Subgroups — #15867651

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	#13115773	C₂	1	1	yes	maximal, characteristic
3	#13115554	C₂	1	1	yes	maximal, characteristic
4	#13115552	C₂	1	1	yes	maximal, characteristic
5	#13115401	C₂	1	2	yes	maximal
6	#13115399	C₂	1	2	yes	maximal
7	#13114691	C₂	1	1	yes	maximal, characteristic
8	#13114688	C₂	1	2	yes	maximal
9	#13114583	C₂	1	2	yes	maximal
10	C₄×#88055	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₁₃	C₄	1	1	yes	characteristic
14	C₂×Q₈×Dic₁₃	C₄	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×#88055	C₂²	1	1	yes	characteristic
18	C₂×#88055	C₂²	1	1	yes	characteristic
19	C₂×#88055	C₂²	1	1	yes	characteristic
20	C₂×#88055	C₂²	1	2	yes	—
21	C₂×#88055	C₂²	1	1	yes	characteristic
22	C₂×#88054	C₂²	1	2	yes	—
23	C₂×#88054	C₂²	1	2	yes	—
24	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
25	C₄⋊C₄×Dic₁₃	C₄	1	2	yes	—
26	C₄⋊C₄×Dic₁₃	C₄	1	2	yes	—
27	C₄⋊C₄×Dic₁₃	C₄	1	1	yes	characteristic
28	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
30	C₄²×Dic₁₃	C₂²	1	2	yes	—
31	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₁₃×#336	C₂²	1	2	yes	—
36	#11718142	C₂²	1	2	yes	—
37	#11718142	C₂²	1	2	yes	—
38	#11718142	C₂²	1	2	yes	—
39	#11718116	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₄×Q₈×C₁₃	—	2	2	no	—
46	C₄×Q₈×C₁₃	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	Q₈×Dic₁₃	—	2	4	no	—
52	Q₈×Dic₁₃	—	2	4	no	—
53	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
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	2	yes	—
61	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
66	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	2	yes	—
69	C₂²×#1055	C₂³	1	1	yes	characteristic
70	C₂²×#1055	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₄×C₈×C₁₃	—	2	2	no	—
73	#88071	C₂×C₄	1	2	yes	—
74	#88071	C₂×C₄	1	2	yes	—
75	#88071	C₂×C₄	1	2	yes	—
76	#88055	—	2	2	no	—
77	#88055	—	2	2	no	—
78	#88055	—	2	4	no	—
79	#88055	—	2	2	no	—
80	#88055	Q₈	1	4	yes	complemented
81	#88054	—	2	4	no	—
82	#88054	—	2	4	no	—
83	C₄⋊#1055	—	2	2	no	—
84	C₄×#1055	—	2	2	no	—
85	#21345	—	13	1	no	maximal, Sylow
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	M₁₆	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₁₃	—	2	1	no	—
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂×C₈×C₁₃	#41	1	2	yes	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	#41	1	2	yes	—
114	C₄²×C₁₃	#41	1	2	yes	—
115	C₄⋊Dic₁₃	—	2	4	no	—
116	C₄⋊Dic₁₃	—	2	2	no	—
117	C₄⋊Dic₁₃	—	2	4	no	—
118	C₄⋊Dic₁₃	M₁₆	1	4	yes	—
119	C₄×Dic₁₃	—	2	4	no	—
120	C₄×Dic₁₃	—	2	2	no	—
121	C₄×Dic₁₃	—	2	2	no	—
122	C₄×Dic₁₃	—	2	2	no	—
123	C₄×Dic₁₃	—	2	2	no	—
124	C₄×Dic₁₃	—	2	1	no	—
125	C₄×Dic₁₃	—	2	1	no	—
126	C₄×Dic₁₃	—	2	4	no	—
127	C₄×Dic₁₃	—	4	2	no	—
128	C₄×Dic₁₃	—	4	1	no	—
129	C₄×Dic₁₃	—	4	1	no	—
130	C₄×Dic₁₃	—	4	2	no	—
131	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
132	C₄×Dic₁₃	#41	1	2	yes	—
133	C₂×#1055	—	2	1	no	—
134	C₂×#1055	—	2	1	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	2	1	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	—	2	2	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	C₂×Q₈	1	2	yes	—
141	C₂×#1055	#41	1	2	yes	—
142	C₄²×Q₈	—	13	1	no	—
143	#1984	—	13	1	no	—
144	#1984	D₁₃	1	1	yes	characteristic
145	#1939	—	13	1	no	—
146	#1939	—	13	1	no	—
147	#1917	—	13	2	no	—
148	#1917	—	13	2	no	—
149	#1767	—	13	1	no	—
150	#1767	—	13	2	no	—
151	#1745	—	13	2	no	—
152	C₄×#97	—	13	1	no	—
153	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
154	Q₈×C₁₃	—	2	8	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	#117	1	2	yes	—
163	C₂×C₄×C₁₃	#117	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
165	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
167	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂×Dic₁₃	—	2	2	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	1	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	—	2	1	no	—
187	C₂×Dic₁₃	—	2	2	no	—
188	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
189	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
190	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	4	2	no	—
194	#1055	—	2	2	no	—
195	#1055	—	2	2	no	—
196	#1055	—	4	2	no	—
197	C₂×C₄×Q₈	—	13	1	no	—
198	C₂×C₄×Q₈	—	13	1	no	—
199	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₈	—	13	2	no	—
201	C₂×C₄⋊C₈	—	13	2	no	—
202	C₂×C₄⋊C₈	—	13	1	no	—
203	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
204	C₂×#97	—	13	1	no	—
205	C₂×#97	—	13	1	no	—
206	C₂×#97	—	13	1	no	—
207	C₂×#97	—	13	1	no	—
208	C₂×#97	—	13	2	no	—
209	C₂×C₄×C₈	—	13	1	no	—
210	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
211	C₄×C₄⋊C₄	—	13	1	no	—
212	C₄×C₄⋊C₄	—	13	2	no	—
213	C₄×C₄⋊C₄	—	13	2	no	—
214	C₄×C₄⋊C₄	—	13	1	no	—
215	C₄×C₄⋊C₄	—	13	2	no	—
216	C₄×C₄⋊C₄	—	13	1	no	—
217	C₄³	—	13	1	no	—
218	C₄³	—	13	2	no	—
219	#336	—	13	2	no	—
220	#336	—	13	2	no	—
221	#336	—	13	2	no	—
222	#336	—	13	2	no	—
223	#336	—	13	2	no	—
224	#336	C₂×D₁₃	1	2	yes	—
225	#336	C₂×D₁₃	1	2	yes	—
226	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
228	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
229	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
230	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
231	C₂²×C₁₃	#568	1	1	yes	characteristic
232	C₂²×C₁₃	#568	1	1	yes	characteristic
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	#432	1	4	yes	—
237	C₄×C₁₃	#529	1	1	yes	characteristic
238	C₄×C₁₃	#529	1	1	yes	characteristic
239	C₄×C₁₃	#533	1	1	yes	characteristic
240	C₄×C₁₃	#533	1	1	yes	characteristic
241	Dic₁₃	—	2	2	no	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	—	2	4	no	—
244	Dic₁₃	—	4	1	no	—
245	Dic₁₃	—	4	2	no	—
246	Dic₁₃	—	4	1	no	—
247	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	2	no	—
251	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
252	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	26	4	no	—
257	C₄×Q₈	—	26	4	no	—
258	C₂×C₄⋊C₄	—	13	1	no	—
259	C₂×C₄⋊C₄	—	13	2	no	—
260	C₂×C₄⋊C₄	—	13	2	no	—
261	C₂×C₄⋊C₄	—	13	1	no	—
262	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	2	no	—
266	C₂×C₄²	—	13	2	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	2	no	—
271	C₂×C₄²	—	13	2	no	—
272	C₂×C₄²	—	13	2	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
276	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	26	4	no	—
279	C₄⋊C₈	—	26	4	no	—
280	C₄⋊C₈	—	26	2	no	—
281	#97	—	13	4	no	—
282	#97	—	26	2	no	—
283	#97	—	26	4	no	—
284	#97	—	26	2	no	—
285	#97	—	26	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	26	2	no	—
288	#95	—	13	2	no	—
289	#95	—	13	2	no	—
290	#95	—	13	2	no	—
291	C₂×C₁₃	#2295	1	1	yes	characteristic
292	C₂×C₁₃	C₂×#432	1	1	yes	characteristic
293	C₂×C₁₃	#2923	1	1	yes	characteristic
294	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
295	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
296	C₂×C₁₃	#2970	1	1	yes	characteristic
297	C₂×C₁₃	#2971	1	1	yes	characteristic
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	#6094	1	4	yes	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	2	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
308	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	26	1	no	—
322	C₂×C₈	—	26	1	no	—
323	C₂×C₈	—	26	1	no	—
324	C₂×C₈	—	26	1	no	—
325	C₂×C₈	—	26	2	no	—
326	C₂×C₈	—	26	2	no	—
327	C₂×C₈	—	26	2	no	—
328	C₂×C₈	Q₈×D₁₃	1	2	yes	—
329	C₂×C₈	#6131	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	13	4	no	—
333	C₄⋊C₄	—	26	4	no	—
334	C₄⋊C₄	—	26	4	no	—
335	C₄⋊C₄	—	26	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	13	2	no	—
339	C₄²	—	13	2	no	—
340	C₄²	—	26	4	no	—
341	C₄²	—	26	4	no	—
342	C₄²	—	26	2	no	—
343	C₄²	—	26	2	no	—
344	C₄²	—	26	1	no	—
345	C₄²	—	26	2	no	—
346	C₄²	—	26	1	no	—
347	C₄²	—	26	2	no	—
348	C₄²	—	52	1	no	—
349	C₄²	—	52	1	no	—
350	C₄²	—	52	2	no	—
351	C₄²	—	52	2	no	—
352	C₄²	#6129	1	2	yes	—
353	C₄²	#6129	1	2	yes	—
354	C₁₃	#21345	1	1	yes	characteristic, complemented, Sylow
355	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
356	Q₈	—	2	8	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	13	4	no	—
365	C₂×C₄	—	13	2	no	—
366	C₂×C₄	—	13	2	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	1	no	—
376	C₂×C₄	—	26	1	no	—
377	C₂×C₄	—	26	1	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	1	no	—
380	C₂×C₄	—	26	1	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	#88131	1	2	yes	—
383	C₂×C₄	#88131	1	2	yes	—
384	C₂×C₄	C₂×#6094	1	4	yes	—
385	C₂×C₄	C₂×#6094	1	2	yes	—
386	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
387	C₂×C₄	C₂×#6129	1	1	yes	characteristic
388	C₂×C₄	C₂×#6129	1	1	yes	characteristic
389	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#6131	1	1	yes	characteristic
391	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
392	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	26	2	no	—
397	C₈	—	26	2	no	—
398	C₈	—	52	2	no	—
399	C₂²	C₂×#88131	1	1	yes	characteristic
400	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
401	C₂²	C₄×#6131	1	1	yes	characteristic
402	C₂²	C₂²×#6094	1	1	yes	characteristic
403	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
404	C₂²	#11719455	1	1	yes	characteristic
405	C₂²	#11719455	1	1	yes	characteristic
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	26	4	no	—
410	C₄	—	26	2	no	—
411	C₄	—	26	2	no	—
412	C₄	—	52	1	no	—
413	C₄	—	52	1	no	—
414	C₄	—	52	2	no	—
415	C₄	#11718380	1	4	yes	—
416	C₄	#11719327	1	1	yes	characteristic
417	C₄	#11719329	1	1	yes	characteristic
418	C₄	#11719385	1	1	yes	characteristic
419	C₄	#11719433	1	1	yes	characteristic
420	C₂	#13117311	1	1	yes	characteristic
421	C₂	C₂×#11718380	1	1	yes	characteristic
422	C₂	#13123483	1	1	yes	characteristic
423	C₂	Q₈×#6094	1	1	yes	characteristic
424	C₂	#13123788	1	1	yes	characteristic
425	C₂	#13123849	1	1	yes	characteristic
426	C₂	#13123855	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1984	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1984	D₁₃
hypocenter	C₁₃	#21345
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

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

N	H ≅ G/N	type
80. #88055	Q₈	semidirect
354. C₁₃	#21345	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×Dic₁₃	2
#13115773	2
#13115554	2
#13115552	2
#13115401	2
#13115399	2
#13114691	2
#13114688	2
#13114583	2
C₄×#88055	2
C₁₃×#1984	2
#21345	13