Subgroups — #31814770

Order 17792.

516 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	C₂×#17984837	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17984835	C₂	1	1	yes	maximal, characteristic, complemented
3	#22580853	C₂	1	1	yes	maximal, characteristic
4	#22580853	C₂	1	1	yes	maximal, characteristic
5	#22580853	C₂	1	1	yes	maximal, characteristic
6	#22580850	C₂	1	1	yes	maximal, characteristic, complemented
7	#22580850	C₂	1	1	yes	maximal, characteristic, complemented
8	#22580848	C₂	1	1	yes	maximal, characteristic, complemented
9	#22580846	C₂	1	1	yes	maximal, characteristic, complemented
10	#22580845	C₂	1	1	yes	maximal, characteristic, complemented
11	#22580844	C₂	1	1	yes	maximal, characteristic, complemented
12	#22580842	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580841	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#388×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
17	#17984837	—	2	4	no	—
18	#17984835	—	2	4	no	—
19	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
42	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
43	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
44	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
45	C₁₃₉⋊#95	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
51	#95×C₁₃₉	C₂²	1	1	yes	characteristic
52	#95×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂³×D₁₃₉	C₂³	1	1	yes	characteristic
54	C₂×C₂²⋊D₁₃₉	—	2	2	no	—
55	C₂×C₂²⋊D₁₃₉	—	2	2	no	—
56	C₂×C₂²⋊D₁₃₉	—	2	2	no	—
57	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₁₃₉	—	2	2	no	—
65	C₄⋊Dic₁₃₉	—	2	2	no	—
66	Dic₁₃₉⋊C₄	—	2	2	no	—
67	Dic₁₃₉⋊C₄	—	2	2	no	—
68	Dic₁₃₉⋊C₄	—	2	2	no	—
69	Dic₁₃₉⋊C₄	—	2	2	no	—
70	Dic₁₃₉⋊C₄	—	2	2	no	—
71	Dic₁₃₉⋊C₄	—	2	2	no	—
72	C₂²⋊Dic₁₃₉	—	2	2	no	—
73	C₂²⋊Dic₁₃₉	—	2	2	no	—
74	C₂²⋊Dic₁₃₉	—	2	2	no	—
75	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
76	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
77	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
78	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
79	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
80	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
81	C₄×Dic₁₃₉	—	2	2	no	—
82	C₄×Dic₁₃₉	—	2	2	no	—
83	C₄×Dic₁₃₉	—	2	2	no	—
84	C₄×Dic₁₃₉	—	2	2	no	—
85	C₄×Dic₁₃₉	—	2	2	no	—
86	C₄×Dic₁₃₉	D₄	1	4	yes	complemented
87	C₂⁴×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₄×C₁₃₉	—	2	2	no	—
95	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
96	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
97	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
98	C₄²×C₁₃₉	—	2	2	no	—
99	C₂²×D₁₃₉	—	2	1	no	—
100	C₂²×D₁₃₉	—	2	1	no	—
101	C₂²×D₁₃₉	—	2	1	no	—
102	C₂²×D₁₃₉	—	2	1	no	—
103	C₂²×D₁₃₉	—	2	1	no	—
104	C₂²×D₁₃₉	—	2	1	no	—
105	C₂²×D₁₃₉	—	2	1	no	—
106	C₂²⋊D₁₃₉	—	4	4	no	—
107	C₂×Dic₁₃₉	—	2	1	no	—
108	C₂×Dic₁₃₉	—	2	1	no	—
109	C₂×Dic₁₃₉	—	2	1	no	—
110	C₂×Dic₁₃₉	—	2	1	no	—
111	C₂×Dic₁₃₉	—	2	1	no	—
112	C₂×Dic₁₃₉	—	2	1	no	—
113	C₂×Dic₁₃₉	—	2	1	no	—
114	C₂×Dic₁₃₉	—	2	1	no	—
115	C₂×Dic₁₃₉	—	2	1	no	—
116	C₂×Dic₁₃₉	—	2	1	no	—
117	C₂×Dic₁₃₉	—	2	1	no	—
118	C₂×Dic₁₃₉	—	2	1	no	—
119	C₂×Dic₁₃₉	—	2	1	no	—
120	C₂×Dic₁₃₉	—	2	1	no	—
121	C₂×Dic₁₃₉	—	2	1	no	—
122	C₂×Dic₁₃₉	C₂×D₄	1	2	yes	—
123	C₂×Dic₁₃₉	C₂×D₄	1	2	yes	—
124	C₂×Dic₁₃₉	#41	1	2	yes	—
125	C₂×Dic₁₃₉	#41	1	2	yes	—
126	C₂×Dic₁₃₉	#41	1	2	yes	—
127	C₂×Dic₁₃₉	#41	1	2	yes	—
128	C₂³×C₁₃₉	—	2	1	no	—
129	C₂³×C₁₃₉	—	2	1	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	2	1	no	—
132	C₂³×C₁₃₉	—	2	1	no	—
133	C₂³×C₁₃₉	—	2	1	no	—
134	C₂³×C₁₃₉	—	2	1	no	—
135	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₄×C₁₃₉	—	2	1	no	—
137	C₂×C₄×C₁₃₉	—	2	1	no	—
138	C₂×C₄×C₁₃₉	—	2	1	no	—
139	C₂×C₄×C₁₃₉	—	2	1	no	—
140	C₂×C₄×C₁₃₉	—	2	1	no	—
141	C₂×C₄×C₁₃₉	—	2	1	no	—
142	C₂×C₄×C₁₃₉	—	2	1	no	—
143	C₂×C₄×C₁₃₉	—	2	1	no	—
144	C₂×C₄×C₁₃₉	—	2	1	no	—
145	C₂×C₄×C₁₃₉	—	2	1	no	—
146	C₂×C₄×C₁₃₉	—	2	1	no	—
147	C₂×C₄×C₁₃₉	—	2	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	C₂×D₄	1	2	yes	—
152	C₂×C₄×C₁₃₉	#41	1	2	yes	—
153	C₂×C₄×C₁₃₉	#41	1	2	yes	—
154	C₂²×C₁₃₉	—	4	1	no	—
155	C₂²×C₁₃₉	—	4	1	no	—
156	C₂²×C₁₃₉	—	4	1	no	—
157	C₂²×C₁₃₉	—	4	1	no	—
158	C₂²×C₁₃₉	—	4	1	no	—
159	C₂²×C₁₃₉	—	4	1	no	—
160	C₂²×C₁₃₉	—	4	1	no	—
161	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
162	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
163	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
165	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
166	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
167	C₂²×C₁₃₉	C₂×#41	1	1	yes	characteristic
168	C₂×D₁₃₉	—	4	1	no	—
169	C₂×D₁₃₉	—	4	1	no	—
170	C₂×D₁₃₉	—	4	1	no	—
171	C₂×D₁₃₉	—	4	1	no	—
172	C₂×D₁₃₉	—	4	1	no	—
173	C₂×D₁₃₉	—	4	1	no	—
174	C₂×D₁₃₉	—	4	1	no	—
175	C₄×C₁₃₉	—	2	2	no	—
176	C₄×C₁₃₉	—	2	2	no	—
177	C₄×C₁₃₉	—	2	2	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	—	4	1	no	—
180	C₄×C₁₃₉	—	4	1	no	—
181	Dic₁₃₉	—	2	2	no	—
182	Dic₁₃₉	—	2	2	no	—
183	Dic₁₃₉	—	2	2	no	—
184	Dic₁₃₉	—	4	1	no	—
185	Dic₁₃₉	—	4	1	no	—
186	Dic₁₃₉	—	4	1	no	—
187	Dic₁₃₉	#126	1	4	yes	complemented
188	C₂×C₁₃₉	—	8	1	no	—
189	C₂×C₁₃₉	C₂×#126	1	1	yes	characteristic
190	C₂×C₁₃₉	#529	1	1	yes	characteristic
191	C₂×C₁₃₉	#529	1	1	yes	characteristic
192	C₂×C₁₃₉	#529	1	1	yes	characteristic
193	C₂×C₁₃₉	#532	1	1	yes	characteristic
194	C₂×C₁₃₉	#532	1	1	yes	characteristic
195	C₂×C₁₃₉	#532	1	1	yes	characteristic
196	D₁₃₉	—	8	1	no	—
197	C₁₃₉	#2860	1	1	yes	characteristic, complemented, Sylow
198	#2860	—	139	1	no	maximal, Sylow
199	C₂×#126	—	139	1	no	—
200	C₂×#126	—	139	1	no	—
201	#390	—	139	1	no	—
202	#390	—	139	1	no	—
203	#390	—	139	1	no	—
204	#389	—	139	1	no	—
205	#389	—	139	1	no	—
206	#389	—	139	1	no	—
207	#388	—	139	1	no	—
208	#388	—	139	1	no	—
209	#388	—	139	1	no	—
210	#388	—	139	1	no	—
211	#388	—	139	1	no	—
212	#388	D₁₃₉	1	1	yes	characteristic, complemented
213	C₄³	—	139	1	no	—
214	C₂²×D₄	—	139	1	no	—
215	#126	—	278	4	no	—
216	#126	—	278	4	no	—
217	C₂×C₄⋊C₄	—	139	1	no	—
218	C₂×C₄⋊C₄	—	139	1	no	—
219	C₂×C₄⋊C₄	—	139	1	no	—
220	C₂×C₄⋊C₄	—	139	1	no	—
221	C₂×C₄⋊C₄	—	139	1	no	—
222	C₂×C₄⋊C₄	—	139	1	no	—
223	C₂×C₄⋊C₄	—	139	1	no	—
224	C₂×C₄⋊C₄	—	139	1	no	—
225	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
226	C₂×C₂²⋊C₄	—	139	1	no	—
227	C₂×C₂²⋊C₄	—	139	1	no	—
228	C₂×C₂²⋊C₄	—	139	1	no	—
229	C₂×C₂²⋊C₄	—	139	1	no	—
230	C₂×C₂²⋊C₄	—	139	1	no	—
231	C₂×C₂²⋊C₄	—	139	1	no	—
232	C₂×C₂²⋊C₄	—	139	1	no	—
233	C₂×C₂²⋊C₄	—	139	1	no	—
234	C₂×C₂²⋊C₄	—	139	1	no	—
235	C₂×C₂²⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
238	C₂×C₄²	—	139	1	no	—
239	C₂×C₄²	—	139	1	no	—
240	C₂×C₄²	—	139	1	no	—
241	C₂×C₄²	—	139	1	no	—
242	C₂×C₄²	—	139	1	no	—
243	C₂×C₄²	—	139	1	no	—
244	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
245	#95	—	139	1	no	—
246	#95	—	139	1	no	—
247	#95	—	139	1	no	—
248	#95	—	139	1	no	—
249	#95	C₂×D₁₃₉	1	1	yes	characteristic
250	#95	C₂×D₁₃₉	1	1	yes	characteristic
251	C₂⁴	—	139	1	no	—
252	C₂⁴	C₂²×D₁₃₉	1	1	yes	characteristic
253	C₂×D₄	—	278	2	no	—
254	C₂×D₄	—	278	2	no	—
255	C₂×D₄	—	278	2	no	—
256	C₂²×C₄	—	139	1	no	—
257	C₂²×C₄	—	139	1	no	—
258	C₂²×C₄	—	139	1	no	—
259	C₂²×C₄	—	139	1	no	—
260	C₂²×C₄	—	139	1	no	—
261	C₂²×C₄	—	139	1	no	—
262	C₂²×C₄	—	139	1	no	—
263	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	278	2	no	—
271	C₄⋊C₄	—	278	2	no	—
272	C₄⋊C₄	—	278	2	no	—
273	C₄⋊C₄	—	278	2	no	—
274	C₄⋊C₄	—	278	2	no	—
275	C₄⋊C₄	—	278	2	no	—
276	C₄⋊C₄	—	278	2	no	—
277	C₄⋊C₄	—	278	2	no	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	—	278	2	no	—
282	C₂²⋊C₄	—	278	2	no	—
283	C₂²⋊C₄	—	278	2	no	—
284	C₂²⋊C₄	—	278	2	no	—
285	C₂²⋊C₄	—	278	2	no	—
286	C₂²⋊C₄	—	278	2	no	—
287	C₂²⋊C₄	—	278	2	no	—
288	C₂²⋊C₄	—	278	2	no	—
289	C₂²⋊C₄	—	278	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	278	2	no	—
292	C₄²	—	278	2	no	—
293	C₄²	—	278	2	no	—
294	C₄²	—	278	2	no	—
295	C₄²	—	278	2	no	—
296	C₄²	—	139	4	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	278	1	no	—
305	C₂³	—	278	1	no	—
306	C₂³	—	278	1	no	—
307	C₂³	—	278	1	no	—
308	C₂³	—	278	1	no	—
309	C₂³	—	278	1	no	—
310	C₂³	—	278	1	no	—
311	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
312	D₄	—	556	4	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	278	1	no	—
329	C₂×C₄	—	278	1	no	—
330	C₂×C₄	—	278	1	no	—
331	C₂×C₄	—	278	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	—	278	1	no	—
339	C₂×C₄	—	278	1	no	—
340	C₂×C₄	—	278	1	no	—
341	C₂×C₄	—	278	1	no	—
342	C₂×C₄	—	278	1	no	—
343	C₂×C₄	—	139	2	no	—
344	C₂×C₄	—	139	2	no	—
345	C₂×C₄	—	139	2	no	—
346	C₂×C₄	—	139	2	no	—
347	C₂×C₄	—	139	2	no	—
348	C₂×C₄	—	139	2	no	—
349	C₂×C₄	D₄×D₁₃₉	1	2	yes	—
350	C₂×C₄	#14555784	1	2	yes	—
351	C₂×C₄	#14555785	1	2	yes	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	556	1	no	—
360	C₂²	—	556	1	no	—
361	C₂²	—	556	1	no	—
362	C₂²	—	556	1	no	—
363	C₂²	—	556	1	no	—
364	C₂²	—	556	1	no	—
365	C₂²	—	556	1	no	—
366	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
367	C₂²	#41×D₁₃₉	1	1	yes	characteristic
368	C₂²	#41×D₁₃₉	1	1	yes	characteristic
369	C₂²	#41×D₁₃₉	1	1	yes	characteristic
370	C₂²	#41×D₁₃₉	1	1	yes	characteristic
371	C₂²	C₂×#14555784	1	1	yes	characteristic
372	C₂²	C₂×#14555785	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	278	2	no	—
380	C₄	—	278	2	no	—
381	C₄	—	278	2	no	—
382	C₄	—	556	1	no	—
383	C₄	—	556	1	no	—
384	C₄	—	556	1	no	—
385	C₄	—	139	4	no	—
386	C₂	—	8	1	no	—
387	C₂	—	1112	1	no	—
388	C₂	#126×D₁₃₉	1	1	yes	characteristic
389	C₂	#22581480	1	1	yes	characteristic
390	C₂	#22581481	1	1	yes	characteristic
391	C₂	#22581483	1	1	yes	characteristic
392	C₂	#22581498	1	1	yes	characteristic
393	C₂	#22581500	1	1	yes	characteristic
394	C₂	#22581502	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃₉
commutator, socle, cosocle	C₂³×C₁₃₉	C₂⁴
Fitting	#388×C₁₃₉	C₂
prime radical	C₂²×C₂²⋊D₁₃₉	C₂²
hypercenter	#388	D₁₃₉
hypocenter	C₁₃₉	#2860
LCS	G ▷ C₂³×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ #388

Complements

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

N	H ≅ G/N	type
1. C₂×#17984837	C₂	semidirect
2. C₂×#17984835	C₂	semidirect
6. #22580850	C₂	semidirect
7. #22580850	C₂	semidirect
8. #22580848	C₂	semidirect
9. #22580846	C₂	semidirect
10. #22580845	C₂	semidirect
11. #22580844	C₂	semidirect
12. #22580842	C₂	semidirect
13. #22580841	C₂	semidirect
14. C₄²×Dic₁₃₉	C₂	semidirect
15. #388×C₁₃₉	C₂	semidirect
86. C₄×Dic₁₃₉	D₄	semidirect
187. Dic₁₃₉	#126	semidirect
197. C₁₃₉	#2860	semidirect
212. #388	D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17984837	2
C₂×#17984835	2
#22580853	2
#22580850	2
#22580848	2
#22580846	2
#22580845	2
#22580844	2
#22580842	2
#22580841	2
C₄²×Dic₁₃₉	2
#388×C₁₃₉	2
#2860	139