Subgroups — #15832212

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123963	C₂	1	2	yes	maximal
2	C₈×#6127	C₂	1	1	yes	maximal, characteristic
3	#13113626	C₂	1	2	yes	maximal, complemented
4	#13113622	C₂	1	2	yes	maximal, complemented
5	#13113620	C₂	1	2	yes	maximal, complemented
6	#13113596	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113590	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113581	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11718049	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#6127	C₂²	1	1	yes	characteristic
13	C₁₃×#432	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
16	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
19	#11718586	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	2	yes	—
21	#11718498	C₂²	1	2	yes	—
22	#11718496	C₂²	1	2	yes	—
23	#11718494	C₂²	1	2	yes	—
24	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	#11718391	—	2	2	no	—
26	#11718386	—	2	2	no	—
27	#11718367	—	2	2	no	—
28	#11718362	—	2	2	no	—
29	C₈×D₅₂	C₄	1	1	yes	characteristic
30	C₈×D₅₂	C₄	1	1	yes	characteristic
31	#11718346	C₂²	1	1	yes	characteristic
32	#11718346	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
35	C₈×Dic₂₆	C₄	1	1	yes	characteristic
36	C₈×Dic₂₆	C₄	1	1	yes	characteristic
37	C₁₃×#335	C₂²	1	2	yes	—
38	C₁₃×#334	C₂²	1	1	yes	characteristic
39	C₁₃×#334	C₂²	1	1	yes	characteristic
40	#11718072	C₂²	1	2	yes	—
41	#11718072	C₂²	1	2	yes	—
42	#11718071	C₂²	1	2	yes	—
43	#11718071	C₂²	1	2	yes	—
44	#11718049	C₂²	1	2	yes	—
45	#11718049	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	1	yes	characteristic
47	C₂×#6127	Q₈	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	D₄	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	D₄	1	1	yes	characteristic
55	#88180	Q₈	1	1	yes	characteristic
56	C₂²×#1055	—	2	2	no	—
57	C₂×#6094	—	2	2	no	—
58	C₂×C₈×D₁₃	—	2	2	no	—
59	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
64	C₄×D₅₂	D₄	1	1	yes	characteristic
65	#88126	Q₈	1	1	yes	characteristic
66	#88126	Q₈	1	1	yes	characteristic
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₄²×D₁₃	C₂³	1	1	yes	characteristic
69	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₂₆	D₄	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×C₂²⋊C₈	—	2	2	no	—
74	C₁₃×#97	—	2	2	no	—
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
81	#88060	—	2	2	no	—
82	#88060	—	2	2	no	—
83	#88060	C₂×C₄	1	1	yes	characteristic
84	#88060	C₂×C₄	1	1	yes	characteristic
85	#88060	C₂×C₄	1	1	yes	characteristic
86	#88060	C₂×C₄	1	1	yes	characteristic
87	#88055	—	2	2	no	—
88	#88054	—	2	2	no	—
89	#88054	—	2	2	no	—
90	#88054	C₂×C₄	1	1	yes	characteristic
91	#88054	C₂×C₄	1	1	yes	characteristic
92	#88054	C₂×C₄	1	1	yes	characteristic
93	#88054	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₃	—	2	2	no	—
95	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
99	C₄⋊#1055	—	2	2	no	—
100	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#1055	C₂³	1	2	yes	—
103	C₄⋊#1055	C₂³	1	2	yes	—
104	C₄×#1055	C₂³	1	1	yes	characteristic
105	C₄×#1055	C₂³	1	1	yes	characteristic
106	#17834	—	13	1	no	maximal, Sylow
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
112	#6127	—	2	4	no	—
113	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	4	1	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
132	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
135	#6103	C₄⋊C₄	1	1	yes	characteristic
136	#6103	C₄⋊C₄	1	1	yes	characteristic
137	#6103	C₄⋊C₄	1	1	yes	characteristic
138	#6103	C₄⋊C₄	1	1	yes	characteristic
139	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
141	#6101	C₄⋊C₄	1	1	yes	characteristic
142	#6101	C₄⋊C₄	1	1	yes	characteristic
143	#6101	C₄⋊C₄	1	1	yes	characteristic
144	#6101	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	8	2	no	—
154	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
158	#6094	—	8	2	no	—
159	C₈×D₁₃	—	2	2	no	—
160	C₈×D₁₃	—	2	2	no	—
161	C₈×D₁₃	—	4	1	no	—
162	C₈×D₁₃	—	4	1	no	—
163	C₈×D₁₃	—	8	2	no	—
164	#2990	—	13	2	no	—
165	C₈×#41	—	13	1	no	—
166	#1574	—	13	2	no	—
167	#1573	—	13	2	no	—
168	#1573	—	13	2	no	—
169	#1568	—	13	1	no	—
170	#1568	D₁₃	1	1	yes	characteristic, complemented
171	#1566	—	13	1	no	—
172	#1564	—	13	1	no	—
173	C₂×#334	—	13	1	no	—
174	C₂×#334	—	13	1	no	—
175	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
188	C₂²⋊D₁₃	—	2	2	no	—
189	C₂²⋊D₁₃	#108	1	4	yes	—
190	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	D₅₂	—	2	2	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	1	no	—
199	C₄×D₁₃	—	2	1	no	—
200	C₄×D₁₃	—	2	1	no	—
201	C₄×D₁₃	—	2	1	no	—
202	C₄×D₁₃	—	2	2	no	—
203	C₄×D₁₃	—	2	2	no	—
204	C₄×D₁₃	—	2	2	no	—
205	Dic₂₆	—	2	2	no	—
206	C₈×C₁₃	—	2	1	no	—
207	C₈×C₁₃	—	2	1	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	#131	1	2	yes	—
212	#1055	—	2	1	no	—
213	#1055	—	2	1	no	—
214	#1055	—	2	1	no	—
215	#1055	—	2	1	no	—
216	#1055	—	4	2	no	—
217	#1055	—	4	2	no	—
218	C₄×#41	—	13	1	no	—
219	#446	—	26	2	no	—
220	C₈×Q₈	—	13	1	no	—
221	C₈×Q₈	—	13	1	no	—
222	#435	—	26	2	no	—
223	#435	—	26	2	no	—
224	C₈×D₄	—	13	1	no	—
225	C₈×D₄	—	13	1	no	—
226	C₈×D₄	—	13	1	no	—
227	C₈×D₄	—	13	1	no	—
228	C₈×D₄	—	13	1	no	—
229	C₈×D₄	—	13	1	no	—
230	C₈×D₄	—	26	2	no	—
231	#432	—	13	2	no	—
232	#432	C₂×D₁₃	1	2	yes	—
233	#431	—	13	1	no	—
234	#431	—	13	1	no	—
235	#431	—	13	1	no	—
236	#431	—	13	2	no	—
237	#423	—	13	2	no	—
238	C₂×C₄⋊C₈	—	13	2	no	—
239	C₂×C₄⋊C₈	—	13	2	no	—
240	C₂×C₄×C₈	—	13	1	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
243	#335	—	13	2	no	—
244	#335	—	13	2	no	—
245	#335	C₂×D₁₃	1	2	yes	—
246	#334	—	13	2	no	—
247	#334	—	13	2	no	—
248	#334	—	13	1	no	—
249	#334	—	13	1	no	—
250	#334	—	13	2	no	—
251	#334	C₂×D₁₃	1	1	yes	characteristic
252	#334	C₂×D₁₃	1	1	yes	characteristic
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	C₂×#108	1	2	yes	—
256	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
257	C₂×D₁₃	—	2	1	no	—
258	C₂×D₁₃	—	2	1	no	—
259	C₂×D₁₃	—	2	1	no	—
260	C₂×D₁₃	—	2	1	no	—
261	C₂×D₁₃	—	2	1	no	—
262	C₂×D₁₃	C₂×#108	1	2	yes	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
268	C₄×C₁₃	#568	1	1	yes	characteristic
269	C₄×C₁₃	#577	1	2	yes	—
270	Dic₁₃	—	2	1	no	—
271	Dic₁₃	—	2	1	no	—
272	Dic₁₃	—	2	1	no	—
273	Dic₁₃	—	2	1	no	—
274	Dic₁₃	—	2	1	no	—
275	Dic₁₃	C₂×#108	1	2	yes	—
276	C₂×#41	—	13	1	no	—
277	C₂×M₁₆	—	26	2	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	13	1	no	—
281	C₂²×C₈	—	13	1	no	—
282	C₂²×C₈	—	26	2	no	—
283	C₂²×C₈	—	26	2	no	—
284	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
285	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
286	C₄×Q₈	—	13	1	no	—
287	C₄×Q₈	—	13	1	no	—
288	C₄×D₄	—	13	1	no	—
289	C₄×D₄	—	13	1	no	—
290	C₄×D₄	—	13	1	no	—
291	C₄×D₄	—	13	1	no	—
292	C₄×D₄	—	13	1	no	—
293	C₄×D₄	—	13	1	no	—
294	#117	—	13	1	no	—
295	#117	—	13	1	no	—
296	#117	—	13	1	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	—	13	1	no	—
299	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
300	C₄⋊C₈	—	13	1	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	13	1	no	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	13	1	no	—
305	C₄⋊C₈	—	13	1	no	—
306	C₄⋊C₈	—	13	2	no	—
307	C₄⋊C₈	—	13	2	no	—
308	C₄⋊C₈	—	26	2	no	—
309	C₄⋊C₈	—	26	2	no	—
310	C₄⋊C₈	—	26	2	no	—
311	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
312	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	13	1	no	—
315	C₂²⋊C₈	—	13	1	no	—
316	C₂²⋊C₈	—	13	1	no	—
317	C₂²⋊C₈	—	13	1	no	—
318	C₂²⋊C₈	—	13	1	no	—
319	C₂²⋊C₈	—	13	1	no	—
320	C₂²⋊C₈	—	26	2	no	—
321	C₂²⋊C₈	—	26	2	no	—
322	#97	—	2	2	no	—
323	#97	—	26	2	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	13	1	no	—
326	C₄×C₈	—	13	1	no	—
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	13	1	no	—
330	C₄×C₈	—	26	2	no	—
331	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
332	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
335	C₂×C₁₃	—	2	2	no	—
336	C₂×C₁₃	#2906	1	1	yes	characteristic
337	C₂×C₁₃	#2912	1	1	yes	characteristic
338	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
339	D₁₃	—	2	2	no	—
340	D₁₃	—	4	1	no	—
341	#41	—	26	4	no	—
342	C₂×Q₈	—	13	1	no	—
343	C₂×D₄	—	13	1	no	—
344	C₂×D₄	—	13	1	no	—
345	C₂×D₄	—	13	1	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
354	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
355	M₁₆	—	104	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	13	1	no	—
362	C₂×C₈	—	13	1	no	—
363	C₂×C₈	—	13	1	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	—	26	2	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	—	26	2	no	—
368	C₂×C₈	—	52	1	no	—
369	C₂×C₈	—	52	1	no	—
370	C₂×C₈	—	104	2	no	—
371	C₂×C₈	—	104	2	no	—
372	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
376	C₄⋊C₄	—	13	1	no	—
377	C₄⋊C₄	—	13	1	no	—
378	C₄⋊C₄	—	13	1	no	—
379	C₄⋊C₄	—	13	1	no	—
380	C₄⋊C₄	—	13	1	no	—
381	C₄⋊C₄	—	13	1	no	—
382	C₂²⋊C₄	—	13	1	no	—
383	C₂²⋊C₄	—	13	1	no	—
384	C₂²⋊C₄	—	13	1	no	—
385	C₂²⋊C₄	—	13	1	no	—
386	C₂²⋊C₄	—	13	1	no	—
387	C₂²⋊C₄	—	13	1	no	—
388	C₄²	—	13	1	no	—
389	C₄²	—	13	1	no	—
390	C₄²	—	13	1	no	—
391	C₄²	—	13	1	no	—
392	C₄²	—	13	1	no	—
393	C₄²	—	13	1	no	—
394	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
395	C₄²	D₄×D₁₃	1	1	yes	characteristic
396	C₄²	Q₈×D₁₃	1	1	yes	characteristic
397	C₄²	C₂³×D₁₃	1	1	yes	characteristic
398	C₁₃	#17834	1	1	yes	characteristic, complemented, Sylow
399	C₂³	—	13	1	no	—
400	C₂³	—	13	1	no	—
401	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
402	Q₈	—	26	2	no	—
403	D₄	—	13	4	no	—
404	D₄	—	26	2	no	—
405	D₄	—	26	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	13	1	no	—
412	C₂×C₄	—	13	1	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	1	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	26	1	no	—
421	C₂×C₄	—	26	1	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	2	no	—
424	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
425	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	26	1	no	—
436	C₈	—	26	1	no	—
437	C₈	—	26	1	no	—
438	C₈	—	26	1	no	—
439	C₈	—	52	2	no	—
440	C₈	—	52	2	no	—
441	C₈	#88161	1	2	yes	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	13	2	no	—
445	C₂²	—	26	1	no	—
446	C₂²	—	26	1	no	—
447	C₂²	—	26	1	no	—
448	C₂²	—	26	1	no	—
449	C₂²	—	26	1	no	—
450	C₂²	D₁₃×#108	1	2	yes	—
451	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	13	2	no	—
457	C₄	—	26	1	no	—
458	C₄	—	26	1	no	—
459	C₄	—	26	1	no	—
460	C₄	—	26	1	no	—
461	C₄	—	26	1	no	—
462	C₄	C₂×#88161	1	1	yes	characteristic
463	C₄	#11719450	1	1	yes	characteristic
464	C₄	#11719475	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	26	2	no	—
467	C₂	—	52	1	no	—
468	C₂	#13123405	1	1	yes	characteristic
469	C₂	#13123428	1	1	yes	characteristic
470	C₂	C₂×D₁₃×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1568	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6127	Q₈
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1568	D₁₃
hypocenter	C₁₃	#17834
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #13113626	C₂	semidirect
4. #13113622	C₂	semidirect
5. #13113620	C₂	semidirect
6. #13113596	C₂	semidirect
7. #13113590	C₂	semidirect
8. #13113581	C₂	semidirect
9. C₂×#11718049	C₂	semidirect
10. D₁₃×#334	C₂	semidirect
11. C₁₃×#1568	C₂	semidirect
170. #1568	D₁₃	semidirect
398. C₁₃	#17834	semidirect

Maximal subgroups

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

subgroup	index
#13123963	2
C₈×#6127	2
#13113626	2
#13113622	2
#13113620	2
#13113596	2
#13113590	2
#13113581	2
C₂×#11718049	2
D₁₃×#334	2
C₁₃×#1568	2
#17834	13