Subgroups — #15832134

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123953	C₂	1	1	yes	maximal, characteristic
2	#13123480	C₂	1	1	yes	maximal, characteristic
3	#13113627	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113624	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113622	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113619	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113617	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113614	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113612	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113610	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113604	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113601	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113597	C₂	1	1	yes	maximal, characteristic, complemented
14	#13113594	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic
16	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₁₃×#446	—	2	1	no	—
18	C₁₃×#436	—	2	1	no	—
19	C₁₃×#435	—	2	1	no	—
20	C₁₃×#435	—	2	1	no	—
21	C₁₃×#432	C₂²	1	1	yes	characteristic
22	C₁₃×#432	C₂²	1	1	yes	characteristic
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	C₁₃×#423	C₂²	1	1	yes	characteristic
25	C₁₃×#423	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	#11718895	C₄	1	2	yes	—
28	#11718685	—	2	1	no	—
29	#11718673	—	2	1	no	—
30	#11718672	—	2	1	no	—
31	#11718672	—	2	1	no	—
32	#11718661	C₄	1	2	yes	—
33	#11718661	C₄	1	2	yes	—
34	#11718660	C₄	1	2	yes	—
35	#11718587	C₂²	1	1	yes	characteristic
36	#11718587	C₂²	1	1	yes	characteristic
37	#11718586	C₂²	1	1	yes	characteristic
38	#11718586	C₂²	1	1	yes	characteristic
39	#11718586	C₂²	1	1	yes	characteristic
40	#11718586	C₂²	1	1	yes	characteristic
41	#11718586	C₂²	1	1	yes	characteristic
42	#11718585	C₂²	1	1	yes	characteristic
43	#11718585	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
45	C₄×#6099	C₂²	1	1	yes	characteristic
46	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
47	#11718072	C₂²	1	1	yes	characteristic
48	#11718072	C₂²	1	1	yes	characteristic
49	#11718072	C₂²	1	1	yes	characteristic
50	#11718072	C₂²	1	1	yes	characteristic
51	#11718072	C₂²	1	1	yes	characteristic
52	#11718072	C₂²	1	1	yes	characteristic
53	#11718071	C₂²	1	1	yes	characteristic
54	#11718071	C₂²	1	1	yes	characteristic
55	#11718071	C₂²	1	1	yes	characteristic
56	#11718071	C₂²	1	1	yes	characteristic
57	#11718071	C₂²	1	1	yes	characteristic
58	#11718071	C₂²	1	1	yes	characteristic
59	#11718071	C₂²	1	1	yes	characteristic
60	#11718071	C₂²	1	1	yes	characteristic
61	#11718071	C₂²	1	1	yes	characteristic
62	#11718071	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂²×C₈×C₁₃	—	2	1	no	—
67	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	Q₈	1	1	yes	characteristic
69	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
71	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
72	C₄×D₄×C₁₃	Q₈	1	1	yes	characteristic
73	C₄×D₄×C₁₃	Q₈	1	1	yes	characteristic
74	C₄×D₄×C₁₃	Q₈	1	1	yes	characteristic
75	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
76	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	C₂×C₄	1	2	yes	—
84	C₂²×#1055	—	2	1	no	—
85	C₂²×#1055	C₂×C₄	1	2	yes	—
86	C₁₃×C₄⋊C₈	—	2	1	no	—
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₁₃×C₂²⋊C₈	—	2	1	no	—
94	C₁₃×C₂²⋊C₈	—	2	1	no	—
95	C₁₃×C₂²⋊C₈	—	2	1	no	—
96	C₁₃×#97	—	2	1	no	—
97	C₁₃×#97	—	2	1	no	—
98	C₄×C₈×C₁₃	—	2	1	no	—
99	C₂²⋊#1055	—	2	1	no	—
100	C₂²⋊#1055	—	2	1	no	—
101	C₂²⋊#1055	—	2	1	no	—
102	C₂²⋊#1055	C₂×C₄	1	2	yes	—
103	C₂²⋊#1055	C₂×C₄	1	2	yes	—
104	C₂²⋊#1055	C₂×C₄	1	2	yes	—
105	C₂²⋊#1055	C₂×C₄	1	2	yes	—
106	C₄⋊#1055	—	2	1	no	—
107	C₄⋊#1055	—	2	1	no	—
108	C₄⋊#1055	—	2	1	no	—
109	C₄⋊#1055	C₂×C₄	1	2	yes	—
110	C₄⋊#1055	C₂×C₄	1	2	yes	—
111	C₄⋊#1055	C₂×C₄	1	2	yes	—
112	C₄⋊#1055	C₂×C₄	1	2	yes	—
113	C₄⋊#1055	C₂³	1	1	yes	characteristic
114	C₄⋊#1055	C₂³	1	1	yes	characteristic
115	C₄⋊#1055	C₂³	1	1	yes	characteristic
116	C₄⋊#1055	C₂³	1	1	yes	characteristic
117	#88043	—	2	1	no	—
118	#88043	—	2	1	no	—
119	#88043	C₂×C₄	1	2	yes	—
120	C₄×#1055	—	2	1	no	—
121	C₄×#1055	C₂×C₄	1	2	yes	—
122	C₄×#1055	C₂³	1	1	yes	characteristic
123	C₄×#1055	C₂³	1	1	yes	characteristic
124	C₄×#1055	C₂³	1	1	yes	characteristic
125	C₄×#1055	C₂³	1	1	yes	characteristic
126	#17825	—	13	1	no	maximal, Sylow
127	C₁₃×#41	—	4	2	no	—
128	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
141	C₁₃×M₁₆	—	8	1	no	—
142	C₁₃×M₁₆	—	8	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	8	1	no	—
148	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
154	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
155	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
156	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
157	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
159	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
167	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
169	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
170	#6099	—	4	2	no	—
171	#6099	—	8	1	no	—
172	#6099	—	8	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	1	no	—
175	C₂×#1055	—	2	1	no	—
176	C₂×#1055	—	2	1	no	—
177	C₂×#1055	—	4	2	no	—
178	C₂×#1055	—	8	1	no	—
179	C₂×#1055	C₂²×C₄	1	2	yes	—
180	C₂×#1055	C₂²×C₄	1	2	yes	—
181	C₂×#1055	C₂²×C₄	1	2	yes	—
182	C₂×#1055	C₂²×C₄	1	2	yes	—
183	#2989	—	13	1	no	—
184	#2989	D₁₃	1	1	yes	characteristic
185	#2922	—	13	1	no	—
186	#1574	—	13	1	no	—
187	#1574	—	13	1	no	—
188	#1573	—	13	1	no	—
189	#1573	—	13	1	no	—
190	#1572	—	13	1	no	—
191	#1572	—	13	1	no	—
192	#1571	—	13	1	no	—
193	#1571	—	13	1	no	—
194	#1569	—	13	1	no	—
195	#1569	—	13	1	no	—
196	#1568	—	13	1	no	—
197	#1567	—	13	1	no	—
198	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	Q₈×C₁₃	—	4	1	no	—
202	D₄×C₁₃	—	4	1	no	—
203	D₄×C₁₃	—	4	1	no	—
204	D₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
229	C₈×C₁₃	—	4	1	no	—
230	C₈×C₁₃	—	4	1	no	—
231	C₈×C₁₃	—	4	1	no	—
232	C₈×C₁₃	—	4	1	no	—
233	#1055	—	2	2	no	—
234	#1055	—	2	2	no	—
235	#1055	—	2	2	no	—
236	#1055	—	2	2	no	—
237	#1055	—	4	1	no	—
238	#1055	—	4	1	no	—
239	#1055	—	4	1	no	—
240	#1055	—	4	1	no	—
241	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
242	#446	—	2	1	no	—
243	#446	—	26	1	no	—
244	#436	—	2	1	no	—
245	#436	—	26	1	no	—
246	#435	—	2	1	no	—
247	#435	—	2	1	no	—
248	#435	—	26	1	no	—
249	#435	—	26	1	no	—
250	#433	—	13	2	no	—
251	#433	—	13	2	no	—
252	#432	—	13	1	no	—
253	#432	—	13	1	no	—
254	#432	C₂×D₁₃	1	1	yes	characteristic
255	#432	C₂×D₁₃	1	1	yes	characteristic
256	#431	—	13	1	no	—
257	#431	—	13	1	no	—
258	#431	—	13	1	no	—
259	#431	—	13	1	no	—
260	#431	—	13	1	no	—
261	#431	C₂×D₁₃	1	1	yes	characteristic
262	#424	—	13	2	no	—
263	#423	—	13	1	no	—
264	#423	—	13	1	no	—
265	#423	C₂×D₁₃	1	1	yes	characteristic
266	#423	C₂×D₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	—	13	1	no	—
268	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
269	#408	—	13	2	no	—
270	C₄×M₁₆	—	13	1	no	—
271	C₂×C₄×C₈	—	13	1	no	—
272	#335	—	13	1	no	—
273	#335	—	13	1	no	—
274	#335	—	13	1	no	—
275	#335	—	13	1	no	—
276	#335	—	13	1	no	—
277	#335	—	13	1	no	—
278	#335	—	13	1	no	—
279	#335	—	13	1	no	—
280	#335	—	13	1	no	—
281	#335	—	13	1	no	—
282	#334	—	13	1	no	—
283	#334	—	13	1	no	—
284	#334	—	13	1	no	—
285	#334	—	13	1	no	—
286	#334	—	13	1	no	—
287	#334	—	13	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	2	1	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	#568	1	2	yes	—
309	C₄×C₁₃	#576	1	1	yes	characteristic
310	C₄×C₁₃	#578	1	1	yes	characteristic
311	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	13	2	no	—
315	C₂×M₁₆	—	26	1	no	—
316	C₂×M₁₆	—	26	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	13	2	no	—
319	C₂²×C₈	—	26	1	no	—
320	C₄×Q₈	Dic₂₆	1	1	yes	characteristic
321	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
322	C₄×D₄	Dic₂₆	1	1	yes	characteristic
323	C₄×D₄	Dic₂₆	1	1	yes	characteristic
324	C₄×D₄	Dic₂₆	1	1	yes	characteristic
325	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
326	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
327	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
328	#117	C₄×D₁₃	1	1	yes	characteristic
329	#117	C₄×D₁₃	1	1	yes	characteristic
330	#117	C₄×D₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	—	13	2	no	—
338	C₄⋊C₈	—	13	2	no	—
339	C₄⋊C₈	—	13	2	no	—
340	C₄⋊C₈	—	13	2	no	—
341	C₄⋊C₈	—	13	1	no	—
342	C₄⋊C₈	—	13	1	no	—
343	C₄⋊C₈	—	13	1	no	—
344	C₄⋊C₈	—	13	1	no	—
345	C₄⋊C₈	—	26	1	no	—
346	C₄⋊C₈	—	26	1	no	—
347	C₄⋊C₈	—	26	1	no	—
348	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
349	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
350	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
351	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	2	1	no	—
354	C₂²⋊C₈	—	2	1	no	—
355	C₂²⋊C₈	—	13	2	no	—
356	C₂²⋊C₈	—	13	2	no	—
357	C₂²⋊C₈	—	13	2	no	—
358	C₂²⋊C₈	—	13	2	no	—
359	C₂²⋊C₈	—	26	1	no	—
360	C₂²⋊C₈	—	26	1	no	—
361	C₂²⋊C₈	—	26	1	no	—
362	#97	—	2	1	no	—
363	#97	—	2	1	no	—
364	#97	—	13	2	no	—
365	#97	—	26	1	no	—
366	#97	—	26	1	no	—
367	C₄×C₈	—	2	1	no	—
368	C₄×C₈	—	13	2	no	—
369	C₄×C₈	—	13	1	no	—
370	C₄×C₈	—	13	1	no	—
371	C₄×C₈	—	13	1	no	—
372	C₄×C₈	—	13	1	no	—
373	C₄×C₈	—	26	1	no	—
374	C₂×C₁₃	—	4	1	no	—
375	C₂×C₁₃	—	4	1	no	—
376	C₂×C₁₃	—	4	1	no	—
377	C₂×C₁₃	#2905	1	1	yes	characteristic
378	C₂×C₁₃	#2913	1	1	yes	characteristic
379	C₂×C₁₃	#2916	1	1	yes	characteristic
380	#41	—	4	2	no	—
381	C₂×Q₈	#6101	1	1	yes	characteristic
382	C₂×D₄	#6101	1	1	yes	characteristic
383	C₂×D₄	#6101	1	1	yes	characteristic
384	C₂×D₄	#6101	1	1	yes	characteristic
385	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
386	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
387	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
394	M₁₆	—	8	1	no	—
395	M₁₆	—	8	1	no	—
396	M₁₆	—	52	2	no	—
397	M₁₆	—	104	1	no	—
398	M₁₆	—	104	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	8	1	no	—
404	C₂×C₈	—	13	2	no	—
405	C₂×C₈	—	13	2	no	—
406	C₂×C₈	—	13	2	no	—
407	C₂×C₈	—	13	2	no	—
408	C₂×C₈	—	26	1	no	—
409	C₂×C₈	—	26	1	no	—
410	C₂×C₈	—	26	1	no	—
411	C₂×C₈	—	26	1	no	—
412	C₂×C₈	—	52	2	no	—
413	C₂×C₈	—	104	1	no	—
414	C₄⋊C₄	#6101	1	1	yes	characteristic
415	C₄⋊C₄	#6101	1	1	yes	characteristic
416	C₄⋊C₄	#6101	1	1	yes	characteristic
417	C₄⋊C₄	#6101	1	1	yes	characteristic
418	C₄⋊C₄	#6101	1	1	yes	characteristic
419	C₄⋊C₄	#6101	1	1	yes	characteristic
420	C₂²⋊C₄	#6101	1	1	yes	characteristic
421	C₂²⋊C₄	#6101	1	1	yes	characteristic
422	C₂²⋊C₄	#6101	1	1	yes	characteristic
423	C₂²⋊C₄	#6101	1	1	yes	characteristic
424	C₂²⋊C₄	#6101	1	1	yes	characteristic
425	C₂²⋊C₄	#6101	1	1	yes	characteristic
426	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
427	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
428	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
429	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
433	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
434	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
435	C₄²	C₂³×D₁₃	1	1	yes	characteristic
436	C₁₃	#17825	1	1	yes	characteristic, complemented, Sylow
437	C₂³	C₂×#6101	1	1	yes	characteristic
438	C₂³	C₂×#6101	1	1	yes	characteristic
439	C₂³	C₂×#6101	1	1	yes	characteristic
440	Q₈	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	C₂×#6101	1	1	yes	characteristic
457	C₂×C₄	C₂×#6101	1	1	yes	characteristic
458	C₂×C₄	C₂×#6101	1	1	yes	characteristic
459	C₂×C₄	C₂×#6101	1	1	yes	characteristic
460	C₂×C₄	C₂×#6101	1	1	yes	characteristic
461	C₂×C₄	C₂×#6101	1	1	yes	characteristic
462	C₂×C₄	C₂×#6101	1	1	yes	characteristic
463	C₂×C₄	C₂×#6101	1	1	yes	characteristic
464	C₂×C₄	C₂×#6101	1	1	yes	characteristic
465	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
468	C₈	—	4	1	no	—
469	C₈	—	4	1	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	26	2	no	—
473	C₈	—	26	2	no	—
474	C₈	—	26	2	no	—
475	C₈	—	26	2	no	—
476	C₈	—	52	1	no	—
477	C₈	—	52	1	no	—
478	C₈	—	52	1	no	—
479	C₈	—	52	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	C₂²×#6101	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	#11719450	1	2	yes	—
501	C₄	#11719540	1	1	yes	characteristic
502	C₄	#11719543	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	1	no	—
505	C₂	—	4	1	no	—
506	C₂	#13123399	1	1	yes	characteristic
507	C₂	#13123434	1	1	yes	characteristic
508	C₂	#13123445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2989	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×C₁₃×#41	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2989	D₁₃
hypocenter	C₁₃	#17825
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2989

Complements

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

N	H ≅ G/N	type
3. #13113627	C₂	semidirect
4. #13113624	C₂	semidirect
5. #13113622	C₂	semidirect
6. #13113619	C₂	semidirect
7. #13113617	C₂	semidirect
8. #13113614	C₂	semidirect
9. #13113612	C₂	semidirect
10. #13113610	C₂	semidirect
11. #13113604	C₂	semidirect
12. #13113601	C₂	semidirect
13. #13113597	C₂	semidirect
14. #13113594	C₂	semidirect
436. C₁₃	#17825	semidirect

Maximal subgroups

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

subgroup	index
#13123953	2
#13123480	2
#13113627	2
#13113624	2
#13113622	2
#13113619	2
#13113617	2
#13113614	2
#13113612	2
#13113610	2
#13113604	2
#13113601	2
#13113597	2
#13113594	2
C₁₃×#2989	2
#17825	13