Subgroups — #31815451

Order 17792.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581462	C₂	1	1	yes	maximal, characteristic
2	#22581031	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581028	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581027	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581026	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581022	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581018	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₂²⋊D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581015	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581013	C₂	1	1	yes	maximal, characteristic, complemented
11	#22580919	C₂	1	1	yes	maximal, characteristic, complemented
12	#22580918	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580916	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555785	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#14555769	C₂²	1	1	yes	characteristic
19	C₂×#14555769	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
24	#17984827	C₄	1	1	yes	characteristic
25	#17984824	C₄	1	1	yes	characteristic
26	#17984820	C₄	1	1	yes	characteristic
27	#17984819	C₄	1	1	yes	characteristic
28	#17984815	C₄	1	1	yes	characteristic
29	#17984814	C₄	1	1	yes	characteristic
30	#17984812	C₄	1	1	yes	characteristic
31	#17984810	C₄	1	1	yes	characteristic
32	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
35	#17984799	C₂²	1	1	yes	characteristic
36	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂²⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
42	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	#17984752	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#97×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₃₉	C₂×C₄	1	1	yes	characteristic
60	#14555785	—	4	1	no	—
61	#14555785	—	4	1	no	—
62	C₂×Dic₂₇₈	C₂×C₄	1	1	yes	characteristic
63	C₂×D₅₅₆	C₂×C₄	1	1	yes	characteristic
64	C₂×D₅₅₆	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₃₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₃₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₃₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₃₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₁₃₉	—	4	1	no	—
71	C₂×C₄×D₁₃₉	—	4	1	no	—
72	C₂×C₄×D₁₃₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×D₁₃₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
75	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
77	#14555769	—	4	1	no	—
78	#14555769	—	4	1	no	—
79	#14555768	—	4	1	no	—
80	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
84	C₈×D₁₃₉	—	4	1	no	—
85	C₈×D₁₃₉	—	4	1	no	—
86	C₈×D₁₃₉	—	4	1	no	—
87	C₄⋊Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
88	Dic₁₃₉⋊C₄	C₂×C₄	1	1	yes	characteristic
89	Dic₁₃₉⋊C₄	C₂×C₄	1	1	yes	characteristic
90	Dic₁₃₉⋊C₄	C₂×C₄	1	1	yes	characteristic
91	Dic₁₃₉⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₁₃₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₁₃₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₁₃₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₁₃₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₁₃₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₁₃₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	M₁₆×C₁₃₉	—	4	1	no	—
105	C₂×C₈×C₁₃₉	—	4	1	no	—
106	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
113	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂²×D₁₃₉	—	2	2	no	—
115	C₂²×D₁₃₉	—	4	1	no	—
116	C₂²×D₁₃₉	—	4	1	no	—
117	C₂²×D₁₃₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×D₁₃₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×D₁₃₉	C₂²×C₄	1	1	yes	characteristic
120	Dic₂₇₈	—	4	1	no	—
121	D₅₅₆	—	2	2	no	—
122	D₅₅₆	—	4	1	no	—
123	C₂²⋊D₁₃₉	—	2	2	no	—
124	C₂²⋊D₁₃₉	—	4	1	no	—
125	C₂²⋊D₁₃₉	—	4	1	no	—
126	C₂²⋊D₁₃₉	—	4	1	no	—
127	C₂×Dic₁₃₉	—	4	1	no	—
128	C₂×Dic₁₃₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₁₃₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₁₃₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×Dic₁₃₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₁₃₉	C₂²×C₄	1	1	yes	characteristic
133	C₄×D₁₃₉	—	2	1	no	—
134	C₄×D₁₃₉	—	2	1	no	—
135	C₄×D₁₃₉	—	2	1	no	—
136	C₄×D₁₃₉	—	2	1	no	—
137	C₄×D₁₃₉	—	2	1	no	—
138	C₄×D₁₃₉	—	2	1	no	—
139	C₄×D₁₃₉	—	4	1	no	—
140	C₄×D₁₃₉	—	4	1	no	—
141	C₁₃₉⋊C₈	—	2	1	no	—
142	C₁₃₉⋊C₈	—	2	1	no	—
143	C₁₃₉⋊C₈	—	2	1	no	—
144	C₁₃₉⋊C₈	—	2	1	no	—
145	C₂³×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
147	D₄×C₁₃₉	—	4	1	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	1	no	—
152	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
157	C₈×C₁₃₉	—	2	1	no	—
158	C₈×C₁₃₉	—	2	1	no	—
159	C₈×C₁₃₉	—	2	1	no	—
160	C₈×C₁₃₉	—	2	1	no	—
161	C₂²×C₁₃₉	—	2	1	no	—
162	C₂²×C₁₃₉	—	2	1	no	—
163	C₂²×C₁₃₉	—	2	1	no	—
164	C₂²×C₁₃₉	—	2	1	no	—
165	C₂²×C₁₃₉	—	2	1	no	—
166	C₂²×C₁₃₉	—	2	1	no	—
167	C₂²×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×D₁₃₉	—	2	1	no	—
169	C₂×D₁₃₉	—	2	1	no	—
170	C₂×D₁₃₉	—	2	1	no	—
171	C₂×D₁₃₉	—	2	1	no	—
172	C₂×D₁₃₉	—	2	1	no	—
173	C₂×D₁₃₉	—	2	1	no	—
174	C₂×D₁₃₉	—	2	1	no	—
175	C₂×D₁₃₉	—	2	1	no	—
176	C₂×D₁₃₉	—	4	4	no	—
177	C₂×D₁₃₉	#131	1	2	yes	—
178	C₄×C₁₃₉	—	2	1	no	—
179	C₄×C₁₃₉	—	2	1	no	—
180	C₄×C₁₃₉	—	2	1	no	—
181	C₄×C₁₃₉	—	2	1	no	—
182	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
183	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
184	Dic₁₃₉	—	2	1	no	—
185	Dic₁₃₉	—	2	1	no	—
186	Dic₁₃₉	—	2	1	no	—
187	Dic₁₃₉	—	2	1	no	—
188	Dic₁₃₉	—	2	1	no	—
189	C₂×C₁₃₉	—	4	1	no	—
190	C₂×C₁₃₉	—	4	1	no	—
191	C₂×C₁₃₉	#518	1	1	yes	characteristic
192	C₂×C₁₃₉	C₂×#131	1	1	yes	characteristic
193	C₂×C₁₃₉	#568	1	1	yes	characteristic
194	D₁₃₉	—	2	2	no	—
195	D₁₃₉	—	4	1	no	—
196	D₁₃₉	—	4	1	no	—
197	C₁₃₉	#2976	1	1	yes	characteristic, complemented, Sylow
198	#2976	—	139	1	no	maximal, Sylow
199	#525	—	139	1	no	—
200	#436	—	139	1	no	—
201	#436	—	139	1	no	—
202	#435	—	139	1	no	—
203	#435	—	139	1	no	—
204	#435	—	139	1	no	—
205	#435	D₁₃₉	1	1	yes	characteristic, complemented
206	C₈×D₄	—	139	1	no	—
207	C₈×D₄	—	139	1	no	—
208	#433	—	139	1	no	—
209	#433	—	139	1	no	—
210	#408	—	139	1	no	—
211	#408	—	139	1	no	—
212	#407	—	139	1	no	—
213	C₂×C₂²⋊C₈	—	139	1	no	—
214	C₂×#41	—	139	1	no	—
215	C₂³×C₄	—	139	1	no	—
216	C₂×M₁₆	—	139	1	no	—
217	C₂×M₁₆	—	139	1	no	—
218	C₂×M₁₆	—	139	1	no	—
219	C₂×M₁₆	C₂×D₁₃₉	1	1	yes	characteristic
220	C₂²×C₈	—	139	1	no	—
221	C₂²×C₈	—	139	1	no	—
222	C₂²×C₈	—	139	1	no	—
223	C₂²×C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
224	#123	—	139	1	no	—
225	#123	—	139	1	no	—
226	C₂²⋊Q₈	—	139	1	no	—
227	C₂²⋊Q₈	—	139	1	no	—
228	#121	—	139	1	no	—
229	#121	—	139	1	no	—
230	#120	—	139	1	no	—
231	#120	—	139	1	no	—
232	C₄×D₄	—	139	1	no	—
233	C₄×D₄	—	139	1	no	—
234	C₄×D₄	—	139	1	no	—
235	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
236	#117	—	139	1	no	—
237	C₄⋊C₈	—	139	1	no	—
238	C₄⋊C₈	—	139	1	no	—
239	C₄⋊C₈	—	139	1	no	—
240	C₄⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
241	C₂²⋊C₈	—	139	1	no	—
242	C₂²⋊C₈	—	139	1	no	—
243	C₂²⋊C₈	—	139	1	no	—
244	C₂²⋊C₈	—	139	1	no	—
245	C₂²⋊C₈	—	139	1	no	—
246	C₂²⋊C₈	—	139	1	no	—
247	C₂²⋊C₈	—	139	1	no	—
248	C₂²⋊C₈	—	139	1	no	—
249	C₂²⋊C₈	—	139	1	no	—
250	C₂²⋊C₈	—	139	1	no	—
251	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic
252	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
253	#97	—	139	1	no	—
254	#97	C₂×D₁₃₉	1	1	yes	characteristic, complemented
255	C₄×C₈	—	139	1	no	—
256	C₄×C₈	—	139	1	no	—
257	C₂⁴	—	139	1	no	—
258	#41	—	556	1	no	—
259	#41	—	556	1	no	—
260	C₂×Q₈	—	139	1	no	—
261	C₂×D₄	—	139	1	no	—
262	C₂×D₄	—	139	1	no	—
263	C₂×D₄	—	139	1	no	—
264	C₂×D₄	—	139	1	no	—
265	C₂×D₄	—	139	1	no	—
266	C₂×D₄	—	139	1	no	—
267	C₂×D₄	C₄×D₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	—	556	1	no	—
269	C₂²×C₄	—	556	1	no	—
270	C₂²×C₄	—	139	1	no	—
271	C₂²×C₄	—	139	1	no	—
272	C₂²×C₄	—	139	1	no	—
273	C₂²×C₄	—	139	1	no	—
274	C₂²×C₄	—	139	1	no	—
275	C₂²×C₄	—	139	1	no	—
276	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
278	M₁₆	—	4	1	no	—
279	M₁₆	—	556	1	no	—
280	M₁₆	—	556	1	no	—
281	M₁₆	—	556	1	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	556	1	no	—
284	C₂×C₈	—	556	1	no	—
285	C₂×C₈	—	556	1	no	—
286	C₂×C₈	—	139	1	no	—
287	C₂×C₈	—	139	1	no	—
288	C₂×C₈	—	139	1	no	—
289	C₂×C₈	—	139	1	no	—
290	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
292	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
293	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
294	C₄⋊C₄	—	139	1	no	—
295	C₄⋊C₄	—	139	1	no	—
296	C₄⋊C₄	—	139	1	no	—
297	C₄⋊C₄	—	139	1	no	—
298	C₄⋊C₄	—	139	1	no	—
299	C₄⋊C₄	C₄×D₁₃₉	1	1	yes	characteristic
300	C₂²⋊C₄	—	139	1	no	—
301	C₂²⋊C₄	—	139	1	no	—
302	C₂²⋊C₄	—	139	1	no	—
303	C₂²⋊C₄	—	139	1	no	—
304	C₂²⋊C₄	—	139	1	no	—
305	C₂²⋊C₄	—	139	1	no	—
306	C₂²⋊C₄	—	139	1	no	—
307	C₂²⋊C₄	—	139	1	no	—
308	C₂²⋊C₄	C₄×D₁₃₉	1	1	yes	characteristic
309	C₂²⋊C₄	C₄×D₁₃₉	1	1	yes	characteristic
310	C₄²	—	139	1	no	—
311	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
312	C₂³	—	278	2	no	—
313	C₂³	—	556	1	no	—
314	C₂³	—	556	1	no	—
315	C₂³	—	139	1	no	—
316	C₂³	—	139	1	no	—
317	C₂³	—	139	1	no	—
318	C₂³	C₂×C₄×D₁₃₉	1	1	yes	characteristic
319	C₂³	C₂×C₄×D₁₃₉	1	1	yes	characteristic
320	Q₈	—	556	1	no	—
321	D₄	—	4	1	no	—
322	D₄	—	278	2	no	—
323	D₄	—	278	2	no	—
324	D₄	—	556	1	no	—
325	D₄	—	556	1	no	—
326	D₄	—	556	1	no	—
327	D₄	—	556	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	278	1	no	—
333	C₂×C₄	—	278	1	no	—
334	C₂×C₄	—	278	1	no	—
335	C₂×C₄	—	278	1	no	—
336	C₂×C₄	—	278	1	no	—
337	C₂×C₄	—	278	1	no	—
338	C₂×C₄	—	556	1	no	—
339	C₂×C₄	—	556	1	no	—
340	C₂×C₄	—	556	1	no	—
341	C₂×C₄	—	139	1	no	—
342	C₂×C₄	—	139	1	no	—
343	C₂×C₄	—	139	1	no	—
344	C₂×C₄	—	139	1	no	—
345	C₂×C₄	—	139	1	no	—
346	C₂×C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
350	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	278	1	no	—
356	C₈	—	278	1	no	—
357	C₈	—	278	1	no	—
358	C₈	—	278	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	278	1	no	—
366	C₂²	—	278	1	no	—
367	C₂²	—	278	1	no	—
368	C₂²	—	278	1	no	—
369	C₂²	—	278	1	no	—
370	C₂²	—	278	1	no	—
371	C₂²	—	278	1	no	—
372	C₂²	—	278	1	no	—
373	C₂²	—	556	4	no	—
374	C₂²	—	139	2	no	—
375	C₂²	C₂²×C₄×D₁₃₉	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	278	1	no	—
381	C₄	—	278	1	no	—
382	C₄	—	278	1	no	—
383	C₄	—	278	1	no	—
384	C₄	—	278	1	no	—
385	C₄	#17984887	1	1	yes	characteristic
386	C₄	#17984888	1	1	yes	characteristic
387	C₂	—	4	1	no	—
388	C₂	—	4	1	no	—
389	C₂	—	278	2	no	—
390	C₂	—	556	1	no	—
391	C₂	—	556	1	no	—
392	C₂	#22581425	1	1	yes	characteristic
393	C₂	#131×D₁₃₉	1	1	yes	characteristic
394	C₂	#22581719	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃₉
commutator, socle	C₂²×C₁₃₉	C₂³×C₄
Fitting	#435×C₁₃₉	C₂
prime radical	#22581462	C₂
cosocle	C₂×C₄×C₁₃₉	C₂⁴
hypercenter	#435	D₁₃₉
hypocenter	C₁₃₉	#2976
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #22581031	C₂	semidirect
3. #22581028	C₂	semidirect
4. #22581027	C₂	semidirect
5. #22581026	C₂	semidirect
6. #22581022	C₂	semidirect
7. #22581018	C₂	semidirect
8. C₈×C₂²⋊D₁₃₉	C₂	semidirect
9. #22581015	C₂	semidirect
10. #22581013	C₂	semidirect
11. #22580919	C₂	semidirect
12. #22580918	C₂	semidirect
13. #22580916	C₂	semidirect
14. C₂²⋊C₈×D₁₃₉	C₂	semidirect
15. #435×C₁₃₉	C₂	semidirect
19. C₂×#14555769	C₂²	semidirect
20. C₂×#14555768	C₂²	semidirect
23. C₂×C₈×D₁₃₉	C₂²	semidirect
36. C₄⋊(C₁₃₉⋊C₈)	C₂²	semidirect
37. Dic₁₃₉⋊C₈	C₂²	semidirect
38. Dic₁₃₉⋊C₈	C₂²	semidirect
40. C₂²⋊(C₁₃₉⋊C₈)	C₂²	semidirect
47. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
48. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
49. #17984752	C₂²	semidirect
50. C₄×C₁₃₉⋊C₈	C₂²	semidirect
51. C₈×Dic₁₃₉	C₂²	semidirect
53. C₂²×C₈×C₁₃₉	C₂²	semidirect
55. C₄⋊C₈×C₁₃₉	C₂²	semidirect
57. C₂²⋊C₈×C₁₃₉	C₂²	semidirect
58. #97×C₁₃₉	C₂²	semidirect
197. C₁₃₉	#2976	semidirect
205. #435	D₁₃₉	semidirect
223. C₂²×C₈	C₂×D₁₃₉	semidirect
240. C₄⋊C₈	C₂×D₁₃₉	semidirect
252. C₂²⋊C₈	C₂×D₁₃₉	semidirect
254. #97	C₂×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#22581462	2
#22581031	2
#22581028	2
#22581027	2
#22581026	2
#22581022	2
#22581018	2
C₈×C₂²⋊D₁₃₉	2
#22581015	2
#22581013	2
#22580919	2
#22580918	2
#22580916	2
C₂²⋊C₈×D₁₃₉	2
#435×C₁₃₉	2
#2976	139