
284	#390	C₂²×C₁₃₉	1	8	yes	—
285	#389	C₂²×C₁₃₉	1	4	yes	—
286	#389	C₂²×C₁₃₉	1	4	yes	—
287	#388	C₂²×C₁₃₉	1	8	yes	—
288	#388	C₂²×C₁₃₉	1	8	yes	—
289	#386	C₂²×C₁₃₉	1	8	yes	—
290	#384	C₂²×C₁₃₉	1	1	yes	characteristic
291	#384	C₂²×C₁₃₉	1	2	yes	—
292	#382	C₂²×C₁₃₉	1	2	yes	—
293	#382	C₂²×C₁₃₉	1	4	yes	—
294	#381	C₂²×C₁₃₉	1	4	yes	—
295	#380	C₂²×C₁₃₉	1	4	yes	—
296	#380	C₂²×C₁₃₉	1	4	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
302	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
305	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
306	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
308	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
309	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
310	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
314	#127	—	2	4	no	—
315	#125	—	4	4	no	—
316	#121	—	2	16	no	—
317	#121	—	4	8	no	—
318	#121	—	4	8	no	—
319	C₄×D₄	—	2	8	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	—	4	8	no	—
323	#117	—	4	8	no	—
324	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
341	C₂×C₄²	—	2	8	no	—
342	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
343	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
344	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
346	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
347	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
348	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
349	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
351	#95	C₂³×C₁₃₉	1	1	yes	characteristic
352	#95	C₂³×C₁₃₉	1	1	yes	characteristic
353	#95	C₂³×C₁₃₉	1	2	yes	—
354	#95	C₂³×C₁₃₉	1	2	yes	—
355	#95	C₂³×C₁₃₉	1	4	yes	—
356	#95	C₂³×C₁₃₉	1	8	yes	—
357	#95	C₂³×C₁₃₉	1	8	yes	—
358	#95	C₂³×C₁₃₉	1	4	yes	—
359	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
360	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	16	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	8	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
383	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
387	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	4	8	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	16	no	—
406	C₂²⋊C₄	—	4	8	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₂²⋊C₄	—	4	8	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	4	no	—
414	C₄²	—	2	4	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	4	8	no	—
417	C₄²	#41×C₁₃₉	1	4	yes	—
418	C₄²	#41×C₁₃₉	1	4	yes	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	4	no	—
430	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
431	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
432	D₄	—	2	8	no	—
433	D₄	—	4	16	no	—
434	D₄	—	4	8	no	—
435	D₄	—	8	16	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	16	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
459	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
460	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
461	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
462	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
463	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
464	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
465	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
466	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	8	no	—
479	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
480	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
481	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
482	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
483	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	4	no	—
486	C₄	—	2	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	8	no	—
491	C₄	—	4	2	no	—
492	C₄	#553×C₁₃₉	1	8	yes	—
493	C₄	#555×C₁₃₉	1	4	yes	—
494	C₂	—	4	4	no	—
495	C₂	—	8	4	no	—
496	C₂	#3444×C₁₃₉	1	1	yes	characteristic
497	C₂	C₂×#553×C₁₃₉	1	2	yes	—
498	C₂	C₂×#555×C₁₃₉	1	1	yes	characteristic
499	C₂	#3508×C₁₃₉	1	1	yes	characteristic
500	C₂	#3508×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. #2859×C₁₃₉	C₂	semidirect
2. #2856×C₁₃₉	C₂	semidirect
3. #2535×C₁₃₉	C₂	semidirect
4. #2513×C₁₃₉	C₂	semidirect
5. #2490×C₁₃₉	C₂	semidirect
6. #2420×C₁₃₉	C₂	semidirect
7. #2414×C₁₃₉	C₂	semidirect
8. #2363×C₁₃₉	C₂	semidirect
9. #2357×C₁₃₉	C₂	semidirect
10. C₄×#127×C₁₃₉	C₂	semidirect
11. #2285×C₁₃₉	C₂	semidirect
12. C₄²×D₄×C₁₃₉	C₂	semidirect
250. #36211	C₁₃₉	direct (N × H)
251. C₁₃₉	#36211	direct (N × H)
252. #2859	C₂×C₁₃₉	semidirect
253. #2856	C₂×C₁₃₉	semidirect
254. #2535	C₂×C₁₃₉	semidirect
255. #2513	C₂×C₁₃₉	semidirect
256. #2490	C₂×C₁₃₉	semidirect
257. #2420	C₂×C₁₃₉	semidirect
258. #2414	C₂×C₁₃₉	semidirect
259. #2363	C₂×C₁₃₉	semidirect
260. #2357	C₂×C₁₃₉	semidirect
261. C₄×#127	C₂×C₁₃₉	semidirect
262. #2285	C₂×C₁₃₉	semidirect
263. C₄²×D₄	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2859×C₁₃₉	2
#2856×C₁₃₉	2
#2535×C₁₃₉	2
#2513×C₁₃₉	2
#2490×C₁₃₉	2
#2420×C₁₃₉	2
#2414×C₁₃₉	2
#2363×C₁₃₉	2
#2357×C₁₃₉	2
C₄×#127×C₁₃₉	2
#2285×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36211	139

Subgroups — C139×#36211 #48030807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36211 #48030807