Subgroups — #15881721

Order 3328.

760 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×#1055	C₂	1	1	yes	maximal, characteristic
2	#13117314	C₂	1	1	yes	maximal, characteristic
3	#13115559	C₂	1	2	yes	maximal
4	#13115554	C₂	1	1	yes	maximal, characteristic
5	#13115552	C₂	1	1	yes	maximal, characteristic
6	#13115552	C₂	1	2	yes	maximal
7	#13114989	C₂	1	2	yes	maximal
8	#13114987	C₂	1	1	yes	maximal, characteristic
9	#13114696	C₂	1	2	yes	maximal
10	C₄×#88054	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#446	—	2	4	no	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#97	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718891	C₄	1	1	yes	characteristic
19	#11718891	C₄	1	1	yes	characteristic
20	C₂×#88054	C₂²	1	1	yes	characteristic
21	C₂×#88054	C₂²	1	2	yes	—
22	C₂×#88054	C₂²	1	2	yes	—
23	C₂×#88054	C₂²	1	2	yes	—
24	C₂×#88054	C₂²	1	2	yes	—
25	C₂×#88054	C₂²	1	1	yes	characteristic
26	Q₈×#1055	—	2	4	no	—
27	#11718646	C₄	1	1	yes	characteristic
28	#11718646	C₄	1	1	yes	characteristic
29	#11718642	C₄	1	2	yes	—
30	#11718642	C₄	1	2	yes	—
31	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
33	#11718593	C₂²	1	2	yes	—
34	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	C₂²	1	2	yes	—
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄×#1055	C₂²	1	2	yes	—
39	#11718142	C₂²	1	1	yes	characteristic
40	#11718142	C₂²	1	1	yes	characteristic
41	#11718142	C₂²	1	2	yes	—
42	#11718142	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₁₃	D₄	1	4	yes	—
48	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
63	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
64	C₂²×#1055	C₂³	1	1	yes	characteristic
65	C₂²×#1055	C₂³	1	2	yes	—
66	C₂²×#1055	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×C₄⋊C₈	—	2	4	no	—
69	C₁₃×#97	—	2	4	no	—
70	C₄×C₈×C₁₃	—	2	2	no	—
71	#88071	C₂×C₄	1	2	yes	—
72	#88071	C₂×C₄	1	2	yes	—
73	#88071	C₂×C₄	1	2	yes	—
74	#88071	C₂×C₄	1	2	yes	—
75	#88071	C₂×C₄	1	2	yes	—
76	#88071	C₂×C₄	1	2	yes	—
77	#88071	C₂×C₄	1	2	yes	—
78	#88054	—	2	2	no	—
79	#88054	—	2	4	no	—
80	#88054	—	4	2	no	—
81	#88054	—	4	2	no	—
82	#88054	—	4	2	no	—
83	#88054	Q₈	1	4	yes	complemented
84	C₄⋊#1055	—	2	2	no	—
85	C₄⋊#1055	—	2	4	no	—
86	C₄×#1055	—	2	2	no	—
87	C₄×#1055	—	2	4	no	—
88	#22721	—	13	1	no	maximal, Sylow
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
112	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
113	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
114	C₄²×C₁₃	C₂×D₄	1	2	yes	—
115	C₄²×C₁₃	C₂×D₄	1	4	yes	—
116	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
117	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
118	C₄⋊Dic₁₃	—	2	2	no	—
119	C₄⋊Dic₁₃	—	2	2	no	—
120	C₄⋊Dic₁₃	—	2	4	no	—
121	C₄⋊Dic₁₃	—	4	2	no	—
122	C₄×Dic₁₃	—	2	2	no	—
123	C₄×Dic₁₃	—	2	2	no	—
124	C₄×Dic₁₃	—	2	1	no	—
125	C₄×Dic₁₃	—	2	2	no	—
126	C₄×Dic₁₃	—	2	1	no	—
127	C₄×Dic₁₃	—	2	2	no	—
128	C₄×Dic₁₃	—	2	2	no	—
129	C₄×Dic₁₃	—	4	1	no	—
130	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
131	C₄×Dic₁₃	#41	1	2	yes	—
132	C₂×#1055	—	2	1	no	—
133	C₂×#1055	—	2	1	no	—
134	C₂×#1055	—	2	1	no	—
135	C₂×#1055	—	2	2	no	—
136	C₂×#1055	—	2	1	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	—	2	1	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	C₂×Q₈	1	2	yes	—
141	C₂×#446	D₁₃	1	1	yes	characteristic
142	C₂×C₈×Q₈	—	13	1	no	—
143	#2295	—	13	1	no	—
144	#1940	—	13	2	no	—
145	#1939	—	13	2	no	—
146	#1939	—	13	1	no	—
147	#1939	—	13	1	no	—
148	#1843	—	13	2	no	—
149	#1842	—	13	1	no	—
150	#1768	—	13	2	no	—
151	C₄×C₄⋊C₈	—	13	1	no	—
152	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	Q₈×C₁₃	—	2	8	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₃	#131	1	2	yes	—
165	C₂×C₄×C₁₃	#131	1	2	yes	—
166	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×Dic₁₃	—	2	1	no	—
173	C₂×Dic₁₃	—	2	1	no	—
174	C₂×Dic₁₃	—	2	1	no	—
175	C₂×Dic₁₃	—	2	1	no	—
176	C₂×Dic₁₃	—	2	1	no	—
177	C₂×Dic₁₃	—	2	1	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	1	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	C₂×Dic₁₃	—	2	1	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	—	2	2	no	—
187	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
188	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
189	C₂×Dic₁₃	#131	1	2	yes	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	4	1	no	—
192	C₈×C₁₃	—	4	2	no	—
193	#1055	—	2	2	no	—
194	#1055	—	4	1	no	—
195	#1055	—	4	2	no	—
196	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
197	#446	—	2	4	no	—
198	C₈×Q₈	—	26	4	no	—
199	C₂×C₄⋊C₈	—	13	1	no	—
200	C₂×C₄⋊C₈	—	13	2	no	—
201	C₂×C₄⋊C₈	—	13	1	no	—
202	C₂×C₄⋊C₈	—	13	1	no	—
203	C₂×C₄⋊C₈	—	13	2	no	—
204	C₂×C₄⋊C₈	—	13	2	no	—
205	C₂×C₄⋊C₈	—	13	2	no	—
206	C₂×C₄⋊C₈	—	13	2	no	—
207	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
209	C₂×#97	C₂×D₁₃	1	2	yes	—
210	C₂×C₄×C₈	—	13	1	no	—
211	C₂×C₄×C₈	—	13	2	no	—
212	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
213	#391	—	13	1	no	—
214	#391	—	13	1	no	—
215	#389	—	13	1	no	—
216	#389	—	13	1	no	—
217	#387	—	13	2	no	—
218	#387	—	13	2	no	—
219	C₄×C₄⋊C₄	—	13	1	no	—
220	C₄×C₄⋊C₄	—	13	2	no	—
221	#376	—	13	2	no	—
222	C₄³	—	13	1	no	—
223	#336	—	13	1	no	—
224	#336	—	13	2	no	—
225	#336	—	13	2	no	—
226	#336	—	13	1	no	—
227	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₂²×C₁₃	#520	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
232	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
233	C₂²×C₁₃	#568	1	1	yes	characteristic
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	#424	1	4	yes	—
238	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
239	C₄×C₁₃	#550	1	1	yes	characteristic
240	C₄×C₁₃	#557	1	1	yes	characteristic
241	C₄×C₁₃	Q₈²	1	1	yes	characteristic
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	—	2	2	no	—
244	Dic₁₃	—	2	2	no	—
245	Dic₁₃	—	4	1	no	—
246	Dic₁₃	—	4	2	no	—
247	Dic₁₃	—	4	2	no	—
248	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	2	no	—
251	C₂²×C₈	—	13	1	no	—
252	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
254	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
255	C₄×Q₈	Dic₂₆	1	4	yes	—
256	C₄×Q₈	C₂²⋊D₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	—	13	2	no	—
258	C₂×C₄⋊C₄	—	13	1	no	—
259	C₂×C₄⋊C₄	—	13	1	no	—
260	C₂×C₄⋊C₄	—	13	2	no	—
261	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	2	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
271	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	13	4	no	—
275	C₄⋊C₈	—	26	4	no	—
276	C₄⋊C₈	—	26	2	no	—
277	C₄⋊C₈	—	26	2	no	—
278	C₄⋊C₈	—	26	4	no	—
279	C₄⋊C₈	—	52	2	no	—
280	C₄⋊C₈	—	52	2	no	—
281	C₄⋊C₈	—	52	2	no	—
282	#97	—	2	4	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	26	2	no	—
285	C₄×C₈	—	26	4	no	—
286	#95	—	13	2	no	—
287	#95	—	13	2	no	—
288	#95	—	13	2	no	—
289	#95	—	13	2	no	—
290	#95	—	13	2	no	—
291	#95	—	13	2	no	—
292	#95	—	13	2	no	—
293	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
295	C₂×C₁₃	#2906	1	1	yes	characteristic
296	C₂×C₁₃	#2960	1	1	yes	characteristic
297	C₂×C₁₃	#2962	1	1	yes	characteristic
298	C₂×C₁₃	#2993	1	1	yes	characteristic
299	C₂×C₁₃	#2994	1	1	yes	characteristic
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	#6101	1	4	yes	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	2	no	—
307	C₂²×C₄	—	13	2	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
312	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	13	2	no	—
323	C₂×C₈	—	26	1	no	—
324	C₂×C₈	—	26	1	no	—
325	C₂×C₈	—	26	2	no	—
326	C₂×C₈	—	26	1	no	—
327	C₂×C₈	—	26	2	no	—
328	C₂×C₈	—	26	1	no	—
329	C₂×C₈	—	26	1	no	—
330	C₂×C₈	—	26	2	no	—
331	C₂×C₈	Q₈×D₁₃	1	2	yes	—
332	C₄⋊C₄	—	26	4	no	—
333	C₄⋊C₄	—	26	2	no	—
334	C₄⋊C₄	—	26	2	no	—
335	C₄⋊C₄	—	52	2	no	—
336	C₄⋊C₄	#6101	1	8	yes	—
337	C₄⋊C₄	#6101	1	4	yes	—
338	C₄²	—	13	2	no	—
339	C₄²	—	13	2	no	—
340	C₄²	—	26	2	no	—
341	C₄²	—	26	2	no	—
342	C₄²	—	26	2	no	—
343	C₄²	—	26	1	no	—
344	C₄²	—	26	2	no	—
345	C₄²	—	26	1	no	—
346	C₄²	—	26	2	no	—
347	C₄²	—	52	1	no	—
348	C₄²	C₂×Dic₂₆	1	4	yes	—
349	C₄²	C₂×Dic₂₆	1	2	yes	—
350	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
351	C₄²	C₂×C₂²⋊D₁₃	1	4	yes	—
352	C₁₃	#22721	1	1	yes	characteristic, complemented, Sylow
353	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
354	Q₈	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	13	2	no	—
362	C₂×C₄	—	13	2	no	—
363	C₂×C₄	—	13	2	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	—	26	1	no	—
366	C₂×C₄	—	26	1	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	26	1	no	—
369	C₂×C₄	—	26	1	no	—
370	C₂×C₄	—	26	1	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	26	2	no	—
374	C₂×C₄	—	26	1	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	1	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	#88161	1	2	yes	—
380	C₂×C₄	#88161	1	2	yes	—
381	C₂×C₄	C₂×#6101	1	2	yes	—
382	C₂×C₄	C₂×#6101	1	4	yes	—
383	C₂×C₄	C₂×#6101	1	4	yes	—
384	C₂×C₄	C₂×#6101	1	2	yes	—
385	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
386	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
387	C₂×C₄	#88254	1	1	yes	characteristic
388	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
389	C₂×C₄	#88256	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	26	2	no	—
395	C₈	—	52	2	no	—
396	C₈	—	52	1	no	—
397	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
398	C₂²	#11719279	1	1	yes	characteristic
399	C₂²	C₂×#88161	1	1	yes	characteristic
400	C₂²	C₂×#88161	1	1	yes	characteristic
401	C₂²	D₁₃×#131	1	1	yes	characteristic
402	C₂²	#11719455	1	1	yes	characteristic
403	C₂²	C₂²×#6101	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	26	2	no	—
408	C₄	—	26	2	no	—
409	C₄	—	26	2	no	—
410	C₄	—	52	1	no	—
411	C₄	—	52	2	no	—
412	C₄	—	52	2	no	—
413	C₄	#11718780	1	4	yes	—
414	C₄	Q₈×Dic₂₆	1	1	yes	characteristic
415	C₄	#11719274	1	1	yes	characteristic
416	C₄	Q₈×C₂²⋊D₁₃	1	1	yes	characteristic
417	C₄	#11719539	1	1	yes	characteristic
418	C₂	Q₈×#6101	1	1	yes	characteristic
419	C₂	C₂×#11718780	1	1	yes	characteristic
420	C₂	#13123402	1	1	yes	characteristic
421	C₂	#13123767	1	1	yes	characteristic
422	C₂	#13123784	1	1	yes	characteristic
423	C₂	#13123988	1	1	yes	characteristic
424	C₂	#13123999	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₁₃×#446	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#446	D₁₃
hypocenter	C₁₃	#22721
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
83. #88054	Q₈	semidirect
352. C₁₃	#22721	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×#1055	2
#13117314	2
#13115559	2
#13115554	2
#13115552	2
#13114989	2
#13114987	2
#13114696	2
C₄×#88054	2
C₂×C₁₃×#446	2
#22721	13