Subgroups — #15768646

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718121	C₂	1	2	yes	maximal
3	C₂×#11718121	C₂	1	2	yes	maximal
4	#13113066	C₂	1	1	yes	maximal, characteristic
5	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
9	C₂³×#1055	C₂²	1	1	yes	characteristic
10	C₂³×#1055	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#95	—	2	1	no	—
12	C₂×C₁₃×#95	—	2	1	no	—
13	C₂×#88071	—	2	1	no	—
14	C₂×#88071	—	2	1	no	—
15	C₂×C₄×#1055	—	2	4	no	—
16	C₂×C₄×#1055	C₄	1	4	yes	complemented
17	#11718121	—	2	4	no	—
18	#11718121	C₄	1	8	yes	complemented
19	C₂³×C₄×C₁₃	—	2	2	no	—
20	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂³×Dic₁₃	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₃	—	2	2	no	—
31	C₂×C₄²×C₁₃	—	2	2	no	—
32	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
34	C₂×C₄⋊Dic₁₃	—	2	2	no	—
35	C₂×C₄⋊Dic₁₃	—	2	2	no	—
36	C₂×C₄⋊Dic₁₃	—	2	2	no	—
37	C₂×C₄⋊Dic₁₃	—	2	2	no	—
38	C₂×C₄⋊Dic₁₃	—	2	2	no	—
39	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
40	C₂²×#1055	—	2	2	no	—
41	C₂²×#1055	—	2	2	no	—
42	C₂²×#1055	—	2	1	no	—
43	C₂²×#1055	—	2	1	no	—
44	C₂²×#1055	—	2	1	no	—
45	C₂²×#1055	—	2	1	no	—
46	C₂²×#1055	C₂×C₄	1	2	yes	—
47	C₂²×#1055	C₂×C₄	1	4	yes	—
48	C₂²×#1055	C₂×C₄	1	2	yes	—
49	C₂²×#1055	D₄	1	4	yes	—
50	C₁₃×#95	—	4	2	no	—
51	C₁₃×#95	—	4	2	no	—
52	#88071	—	4	2	no	—
53	#88071	—	4	2	no	—
54	C₄×#1055	—	2	8	no	—
55	#10820	—	13	1	no	maximal, Sylow
56	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₃	—	4	2	no	—
63	C₂²×C₄×C₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₃	—	4	2	no	—
65	C₂²×C₄×C₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₃	—	4	2	no	—
68	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₃	D₈	1	2	yes	—
71	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
73	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	#41	1	2	yes	—
79	C₂²×C₄×C₁₃	#41	1	2	yes	—
80	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
84	C₂²×Dic₁₃	—	2	4	no	—
85	C₂²×Dic₁₃	—	4	2	no	—
86	C₂²×Dic₁₃	—	4	2	no	—
87	C₂²×Dic₁₃	—	4	2	no	—
88	C₂²×Dic₁₃	—	4	2	no	—
89	C₂²×Dic₁₃	—	4	2	no	—
90	C₂²×Dic₁₃	—	4	2	no	—
91	C₁₃×C₄⋊C₄	—	2	4	no	—
92	C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₁₃×C₄⋊C₄	—	4	2	no	—
94	C₁₃×C₄⋊C₄	—	4	2	no	—
95	C₄²×C₁₃	—	2	2	no	—
96	C₄²×C₁₃	—	2	2	no	—
97	C₄²×C₁₃	—	2	4	no	—
98	C₄⋊Dic₁₃	—	2	4	no	—
99	C₄⋊Dic₁₃	—	2	4	no	—
100	C₄⋊Dic₁₃	—	4	2	no	—
101	C₄⋊Dic₁₃	—	4	2	no	—
102	C₂×#1055	—	2	2	no	—
103	C₂×#1055	—	2	2	no	—
104	C₂×#1055	—	2	2	no	—
105	C₂×#1055	—	2	2	no	—
106	C₂×#1055	—	2	4	no	—
107	C₂×#1055	—	2	4	no	—
108	C₂×#1055	—	2	4	no	—
109	C₂×#1055	—	2	4	no	—
110	C₂×#1055	C₄²	1	4	yes	—
111	C₂×#1055	C₂²⋊C₄	1	4	yes	—
112	C₂²×C₄×C₈	—	13	1	no	—
113	C₂×#340	—	13	2	no	—
114	C₂×#340	—	13	2	no	—
115	C₄⋊#95	—	13	1	no	—
116	C₄⋊#95	D₁₃	1	1	yes	characteristic
117	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₁₃	C₄×D₄	1	2	yes	—
119	C₂³×C₁₃	#121	1	2	yes	—
120	C₂³×C₁₃	#124	1	1	yes	characteristic
121	C₂³×C₁₃	#124	1	1	yes	characteristic
122	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
123	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
124	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
125	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
126	C₂³×C₁₃	#135	1	2	yes	—
127	C₂³×C₁₃	#135	1	2	yes	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	4	4	no	—
137	C₂×C₄×C₁₃	—	4	4	no	—
138	C₂×C₄×C₁₃	—	4	4	no	—
139	C₂×C₄×C₁₃	—	8	2	no	—
140	C₂×C₄×C₁₃	—	8	2	no	—
141	C₂×C₄×C₁₃	—	8	2	no	—
142	C₂×C₄×C₁₃	—	8	2	no	—
143	C₂×C₄×C₁₃	#106	1	4	yes	—
144	C₂×C₄×C₁₃	#107	1	4	yes	—
145	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#117	1	2	yes	—
150	C₂×C₄×C₁₃	#117	1	2	yes	—
151	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₃	#123	1	2	yes	—
158	C₂×C₄×C₁₃	#123	1	2	yes	—
159	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#126	1	2	yes	—
162	C₂×C₄×C₁₃	#126	1	2	yes	—
163	C₂×Dic₁₃	—	4	4	no	—
164	C₂×Dic₁₃	—	4	4	no	—
165	C₂×Dic₁₃	—	4	4	no	—
166	C₂×Dic₁₃	—	8	2	no	—
167	C₂×Dic₁₃	—	8	2	no	—
168	C₂×Dic₁₃	—	8	2	no	—
169	C₂×Dic₁₃	—	8	2	no	—
170	#1055	—	2	4	no	—
171	#1055	—	2	4	no	—
172	C₂³×C₈	—	13	1	no	—
173	C₂³×C₈	—	13	1	no	—
174	C₂²×C₄⋊C₄	—	13	2	no	—
175	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
176	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
177	C₂×C₄×C₈	—	13	4	no	—
178	C₂×C₄×C₈	—	26	4	no	—
179	C₂×#95	—	2	1	no	—
180	C₂×#95	—	2	1	no	—
181	C₂×#95	—	26	1	no	—
182	C₂×#95	—	26	1	no	—
183	#340	—	13	8	no	—
184	#340	—	26	4	no	—
185	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×C₁₃	#380	1	1	yes	characteristic
187	C₂²×C₁₃	#382	1	1	yes	characteristic
188	C₂²×C₁₃	#388	1	2	yes	—
189	C₂²×C₁₃	#388	1	2	yes	—
190	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
191	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
192	C₂²×C₁₃	#427	1	1	yes	characteristic
193	C₂²×C₁₃	#427	1	1	yes	characteristic
194	C₂²×C₁₃	C₄×D₈	1	2	yes	—
195	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
196	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
197	C₂²×C₁₃	C₄×Q₁₆	1	2	yes	—
198	C₂²×C₁₃	#465	1	2	yes	—
199	C₂²×C₁₃	#465	1	2	yes	—
200	C₂²×C₁₃	#466	1	2	yes	—
201	C₂²×C₁₃	#467	1	2	yes	—
202	C₂²×C₁₃	#486	1	1	yes	characteristic
203	C₂²×C₁₃	#486	1	1	yes	characteristic
204	C₂²×C₁₃	#487	1	1	yes	characteristic
205	C₂²×C₁₃	#487	1	1	yes	characteristic
206	C₂²×C₁₃	#488	1	2	yes	—
207	C₂²×C₁₃	#488	1	2	yes	—
208	C₄×C₁₃	—	2	4	no	—
209	C₄×C₁₃	—	2	4	no	—
210	C₄×C₁₃	—	8	4	no	—
211	C₄×C₁₃	#376	1	1	yes	characteristic
212	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₄×C₁₃	#381	1	1	yes	characteristic
214	C₄×C₁₃	#383	1	1	yes	characteristic
215	C₄×C₁₃	#387	1	2	yes	—
216	C₄×C₁₃	#387	1	2	yes	—
217	Dic₁₃	—	8	4	no	—
218	C₂³×C₄	—	2	2	no	—
219	C₂³×C₄	—	26	2	no	—
220	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
221	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
223	C₂²×C₈	—	13	4	no	—
224	C₂²×C₈	—	13	2	no	—
225	C₂²×C₈	—	13	2	no	—
226	C₂²×C₈	—	13	4	no	—
227	C₂²×C₈	—	26	2	no	—
228	C₂²×C₈	—	26	2	no	—
229	C₂²×C₈	—	26	1	no	—
230	C₂²×C₈	—	26	1	no	—
231	C₂²×C₈	—	26	1	no	—
232	C₂²×C₈	—	26	1	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	13	4	no	—
239	C₂×C₄⋊C₄	—	26	2	no	—
240	C₂×C₄⋊C₄	—	26	2	no	—
241	C₂×C₄⋊C₄	—	26	2	no	—
242	C₂×C₄⋊C₄	—	26	2	no	—
243	C₂×C₄⋊C₄	—	26	2	no	—
244	C₂×C₄⋊C₄	C₄×D₁₃	1	4	yes	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	Dic₂₆	1	2	yes	—
248	C₂×C₄²	C₄×D₁₃	1	2	yes	—
249	C₄×C₈	—	26	8	no	—
250	#95	—	4	2	no	—
251	#95	—	4	2	no	—
252	#95	—	52	2	no	—
253	#95	—	52	2	no	—
254	C₂×C₁₃	#1434	1	1	yes	characteristic
255	C₂×C₁₃	C₄×#106	1	1	yes	characteristic
256	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
257	C₂×C₁₃	#1807	1	1	yes	characteristic
258	C₂×C₁₃	#1808	1	1	yes	characteristic
259	C₂×C₁₃	#1834	1	1	yes	characteristic
260	C₂×C₁₃	#1835	1	1	yes	characteristic
261	C₂×C₁₃	#1933	1	2	yes	—
262	C₂×C₁₃	#1933	1	2	yes	—
263	C₂×C₁₃	#1934	1	2	yes	—
264	C₂×C₁₃	#1934	1	2	yes	—
265	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	26	4	no	—
278	C₂²×C₄	—	52	2	no	—
279	C₂²×C₄	—	52	2	no	—
280	C₂²×C₄	—	52	2	no	—
281	C₂²×C₄	—	52	2	no	—
282	C₂²×C₄	—	52	2	no	—
283	C₂²×C₄	—	52	2	no	—
284	C₂²×C₄	#6101	1	2	yes	—
285	C₂²×C₄	#6101	1	2	yes	—
286	C₂²×C₄	#6104	1	2	yes	—
287	C₂²×C₄	#6105	1	2	yes	—
288	C₂²×C₄	#6106	1	2	yes	—
289	C₂²×C₄	#6107	1	2	yes	—
290	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
292	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
293	C₂²×C₄	#6127	1	2	yes	—
294	C₂²×C₄	D₄×D₁₃	1	2	yes	—
295	C₂²×C₄	#6129	1	2	yes	—
296	C₂²×C₄	#6129	1	1	yes	characteristic
297	C₂²×C₄	#6129	1	1	yes	characteristic
298	C₂²×C₄	#6131	1	1	yes	characteristic
299	C₂²×C₄	#6131	1	1	yes	characteristic
300	C₂×C₈	—	13	4	no	—
301	C₂×C₈	—	13	4	no	—
302	C₂×C₈	—	26	2	no	—
303	C₂×C₈	—	26	2	no	—
304	C₂×C₈	—	26	4	no	—
305	C₂×C₈	—	26	4	no	—
306	C₂×C₈	—	26	2	no	—
307	C₂×C₈	—	26	2	no	—
308	C₂×C₈	—	26	4	no	—
309	C₂×C₈	—	26	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	26	4	no	—
315	C₄⋊C₄	—	26	4	no	—
316	C₄⋊C₄	—	52	2	no	—
317	C₄⋊C₄	—	52	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	2	no	—
321	C₁₃	#10820	1	1	yes	characteristic, complemented, Sylow
322	C₂³	C₂×#6101	1	1	yes	characteristic
323	C₂³	C₄×C₂²⋊D₁₃	1	2	yes	—
324	C₂³	C₂×#6104	1	1	yes	characteristic
325	C₂³	C₂×#6105	1	1	yes	characteristic
326	C₂³	#88190	1	1	yes	characteristic
327	C₂³	#88193	1	2	yes	—
328	C₂³	C₂×#6106	1	1	yes	characteristic
329	C₂³	C₂×#6107	1	1	yes	characteristic
330	C₂³	#88201	1	1	yes	characteristic
331	C₂³	#88204	1	2	yes	—
332	C₂³	#88204	1	2	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	52	4	no	—
349	C₂×C₄	—	52	4	no	—
350	C₂×C₄	—	52	4	no	—
351	C₂×C₄	—	104	2	no	—
352	C₂×C₄	—	104	2	no	—
353	C₂×C₄	—	104	2	no	—
354	C₂×C₄	—	104	2	no	—
355	C₂×C₄	#88047	1	4	yes	—
356	C₂×C₄	#88048	1	4	yes	—
357	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
358	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
359	C₂×C₄	#88126	1	1	yes	characteristic
360	C₂×C₄	#88131	1	1	yes	characteristic
361	C₂×C₄	#88131	1	2	yes	—
362	C₂×C₄	#88132	1	2	yes	—
363	C₂×C₄	#88133	1	2	yes	—
364	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
365	C₂×C₄	#88135	1	2	yes	—
366	C₂×C₄	#88137	1	2	yes	—
367	C₂×C₄	#88144	1	1	yes	characteristic
368	C₂×C₄	#88144	1	1	yes	characteristic
369	C₂×C₄	#88146	1	2	yes	—
370	C₂×C₄	#88146	1	1	yes	characteristic
371	C₂×C₄	#88146	1	1	yes	characteristic
372	C₂×C₄	#88147	1	2	yes	—
373	C₂×C₄	#88148	1	2	yes	—
374	C₂×C₄	#88152	1	2	yes	—
375	C₈	—	26	4	no	—
376	C₈	—	26	4	no	—
377	C₂²	C₄×#6101	1	1	yes	characteristic
378	C₂²	#11718603	1	1	yes	characteristic
379	C₂²	#11718606	1	2	yes	—
380	C₂²	C₂×#88047	1	1	yes	characteristic
381	C₂²	C₂×#88048	1	1	yes	characteristic
382	C₂²	#11718638	1	1	yes	characteristic
383	C₂²	#11718651	1	2	yes	—
384	C₂²	#11718659	1	1	yes	characteristic
385	C₂²	#11718659	1	1	yes	characteristic
386	C₂²	C₄×#6104	1	2	yes	—
387	C₂²	C₄×#6105	1	2	yes	—
388	C₂²	C₄×#6106	1	2	yes	—
389	C₂²	C₄×#6107	1	2	yes	—
390	C₂²	#11718699	1	2	yes	—
391	C₂²	#11718702	1	2	yes	—
392	C₂²	#11718709	1	2	yes	—
393	C₂²	#11718712	1	2	yes	—
394	C₂²	#11718717	1	2	yes	—
395	C₂²	#11718729	1	2	yes	—
396	C₂²	#11718731	1	1	yes	characteristic
397	C₂²	#11718742	1	1	yes	characteristic
398	C₂²	#11718749	1	1	yes	characteristic
399	C₂²	#11718754	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	8	4	no	—
403	C₄	—	104	4	no	—
404	C₄	#11718309	1	1	yes	characteristic
405	C₄	#11718312	1	1	yes	characteristic
406	C₄	#11718315	1	2	yes	—
407	C₄	#11718316	1	2	yes	—
408	C₄	#11718325	1	1	yes	characteristic
409	C₄	#11718327	1	1	yes	characteristic
410	C₂	#13113062	1	1	yes	characteristic
411	C₂	C₄×#88048	1	1	yes	characteristic
412	C₂	C₄×#88047	1	1	yes	characteristic
413	C₂	#13114859	1	1	yes	characteristic
414	C₂	#13114863	1	1	yes	characteristic
415	C₂	#13114963	1	1	yes	characteristic
416	C₂	#13114966	1	1	yes	characteristic
417	C₂	#13115511	1	2	yes	—
418	C₂	#13115515	1	2	yes	—
419	C₂	#13115518	1	2	yes	—
420	C₂	#13115522	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₁₃×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₄⋊#95	D₁₃
hypocenter	C₁₃	#10820
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
16. C₂×C₄×#1055	C₄	semidirect
18. #11718121	C₄	semidirect
321. C₁₃	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×#1055	2
C₂×#11718121	2
#13113066	2
C₁₃×C₄⋊#95	2
#10820	13