Subgroups — #15870441

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718685	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718658	C₂	1	1	yes	maximal, characteristic
3	#13115777	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115560	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115395	C₂	1	2	yes	maximal, complemented
6	#13115016	C₂	1	2	yes	maximal
7	#13114820	C₂	1	1	yes	maximal, characteristic
8	#13114705	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114620	C₂	1	2	yes	maximal
11	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂³×#1055	C₂²	1	1	yes	characteristic
16	C₁₃×#400	C₄	1	1	yes	characteristic
17	C₁₃×#399	C₄	1	1	yes	characteristic
18	C₁₃×#398	C₄	1	2	yes	—
19	C₁₃×#396	C₄	1	2	yes	—
20	C₁₃×#395	C₄	1	1	yes	characteristic
21	C₁₃×#393	C₄	1	1	yes	characteristic
22	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
26	#11718685	—	2	4	no	—
27	#11718658	—	2	4	no	—
28	C₂×C₄⋊#1055	C₂²	1	2	yes	—
29	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊#1055	C₂²	1	2	yes	—
31	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
32	C₂×#88043	C₂²	1	1	yes	characteristic
33	C₂×#88043	C₂²	1	2	yes	—
34	C₂×#88043	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	2	yes	—
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	#11718116	C₂²	1	2	yes	—
39	#11718116	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	#11718116	C₂²	1	2	yes	—
42	#11718116	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₄×Q₈×C₁₃	—	2	2	no	—
46	C₄×Q₈×C₁₃	—	2	2	no	—
47	C₁₃×#117	—	2	2	no	—
48	C₁₃×#117	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×#6099	—	2	2	no	—
65	C₂×#6099	—	2	2	no	—
66	C₂×#6099	Q₈	1	4	yes	complemented
67	C₂²×#1055	—	2	2	no	—
68	C₂²×#1055	—	2	2	no	—
69	C₂²×#1055	—	2	2	no	—
70	C₂²×#1055	C₂³	1	2	yes	—
71	C₂²×#1055	C₂³	1	2	yes	—
72	C₂²×#1055	C₂³	1	1	yes	characteristic
73	C₂²×#1055	C₂³	1	1	yes	characteristic
74	C₂²×#1055	C₂³	1	1	yes	characteristic
75	C₂²×#1055	C₂³	1	1	yes	characteristic
76	C₁₃×#95	C₂×C₄	1	2	yes	—
77	C₁₃×#95	C₂×C₄	1	2	yes	—
78	C₁₃×#95	C₂×C₄	1	2	yes	—
79	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#95	C₂×C₄	1	2	yes	—
82	C₂²⋊#1055	—	2	4	no	—
83	C₄⋊#1055	—	2	2	no	—
84	C₄⋊#1055	—	2	2	no	—
85	C₄⋊#1055	—	2	4	no	—
86	C₄⋊#1055	—	2	4	no	—
87	#88043	—	2	2	no	—
88	#88043	—	2	2	no	—
89	#88043	—	2	4	no	—
90	C₄×#1055	—	2	2	no	—
91	C₄×#1055	—	2	4	no	—
92	C₄×#1055	D₄	1	4	yes	—
93	#21604	—	13	1	no	maximal, Sylow
94	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₁₃×C₂²⋊C₄	—	2	4	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	1	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	#41	1	2	yes	—
132	#6099	—	2	8	no	—
133	C₂×#1055	—	2	8	no	—
134	C₂×#1055	—	2	1	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	2	1	no	—
137	C₂×#1055	—	2	1	no	—
138	C₂×#1055	—	2	1	no	—
139	C₂×#1055	—	2	1	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	C₂×D₄	1	2	yes	—
147	C₂×#1055	C₂×D₄	1	2	yes	—
148	C₂×#1055	C₂×Q₈	1	2	yes	—
149	C₂×#1055	C₂×Q₈	1	2	yes	—
150	C₂×#1055	#41	1	2	yes	—
151	C₂×#1055	#41	1	2	yes	—
152	C₂×#446	—	13	1	no	—
153	C₂×#405	—	13	1	no	—
154	#2396	D₁₃	1	1	yes	characteristic
155	#1985	—	13	1	no	—
156	#1940	—	13	1	no	—
157	#1916	—	13	2	no	—
158	#1850	—	13	2	no	—
159	#1798	—	13	1	no	—
160	#1770	—	13	2	no	—
161	C₈×C₄⋊C₄	—	13	1	no	—
162	#1753	—	13	2	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
168	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
196	C₂×C₄×C₁₃	#131	1	4	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	#1055	—	2	2	no	—
204	#1055	—	2	2	no	—
205	#1055	—	2	2	no	—
206	#1055	—	4	2	no	—
207	#1055	—	4	2	no	—
208	#1055	C₂²⋊Q₈	1	4	yes	—
209	C₂²×M₁₆	—	13	1	no	—
210	C₂³×C₈	—	13	1	no	—
211	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
212	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
213	#446	—	26	4	no	—
214	C₂×C₄⋊C₈	—	13	1	no	—
215	C₂×C₄⋊C₈	—	13	1	no	—
216	C₂×C₄⋊C₈	—	13	2	no	—
217	C₂×C₄⋊C₈	—	13	2	no	—
218	C₂×C₂²⋊C₈	—	13	2	no	—
219	#405	—	26	4	no	—
220	C₂×#97	—	13	1	no	—
221	C₂×#97	—	13	1	no	—
222	C₂×#97	—	13	2	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	C₂×C₄×C₈	—	13	2	no	—
226	#400	Dic₁₃	1	1	yes	characteristic
227	#399	Dic₁₃	1	1	yes	characteristic
228	#398	Dic₁₃	1	2	yes	—
229	#396	Dic₁₃	1	2	yes	—
230	#395	Dic₁₃	1	1	yes	characteristic
231	#393	Dic₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
233	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
235	#336	—	13	2	no	—
236	#336	—	13	2	no	—
237	#336	—	13	2	no	—
238	#336	—	13	2	no	—
239	#336	—	13	2	no	—
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
247	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#131	1	2	yes	—
249	C₂²×C₁₃	#568	1	2	yes	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	4	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
260	C₄×C₁₃	#525	1	1	yes	characteristic
261	C₄×C₁₃	#529	1	1	yes	characteristic
262	C₄×C₁₃	#533	1	1	yes	characteristic
263	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
264	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
265	C₂×M₁₆	—	13	4	no	—
266	C₂×M₁₆	—	26	2	no	—
267	C₂×M₁₆	—	26	2	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	13	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	2	no	—
273	C₂²×C₈	—	13	2	no	—
274	C₂²×C₈	—	26	2	no	—
275	C₂²×C₈	—	26	2	no	—
276	C₂²×C₈	—	26	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
294	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
295	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
296	C₄⋊C₈	—	26	4	no	—
297	C₄⋊C₈	—	26	4	no	—
298	C₄⋊C₈	—	26	2	no	—
299	C₄⋊C₈	—	26	2	no	—
300	C₂²⋊C₈	—	26	4	no	—
301	#97	—	26	2	no	—
302	#97	—	26	4	no	—
303	#97	—	26	2	no	—
304	C₄×C₈	—	13	4	no	—
305	C₄×C₈	—	26	2	no	—
306	C₄×C₈	—	26	4	no	—
307	#95	C₂×Dic₁₃	1	2	yes	—
308	#95	C₂×Dic₁₃	1	2	yes	—
309	#95	C₂×Dic₁₃	1	2	yes	—
310	#95	C₂×Dic₁₃	1	1	yes	characteristic
311	#95	C₂×Dic₁₃	1	1	yes	characteristic
312	#95	C₂×Dic₁₃	1	2	yes	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
315	C₂×C₁₃	#2930	1	1	yes	characteristic
316	C₂×C₁₃	#2931	1	1	yes	characteristic
317	C₂×C₁₃	#2962	1	2	yes	—
318	C₂×C₁₃	#2968	1	2	yes	—
319	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
327	C₂²×C₄	#6131	1	2	yes	—
328	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
329	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
332	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
333	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
337	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
338	M₁₆	—	26	8	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	2	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	26	8	no	—
346	C₂×C₈	—	26	1	no	—
347	C₂×C₈	—	26	1	no	—
348	C₂×C₈	—	26	1	no	—
349	C₂×C₈	—	26	1	no	—
350	C₂×C₈	—	26	1	no	—
351	C₂×C₈	—	26	1	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	D₄×D₁₃	1	2	yes	—
376	C₄²	#6129	1	2	yes	—
377	C₁₃	#21604	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	2	1	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	Q₈×Dic₁₃	1	2	yes	—
383	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
409	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
410	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
411	C₂×C₄	#88202	1	4	yes	—
412	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#6129	1	1	yes	characteristic
414	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#6131	1	1	yes	characteristic
416	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
417	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
418	C₈	—	13	4	no	—
419	C₈	—	26	2	no	—
420	C₈	—	26	2	no	—
421	C₈	—	26	2	no	—
422	C₈	—	52	2	no	—
423	C₈	—	52	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
430	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
431	C₂²	C₂×#88202	1	2	yes	—
432	C₂²	#11719524	1	2	yes	—
433	C₂²	#41×Dic₁₃	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	#11719327	1	1	yes	characteristic
444	C₄	#11719329	1	1	yes	characteristic
445	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
446	C₄	#11719332	1	1	yes	characteristic
447	C₂	—	4	2	no	—
448	C₂	C₂²⋊Q₈×Dic₁₃	1	1	yes	characteristic
449	C₂	#13123540	1	1	yes	characteristic
450	C₂	#13123548	1	1	yes	characteristic
451	C₂	#13123785	1	2	yes	—
452	C₂	#13123832	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	#21604
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. C₂×#11718685	C₂	semidirect
3. #13115777	C₂	semidirect
4. #13115560	C₂	semidirect
5. #13115395	C₂	semidirect
8. #13114705	C₂	semidirect
9. C₄⋊C₄×#1055	C₂	semidirect
66. C₂×#6099	Q₈	semidirect
377. C₁₃	#21604	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718685	2
C₂×#11718658	2
#13115777	2
#13115560	2
#13115395	2
#13115016	2
#13114820	2
#13114705	2
C₄⋊C₄×#1055	2
#13114620	2
C₁₃×#2396	2
#21604	13