Subgroups — C₁₃₉×#33531 #48028127

Order 35584.

1122 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#3058×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2190×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2145×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2115×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#585×C₁₃₉	—	2	1	no	—
8	#578×C₁₃₉	—	2	2	no	—
9	#577×C₁₃₉	—	2	4	no	—
10	#576×C₁₃₉	—	2	2	no	—
11	#575×C₁₃₉	—	2	1	no	—
12	#575×C₁₃₉	C₂²	1	4	yes	complemented
13	C₂×#135×C₁₃₉	—	2	2	no	—
14	C₂×#135×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×#131×C₁₃₉	C₂²	1	1	yes	characteristic
17	#535×C₁₃₉	—	2	1	no	—
18	#509×C₁₃₉	—	2	4	no	—
19	#509×C₁₃₉	C₂²	1	8	yes	complemented
20	C₂×SD₃₂×C₁₃₉	—	2	2	no	—
21	C₂×D₁₆×C₁₃₉	—	2	2	no	—
22	C₂×M₃₂×C₁₃₉	C₂²	1	2	yes	complemented
23	#469×C₁₃₉	C₂²	1	4	yes	complemented
24	#466×C₁₃₉	—	2	2	no	—
25	#427×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	#418×C₁₃₉	—	2	1	no	—
27	#360×C₁₃₉	C₂²	1	8	yes	complemented
28	#349×C₁₃₉	C₂²	1	4	yes	complemented
29	2₋¹⁺⁴×C₁₃₉	—	2	4	no	—
30	2₋¹⁺⁴×C₁₃₉	—	4	1	no	—
31	H(5,𝔽₂)×C₁₃₉	—	2	4	no	—
32	H(5,𝔽₂)×C₁₃₉	—	4	2	no	—
33	H(5,𝔽₂)×C₁₃₉	—	4	1	no	—
34	C₂×#41×C₁₃₉	—	2	4	no	—
35	C₂×#41×C₁₃₉	—	2	2	no	—
36	C₂×#41×C₁₃₉	—	4	4	no	—
37	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₃₉	—	2	1	no	—
39	#137×C₁₃₉	—	2	4	no	—
40	#137×C₁₃₉	—	2	8	no	—
41	AGL(1,ℤ/8)×C₁₃₉	—	2	4	no	—
42	AGL(1,ℤ/8)×C₁₃₉	—	2	8	no	—
43	#135×C₁₃₉	—	2	4	no	—
44	#135×C₁₃₉	—	2	4	no	—
45	#135×C₁₃₉	—	2	2	no	—
46	#135×C₁₃₉	—	2	4	no	—
47	#135×C₁₃₉	—	2	2	no	—
48	#135×C₁₃₉	D₄	1	4	yes	complemented
49	#135×C₁₃₉	C₂³	1	4	yes	—
50	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
51	C₂×Q₁₆×C₁₃₉	D₄	1	2	yes	complemented
52	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
53	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
54	C₂×D₈×C₁₃₉	—	2	2	no	—
55	C₂×D₈×C₁₃₉	—	2	2	no	—
56	C₂×D₈×C₁₃₉	—	2	2	no	—
57	C₂×D₈×C₁₃₉	—	2	1	no	—
58	C₂×D₈×C₁₃₉	D₄	1	2	yes	complemented
59	C₂×D₈×C₁₃₉	C₂³	1	2	yes	—
60	#131×C₁₃₉	—	2	2	no	—
61	#131×C₁₃₉	—	2	2	no	—
62	C₂×M₁₆×C₁₃₉	D₄	1	1	yes	characteristic
63	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃₉	D₄	1	2	yes	—
65	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
66	#127×C₁₃₉	—	4	1	no	—
67	#124×C₁₃₉	—	4	1	no	—
68	#121×C₁₃₉	—	2	4	no	—
69	#120×C₁₃₉	—	4	2	no	—
70	#117×C₁₃₉	—	2	1	no	—
71	SD₃₂×C₁₃₉	—	2	8	no	—
72	D₁₆×C₁₃₉	—	2	8	no	—
73	M₃₂×C₁₃₉	—	2	2	no	—
74	M₃₂×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₁₆×C₁₃₉	—	2	2	no	—
76	#107×C₁₃₉	—	2	1	no	—
77	#106×C₁₃₉	C₂³	1	2	yes	—
78	#102×C₁₃₉	—	2	4	no	—
79	C₂⁴×C₁₃₉	—	4	1	no	—
80	#41×C₁₃₉	—	2	2	no	—
81	#41×C₁₃₉	—	2	2	no	—
82	#41×C₁₃₉	—	2	8	no	—
83	#41×C₁₃₉	—	2	4	no	—
84	#41×C₁₃₉	—	2	4	no	—
85	#41×C₁₃₉	—	4	4	no	—
86	#41×C₁₃₉	—	4	8	no	—
87	#41×C₁₃₉	—	4	4	no	—
88	#41×C₁₃₉	—	4	4	no	—
89	#41×C₁₃₉	—	4	4	no	—
90	#41×C₁₃₉	—	4	2	no	—
91	#41×C₁₃₉	—	4	2	no	—
92	C₂×Q₈×C₁₃₉	—	2	4	no	—
93	C₂×Q₈×C₁₃₉	—	2	2	no	—
94	C₂×Q₈×C₁₃₉	—	4	4	no	—
95	C₂×Q₈×C₁₃₉	D₈	1	1	yes	characteristic
96	C₂×D₄×C₁₃₉	—	2	4	no	—
97	C₂×D₄×C₁₃₉	—	2	2	no	—
98	C₂×D₄×C₁₃₉	—	2	2	no	—
99	C₂×D₄×C₁₃₉	—	4	8	no	—
100	C₂×D₄×C₁₃₉	—	4	4	no	—
101	C₂×D₄×C₁₃₉	—	4	4	no	—
102	C₂×D₄×C₁₃₉	—	4	2	no	—
103	C₂×D₄×C₁₃₉	—	4	4	no	—
104	C₂×D₄×C₁₃₉	—	4	2	no	—
105	C₂×D₄×C₁₃₉	—	4	1	no	—
106	C₂×D₄×C₁₃₉	—	4	2	no	—
107	C₂×D₄×C₁₃₉	D₈	1	2	yes	—
108	C₂×D₄×C₁₃₉	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	—	4	4	no	—
110	C₂²×C₄×C₁₃₉	—	4	2	no	—
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₁₃₉	—	2	4	no	—
114	Q₁₆×C₁₃₉	—	2	2	no	—
115	Q₁₆×C₁₃₉	C₂×D₄	1	4	yes	—
116	SD₁₆×C₁₃₉	—	2	8	no	—
117	SD₁₆×C₁₃₉	—	2	4	no	—
118	SD₁₆×C₁₃₉	—	2	4	no	—
119	D₈×C₁₃₉	—	2	4	no	—
120	D₈×C₁₃₉	—	2	2	no	—
121	D₈×C₁₃₉	—	2	4	no	—
122	D₈×C₁₃₉	—	4	1	no	—
123	D₈×C₁₃₉	—	4	1	no	—
124	D₈×C₁₃₉	C₂×D₄	1	4	yes	—
125	M₁₆×C₁₃₉	—	2	2	no	—
126	M₁₆×C₁₃₉	—	2	4	no	—
127	C₂×C₈×C₁₃₉	—	2	2	no	—
128	C₂×C₈×C₁₃₉	—	2	2	no	—
129	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₁₃₉	—	2	2	no	—
135	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
136	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
137	C₄²×C₁₃₉	—	4	1	no	—
138	C₁₆×C₁₃₉	—	2	4	no	—
139	C₂³×C₁₃₉	—	4	4	no	—
140	C₂³×C₁₃₉	—	4	2	no	—
141	C₂³×C₁₃₉	—	4	2	no	—
142	C₂³×C₁₃₉	—	8	2	no	—
143	C₂³×C₁₃₉	—	16	2	no	—
144	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
145	C₂³×C₁₃₉	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₁₃₉	—	2	2	no	—
147	Q₈×C₁₃₉	—	2	4	no	—
148	Q₈×C₁₃₉	—	4	4	no	—
149	Q₈×C₁₃₉	—	4	2	no	—
150	D₄×C₁₃₉	—	2	4	no	—
151	D₄×C₁₃₉	—	2	4	no	—
152	D₄×C₁₃₉	—	2	2	no	—
153	D₄×C₁₃₉	—	4	4	no	—
154	D₄×C₁₃₉	—	4	8	no	—
155	D₄×C₁₃₉	—	4	4	no	—
156	D₄×C₁₃₉	—	4	4	no	—
157	D₄×C₁₃₉	—	4	2	no	—
158	D₄×C₁₃₉	—	4	2	no	—
159	D₄×C₁₃₉	—	4	2	no	—
160	D₄×C₁₃₉	—	8	2	no	—
161	D₄×C₁₃₉	—	16	4	no	—
162	C₂×C₄×C₁₃₉	—	2	2	no	—
163	C₂×C₄×C₁₃₉	—	2	2	no	—
164	C₂×C₄×C₁₃₉	—	4	8	no	—
165	C₂×C₄×C₁₃₉	—	4	4	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	4	no	—
168	C₂×C₄×C₁₃₉	—	4	4	no	—
169	C₂×C₄×C₁₃₉	—	4	2	no	—
170	C₂×C₄×C₁₃₉	#120	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
172	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₁₃₉	—	2	2	no	—
176	C₈×C₁₃₉	#120	1	1	yes	characteristic
177	C₈×C₁₃₉	#120	1	1	yes	characteristic
178	C₈×C₁₃₉	C₂²×D₄	1	2	yes	—
179	C₂²×C₁₃₉	—	2	2	no	—
180	C₂²×C₁₃₉	—	4	1	no	—
181	C₂²×C₁₃₉	—	4	2	no	—
182	C₂²×C₁₃₉	—	4	4	no	—
183	C₂²×C₁₃₉	—	8	4	no	—
184	C₂²×C₁₃₉	—	8	2	no	—
185	C₂²×C₁₃₉	—	16	2	no	—
186	C₂²×C₁₃₉	—	16	4	no	—
187	C₂²×C₁₃₉	—	16	4	no	—
188	C₂²×C₁₃₉	#447	1	2	yes	—
189	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
190	C₄×C₁₃₉	—	2	2	no	—
191	C₄×C₁₃₉	—	4	4	no	—
192	C₄×C₁₃₉	—	8	2	no	—
193	C₄×C₁₃₉	#447	1	2	yes	—
194	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
195	C₄×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂×C₁₃₉	—	2	1	no	—
197	C₂×C₁₃₉	—	2	2	no	—
198	C₂×C₁₃₉	—	4	2	no	—
199	C₂×C₁₃₉	—	8	4	no	—
200	C₂×C₁₃₉	—	16	2	no	—
201	C₂×C₁₃₉	C₂×#447	1	1	yes	characteristic
202	#33531	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₉	#33531	1	1	yes	characteristic, direct product factor, Sylow
204	#3584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
205	C₂×#509	C₂×C₁₃₉	1	2	yes	complemented
206	#3058	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	#2190	C₂×C₁₃₉	1	8	yes	complemented
208	#2145	C₂×C₁₃₉	1	2	yes	complemented
209	#2115	C₂×C₁₃₉	1	1	yes	characteristic, complemented
210	#585	—	2	1	no	—
211	#578	—	2	2	no	—
212	#577	—	2	4	no	—
213	#576	—	2	2	no	—
214	#575	—	2	1	no	—
215	#575	C₂²×C₁₃₉	1	4	yes	complemented
216	C₂×#135	—	2	2	no	—
217	C₂×#135	C₂²×C₁₃₉	1	2	yes	—
218	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
219	C₂×#131	C₂²×C₁₃₉	1	1	yes	characteristic
220	#535	—	2	1	no	—
221	#509	—	2	4	no	—
222	#509	C₂²×C₁₃₉	1	8	yes	complemented
223	C₂×SD₃₂	—	2	2	no	—
224	C₂×D₁₆	—	2	2	no	—
225	C₂×M₃₂	C₂²×C₁₃₉	1	2	yes	complemented
226	#469	C₂²×C₁₃₉	1	4	yes	complemented
227	#466	—	2	2	no	—
228	#427	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
229	#418	—	2	1	no	—
230	#360	C₂²×C₁₃₉	1	8	yes	complemented
231	#349	C₂²×C₁₃₉	1	4	yes	complemented
232	2₋¹⁺⁴	—	2	4	no	—
233	2₋¹⁺⁴	—	4	1	no	—
234	H(5,𝔽₂)	—	2	4	no	—
235	H(5,𝔽₂)	—	4	2	no	—
236	H(5,𝔽₂)	—	4	1	no	—
237	C₂×#41	—	2	4	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	4	4	no	—
240	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
241	C₂²×D₄	—	2	1	no	—
242	#137	—	2	4	no	—
243	#137	—	2	8	no	—
244	AGL(1,ℤ/8)	—	2	4	no	—
245	AGL(1,ℤ/8)	—	2	8	no	—
246	#135	—	2	4	no	—
247	#135	—	2	4	no	—
248	#135	—	2	2	no	—
249	#135	—	2	4	no	—
250	#135	—	2	2	no	—
251	#135	D₄×C₁₃₉	1	4	yes	complemented
252	#135	C₂³×C₁₃₉	1	4	yes	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	D₄×C₁₃₉	1	2	yes	complemented
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×D₈	—	2	2	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	—	2	1	no	—
261	C₂×D₈	D₄×C₁₃₉	1	2	yes	complemented
262	C₂×D₈	C₂³×C₁₃₉	1	2	yes	—
263	#131	—	2	2	no	—
264	#131	—	2	2	no	—
265	C₂×M₁₆	D₄×C₁₃₉	1	1	yes	characteristic
266	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
267	C₂²×C₈	D₄×C₁₃₉	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
269	#127	—	4	1	no	—
270	#124	—	4	1	no	—
271	#121	—	2	4	no	—
272	#120	—	4	2	no	—
273	#117	—	2	1	no	—
274	SD₃₂	—	2	8	no	—
275	D₁₆	—	2	8	no	—
276	M₃₂	—	2	2	no	—
277	M₃₂	C₂³×C₁₃₉	1	4	yes	—
278	C₂×C₁₆	—	2	2	no	—
279	#107	—	2	1	no	—
280	#106	C₂³×C₁₃₉	1	2	yes	—
281	#102	—	2	4	no	—
282	C₂⁴	—	4	1	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	8	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	4	4	no	—
289	#41	—	4	8	no	—
290	#41	—	4	4	no	—
291	#41	—	4	4	no	—
292	#41	—	4	4	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	D₈×C₁₃₉	1	1	yes	characteristic
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	8	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	D₈×C₁₃₉	1	2	yes	—
311	C₂×D₄	D₈×C₁₃₉	1	1	yes	characteristic
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
316	Q₁₆	—	2	4	no	—
317	Q₁₆	—	2	2	no	—
318	Q₁₆	C₂×D₄×C₁₃₉	1	4	yes	—
319	SD₁₆	—	2	8	no	—
320	SD₁₆	—	2	4	no	—
321	SD₁₆	—	2	4	no	—
322	D₈	—	2	4	no	—
323	D₈	—	2	2	no	—
324	D₈	—	2	4	no	—
325	D₈	—	4	1	no	—
326	D₈	—	4	1	no	—
327	D₈	C₂×D₄×C₁₃₉	1	4	yes	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	4	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
336	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
337	C₄⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₄²	—	4	1	no	—
341	C₁₆	—	2	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	16	2	no	—
347	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
348	C₂³	C₂×D₈×C₁₃₉	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	4	no	—
352	Q₈	—	4	2	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	8	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	16	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	#120×C₁₃₉	1	2	yes	—
374	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
375	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
376	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	#120×C₁₃₉	1	1	yes	characteristic
380	C₈	#120×C₁₃₉	1	1	yes	characteristic
381	C₈	C₂²×D₄×C₁₃₉	1	2	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	8	4	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	16	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	—	16	4	no	—
391	C₂²	#447×C₁₃₉	1	2	yes	—
392	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	2	no	—
396	C₄	#447×C₁₃₉	1	2	yes	—
397	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
398	C₄	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	16	2	no	—
404	C₂	C₂×#447×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₉	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ C₂×#131×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #3584×C₁₃₉	C₂	semidirect
2. C₂×#509×C₁₃₉	C₂	semidirect
3. #3058×C₁₃₉	C₂	semidirect
4. #2190×C₁₃₉	C₂	semidirect
5. #2145×C₁₃₉	C₂	semidirect
6. #2115×C₁₃₉	C₂	semidirect
12. #575×C₁₃₉	C₂²	semidirect
15. C₂²×D₈×C₁₃₉	C₂²	semidirect
19. #509×C₁₃₉	C₂²	semidirect
22. C₂×M₃₂×C₁₃₉	C₂²	semidirect
23. #469×C₁₃₉	C₂²	semidirect
25. #427×C₁₃₉	C₂²	semidirect
27. #360×C₁₃₉	C₂²	semidirect
28. #349×C₁₃₉	C₂²	semidirect
48. #135×C₁₃₉	D₄	semidirect
51. C₂×Q₁₆×C₁₃₉	D₄	semidirect
58. C₂×D₈×C₁₃₉	D₄	semidirect
202. #33531	C₁₃₉	direct (N × H)
203. C₁₃₉	#33531	direct (N × H)
204. #3584	C₂×C₁₃₉	semidirect
205. C₂×#509	C₂×C₁₃₉	semidirect
206. #3058	C₂×C₁₃₉	semidirect
207. #2190	C₂×C₁₃₉	semidirect
208. #2145	C₂×C₁₃₉	semidirect
209. #2115	C₂×C₁₃₉	semidirect
215. #575	C₂²×C₁₃₉	semidirect
218. C₂²×D₈	C₂²×C₁₃₉	semidirect
222. #509	C₂²×C₁₃₉	semidirect
225. C₂×M₃₂	C₂²×C₁₃₉	semidirect
226. #469	C₂²×C₁₃₉	semidirect
228. #427	C₂²×C₁₃₉	semidirect
230. #360	C₂²×C₁₃₉	semidirect
231. #349	C₂²×C₁₃₉	semidirect
251. #135	D₄×C₁₃₉	semidirect
254. C₂×Q₁₆	D₄×C₁₃₉	semidirect
261. C₂×D₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3584×C₁₃₉	2
C₂×#509×C₁₃₉	2
#3058×C₁₃₉	2
#2190×C₁₃₉	2
#2145×C₁₃₉	2
#2115×C₁₃₉	2
#33531	139

Subgroups — C139×#33531 #48028127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33531 #48028127