Subgroups — #15832164

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6127	C₂	1	1	yes	maximal, characteristic
2	#13123503	C₂	1	2	yes	maximal
3	#13113617	C₂	1	2	yes	maximal, complemented
4	#13113613	C₂	1	2	yes	maximal, complemented
5	#13113605	C₂	1	2	yes	maximal, complemented
6	#13113598	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113583	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#335	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	2	yes	—
20	#11718586	C₂²	1	1	yes	characteristic
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	#11718388	—	2	2	no	—
26	#11718381	—	2	2	no	—
27	#11718370	—	2	2	no	—
28	#11718369	—	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	1	yes	characteristic
38	C₁₃×#335	C₂²	1	1	yes	characteristic
39	C₁₃×#334	C₂²	1	2	yes	—
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	#11718050	C₂²	1	1	yes	characteristic
45	#11718050	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	2	yes	—
47	C₂×#6127	D₄	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	Q₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
55	#88180	D₄	1	1	yes	characteristic
56	C₂×#6094	—	2	2	no	—
57	C₂×C₈×D₁₃	—	2	2	no	—
58	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
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	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
63	C₄×D₅₂	Q₈	1	1	yes	characteristic
64	#88126	D₄	1	1	yes	characteristic
65	#88126	D₄	1	1	yes	characteristic
66	C₄²×D₁₃	C₂³	1	1	yes	characteristic
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₂₆	Q₈	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₂²⋊C₈	—	2	2	no	—
73	C₁₃×#97	—	2	2	no	—
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²⋊#1055	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#1055	C₂³	1	2	yes	—
102	C₄⋊#1055	C₂³	1	2	yes	—
103	C₄×#1055	—	2	2	no	—
104	C₄×#1055	C₂³	1	1	yes	characteristic
105	C₄×#1055	C₂³	1	1	yes	characteristic
106	#17829	—	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	2	no	—
113	#6127	—	2	2	no	—
114	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
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	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
133	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
135	C₂²⋊Dic₁₃	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	#6103	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
141	C₄⋊Dic₁₃	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	#6101	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	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	—	4	4	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	—	4	4	no	—
164	C₈×#41	—	13	1	no	—
165	#2925	—	13	2	no	—
166	#1572	—	13	2	no	—
167	#1572	—	13	2	no	—
168	#1570	—	13	2	no	—
169	#1568	—	13	1	no	—
170	#1568	D₁₃	1	1	yes	characteristic, complemented
171	#1567	—	13	1	no	—
172	#1564	—	13	1	no	—
173	#1564	—	13	1	no	—
174	C₂×#335	—	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	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
189	C₂²⋊D₁₃	—	2	2	no	—
190	C₂²⋊D₁₃	—	2	2	no	—
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	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	D₅₂	—	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	1	no	—
203	C₄×D₁₃	—	2	1	no	—
204	C₄×D₁₃	—	4	1	no	—
205	C₄×D₁₃	—	4	1	no	—
206	C₄×D₁₃	#135	1	2	yes	—
207	C₄×D₁₃	#135	1	2	yes	—
208	Dic₂₆	—	2	2	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	2	1	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₈×C₁₃	—	4	2	no	—
214	C₈×C₁₃	#131	1	2	yes	—
215	#1055	—	2	1	no	—
216	#1055	—	2	1	no	—
217	#1055	—	2	1	no	—
218	#1055	—	2	1	no	—
219	#1055	—	4	2	no	—
220	#1055	—	4	2	no	—
221	C₄×#41	—	13	1	no	—
222	C₈×Q₈	—	13	1	no	—
223	C₈×Q₈	—	13	1	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	#433	—	26	2	no	—
231	#433	—	26	2	no	—
232	#432	—	13	2	no	—
233	#432	C₂×D₁₃	1	2	yes	—
234	#431	—	13	1	no	—
235	#431	—	13	1	no	—
236	#431	—	13	1	no	—
237	#431	—	13	2	no	—
238	#431	—	13	2	no	—
239	#423	—	13	2	no	—
240	C₂×C₄⋊C₈	—	13	2	no	—
241	#408	—	26	2	no	—
242	#405	—	26	2	no	—
243	C₂×C₄×C₈	—	13	1	no	—
244	C₂×C₄×C₈	—	13	1	no	—
245	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
246	#335	—	13	2	no	—
247	#335	—	13	2	no	—
248	#335	—	13	1	no	—
249	#335	—	13	1	no	—
250	#335	C₂×D₁₃	1	1	yes	characteristic
251	#335	C₂×D₁₃	1	1	yes	characteristic
252	#334	—	13	2	no	—
253	#334	—	13	2	no	—
254	#334	—	13	2	no	—
255	#334	C₂×D₁₃	1	2	yes	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
260	C₂×D₁₃	—	2	1	no	—
261	C₂×D₁₃	—	2	1	no	—
262	C₂×D₁₃	—	2	1	no	—
263	C₂×D₁₃	—	2	1	no	—
264	C₂×D₁₃	—	2	1	no	—
265	C₂×D₁₃	#427	1	2	yes	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
271	C₄×C₁₃	#568	1	1	yes	characteristic
272	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
273	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
274	Dic₁₃	—	2	1	no	—
275	Dic₁₃	—	2	1	no	—
276	Dic₁₃	—	2	1	no	—
277	Dic₁₃	—	2	1	no	—
278	Dic₁₃	—	2	1	no	—
279	Dic₁₃	#427	1	2	yes	—
280	C₂×#41	—	13	1	no	—
281	C₂×M₁₆	—	26	2	no	—
282	C₂²×C₈	—	13	1	no	—
283	C₂²×C₈	—	13	1	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	13	1	no	—
286	C₂²×C₈	—	26	2	no	—
287	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
289	C₄×Q₈	—	13	1	no	—
290	C₄×Q₈	—	13	1	no	—
291	C₄×D₄	—	13	1	no	—
292	C₄×D₄	—	13	1	no	—
293	C₄×D₄	—	13	1	no	—
294	C₄×D₄	—	13	1	no	—
295	C₄×D₄	—	13	1	no	—
296	C₄×D₄	—	13	1	no	—
297	#117	—	13	1	no	—
298	#117	—	13	1	no	—
299	#117	—	13	1	no	—
300	C₂×C₄²	—	13	1	no	—
301	C₂×C₄²	—	13	1	no	—
302	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	13	1	no	—
305	C₄⋊C₈	—	13	1	no	—
306	C₄⋊C₈	—	13	1	no	—
307	C₄⋊C₈	—	13	1	no	—
308	C₄⋊C₈	—	13	1	no	—
309	C₄⋊C₈	—	13	2	no	—
310	C₄⋊C₈	—	13	2	no	—
311	C₄⋊C₈	—	26	2	no	—
312	C₄⋊C₈	—	26	2	no	—
313	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
314	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
315	C₂²⋊C₈	—	2	2	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	—	13	1	no	—
321	C₂²⋊C₈	—	13	1	no	—
322	C₂²⋊C₈	—	26	2	no	—
323	C₂²⋊C₈	—	26	2	no	—
324	C₂²⋊C₈	—	26	2	no	—
325	#97	—	2	2	no	—
326	#97	—	26	2	no	—
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	13	1	no	—
330	C₄×C₈	—	13	1	no	—
331	C₄×C₈	—	13	1	no	—
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	26	2	no	—
334	C₄×C₈	—	26	2	no	—
335	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
336	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
338	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
339	C₂×C₁₃	—	4	1	no	—
340	C₂×C₁₃	#2906	1	1	yes	characteristic
341	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
342	C₂×C₁₃	#2916	1	1	yes	characteristic
343	D₁₃	—	2	2	no	—
344	D₁₃	—	4	1	no	—
345	#41	—	26	2	no	—
346	#41	—	26	2	no	—
347	C₂×Q₈	—	13	1	no	—
348	C₂×D₄	—	13	1	no	—
349	C₂×D₄	—	13	1	no	—
350	C₂×D₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
359	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
360	M₁₆	—	52	4	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	13	1	no	—
366	C₂×C₈	—	13	1	no	—
367	C₂×C₈	—	13	1	no	—
368	C₂×C₈	—	13	1	no	—
369	C₂×C₈	—	26	2	no	—
370	C₂×C₈	—	26	2	no	—
371	C₂×C₈	—	26	2	no	—
372	C₂×C₈	—	26	2	no	—
373	C₂×C₈	—	52	1	no	—
374	C₂×C₈	—	52	1	no	—
375	C₂×C₈	—	52	4	no	—
376	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₄⋊C₄	—	13	1	no	—
381	C₄⋊C₄	—	13	1	no	—
382	C₄⋊C₄	—	13	1	no	—
383	C₄⋊C₄	—	13	1	no	—
384	C₄⋊C₄	—	13	1	no	—
385	C₄⋊C₄	—	13	1	no	—
386	C₂²⋊C₄	—	13	1	no	—
387	C₂²⋊C₄	—	13	1	no	—
388	C₂²⋊C₄	—	13	1	no	—
389	C₂²⋊C₄	—	13	1	no	—
390	C₂²⋊C₄	—	13	1	no	—
391	C₂²⋊C₄	—	13	1	no	—
392	C₄²	—	13	1	no	—
393	C₄²	—	13	1	no	—
394	C₄²	—	13	1	no	—
395	C₄²	—	13	1	no	—
396	C₄²	—	13	1	no	—
397	C₄²	—	13	1	no	—
398	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
399	C₄²	D₄×D₁₃	1	1	yes	characteristic
400	C₄²	Q₈×D₁₃	1	1	yes	characteristic
401	C₄²	C₂³×D₁₃	1	1	yes	characteristic
402	C₁₃	#17829	1	1	yes	characteristic, complemented, Sylow
403	C₂³	—	13	1	no	—
404	C₂³	—	13	1	no	—
405	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
406	Q₈	—	26	2	no	—
407	D₄	—	26	2	no	—
408	D₄	—	26	2	no	—
409	D₄	—	26	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	13	2	no	—
417	C₂×C₄	—	13	2	no	—
418	C₂×C₄	—	13	1	no	—
419	C₂×C₄	—	13	1	no	—
420	C₂×C₄	—	13	1	no	—
421	C₂×C₄	—	13	1	no	—
422	C₂×C₄	—	13	1	no	—
423	C₂×C₄	—	26	1	no	—
424	C₂×C₄	—	26	1	no	—
425	C₂×C₄	—	26	1	no	—
426	C₂×C₄	—	26	1	no	—
427	C₂×C₄	—	26	1	no	—
428	C₂×C₄	—	26	1	no	—
429	C₂×C₄	—	52	1	no	—
430	C₂×C₄	—	52	1	no	—
431	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
432	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
433	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	26	1	no	—
443	C₈	—	26	1	no	—
444	C₈	—	26	1	no	—
445	C₈	—	26	1	no	—
446	C₈	—	52	2	no	—
447	C₈	—	52	2	no	—
448	C₈	#88161	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	13	2	no	—
453	C₂²	—	26	1	no	—
454	C₂²	—	26	1	no	—
455	C₂²	—	26	1	no	—
456	C₂²	—	26	1	no	—
457	C₂²	—	26	1	no	—
458	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	13	2	no	—
464	C₄	—	26	1	no	—
465	C₄	—	26	1	no	—
466	C₄	—	26	1	no	—
467	C₄	—	26	1	no	—
468	C₄	—	26	1	no	—
469	C₄	C₂×#88161	1	1	yes	characteristic
470	C₄	#11719450	1	1	yes	characteristic
471	C₄	D₁₃×#135	1	1	yes	characteristic
472	C₄	D₁₃×#135	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	26	2	no	—
475	C₂	—	52	1	no	—
476	C₂	#13123405	1	1	yes	characteristic
477	C₂	D₁₃×#427	1	1	yes	characteristic
478	C₂	#13123444	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	D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1568	D₁₃
hypocenter	C₁₃	#17829
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. #13113617	C₂	semidirect
4. #13113613	C₂	semidirect
5. #13113605	C₂	semidirect
6. #13113598	C₂	semidirect
7. #13113593	C₂	semidirect
8. #13113584	C₂	semidirect
9. #13113583	C₂	semidirect
10. D₁₃×#335	C₂	semidirect
11. C₁₃×#1568	C₂	semidirect
170. #1568	D₁₃	semidirect
402. C₁₃	#17829	semidirect

Maximal subgroups

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

subgroup	index
C₈×#6127	2
#13123503	2
#13113617	2
#13113613	2
#13113605	2
#13113598	2
#13113593	2
#13113584	2
#13113583	2
D₁₃×#335	2
C₁₃×#1568	2
#17829	13