Subgroups — C₁₃₉×#36128 #48030724

Order 35584.

3562 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2867×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2548×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2541×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2431×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2428×C₁₃₉	C₂	1	8	yes	maximal, complemented
9	#2366×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	C₄×C₄⋊Q₈×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	#550×C₁₃₉	—	2	16	no	—
14	#532×C₁₃₉	—	2	16	no	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	8	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
33	#394×C₁₃₉	C₂²	1	8	yes	—
34	#392×C₁₃₉	C₂²	1	16	yes	—
35	#391×C₁₃₉	C₂²	1	2	yes	—
36	#390×C₁₃₉	C₂²	1	8	yes	—
37	#390×C₁₃₉	C₂²	1	4	yes	—
38	#390×C₁₃₉	C₂²	1	8	yes	—
39	#389×C₁₃₉	C₂²	1	4	yes	—
40	#386×C₁₃₉	C₂²	1	16	yes	—
41	#384×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	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	2	yes	—
52	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
53	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
56	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
64	#127×C₁₃₉	—	2	16	no	—
65	#127×C₁₃₉	—	2	8	no	—
66	#127×C₁₃₉	—	2	8	no	—
67	#127×C₁₃₉	—	2	16	no	—
68	#127×C₁₃₉	—	4	8	no	—
69	#127×C₁₃₉	—	4	4	no	—
70	#124×C₁₃₉	—	2	16	no	—
71	#121×C₁₃₉	—	2	16	no	—
72	#121×C₁₃₉	—	2	32	no	—
73	#121×C₁₃₉	—	2	32	no	—
74	#121×C₁₃₉	—	4	16	no	—
75	C₄×Q₈×C₁₃₉	—	2	8	no	—
76	C₄×D₄×C₁₃₉	—	2	32	no	—
77	C₄×D₄×C₁₃₉	—	2	16	no	—
78	C₄×D₄×C₁₃₉	—	2	8	no	—
79	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₃₉	—	2	8	no	—
92	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
100	#95×C₁₃₉	C₂³	1	4	yes	—
101	#95×C₁₃₉	C₂³	1	2	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	C₂⁴×C₁₃₉	C₂⁴	1	8	yes	—
104	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
105	#41×C₁₃₉	—	4	64	no	—
106	C₂×Q₈×C₁₃₉	—	2	4	no	—
107	C₂×Q₈×C₁₃₉	—	2	4	no	—
108	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
109	C₂×D₄×C₁₃₉	—	2	16	no	—
110	C₂×D₄×C₁₃₉	—	2	16	no	—
111	C₂×D₄×C₁₃₉	—	2	16	no	—
112	C₂×D₄×C₁₃₉	—	2	8	no	—
113	C₂×D₄×C₁₃₉	—	2	16	no	—
114	C₂×D₄×C₁₃₉	—	2	8	no	—
115	C₂×D₄×C₁₃₉	—	2	8	no	—
116	C₂×D₄×C₁₃₉	—	2	8	no	—
117	C₂×D₄×C₁₃₉	—	2	4	no	—
118	C₂×D₄×C₁₃₉	—	2	16	no	—
119	C₂×D₄×C₁₃₉	—	2	16	no	—
120	C₂×D₄×C₁₃₉	—	2	16	no	—
121	C₂×D₄×C₁₃₉	—	2	16	no	—
122	C₂×D₄×C₁₃₉	—	2	8	no	—
123	C₂×D₄×C₁₃₉	—	4	8	no	—
124	C₂×D₄×C₁₃₉	—	4	16	no	—
125	C₂×D₄×C₁₃₉	—	4	8	no	—
126	C₂×D₄×C₁₃₉	—	4	8	no	—
127	C₂×D₄×C₁₃₉	—	4	8	no	—
128	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₃₉	—	2	4	no	—
130	C₂²×C₄×C₁₃₉	—	2	4	no	—
131	C₂²×C₄×C₁₃₉	—	2	8	no	—
132	C₂²×C₄×C₁₃₉	—	2	16	no	—
133	C₂²×C₄×C₁₃₉	—	2	16	no	—
134	C₂²×C₄×C₁₃₉	—	2	8	no	—
135	C₂²×C₄×C₁₃₉	—	2	8	no	—
136	C₂²×C₄×C₁₃₉	—	4	8	no	—
137	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
138	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₄⋊C₄×C₁₃₉	—	2	8	no	—
148	C₄⋊C₄×C₁₃₉	—	2	4	no	—
149	C₄⋊C₄×C₁₃₉	—	2	4	no	—
150	C₄⋊C₄×C₁₃₉	—	2	8	no	—
151	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
153	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
155	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₃₉	—	4	16	no	—
157	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
158	C₄²×C₁₃₉	—	2	8	no	—
159	C₄²×C₁₃₉	—	2	4	no	—
160	C₄²×C₁₃₉	—	2	8	no	—
161	C₄²×C₁₃₉	—	2	2	no	—
162	C₄²×C₁₃₉	—	2	4	no	—
163	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
164	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
165	C₄²×C₁₃₉	#41	1	8	yes	complemented
166	C₂³×C₁₃₉	—	2	2	no	—
167	C₂³×C₁₃₉	—	2	4	no	—
168	C₂³×C₁₃₉	—	2	2	no	—
169	C₂³×C₁₃₉	—	2	4	no	—
170	C₂³×C₁₃₉	—	2	8	no	—
171	C₂³×C₁₃₉	—	2	8	no	—
172	C₂³×C₁₃₉	—	2	16	no	—
173	C₂³×C₁₃₉	—	2	16	no	—
174	C₂³×C₁₃₉	—	2	8	no	—
175	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
176	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
177	Q₈×C₁₃₉	—	2	16	no	—
178	D₄×C₁₃₉	—	2	8	no	—
179	D₄×C₁₃₉	—	4	32	no	—
180	D₄×C₁₃₉	—	4	16	no	—
181	D₄×C₁₃₉	—	4	16	no	—
182	D₄×C₁₃₉	—	4	32	no	—
183	D₄×C₁₃₉	—	8	8	no	—
184	D₄×C₁₃₉	—	8	16	no	—
185	D₄×C₁₃₉	—	8	16	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	2	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₄×C₁₃₉	—	2	16	no	—
194	C₂×C₄×C₁₃₉	—	2	4	no	—
195	C₂×C₄×C₁₃₉	—	2	4	no	—
196	C₂×C₄×C₁₃₉	—	2	4	no	—
197	C₂×C₄×C₁₃₉	—	2	4	no	—
198	C₂×C₄×C₁₃₉	—	2	8	no	—
199	C₂×C₄×C₁₃₉	—	4	32	no	—
200	C₂×C₄×C₁₃₉	—	4	16	no	—
201	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
204	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
209	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
210	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
211	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
212	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
213	C₂²×C₁₃₉	—	2	4	no	—
214	C₂²×C₁₃₉	—	2	4	no	—
215	C₂²×C₁₃₉	—	2	4	no	—
216	C₂²×C₁₃₉	—	4	4	no	—
217	C₂²×C₁₃₉	—	4	4	no	—
218	C₂²×C₁₃₉	—	4	8	no	—
219	C₂²×C₁₃₉	—	4	8	no	—
220	C₂²×C₁₃₉	—	4	16	no	—
221	C₂²×C₁₃₉	—	4	8	no	—
222	C₂²×C₁₃₉	—	4	16	no	—
223	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
224	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
225	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
226	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
228	C₄×C₁₃₉	—	2	4	no	—
229	C₄×C₁₃₉	—	2	8	no	—
230	C₄×C₁₃₉	—	2	2	no	—
231	C₄×C₁₃₉	—	2	4	no	—
232	C₄×C₁₃₉	—	4	4	no	—
233	C₄×C₁₃₉	—	4	4	no	—
234	C₄×C₁₃₉	#532	1	4	yes	complemented
235	C₄×C₁₃₉	D₄²	1	4	yes	—
236	C₄×C₁₃₉	#550	1	8	yes	complemented
237	C₂×C₁₃₉	—	4	4	no	—
238	C₂×C₁₃₉	—	8	8	no	—
239	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
240	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
241	C₂×C₁₃₉	C₂×#550	1	2	yes	—
242	C₂×C₁₃₉	#3498	1	1	yes	characteristic
243	C₂×C₁₃₉	#3508	1	2	yes	—
244	#36128	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₁₃₉	#36128	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×#550	C₂×C₁₃₉	1	2	yes	complemented
247	C₂×#532	C₂×C₁₃₉	1	2	yes	complemented
248	#2867	C₂×C₁₃₉	1	1	yes	characteristic, complemented
249	#2856	C₂×C₁₃₉	1	2	yes	complemented
250	#2548	C₂×C₁₃₉	1	2	yes	complemented
251	#2541	C₂×C₁₃₉	1	4	yes	complemented
252	#2431	C₂×C₁₃₉	1	4	yes	complemented
253	#2428	C₂×C₁₃₉	1	8	yes	complemented
254	#2366	C₂×C₁₃₉	1	4	yes	complemented
255	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
256	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
257	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
258	#550	—	2	16	no	—
259	#532	—	2	16	no	—
260	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
261	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
262	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
263	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
264	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
265	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
266	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
267	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
268	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
269	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
270	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
271	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
272	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
274	C₂×C₄×D₄	C₂²×C₁₃₉	1	8	yes	—
275	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
276	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
277	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
278	#394	C₂²×C₁₃₉	1	8	yes	—
279	#392	C₂²×C₁₃₉	1	16	yes	—
280	#391	C₂²×C₁₃₉	1	2	yes	—
281	#390	C₂²×C₁₃₉	1	8	yes	—
282	#390	C₂²×C₁₃₉	1	4	yes	—
283	#390	C₂²×C₁₃₉	1	8	yes	—
284	#389	C₂²×C₁₃₉	1	4	yes	—
285	#386	C₂²×C₁₃₉	1	16	yes	—
286	#384	C₂²×C₁₃₉	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
288	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
289	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
291	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
292	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
293	C₂×#41	—	2	16	no	—
294	C₂×#41	—	2	16	no	—
295	C₂×#41	—	4	8	no	—
296	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
297	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
298	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
299	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
300	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
301	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
302	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
303	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
304	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
305	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
306	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
307	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
308	C₄⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
309	#127	—	2	16	no	—
310	#127	—	2	8	no	—
311	#127	—	2	8	no	—
312	#127	—	2	16	no	—
313	#127	—	4	8	no	—
314	#127	—	4	4	no	—
315	#124	—	2	16	no	—
316	#121	—	2	16	no	—
317	#121	—	2	32	no	—
318	#121	—	2	32	no	—
319	#121	—	4	16	no	—
320	C₄×Q₈	—	2	8	no	—
321	C₄×D₄	—	2	32	no	—
322	C₄×D₄	—	2	16	no	—
323	C₄×D₄	—	2	8	no	—
324	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
325	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
336	C₂×C₄²	—	2	8	no	—
337	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
338	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
340	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
341	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
345	#95	C₂³×C₁₃₉	1	4	yes	—
346	#95	C₂³×C₁₃₉	1	2	yes	—
347	#95	C₂³×C₁₃₉	1	8	yes	—
348	C₂⁴	C₂⁴×C₁₃₉	1	8	yes	—
349	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
350	#41	—	4	64	no	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
354	C₂×D₄	—	2	16	no	—
355	C₂×D₄	—	2	16	no	—
356	C₂×D₄	—	2	16	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	16	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	16	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	2	16	no	—
366	C₂×D₄	—	2	16	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	4	8	no	—
369	C₂×D₄	—	4	16	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	8	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	16	no	—
378	C₂²×C₄	—	2	16	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
383	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
398	C₂²⋊C₄	—	2	16	no	—
399	C₂²⋊C₄	—	2	32	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	4	16	no	—
402	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
403	C₄²	—	2	8	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	8	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
409	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
410	C₄²	#41×C₁₃₉	1	8	yes	complemented
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	16	no	—
418	C₂³	—	2	16	no	—
419	C₂³	—	2	8	no	—
420	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
421	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
422	Q₈	—	2	16	no	—
423	D₄	—	2	8	no	—
424	D₄	—	4	32	no	—
425	D₄	—	4	16	no	—
426	D₄	—	4	16	no	—
427	D₄	—	4	32	no	—
428	D₄	—	8	8	no	—
429	D₄	—	8	16	no	—
430	D₄	—	8	16	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	16	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	4	32	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
453	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
454	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
455	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
456	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
457	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	4	8	no	—
465	C₂²	—	4	16	no	—
466	C₂²	—	4	8	no	—
467	C₂²	—	4	16	no	—
468	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
469	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
470	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
471	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
472	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
473	C₄	—	2	4	no	—
474	C₄	—	2	8	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	#532×C₁₃₉	1	4	yes	complemented
480	C₄	D₄²×C₁₃₉	1	4	yes	—
481	C₄	#550×C₁₃₉	1	8	yes	complemented
482	C₂	—	4	4	no	—
483	C₂	—	8	8	no	—
484	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
485	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
486	C₂	C₂×#550×C₁₃₉	1	2	yes	—
487	C₂	#3498×C₁₃₉	1	1	yes	characteristic
488	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. C₂×#550×C₁₃₉	C₂	semidirect
2. C₂×#532×C₁₃₉	C₂	semidirect
3. #2867×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2548×C₁₃₉	C₂	semidirect
6. #2541×C₁₃₉	C₂	semidirect
7. #2431×C₁₃₉	C₂	semidirect
8. #2428×C₁₃₉	C₂	semidirect
9. #2366×C₁₃₉	C₂	semidirect
10. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
11. C₄²×D₄×C₁₃₉	C₂	semidirect
63. C₄⋊Q₈×C₁₃₉	D₄	semidirect
79. C₄×D₄×C₁₃₉	D₄	semidirect
165. C₄²×C₁₃₉	#41	semidirect
234. C₄×C₁₃₉	#532	semidirect
236. C₄×C₁₃₉	#550	semidirect
244. #36128	C₁₃₉	direct (N × H)
245. C₁₃₉	#36128	direct (N × H)
246. C₂×#550	C₂×C₁₃₉	semidirect
247. C₂×#532	C₂×C₁₃₉	semidirect
248. #2867	C₂×C₁₃₉	semidirect
249. #2856	C₂×C₁₃₉	semidirect
250. #2548	C₂×C₁₃₉	semidirect
251. #2541	C₂×C₁₃₉	semidirect
252. #2431	C₂×C₁₃₉	semidirect
253. #2428	C₂×C₁₃₉	semidirect
254. #2366	C₂×C₁₃₉	semidirect
255. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
256. C₄²×D₄	C₂×C₁₃₉	semidirect
308. C₄⋊Q₈	D₄×C₁₃₉	semidirect
324. C₄×D₄	D₄×C₁₃₉	semidirect
410. C₄²	#41×C₁₃₉	semidirect
479. C₄	#532×C₁₃₉	semidirect
481. C₄	#550×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₃₉	2
C₂×#532×C₁₃₉	2
#2867×C₁₃₉	2
#2856×C₁₃₉	2
#2548×C₁₃₉	2
#2541×C₁₃₉	2
#2431×C₁₃₉	2
#2428×C₁₃₉	2
#2366×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36128	139

Subgroups — C139×#36128 #48030724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36128 #48030724