Subgroups — #183568

Order 512.

668 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	#20462	C₂	1	1	yes	maximal, characteristic
2	#17806	C₂	1	1	yes	maximal, characteristic
3	#17803	C₂	1	1	yes	maximal, characteristic
4	#17326	C₂	1	1	yes	maximal, characteristic
5	#17325	C₂	1	1	yes	maximal, characteristic
6	#8270	C₂	1	1	yes	maximal, characteristic, complemented
7	#8270	C₂	1	1	yes	maximal, characteristic, complemented
8	#8270	C₂	1	1	yes	maximal, characteristic, complemented
9	#8270	C₂	1	1	yes	maximal, characteristic, complemented
10	#8269	C₂	1	1	yes	maximal, characteristic, complemented
11	#8268	C₂	1	1	yes	maximal, characteristic, complemented
12	#8267	C₂	1	1	yes	maximal, characteristic, complemented
13	#8266	C₂	1	1	yes	maximal, characteristic, complemented
14	#7868	C₂	1	1	yes	maximal, characteristic
15	#7866	C₂	1	1	yes	maximal, characteristic
16	#2920	C₂²	1	1	yes	characteristic
17	#2920	C₂²	1	1	yes	characteristic
18	C₂×#431	C₂²	1	1	yes	characteristic
19	C₂×#431	C₂²	1	1	yes	characteristic
20	C₂×#431	C₂²	1	1	yes	characteristic
21	C₂×#431	C₂²	1	1	yes	characteristic
22	C₄×#117	C₂²	1	1	yes	characteristic
23	#1768	C₄	1	2	yes	—
24	#1768	C₄	1	2	yes	—
25	#1750	C₄	1	2	yes	—
26	#1750	C₄	1	2	yes	—
27	#1744	C₂²	1	1	yes	characteristic
28	#1744	C₂²	1	1	yes	characteristic
29	C₄×#97	C₂²	1	1	yes	characteristic
30	C₄²×C₈	C₂²	1	1	yes	characteristic
31	#1574	C₄	1	2	yes	complemented
32	#1574	C₄	1	2	yes	complemented
33	#1573	C₄	1	2	yes	complemented
34	#1573	C₄	1	2	yes	complemented
35	#1572	C₄	1	2	yes	complemented
36	#1572	C₄	1	2	yes	complemented
37	#1571	C₄	1	2	yes	complemented
38	#1570	C₄	1	2	yes	complemented
39	#1564	C₂²	1	1	yes	characteristic
40	#1564	C₂²	1	1	yes	characteristic
41	#1564	C₂²	1	1	yes	characteristic
42	#1564	C₂²	1	1	yes	characteristic
43	#1564	C₂²	1	1	yes	characteristic
44	#1564	C₂²	1	1	yes	characteristic
45	#1564	C₂²	1	1	yes	characteristic
46	#1564	C₂²	1	1	yes	characteristic
47	#1454	—	2	1	no	—
48	#1454	—	2	1	no	—
49	#1453	—	2	1	no	—
50	#1453	—	2	1	no	—
51	#1452	—	2	1	no	—
52	#1452	C₂²	1	1	yes	characteristic
53	#1452	C₂²	1	1	yes	characteristic
54	#1452	C₂²	1	1	yes	characteristic
55	#1452	C₂²	1	1	yes	characteristic
56	#1451	—	2	1	no	—
57	#1450	—	2	1	no	—
58	#1450	C₂²	1	1	yes	characteristic
59	#1450	C₂²	1	1	yes	characteristic
60	#1450	C₂²	1	1	yes	characteristic
61	#1450	C₂²	1	1	yes	characteristic
62	C₈×M₁₆	—	2	1	no	—
63	#1276	C₂²	1	1	yes	characteristic
64	#1276	C₂²	1	1	yes	characteristic
65	#1276	C₂²	1	1	yes	characteristic
66	#1276	C₂²	1	1	yes	characteristic
67	#1276	C₂²	1	1	yes	characteristic
68	#1276	C₂²	1	1	yes	characteristic
69	#1276	C₂²	1	1	yes	characteristic
70	#1276	C₂²	1	1	yes	characteristic
71	C₂×#117	C₂×C₄	1	2	yes	—
72	C₂²×C₄²	C₂³	1	1	yes	characteristic
73	#432	—	2	1	no	—
74	#432	—	2	1	no	—
75	#432	C₂×C₄	1	2	yes	—
76	#432	C₂×C₄	1	2	yes	—
77	#431	—	2	1	no	—
78	#431	—	2	1	no	—
79	#431	—	2	1	no	—
80	#431	—	2	1	no	—
81	#431	—	2	1	no	—
82	#431	—	2	1	no	—
83	#431	C₂×C₄	1	2	yes	—
84	#431	C₂×C₄	1	2	yes	—
85	#431	C₂×C₄	1	1	yes	characteristic
86	#431	C₂×C₄	1	1	yes	characteristic
87	#431	C₂×C₄	1	1	yes	characteristic
88	#431	C₂×C₄	1	1	yes	characteristic
89	#431	C₂×C₄	1	1	yes	characteristic
90	#431	C₂×C₄	1	1	yes	characteristic
91	#431	C₂×C₄	1	1	yes	characteristic
92	#431	C₂×C₄	1	1	yes	characteristic
93	#431	D₄	1	1	yes	characteristic
94	#431	D₄	1	1	yes	characteristic
95	#431	D₄	1	1	yes	characteristic
96	#431	D₄	1	1	yes	characteristic
97	#431	Q₈	1	2	yes	—
98	#431	Q₈	1	2	yes	—
99	#431	C₂³	1	1	yes	characteristic
100	#431	C₂³	1	1	yes	characteristic
101	#431	C₂³	1	1	yes	characteristic
102	#431	C₂³	1	1	yes	characteristic
103	#431	C₂³	1	1	yes	characteristic
104	#431	C₂³	1	1	yes	characteristic
105	#431	C₂³	1	1	yes	characteristic
106	#431	C₂³	1	1	yes	characteristic
107	#423	C₂×C₄	1	2	yes	—
108	#423	C₂×C₄	1	2	yes	—
109	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
110	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
111	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
114	#407	—	2	1	no	—
115	#407	—	2	1	no	—
116	C₂×C₂²⋊C₈	—	2	1	no	—
117	C₂×C₂²⋊C₈	—	2	1	no	—
118	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
121	C₄×M₁₆	—	2	1	no	—
122	C₄×M₁₆	—	2	1	no	—
123	C₂×#97	C₂×C₄	1	2	yes	—
124	C₂×#97	C₂×C₄	1	2	yes	—
125	C₂×C₄×C₈	—	2	1	no	—
126	C₂×C₄×C₈	—	2	1	no	—
127	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
128	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
129	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
132	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
133	C₄×C₄⋊C₄	—	2	1	no	—
134	C₄×C₄⋊C₄	—	2	1	no	—
135	C₄×C₂²⋊C₄	—	2	1	no	—
136	C₄×C₂²⋊C₄	—	2	1	no	—
137	#376	C₂×C₄	1	2	yes	—
138	C₄³	C₂³	1	1	yes	characteristic
139	C₄³	C₂³	1	1	yes	characteristic
140	#336	C₂×C₄	1	2	yes	—
141	#336	C₂×C₄	1	2	yes	—
142	#336	C₂×C₄	1	2	yes	—
143	#336	C₂×C₄	1	2	yes	—
144	#335	C₂×C₄	1	2	yes	—
145	#335	C₂×C₄	1	2	yes	—
146	#335	C₂×C₄	1	2	yes	—
147	#335	C₂×C₄	1	2	yes	—
148	#335	C₂×C₄	1	2	yes	—
149	#335	C₂×C₄	1	2	yes	—
150	#335	C₂×C₄	1	2	yes	—
151	#335	C₂×C₄	1	2	yes	—
152	#334	C₂×C₄	1	2	yes	—
153	#334	C₂×C₄	1	2	yes	—
154	#334	C₂×C₄	1	2	yes	—
155	#334	C₂×C₄	1	2	yes	—
156	#334	C₂×C₄	1	2	yes	—
157	#334	C₂×C₄	1	2	yes	—
158	#334	C₂×C₄	1	2	yes	—
159	#334	C₂×C₄	1	2	yes	—
160	#322	—	2	1	no	—
161	#322	—	2	1	no	—
162	#322	—	2	1	no	—
163	#322	—	2	1	no	—
164	#322	—	2	1	no	—
165	#322	—	2	1	no	—
166	#322	—	2	1	no	—
167	#322	—	2	1	no	—
168	#322	—	2	1	no	—
169	#322	—	2	1	no	—
170	#322	—	2	1	no	—
171	#322	—	2	1	no	—
172	C₈²	—	2	1	no	—
173	C₈²	—	2	1	no	—
174	C₈²	—	2	1	no	—
175	C₈²	—	2	1	no	—
176	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
177	C₂³×C₄	#41	1	1	yes	characteristic
178	C₂³×C₄	#41	1	1	yes	characteristic
179	C₂×M₁₆	—	2	2	no	—
180	C₂×M₁₆	—	2	2	no	—
181	C₂²×C₈	—	2	2	no	—
182	C₂²×C₈	—	2	2	no	—
183	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₈	C₂²×C₄	1	2	yes	—
188	C₂²×C₈	C₂²×C₄	1	2	yes	—
189	#117	—	2	4	no	—
190	#117	—	4	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₂²⋊C₄	—	2	2	no	—
193	C₂×C₄²	—	2	1	no	—
194	C₂×C₄²	—	2	1	no	—
195	C₂×C₄²	—	2	1	no	—
196	C₂×C₄²	—	2	1	no	—
197	C₂×C₄²	C₂²×C₄	1	2	yes	—
198	C₂×C₄²	C₂²×C₄	1	2	yes	—
199	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
206	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
207	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
208	C₂×C₄²	#41	1	1	yes	characteristic
209	C₂×C₄²	#41	1	1	yes	characteristic
210	C₂×C₄²	C₂⁴	1	1	yes	characteristic
211	C₄⋊C₈	—	2	2	no	—
212	C₄⋊C₈	—	2	2	no	—
213	C₄⋊C₈	—	2	2	no	—
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	C₄²	1	1	yes	characteristic
216	C₄⋊C₈	C₄²	1	1	yes	characteristic
217	C₄⋊C₈	C₄²	1	1	yes	characteristic
218	C₄⋊C₈	C₄²	1	1	yes	characteristic
219	C₄⋊C₈	C₄²	1	1	yes	characteristic
220	C₄⋊C₈	C₄²	1	1	yes	characteristic
221	C₄⋊C₈	C₄²	1	1	yes	characteristic
222	C₄⋊C₈	C₄²	1	1	yes	characteristic
223	C₄⋊C₈	C₄⋊C₄	1	2	yes	—
224	C₄⋊C₈	C₄⋊C₄	1	2	yes	—
225	C₄⋊C₈	C₄⋊C₄	1	2	yes	—
226	C₄⋊C₈	C₄⋊C₄	1	2	yes	—
227	C₄⋊C₈	C₂²×C₄	1	2	yes	—
228	C₄⋊C₈	C₂²×C₄	1	2	yes	—
229	C₄⋊C₈	C₂²×C₄	1	2	yes	—
230	C₄⋊C₈	C₂²×C₄	1	2	yes	—
231	C₄⋊C₈	C₂²×C₄	1	2	yes	—
232	C₄⋊C₈	C₂²×C₄	1	2	yes	—
233	C₄⋊C₈	C₂²×C₄	1	2	yes	—
234	C₄⋊C₈	C₂²×C₄	1	2	yes	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	2	2	no	—
237	C₂²⋊C₈	—	2	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	1	no	—
240	C₂²⋊C₈	—	2	1	no	—
241	C₂²⋊C₈	—	2	1	no	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	—	2	1	no	—
246	C₂²⋊C₈	—	2	1	no	—
247	C₂²⋊C₈	C₄²	1	1	yes	characteristic
248	C₂²⋊C₈	C₄²	1	1	yes	characteristic
249	C₂²⋊C₈	C₄²	1	1	yes	characteristic
250	C₂²⋊C₈	C₄²	1	1	yes	characteristic
251	C₂²⋊C₈	C₄²	1	1	yes	characteristic
252	C₂²⋊C₈	C₄²	1	1	yes	characteristic
253	C₂²⋊C₈	C₄²	1	1	yes	characteristic
254	C₂²⋊C₈	C₄²	1	1	yes	characteristic
255	C₂²⋊C₈	C₄⋊C₄	1	2	yes	—
256	C₂²⋊C₈	C₄⋊C₄	1	2	yes	—
257	C₂²⋊C₈	C₄⋊C₄	1	2	yes	—
258	C₂²⋊C₈	C₄⋊C₄	1	2	yes	—
259	#97	—	2	2	no	—
260	#97	—	2	2	no	—
261	#97	—	2	4	no	—
262	#97	—	4	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	4	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	—	4	2	no	—
275	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
276	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
277	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
278	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
279	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
280	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
281	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
282	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
283	C₄×C₈	C₂×D₄	1	1	yes	characteristic
284	C₄×C₈	C₂×D₄	1	1	yes	characteristic
285	C₄×C₈	C₂×D₄	1	1	yes	characteristic
286	C₄×C₈	C₂×D₄	1	1	yes	characteristic
287	C₄×C₈	C₂×Q₈	1	2	yes	—
288	C₄×C₈	C₂×Q₈	1	2	yes	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂⁴	#117	1	1	yes	characteristic
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
302	C₂²×C₄	#117	1	1	yes	characteristic
303	C₂²×C₄	#117	1	1	yes	characteristic
304	C₂²×C₄	#117	1	1	yes	characteristic
305	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
310	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
311	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
312	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×#41	1	1	yes	characteristic
315	C₂²×C₄	C₂×#41	1	1	yes	characteristic
316	M₁₆	—	4	4	no	—
317	M₁₆	—	8	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	4	no	—
335	C₂×C₈	—	8	2	no	—
336	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
341	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
342	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
345	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
346	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
347	C₂×C₈	C₂×C₄⋊C₄	1	2	yes	—
348	C₄⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	4	2	no	—
356	C₄²	—	4	2	no	—
357	C₄²	C₂×C₄²	1	1	yes	characteristic
358	C₄²	C₂×C₄²	1	1	yes	characteristic
359	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
360	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
361	C₄²	C₄×D₄	1	1	yes	characteristic
362	C₄²	C₄×D₄	1	1	yes	characteristic
363	C₄²	C₄×D₄	1	1	yes	characteristic
364	C₄²	C₄×D₄	1	1	yes	characteristic
365	C₄²	C₄×Q₈	1	1	yes	characteristic
366	C₄²	C₄×Q₈	1	1	yes	characteristic
367	C₄²	C₄×Q₈	1	1	yes	characteristic
368	C₄²	C₄×Q₈	1	1	yes	characteristic
369	C₄²	#131	1	4	yes	—
370	C₄²	C₂³×C₄	1	1	yes	characteristic
371	C₄²	C₂³×C₄	1	1	yes	characteristic
372	C₄²	C₂²×D₄	1	1	yes	characteristic
373	C₄²	C₂²×Q₈	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	C₄×C₄⋊C₄	1	1	yes	characteristic
378	C₂³	C₄×C₄⋊C₄	1	1	yes	characteristic
379	C₂³	C₂×#117	1	1	yes	characteristic
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	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	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
406	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
407	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
408	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
409	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
410	C₂×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₄²	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
417	C₂×C₄	C₂×#131	1	2	yes	—
418	C₂×C₄	#568	1	2	yes	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	2	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	8	2	no	—
448	C₂²	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
449	C₂²	#2924	1	2	yes	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	4	no	—
459	C₄	—	8	2	no	—
460	C₄	C₄×#131	1	1	yes	characteristic
461	C₄	#2875	1	1	yes	characteristic
462	C₄	#2906	1	2	yes	—
463	C₄	#2955	1	2	yes	—
464	C₄	#2957	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	4	1	no	—
467	C₂	—	4	1	no	—
468	C₂	#20430	1	1	yes	characteristic
469	C₂	#20444	1	1	yes	characteristic
470	C₂	#20446	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×D₄
commutator	C₂×C₄	C₂²×C₄²
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂²	C₂×C₄×C₄⋊C₄
prime radical	C₂⁴	#117
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄² ◁ C₂×#431 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
6. #8270	C₂	semidirect
7. #8270	C₂	semidirect
8. #8270	C₂	semidirect
9. #8270	C₂	semidirect
10. #8269	C₂	semidirect
11. #8268	C₂	semidirect
12. #8267	C₂	semidirect
13. #8266	C₂	semidirect
31. #1574	C₄	semidirect
32. #1574	C₄	semidirect
33. #1573	C₄	semidirect
34. #1573	C₄	semidirect
35. #1572	C₄	semidirect
36. #1572	C₄	semidirect
37. #1571	C₄	semidirect
38. #1570	C₄	semidirect

Maximal subgroups

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

subgroup	index
#20462	2
#17806	2
#17803	2
#17326	2
#17325	2
#8270	2
#8269	2
#8268	2
#8267	2
#8266	2
#7868	2
#7866	2