Subgroups — C₁₃₉×#35616 #48030212

Order 35584.

5294 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#536×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2435×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2432×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2405×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2309×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×H(5,𝔽₂)×C₁₃₉	—	2	16	no	—
10	C₂×H(5,𝔽₂)×C₁₃₉	—	2	8	no	—
11	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
12	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	—
15	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	—
16	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	#536×C₁₃₉	—	2	16	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
19	C₂×#124×C₁₃₉	—	2	8	no	—
20	C₂×#124×C₁₃₉	C₂²	1	8	yes	complemented
21	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×#123×C₁₃₉	C₂²	1	8	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	8	yes	complemented
24	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	#394×C₁₃₉	C₂²	1	32	yes	complemented
28	#391×C₁₃₉	C₂²	1	4	yes	complemented
29	#390×C₁₃₉	C₂²	1	4	yes	complemented
30	#390×C₁₃₉	C₂²	1	8	yes	complemented
31	#386×C₁₃₉	C₂²	1	8	yes	complemented
32	#385×C₁₃₉	C₂²	1	16	yes	complemented
33	#379×C₁₃₉	C₂²	1	4	yes	complemented
34	#379×C₁₃₉	C₂²	1	16	yes	complemented
35	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	complemented
36	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
37	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
38	H(5,𝔽₂)×C₁₃₉	—	2	128	no	—
39	C₂×#41×C₁₃₉	—	2	16	no	—
40	C₂×#41×C₁₃₉	—	2	16	no	—
41	C₂×#41×C₁₃₉	—	2	16	no	—
42	C₂×#41×C₁₃₉	—	2	8	no	—
43	C₂×#41×C₁₃₉	—	2	8	no	—
44	C₂×#41×C₁₃₉	D₄	1	16	yes	—
45	C₂²×Q₈×C₁₃₉	—	2	4	no	—
46	C₂²×Q₈×C₁₃₉	—	2	8	no	—
47	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
48	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃₉	—	2	16	no	—
50	C₂²×D₄×C₁₃₉	—	2	32	no	—
51	C₂²×D₄×C₁₃₉	—	2	16	no	—
52	C₂²×D₄×C₁₃₉	—	2	16	no	—
53	C₂²×D₄×C₁₃₉	—	2	16	no	—
54	C₂²×D₄×C₁₃₉	—	2	8	no	—
55	C₂²×D₄×C₁₃₉	D₄	1	8	yes	—
56	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
66	#124×C₁₃₉	—	2	32	no	—
67	#124×C₁₃₉	—	2	16	no	—
68	#123×C₁₃₉	—	2	32	no	—
69	C₂²⋊Q₈×C₁₃₉	—	2	32	no	—
70	#117×C₁₃₉	—	2	8	no	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
79	C₂×C₄²×C₁₃₉	—	2	4	no	—
80	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
82	#95×C₁₃₉	C₂³	1	16	yes	—
83	C₂⁴×C₁₃₉	—	2	8	no	—
84	C₂⁴×C₁₃₉	—	2	16	no	—
85	C₂⁴×C₁₃₉	—	2	8	no	—
86	C₂⁴×C₁₃₉	—	4	8	no	—
87	C₂⁴×C₁₃₉	—	4	16	no	—
88	C₂⁴×C₁₃₉	C₂×D₄	1	8	yes	—
89	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
90	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
91	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
92	#41×C₁₃₉	—	2	128	no	—
93	#41×C₁₃₉	—	2	64	no	—
94	C₂×Q₈×C₁₃₉	—	2	4	no	—
95	C₂×Q₈×C₁₃₉	—	2	4	no	—
96	C₂×Q₈×C₁₃₉	—	2	8	no	—
97	C₂×Q₈×C₁₃₉	—	2	8	no	—
98	C₂×Q₈×C₁₃₉	—	2	8	no	—
99	C₂×Q₈×C₁₃₉	—	4	16	no	—
100	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
101	C₂×D₄×C₁₃₉	—	2	128	no	—
102	C₂×D₄×C₁₃₉	—	2	128	no	—
103	C₂×D₄×C₁₃₉	—	2	16	no	—
104	C₂×D₄×C₁₃₉	—	2	16	no	—
105	C₂×D₄×C₁₃₉	—	2	8	no	—
106	C₂×D₄×C₁₃₉	—	2	8	no	—
107	C₂×D₄×C₁₃₉	—	2	32	no	—
108	C₂×D₄×C₁₃₉	—	2	16	no	—
109	C₂×D₄×C₁₃₉	—	2	8	no	—
110	C₂×D₄×C₁₃₉	—	2	4	no	—
111	C₂×D₄×C₁₃₉	—	2	4	no	—
112	C₂×D₄×C₁₃₉	—	2	8	no	—
113	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
114	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
115	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
116	C₂²×C₄×C₁₃₉	—	2	8	no	—
117	C₂²×C₄×C₁₃₉	—	2	16	no	—
118	C₂²×C₄×C₁₃₉	—	2	8	no	—
119	C₂²×C₄×C₁₃₉	—	2	8	no	—
120	C₂²×C₄×C₁₃₉	—	2	4	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	8	no	—
123	C₂²×C₄×C₁₃₉	—	4	4	no	—
124	C₂²×C₄×C₁₃₉	C₂×D₄	1	16	yes	—
125	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃₉	C₂⁴	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	2	yes	—
132	C₄⋊C₄×C₁₃₉	—	2	8	no	—
133	C₄⋊C₄×C₁₃₉	—	2	32	no	—
134	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
135	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
136	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
137	C₂²⋊C₄×C₁₃₉	—	4	16	no	—
138	C₂²⋊C₄×C₁₃₉	—	4	16	no	—
139	C₄²×C₁₃₉	—	2	8	no	—
140	C₄²×C₁₃₉	—	2	8	no	—
141	C₂³×C₁₃₉	—	2	4	no	—
142	C₂³×C₁₃₉	—	2	32	no	—
143	C₂³×C₁₃₉	—	2	4	no	—
144	C₂³×C₁₃₉	—	2	8	no	—
145	C₂³×C₁₃₉	—	2	4	no	—
146	C₂³×C₁₃₉	—	2	16	no	—
147	C₂³×C₁₃₉	—	2	16	no	—
148	C₂³×C₁₃₉	—	2	16	no	—
149	C₂³×C₁₃₉	—	4	16	no	—
150	C₂³×C₁₃₉	—	8	16	no	—
151	C₂³×C₁₃₉	—	8	16	no	—
152	C₂³×C₁₃₉	—	8	32	no	—
153	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
154	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
155	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
156	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
157	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
158	Q₈×C₁₃₉	—	2	16	no	—
159	Q₈×C₁₃₉	—	4	16	no	—
160	D₄×C₁₃₉	—	2	64	no	—
161	D₄×C₁₃₉	—	2	32	no	—
162	D₄×C₁₃₉	—	2	16	no	—
163	D₄×C₁₃₉	—	2	32	no	—
164	C₂×C₄×C₁₃₉	—	2	32	no	—
165	C₂×C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄×C₁₃₉	—	2	32	no	—
168	C₂×C₄×C₁₃₉	—	2	4	no	—
169	C₂×C₄×C₁₃₉	—	2	8	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	—	2	8	no	—
172	C₂×C₄×C₁₃₉	—	2	16	no	—
173	C₂×C₄×C₁₃₉	—	2	8	no	—
174	C₂×C₄×C₁₃₉	—	4	8	no	—
175	C₂×C₄×C₁₃₉	—	4	8	no	—
176	C₂×C₄×C₁₃₉	#120	1	16	yes	—
177	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
178	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
179	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
181	C₂²×C₁₃₉	—	2	4	no	—
182	C₂²×C₁₃₉	—	2	8	no	—
183	C₂²×C₁₃₉	—	2	8	no	—
184	C₂²×C₁₃₉	—	2	8	no	—
185	C₂²×C₁₃₉	—	2	16	no	—
186	C₂²×C₁₃₉	—	2	16	no	—
187	C₂²×C₁₃₉	—	4	8	no	—
188	C₂²×C₁₃₉	—	4	16	no	—
189	C₂²×C₁₃₉	—	4	8	no	—
190	C₂²×C₁₃₉	—	8	16	no	—
191	C₂²×C₁₃₉	—	8	32	no	—
192	C₂²×C₁₃₉	C₂×#120	1	4	yes	—
193	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
194	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
195	C₂²×C₁₃₉	#585	1	4	yes	—
196	C₄×C₁₃₉	—	2	8	no	—
197	C₄×C₁₃₉	—	4	4	no	—
198	C₄×C₁₃₉	—	4	4	no	—
199	C₄×C₁₃₉	—	4	8	no	—
200	C₄×C₁₃₉	C₂×#120	1	8	yes	—
201	C₂×C₁₃₉	—	2	4	no	—
202	C₂×C₁₃₉	—	4	8	no	—
203	C₂×C₁₃₉	—	4	8	no	—
204	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
205	C₂×C₁₃₉	#3485	1	2	yes	—
206	C₂×C₁₃₉	#3500	1	4	yes	—
207	#35616	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₉	#35616	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²×H(5,𝔽₂)	C₂×C₁₃₉	1	1	yes	characteristic
210	C₂×#536	C₂×C₁₃₉	1	2	yes	complemented
211	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
212	#2435	C₂×C₁₃₉	1	8	yes	complemented
213	#2432	C₂×C₁₃₉	1	8	yes	complemented
214	#2405	C₂×C₁₃₉	1	8	yes	complemented
215	#2309	C₂×C₁₃₉	1	1	yes	characteristic, complemented
216	#2297	C₂×C₁₃₉	1	2	yes	complemented
217	C₂×H(5,𝔽₂)	—	2	16	no	—
218	C₂×H(5,𝔽₂)	—	2	8	no	—
219	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
220	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
221	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
222	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	—
223	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	—
224	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
225	#536	—	2	16	no	—
226	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
227	C₂×#124	—	2	8	no	—
228	C₂×#124	C₂²×C₁₃₉	1	8	yes	complemented
229	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
230	C₂×#123	C₂²×C₁₃₉	1	8	yes	complemented
231	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	8	yes	complemented
232	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
233	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
234	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
235	#394	C₂²×C₁₃₉	1	32	yes	complemented
236	#391	C₂²×C₁₃₉	1	4	yes	complemented
237	#390	C₂²×C₁₃₉	1	8	yes	complemented
238	#390	C₂²×C₁₃₉	1	4	yes	complemented
239	#386	C₂²×C₁₃₉	1	8	yes	complemented
240	#385	C₂²×C₁₃₉	1	16	yes	complemented
241	#379	C₂²×C₁₃₉	1	4	yes	complemented
242	#379	C₂²×C₁₃₉	1	16	yes	complemented
243	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	complemented
244	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
245	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
246	H(5,𝔽₂)	—	2	128	no	—
247	C₂×#41	—	2	16	no	—
248	C₂×#41	—	2	16	no	—
249	C₂×#41	—	2	16	no	—
250	C₂×#41	—	2	8	no	—
251	C₂×#41	—	2	8	no	—
252	C₂×#41	D₄×C₁₃₉	1	16	yes	—
253	C₂²×Q₈	—	2	4	no	—
254	C₂²×Q₈	—	2	8	no	—
255	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
256	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
257	C₂²×D₄	—	2	16	no	—
258	C₂²×D₄	—	2	32	no	—
259	C₂²×D₄	—	2	16	no	—
260	C₂²×D₄	—	2	16	no	—
261	C₂²×D₄	—	2	16	no	—
262	C₂²×D₄	—	2	8	no	—
263	C₂²×D₄	D₄×C₁₃₉	1	8	yes	—
264	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
265	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
266	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
267	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
268	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
270	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
271	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
273	C₄⋊Q₈	—	2	16	no	—
274	#124	—	2	32	no	—
275	#124	—	2	16	no	—
276	#123	—	2	32	no	—
277	C₂²⋊Q₈	—	2	32	no	—
278	#117	—	2	8	no	—
279	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
281	C₂×C₂²⋊C₄	—	2	16	no	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
290	#95	C₂³×C₁₃₉	1	16	yes	—
291	C₂⁴	—	2	8	no	—
292	C₂⁴	—	2	16	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	4	8	no	—
295	C₂⁴	—	4	16	no	—
296	C₂⁴	C₂×D₄×C₁₃₉	1	8	yes	—
297	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
298	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
299	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
300	#41	—	2	128	no	—
301	#41	—	2	64	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	8	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	4	16	no	—
308	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
309	C₂×D₄	—	2	128	no	—
310	C₂×D₄	—	2	128	no	—
311	C₂×D₄	—	2	16	no	—
312	C₂×D₄	—	2	16	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	32	no	—
316	C₂×D₄	—	2	16	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
322	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
323	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	16	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	C₂×D₄×C₁₃₉	1	16	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
335	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
337	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	32	no	—
342	C₂²⋊C₄	—	2	32	no	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₂²⋊C₄	—	2	32	no	—
345	C₂²⋊C₄	—	4	16	no	—
346	C₂²⋊C₄	—	4	16	no	—
347	C₄²	—	2	8	no	—
348	C₄²	—	2	8	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	32	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	16	no	—
355	C₂³	—	2	16	no	—
356	C₂³	—	2	16	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	8	16	no	—
359	C₂³	—	8	16	no	—
360	C₂³	—	8	32	no	—
361	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
362	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
363	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
364	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
365	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
366	Q₈	—	2	16	no	—
367	Q₈	—	4	16	no	—
368	D₄	—	2	64	no	—
369	D₄	—	2	32	no	—
370	D₄	—	2	16	no	—
371	D₄	—	2	32	no	—
372	C₂×C₄	—	2	32	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	32	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	16	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	#120×C₁₃₉	1	16	yes	—
385	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
386	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
388	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	2	16	no	—
394	C₂²	—	2	16	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	4	16	no	—
397	C₂²	—	4	8	no	—
398	C₂²	—	8	16	no	—
399	C₂²	—	8	32	no	—
400	C₂²	C₂×#120×C₁₃₉	1	4	yes	—
401	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
402	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
403	C₂²	#585×C₁₃₉	1	4	yes	—
404	C₄	—	2	8	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	8	no	—
408	C₄	C₂×#120×C₁₃₉	1	8	yes	—
409	C₂	—	2	4	no	—
410	C₂	—	4	8	no	—
411	C₂	—	4	8	no	—
412	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
413	C₂	#3485×C₁₃₉	1	2	yes	—
414	C₂	#3500×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×H(5,𝔽₂)×C₁₃₉	C₂
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
2. C₂×#536×C₁₃₉	C₂	semidirect
3. C₂²×#124×C₁₃₉	C₂	semidirect
4. #2435×C₁₃₉	C₂	semidirect
5. #2432×C₁₃₉	C₂	semidirect
6. #2405×C₁₃₉	C₂	semidirect
7. #2309×C₁₃₉	C₂	semidirect
8. #2297×C₁₃₉	C₂	semidirect
13. C₂³×Q₈×C₁₃₉	C₂²	semidirect
18. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
20. C₂×#124×C₁₃₉	C₂²	semidirect
21. C₂×#124×C₁₃₉	C₂²	semidirect
22. C₂×#123×C₁₃₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×#117×C₁₃₉	C₂²	semidirect
25. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
26. C₂²×C₄²×C₁₃₉	C₂²	semidirect
27. #394×C₁₃₉	C₂²	semidirect
28. #391×C₁₃₉	C₂²	semidirect
29. #390×C₁₃₉	C₂²	semidirect
30. #390×C₁₃₉	C₂²	semidirect
31. #386×C₁₃₉	C₂²	semidirect
32. #385×C₁₃₉	C₂²	semidirect
33. #379×C₁₃₉	C₂²	semidirect
34. #379×C₁₃₉	C₂²	semidirect
35. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
207. #35616	C₁₃₉	direct (N × H)
208. C₁₃₉	#35616	direct (N × H)
210. C₂×#536	C₂×C₁₃₉	semidirect
211. C₂²×#124	C₂×C₁₃₉	semidirect
212. #2435	C₂×C₁₃₉	semidirect
213. #2432	C₂×C₁₃₉	semidirect
214. #2405	C₂×C₁₃₉	semidirect
215. #2309	C₂×C₁₃₉	semidirect
216. #2297	C₂×C₁₃₉	semidirect
221. C₂³×Q₈	C₂²×C₁₃₉	semidirect
226. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
228. C₂×#124	C₂²×C₁₃₉	semidirect
229. C₂×#124	C₂²×C₁₃₉	semidirect
230. C₂×#123	C₂²×C₁₃₉	semidirect
231. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
232. C₂×#117	C₂²×C₁₃₉	semidirect
233. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
234. C₂²×C₄²	C₂²×C₁₃₉	semidirect
235. #394	C₂²×C₁₃₉	semidirect
236. #391	C₂²×C₁₃₉	semidirect
237. #390	C₂²×C₁₃₉	semidirect
238. #390	C₂²×C₁₃₉	semidirect
239. #386	C₂²×C₁₃₉	semidirect
240. #385	C₂²×C₁₃₉	semidirect
241. #379	C₂²×C₁₃₉	semidirect
242. #379	C₂²×C₁₃₉	semidirect
243. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₁₃₉	2
C₂×#536×C₁₃₉	2
C₂²×#124×C₁₃₉	2
#2435×C₁₃₉	2
#2432×C₁₃₉	2
#2405×C₁₃₉	2
#2309×C₁₃₉	2
#2297×C₁₃₉	2
#35616	139

Subgroups — C139×#35616 #48030212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35616 #48030212