Subgroups — #15876871

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115773	C₂	1	2	yes	maximal, complemented
2	#13115555	C₂	1	2	yes	maximal, complemented
3	#13115395	C₂	1	2	yes	maximal, complemented
4	#13115395	C₂	1	2	yes	maximal, complemented
5	#13115021	C₂	1	2	yes	maximal
6	#13114820	C₂	1	1	yes	maximal, characteristic
7	C₂²⋊C₄×#1055	C₂	1	2	yes	maximal
8	#13114533	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×#6099	C₂²	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	1	yes	characteristic
14	C₁₃×#400	C₄	1	1	yes	characteristic
15	C₁₃×#399	C₄	1	1	yes	characteristic
16	C₁₃×#398	C₄	1	2	yes	—
17	C₁₃×#396	C₄	1	2	yes	—
18	C₁₃×#395	C₄	1	1	yes	characteristic
19	C₁₃×#393	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
24	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#1055	C₂²	1	2	yes	—
26	C₂×C₄⋊#1055	C₂²	1	2	yes	—
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄×#1055	C₂²	1	2	yes	—
29	C₂×C₄×#1055	C₂²	1	2	yes	—
30	#11718116	C₂²	1	2	yes	—
31	#11718116	C₂²	1	2	yes	—
32	#11718116	C₂²	1	2	yes	—
33	#11718116	C₂²	1	2	yes	—
34	#11718116	C₂²	1	2	yes	—
35	#11718116	C₂²	1	2	yes	—
36	#11718116	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₄×Q₈×C₁₃	—	4	1	no	—
40	C₄×Q₈×C₁₃	—	4	1	no	—
41	C₁₃×#117	—	4	1	no	—
42	C₁₃×#117	—	4	1	no	—
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×#6099	—	2	2	no	—
59	C₂×#6099	—	4	1	no	—
60	C₂×#6099	—	4	1	no	—
61	C₂²×#1055	—	4	1	no	—
62	C₂²×#1055	—	4	1	no	—
63	C₂²×#1055	Q₈	1	4	yes	complemented
64	C₂²×#1055	C₂³	1	2	yes	—
65	C₂²×#1055	C₂³	1	2	yes	—
66	C₂²×#1055	C₂³	1	2	yes	—
67	C₂²×#1055	C₂³	1	2	yes	—
68	C₁₃×#95	C₂×C₄	1	2	yes	—
69	C₁₃×#95	C₂×C₄	1	2	yes	—
70	C₁₃×#95	C₂×C₄	1	2	yes	—
71	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
72	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
73	C₁₃×#95	C₂×C₄	1	2	yes	—
74	C₂²⋊#1055	—	2	4	no	—
75	C₄⋊#1055	—	4	2	no	—
76	C₄⋊#1055	—	4	2	no	—
77	C₄⋊#1055	—	4	1	no	—
78	C₄⋊#1055	—	4	1	no	—
79	C₄×#1055	—	4	2	no	—
80	C₄×#1055	—	4	2	no	—
81	#22288	—	13	1	no	maximal, Sylow
82	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×Q₈×C₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₃	—	4	1	no	—
85	C₂²×C₄×C₁₃	—	2	1	no	—
86	C₂²×C₄×C₁₃	—	2	1	no	—
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
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	1	yes	characteristic
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	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₁₃	#41	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×C₄⋊C₄	—	2	4	no	—
102	C₁₃×C₄⋊C₄	—	2	4	no	—
103	C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₁₃×C₄⋊C₄	—	4	1	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	4	2	no	—
107	C₁₃×C₄⋊C₄	—	4	1	no	—
108	C₁₃×C₂²⋊C₄	—	2	4	no	—
109	C₁₃×C₂²⋊C₄	—	2	4	no	—
110	C₁₃×C₂²⋊C₄	—	4	1	no	—
111	C₁₃×C₂²⋊C₄	—	4	1	no	—
112	C₄²×C₁₃	—	2	1	no	—
113	C₄²×C₁₃	—	2	1	no	—
114	C₄²×C₁₃	—	2	1	no	—
115	C₄²×C₁₃	—	2	1	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	#6099	—	4	4	no	—
121	C₂×#1055	—	2	2	no	—
122	C₂×#1055	—	2	2	no	—
123	C₂×#1055	—	2	2	no	—
124	C₂×#1055	—	2	2	no	—
125	C₂×#1055	—	2	2	no	—
126	C₂×#1055	—	2	2	no	—
127	C₂×#1055	—	2	2	no	—
128	C₂×#1055	—	2	2	no	—
129	C₂×#1055	—	2	2	no	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	—	2	2	no	—
132	C₂×#1055	—	4	4	no	—
133	C₂×#1055	C₂×Q₈	1	4	yes	—
134	#2396	D₁₃	1	1	yes	characteristic
135	#1984	—	13	2	no	—
136	#1939	—	13	2	no	—
137	#1916	—	13	2	no	—
138	#1916	—	13	2	no	—
139	#1851	—	13	2	no	—
140	#1798	—	13	1	no	—
141	C₈×C₂²⋊C₄	—	13	2	no	—
142	#1729	—	13	1	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	—	2	1	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
148	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
149	Q₈×C₁₃	—	4	4	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	2	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	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
175	C₂×C₄×C₁₃	#131	1	4	yes	—
176	C₂×C₄×C₁₃	#131	1	4	yes	—
177	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
183	#1055	—	2	4	no	—
184	#1055	—	4	2	no	—
185	#1055	—	4	2	no	—
186	#1055	—	4	2	no	—
187	C₂²×M₁₆	—	13	1	no	—
188	C₂³×C₈	—	13	1	no	—
189	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
190	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	—	13	1	no	—
192	C₂×C₄⋊C₈	—	13	1	no	—
193	C₂×C₄⋊C₈	—	13	2	no	—
194	C₂×C₄⋊C₈	—	13	2	no	—
195	C₂×C₂²⋊C₈	—	13	2	no	—
196	C₂×C₄×C₈	—	13	2	no	—
197	C₂×C₄×C₈	—	13	2	no	—
198	#400	Dic₁₃	1	1	yes	characteristic
199	#399	Dic₁₃	1	1	yes	characteristic
200	#398	Dic₁₃	1	2	yes	—
201	#396	Dic₁₃	1	2	yes	—
202	#395	Dic₁₃	1	1	yes	characteristic
203	#393	Dic₁₃	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
206	C₄×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
207	#336	—	13	2	no	—
208	#336	—	13	2	no	—
209	#336	—	13	2	no	—
210	#336	—	13	2	no	—
211	#336	—	13	2	no	—
212	#336	—	13	2	no	—
213	#336	—	13	2	no	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	4	no	—
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₂²×C₁₃	#518	1	1	yes	characteristic
221	C₂²×C₁₃	#520	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×#131	1	2	yes	—
223	C₂²×C₁₃	C₂×#131	1	2	yes	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	4	no	—
226	C₄×C₁₃	—	2	4	no	—
227	C₄×C₁₃	—	4	1	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	4	1	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	#538	1	1	yes	characteristic
234	C₄×C₁₃	#539	1	1	yes	characteristic
235	C₄×C₁₃	#543	1	1	yes	characteristic
236	C₄×C₁₃	#544	1	1	yes	characteristic
237	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
239	C₂×M₁₆	—	26	2	no	—
240	C₂×M₁₆	—	52	1	no	—
241	C₂×M₁₆	—	52	1	no	—
242	C₂²×C₈	—	13	2	no	—
243	C₂²×C₈	—	13	4	no	—
244	C₂²×C₈	—	13	2	no	—
245	C₂²×C₈	—	13	2	no	—
246	C₂²×C₈	—	13	2	no	—
247	C₂²×C₈	—	52	1	no	—
248	C₂²×C₈	—	52	1	no	—
249	C₄×Q₈	—	4	1	no	—
250	C₄×Q₈	—	4	1	no	—
251	#117	—	4	1	no	—
252	#117	—	4	1	no	—
253	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
267	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
268	C₄⋊C₈	—	52	1	no	—
269	C₄⋊C₈	—	52	1	no	—
270	C₄⋊C₈	—	52	2	no	—
271	C₄⋊C₈	—	52	2	no	—
272	C₂²⋊C₈	—	26	4	no	—
273	C₄×C₈	—	52	2	no	—
274	C₄×C₈	—	52	2	no	—
275	#95	C₂×Dic₁₃	1	2	yes	—
276	#95	C₂×Dic₁₃	1	2	yes	—
277	#95	C₂×Dic₁₃	1	2	yes	—
278	#95	C₂×Dic₁₃	1	1	yes	characteristic
279	#95	C₂×Dic₁₃	1	1	yes	characteristic
280	#95	C₂×Dic₁₃	1	2	yes	—
281	C₂×C₁₃	—	4	2	no	—
282	C₂×C₁₃	#2329	1	1	yes	characteristic
283	C₂×C₁₃	#2960	1	2	yes	—
284	C₂×C₁₃	#2977	1	1	yes	characteristic
285	C₂×C₁₃	#2979	1	1	yes	characteristic
286	C₂×C₁₃	#2994	1	2	yes	—
287	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
295	C₂²×C₄	#6131	1	2	yes	—
296	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
297	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
300	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
304	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
305	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
306	M₁₆	—	52	4	no	—
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	26	2	no	—
309	C₂×C₈	—	26	2	no	—
310	C₂×C₈	—	26	2	no	—
311	C₂×C₈	—	26	2	no	—
312	C₂×C₈	—	26	2	no	—
313	C₂×C₈	—	26	2	no	—
314	C₂×C₈	—	26	2	no	—
315	C₂×C₈	—	26	2	no	—
316	C₂×C₈	—	26	2	no	—
317	C₂×C₈	—	26	2	no	—
318	C₂×C₈	—	26	2	no	—
319	C₂×C₈	—	52	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₁₃	#22288	1	1	yes	characteristic, complemented, Sylow
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	1	no	—
344	C₂³	Q₈×Dic₁₃	1	2	yes	—
345	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
346	Q₈	—	4	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	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	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
372	C₂×C₄	#88202	1	4	yes	—
373	C₂×C₄	#88202	1	4	yes	—
374	C₂×C₄	#88251	1	1	yes	characteristic
375	C₂×C₄	#88251	1	1	yes	characteristic
376	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂×#6131	1	1	yes	characteristic
378	C₂×C₄	#88256	1	1	yes	characteristic
379	C₂×C₄	#88257	1	1	yes	characteristic
380	C₈	—	26	4	no	—
381	C₈	—	52	2	no	—
382	C₈	—	52	2	no	—
383	C₈	—	52	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	2	no	—
389	C₂²	#11719503	1	1	yes	characteristic
390	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
391	C₂²	C₂×#88202	1	2	yes	—
392	C₂²	C₂×#88202	1	2	yes	—
393	C₂²	#11719532	1	1	yes	characteristic
394	C₄	—	2	4	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	#11719328	1	1	yes	characteristic
404	C₄	#11719339	1	1	yes	characteristic
405	C₄	#11719349	1	1	yes	characteristic
406	C₄	#11719350	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	#13117571	1	1	yes	characteristic
409	C₂	#13123771	1	2	yes	—
410	C₂	#13123892	1	1	yes	characteristic
411	C₂	#13123903	1	1	yes	characteristic
412	C₂	#13123996	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2396	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2396	D₁₃
hypocenter	C₁₃	#22288
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
1. #13115773	C₂	semidirect
2. #13115555	C₂	semidirect
3. #13115395	C₂	semidirect
4. #13115395	C₂	semidirect
63. C₂²×#1055	Q₈	semidirect
339. C₁₃	#22288	semidirect

Maximal subgroups

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

subgroup	index
#13115773	2
#13115555	2
#13115395	2
#13115021	2
#13114820	2
C₂²⋊C₄×#1055	2
#13114533	2
C₁₃×#2396	2
#22288	13