Subgroups — #468×D₁₃₉ #31815988

Order 17792.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊Q₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#22581202	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581201	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581200	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581199	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581198	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581197	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581196	C₂	1	1	yes	maximal, characteristic, complemented
12	#107×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#103×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#468×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₃₉	—	2	1	no	—
18	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#14555774	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14555773	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14555772	C₂²	1	1	yes	characteristic, complemented
23	SD₁₆×D₁₃₉	—	2	4	no	—
24	C₂×#14555769	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
27	M₁₆×D₁₃₉	—	2	4	no	—
28	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
30	#17984822	C₂²	1	1	yes	characteristic, complemented
31	#17984821	C₂²	1	1	yes	characteristic, complemented
32	#17984820	—	2	1	no	—
33	#17984819	—	2	1	no	—
34	#17984818	C₂²	1	1	yes	characteristic, complemented
35	#17984817	C₂²	1	1	yes	characteristic
36	#17984816	C₂²	1	1	yes	characteristic
37	#17984815	—	2	1	no	—
38	#17984814	—	2	1	no	—
39	#17984813	C₂²	1	1	yes	characteristic
40	C₄⋊C₄×D₁₃₉	—	2	1	no	—
41	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
44	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
45	#17984776	C₂²	1	1	yes	characteristic, complemented
46	#17984775	C₂²	1	1	yes	characteristic, complemented
47	#17984775	C₂²	1	1	yes	characteristic, complemented
48	#17984767	C₂²	1	1	yes	characteristic, complemented
49	#17984766	C₂²	1	1	yes	characteristic, complemented
50	#17984765	C₂²	1	1	yes	characteristic, complemented
51	#17984764	C₂²	1	1	yes	characteristic, complemented
52	#17984763	C₂²	1	1	yes	characteristic, complemented
53	#17984762	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#121×C₁₃₉	C₂²	1	1	yes	characteristic
58	#107×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃₉	—	2	1	no	—
62	C₂³×D₁₃₉	D₄	1	1	yes	characteristic
63	C₂×Dic₂₇₈	—	2	1	no	—
64	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
65	Q₈×D₁₃₉	—	2	2	no	—
66	Q₈×D₁₃₉	—	2	2	no	—
67	C₂×D₅₅₆	—	2	1	no	—
68	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
72	D₄×D₁₃₉	—	2	2	no	—
73	D₄×D₁₃₉	—	2	2	no	—
74	D₄×D₁₃₉	—	4	4	no	—
75	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃₉	—	2	2	no	—
77	C₂×C₄×D₁₃₉	—	2	2	no	—
78	C₂×C₄×D₁₃₉	—	2	1	no	—
79	C₂×C₄×D₁₃₉	—	2	1	no	—
80	C₂×C₄×D₁₃₉	—	2	1	no	—
81	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
85	#14555774	—	2	2	no	—
86	#14555773	—	2	2	no	—
87	#14555772	—	2	2	no	—
88	#14555769	—	2	2	no	—
89	#14555768	—	2	2	no	—
90	#14555768	—	2	2	no	—
91	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
93	C₈×D₁₃₉	—	2	2	no	—
94	C₈×D₁₃₉	D₄	1	4	yes	complemented
95	C₄⋊Dic₁₃₉	—	2	1	no	—
96	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
98	Dic₁₃₉⋊C₄	—	2	1	no	—
99	Dic₁₃₉⋊C₄	—	2	1	no	—
100	Dic₁₃₉⋊C₄	—	2	1	no	—
101	Dic₁₃₉⋊C₄	—	2	1	no	—
102	C₂²⋊Dic₁₃₉	—	2	1	no	—
103	C₂²⋊Dic₁₃₉	—	2	1	no	—
104	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
105	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
106	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
107	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
108	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₃₉	—	2	1	no	—
110	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	SD₁₆×C₁₃₉	—	2	2	no	—
113	M₁₆×C₁₃₉	—	2	2	no	—
114	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₃₉	—	2	1	no	—
117	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
120	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
121	C₂²×D₁₃₉	—	2	2	no	—
122	C₂²×D₁₃₉	—	2	2	no	—
123	C₂²×D₁₃₉	—	2	2	no	—
124	C₂²×D₁₃₉	—	2	1	no	—
125	C₂²×D₁₃₉	—	4	2	no	—
126	C₂²×D₁₃₉	—	4	2	no	—
127	C₂²×D₁₃₉	—	4	2	no	—
128	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
130	Dic₂₇₈	—	2	1	no	—
131	Dic₂₇₈	—	2	1	no	—
132	Dic₂₇₈	—	4	2	no	—
133	D₅₅₆	—	2	1	no	—
134	D₅₅₆	—	2	1	no	—
135	D₅₅₆	—	4	2	no	—
136	C₂²⋊D₁₃₉	—	4	2	no	—
137	C₂²⋊D₁₃₉	—	4	2	no	—
138	C₂²⋊D₁₃₉	—	4	2	no	—
139	C₂×Dic₁₃₉	—	2	2	no	—
140	C₂×Dic₁₃₉	—	2	1	no	—
141	C₂×Dic₁₃₉	—	2	1	no	—
142	C₂×Dic₁₃₉	—	2	1	no	—
143	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
145	C₄×D₁₃₉	—	2	2	no	—
146	C₄×D₁₃₉	—	2	1	no	—
147	C₄×D₁₃₉	—	2	1	no	—
148	C₄×D₁₃₉	—	2	2	no	—
149	C₄×D₁₃₉	—	4	2	no	—
150	C₄×D₁₃₉	—	4	2	no	—
151	C₄×D₁₃₉	—	4	2	no	—
152	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
153	C₄×D₁₃₉	#41	1	2	yes	—
154	C₁₃₉⋊C₈	—	2	1	no	—
155	C₁₃₉⋊C₈	C₂×D₄	1	2	yes	complemented
156	C₂³×C₁₃₉	—	2	1	no	—
157	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
158	Q₈×C₁₃₉	—	2	1	no	—
159	Q₈×C₁₃₉	—	2	1	no	—
160	D₄×C₁₃₉	—	2	1	no	—
161	D₄×C₁₃₉	—	2	1	no	—
162	D₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	—	2	1	no	—
164	C₂×C₄×C₁₃₉	—	2	1	no	—
165	C₂×C₄×C₁₃₉	—	2	1	no	—
166	C₂×C₄×C₁₃₉	—	2	1	no	—
167	C₂×C₄×C₁₃₉	—	2	1	no	—
168	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
170	C₈×C₁₃₉	—	2	1	no	—
171	C₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
172	C₂²×C₁₃₉	—	2	1	no	—
173	C₂²×C₁₃₉	—	2	1	no	—
174	C₂²×C₁₃₉	—	2	1	no	—
175	C₂²×C₁₃₉	—	4	1	no	—
176	C₂²×C₁₃₉	—	4	1	no	—
177	C₂²×C₁₃₉	—	4	1	no	—
178	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×D₁₃₉	—	2	1	no	—
180	C₂×D₁₃₉	—	2	1	no	—
181	C₂×D₁₃₉	—	2	1	no	—
182	C₂×D₁₃₉	—	4	4	no	—
183	C₂×D₁₃₉	—	4	1	no	—
184	C₂×D₁₃₉	—	4	1	no	—
185	C₂×D₁₃₉	—	4	1	no	—
186	C₂×D₁₃₉	—	8	4	no	—
187	C₂×D₁₃₉	#121	1	2	yes	—
188	C₂×D₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×D₁₃₉	#137	1	2	yes	—
190	C₄×C₁₃₉	—	2	1	no	—
191	C₄×C₁₃₉	—	4	1	no	—
192	C₄×C₁₃₉	—	4	1	no	—
193	C₄×C₁₃₉	—	4	1	no	—
194	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
196	Dic₁₃₉	—	2	1	no	—
197	Dic₁₃₉	—	4	1	no	—
198	Dic₁₃₉	—	4	1	no	—
199	Dic₁₃₉	—	4	1	no	—
200	Dic₁₃₉	#121	1	2	yes	—
201	C₂×C₁₃₉	—	4	1	no	—
202	C₂×C₁₃₉	—	8	1	no	—
203	C₂×C₁₃₉	C₂×#121	1	1	yes	characteristic
204	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂×C₁₃₉	C₂×#137	1	1	yes	characteristic
206	D₁₃₉	—	4	1	no	—
207	D₁₃₉	—	8	1	no	—
208	D₁₃₉	#468	1	4	yes	direct product factor
209	C₁₃₉	C₂×#468	1	1	yes	characteristic, complemented, Sylow
210	C₂×#468	—	139	1	no	maximal, Sylow
211	C₂²×SD₁₆	—	139	1	no	—
212	C₂²×M₁₆	—	139	1	no	—
213	C₂×C₂²⋊Q₈	—	139	1	no	—
214	C₂×#121	—	139	1	no	—
215	#468	—	139	1	no	—
216	#468	—	139	1	no	—
217	#468	—	139	1	no	—
218	#468	—	139	1	no	—
219	#468	—	139	1	no	—
220	#468	—	139	1	no	—
221	#468	—	139	1	no	—
222	#468	D₁₃₉	1	1	yes	characteristic, direct product factor
223	C₂×#107	—	139	1	no	—
224	C₂×#103	—	139	1	no	—
225	C₂×#102	—	139	1	no	—
226	C₂²×Q₈	—	139	1	no	—
227	C₂²×D₄	—	278	1	no	—
228	C₂²×D₄	—	139	1	no	—
229	C₂³×C₄	—	139	1	no	—
230	C₂×SD₁₆	—	278	4	no	—
231	C₂×SD₁₆	—	139	1	no	—
232	C₂×SD₁₆	—	139	1	no	—
233	C₂×SD₁₆	—	139	1	no	—
234	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
235	C₂×M₁₆	—	278	4	no	—
236	C₂×M₁₆	—	139	1	no	—
237	C₂×M₁₆	—	139	1	no	—
238	C₂×M₁₆	—	139	1	no	—
239	C₂×M₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
240	C₂²×C₈	—	139	1	no	—
241	C₂²×C₈	—	139	1	no	—
242	C₂²⋊Q₈	—	278	1	no	—
243	C₂²⋊Q₈	—	278	1	no	—
244	C₂²⋊Q₈	—	139	1	no	—
245	C₂²⋊Q₈	—	139	1	no	—
246	C₂²⋊Q₈	—	139	1	no	—
247	C₂²⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
248	#121	—	278	1	no	—
249	#121	—	278	1	no	—
250	#121	—	139	1	no	—
251	#121	—	139	1	no	—
252	#121	—	139	1	no	—
253	#121	C₂×D₁₃₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	278	1	no	—
255	C₂×C₄⋊C₄	—	139	1	no	—
256	C₂×C₄⋊C₄	—	139	1	no	—
257	C₂×C₂²⋊C₄	—	278	1	no	—
258	C₂×C₂²⋊C₄	—	278	1	no	—
259	#107	—	139	1	no	—
260	#107	—	139	1	no	—
261	#107	—	139	1	no	—
262	#107	C₂×D₁₃₉	1	1	yes	characteristic, complemented
263	#103	—	139	1	no	—
264	#103	—	139	1	no	—
265	#103	—	139	1	no	—
266	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
267	#102	—	139	1	no	—
268	#102	—	139	1	no	—
269	#102	—	139	1	no	—
270	#102	C₂×D₁₃₉	1	1	yes	characteristic, complemented
271	C₂⁴	—	278	1	no	—
272	C₂⁴	—	139	1	no	—
273	C₂×Q₈	—	278	1	no	—
274	C₂×Q₈	—	278	2	no	—
275	C₂×Q₈	—	278	2	no	—
276	C₂×Q₈	—	139	1	no	—
277	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	278	1	no	—
280	C₂×D₄	—	278	1	no	—
281	C₂×D₄	—	278	1	no	—
282	C₂×D₄	—	278	2	no	—
283	C₂×D₄	—	278	2	no	—
284	C₂×D₄	—	278	1	no	—
285	C₂×D₄	—	556	4	no	—
286	C₂×D₄	—	139	1	no	—
287	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
288	C₂²×C₄	—	278	2	no	—
289	C₂²×C₄	—	278	2	no	—
290	C₂²×C₄	—	278	1	no	—
291	C₂²×C₄	—	278	1	no	—
292	C₂²×C₄	—	278	1	no	—
293	C₂²×C₄	—	139	1	no	—
294	C₂²×C₄	—	139	1	no	—
295	C₂²×C₄	—	139	1	no	—
296	C₂²×C₄	—	139	1	no	—
297	C₂²×C₄	—	139	1	no	—
298	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
299	SD₁₆	—	2	2	no	—
300	SD₁₆	—	278	2	no	—
301	SD₁₆	—	278	2	no	—
302	SD₁₆	—	278	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	278	2	no	—
305	M₁₆	—	278	2	no	—
306	M₁₆	—	278	2	no	—
307	C₂×C₈	—	278	2	no	—
308	C₂×C₈	—	139	1	no	—
309	C₂×C₈	—	139	1	no	—
310	C₂×C₈	—	139	4	no	—
311	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	278	1	no	—
315	C₄⋊C₄	—	278	1	no	—
316	C₄⋊C₄	—	278	1	no	—
317	C₄⋊C₄	—	278	1	no	—
318	C₄⋊C₄	—	278	1	no	—
319	C₄⋊C₄	—	139	1	no	—
320	C₄⋊C₄	—	139	1	no	—
321	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
322	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	278	1	no	—
326	C₂²⋊C₄	—	278	1	no	—
327	C₂²⋊C₄	—	278	1	no	—
328	C₂²⋊C₄	—	278	1	no	—
329	C₂²⋊C₄	—	278	1	no	—
330	C₂²⋊C₄	—	278	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	278	2	no	—
333	C₂³	—	278	2	no	—
334	C₂³	—	278	2	no	—
335	C₂³	—	278	1	no	—
336	C₂³	—	556	2	no	—
337	C₂³	—	556	2	no	—
338	C₂³	—	556	2	no	—
339	C₂³	—	139	1	no	—
340	C₂³	—	139	1	no	—
341	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	278	1	no	—
345	Q₈	—	278	1	no	—
346	Q₈	—	556	2	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	278	1	no	—
351	D₄	—	278	1	no	—
352	D₄	—	556	2	no	—
353	D₄	—	556	2	no	—
354	D₄	—	556	2	no	—
355	D₄	—	556	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	278	2	no	—
362	C₂×C₄	—	278	2	no	—
363	C₂×C₄	—	278	2	no	—
364	C₂×C₄	—	278	1	no	—
365	C₂×C₄	—	278	1	no	—
366	C₂×C₄	—	278	1	no	—
367	C₂×C₄	—	278	1	no	—
368	C₂×C₄	—	278	1	no	—
369	C₂×C₄	—	556	2	no	—
370	C₂×C₄	—	556	2	no	—
371	C₂×C₄	—	556	2	no	—
372	C₂×C₄	—	139	1	no	—
373	C₂×C₄	—	139	1	no	—
374	C₂×C₄	—	139	2	no	—
375	C₂×C₄	—	139	2	no	—
376	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	278	1	no	—
380	C₈	—	139	2	no	—
381	C₈	D₄×D₁₃₉	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	278	1	no	—
389	C₂²	—	278	1	no	—
390	C₂²	—	278	1	no	—
391	C₂²	—	556	4	no	—
392	C₂²	—	556	1	no	—
393	C₂²	—	556	1	no	—
394	C₂²	—	556	1	no	—
395	C₂²	—	1112	4	no	—
396	C₂²	—	139	2	no	—
397	C₂²	—	139	2	no	—
398	C₂²	—	139	2	no	—
399	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	278	1	no	—
405	C₄	—	556	1	no	—
406	C₄	—	556	1	no	—
407	C₄	—	556	1	no	—
408	C₄	—	139	2	no	—
409	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
410	C₄	#41×D₁₃₉	1	1	yes	characteristic
411	C₂	—	4	1	no	—
412	C₂	—	8	1	no	—
413	C₂	—	556	1	no	—
414	C₂	—	1112	1	no	—
415	C₂	—	139	4	no	—
416	C₂	#121×D₁₃₉	1	1	yes	characteristic
417	C₂	AGL(1,ℤ/8)×D₁₃₉	1	1	yes	characteristic
418	C₂	#137×D₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#468×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	#121×D₁₃₉	C₂
hypercenter	#468	D₁₃₉
hypocenter	C₁₃₉	C₂×#468
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₁₃₉	C₂	semidirect
2. C₂×M₁₆×D₁₃₉	C₂	semidirect
3. C₂²⋊Q₈×D₁₃₉	C₂	semidirect
5. #22581202	C₂	semidirect
6. #22581201	C₂	semidirect
7. #22581200	C₂	semidirect
8. #22581199	C₂	semidirect
9. #22581198	C₂	semidirect
10. #22581197	C₂	semidirect
11. #22581196	C₂	semidirect
12. #107×D₁₃₉	C₂	semidirect
13. #103×D₁₃₉	C₂	semidirect
14. #102×D₁₃₉	C₂	semidirect
15. #468×C₁₃₉	C₂	semidirect
20. C₂×#14555774	C₂²	semidirect
21. C₂×#14555773	C₂²	semidirect
22. C₂×#14555772	C₂²	semidirect
24. C₂×#14555769	C₂²	semidirect
25. C₂×#14555768	C₂²	semidirect
26. C₂×#14555768	C₂²	semidirect
30. #17984822	C₂²	semidirect
31. #17984821	C₂²	semidirect
34. #17984818	C₂²	semidirect
45. #17984776	C₂²	semidirect
46. #17984775	C₂²	semidirect
47. #17984775	C₂²	semidirect
48. #17984767	C₂²	semidirect
49. #17984766	C₂²	semidirect
50. #17984765	C₂²	semidirect
51. #17984764	C₂²	semidirect
52. #17984763	C₂²	semidirect
53. #17984762	C₂²	semidirect
54. C₂×SD₁₆×C₁₃₉	C₂²	semidirect
55. C₂×M₁₆×C₁₃₉	C₂²	semidirect
56. C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
58. #107×C₁₃₉	C₂²	semidirect
59. #103×C₁₃₉	C₂²	semidirect
60. #102×C₁₃₉	C₂²	semidirect
94. C₈×D₁₃₉	D₄	semidirect
155. C₁₃₉⋊C₈	C₂×D₄	semidirect
171. C₈×C₁₃₉	C₂×D₄	semidirect
208. D₁₃₉	#468	direct (N × H)
209. C₁₃₉	C₂×#468	semidirect
222. #468	D₁₃₉	direct (N × H)
234. C₂×SD₁₆	C₂×D₁₃₉	semidirect
239. C₂×M₁₆	C₂×D₁₃₉	semidirect
247. C₂²⋊Q₈	C₂×D₁₃₉	semidirect
262. #107	C₂×D₁₃₉	semidirect
266. #103	C₂×D₁₃₉	semidirect
270. #102	C₂×D₁₃₉	semidirect
381. C₈	D₄×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₃₉	2
C₂×M₁₆×D₁₃₉	2
C₂²⋊Q₈×D₁₃₉	2
#121×D₁₃₉	2
#22581202	2
#22581201	2
#22581200	2
#22581199	2
#22581198	2
#22581197	2
#22581196	2
#107×D₁₃₉	2
#103×D₁₃₉	2
#102×D₁₃₉	2
#468×C₁₃₉	2
C₂×#468	139

Subgroups — #468×D139 #31815988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #468×D₁₃₉ #31815988