Subgroups — #61263

Order 256.

912 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	#3494	C₂	1	1	yes	maximal, characteristic
3	#3350	C₂	1	2	yes	maximal, complemented
4	#3348	C₂	1	2	yes	maximal, complemented
5	#3346	C₂	1	2	yes	maximal, complemented
6	#3343	C₂	1	2	yes	maximal, complemented
7	#3340	C₂	1	2	yes	maximal, complemented
8	#3337	C₂	1	2	yes	maximal, complemented
9	#3337	C₂	1	2	yes	maximal, complemented
10	#3335	C₂	1	2	yes	maximal, complemented
11	#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	#3095	C₂	1	1	yes	maximal, characteristic, complemented
15	#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#465	C₂	1	1	yes	maximal, characteristic, complemented
20	#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#427	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×#131	C₂²	1	1	yes	characteristic
26	C₂³×C₈	C₂²	1	1	yes	characteristic
27	#556	C₂²	1	2	yes	complemented
28	#555	C₂²	1	2	yes	—
29	#554	C₂²	1	2	yes	complemented
30	#553	C₂²	1	2	yes	—
31	#553	C₂²	1	2	yes	—
32	#552	—	2	2	no	—
33	#552	C₂²	1	2	yes	complemented
34	#552	C₂²	1	2	yes	complemented
35	#551	—	2	2	no	—
36	#551	—	2	2	no	—
37	#547	C₂²	1	2	yes	—
38	#546	—	2	2	no	—
39	#544	C₂²	1	1	yes	characteristic
40	#544	C₂²	1	1	yes	characteristic
41	#542	—	2	1	no	—
42	#542	—	2	1	no	—
43	#541	—	2	1	no	—
44	#540	—	2	1	no	—
45	#536	C₂²	1	1	yes	characteristic
46	#535	C₂²	1	1	yes	characteristic
47	#533	—	2	1	no	—
48	#532	—	2	1	no	—
49	#529	—	2	1	no	—
50	#529	—	2	1	no	—
51	#525	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×#121	C₂²	1	1	yes	characteristic
54	#520	C₂²	1	1	yes	characteristic
55	#520	C₂²	1	1	yes	characteristic
56	#519	C₂²	1	1	yes	characteristic
57	#518	C₂²	1	1	yes	characteristic
58	C₂×#117	C₂²	1	1	yes	characteristic
59	C₂×#117	C₂²	1	1	yes	characteristic
60	#501	C₂²	1	2	yes	complemented
61	#501	C₂²	1	2	yes	complemented
62	#499	C₂²	1	2	yes	complemented
63	#498	C₂²	1	2	yes	complemented
64	#485	C₂²	1	2	yes	complemented
65	#485	C₂²	1	2	yes	complemented
66	#485	C₂²	1	2	yes	complemented
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	2	yes	complemented
69	#484	C₂²	1	2	yes	complemented
70	#483	C₂²	1	2	yes	complemented
71	#483	C₂²	1	2	yes	complemented
72	#482	C₂²	1	2	yes	—
73	#482	C₂²	1	2	yes	—
74	#482	C₂²	1	2	yes	complemented
75	#482	C₂²	1	2	yes	complemented
76	#481	C₂²	1	2	yes	—
77	#481	C₂²	1	2	yes	complemented
78	#480	C₂²	1	2	yes	—
79	#480	C₂²	1	2	yes	complemented
80	#479	C₂²	1	2	yes	complemented
81	#479	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#478	C₂²	1	2	yes	complemented
84	#477	C₂²	1	2	yes	complemented
85	#476	C₂²	1	2	yes	complemented
86	#475	C₂²	1	2	yes	complemented
87	#474	C₂²	1	2	yes	complemented
88	#468	C₂²	1	2	yes	complemented
89	#468	C₂²	1	2	yes	complemented
90	#465	C₂²	1	2	yes	—
91	#465	C₂²	1	2	yes	—
92	#465	C₂²	1	2	yes	—
93	#465	C₂²	1	2	yes	—
94	#465	C₂²	1	2	yes	complemented
95	#465	C₂²	1	2	yes	complemented
96	#440	C₂²	1	2	yes	complemented
97	#440	C₂²	1	2	yes	complemented
98	C₄×SD₁₆	C₂²	1	2	yes	complemented
99	C₄×SD₁₆	C₂²	1	2	yes	complemented
100	#435	C₂²	1	2	yes	complemented
101	#435	C₂²	1	2	yes	complemented
102	C₈×D₄	C₂²	1	2	yes	complemented
103	C₈×D₄	C₂²	1	2	yes	complemented
104	#428	C₂²	1	1	yes	characteristic
105	#428	C₂²	1	1	yes	characteristic
106	#428	C₂²	1	1	yes	characteristic
107	#428	C₂²	1	1	yes	characteristic
108	#428	C₂²	1	2	yes	complemented
109	#428	C₂²	1	2	yes	complemented
110	#427	C₂²	1	1	yes	characteristic
111	#427	C₂²	1	1	yes	characteristic
112	#427	C₂²	1	1	yes	characteristic
113	#427	C₂²	1	1	yes	characteristic
114	#427	C₂²	1	1	yes	characteristic, complemented
115	#427	C₂²	1	2	yes	complemented
116	#427	C₂²	1	1	yes	characteristic, complemented
117	#427	C₂²	1	1	yes	characteristic, complemented
118	#427	C₂²	1	1	yes	characteristic, complemented
119	C₂×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×#107	C₂²	1	1	yes	characteristic, complemented
121	C₂×#106	C₂²	1	1	yes	characteristic
122	C₂×#106	C₂²	1	1	yes	characteristic, complemented
123	C₂×#106	C₂²	1	2	yes	complemented
124	C₂×#106	C₂²	1	1	yes	characteristic, complemented
125	#424	C₂²	1	1	yes	characteristic
126	#419	C₂²	1	1	yes	characteristic
127	#419	C₂²	1	1	yes	characteristic
128	#418	C₂²	1	1	yes	characteristic
129	#418	C₂²	1	1	yes	characteristic
130	C₂×#103	C₂²	1	1	yes	characteristic
131	C₂×#102	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	#407	C₂²	1	1	yes	characteristic
134	#405	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈	C₂³	1	1	yes	characteristic
138	C₂²×D₄	—	2	1	no	—
139	C₂²×D₄	C₂³	1	1	yes	characteristic
140	C₂³×C₄	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆	—	2	4	no	—
142	C₂×SD₁₆	C₂³	1	2	yes	—
143	C₂×SD₁₆	C₂³	1	2	yes	—
144	#131	—	2	4	no	—
145	C₂×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×M₁₆	C₂³	1	2	yes	—
147	C₂×M₁₆	C₂³	1	1	yes	characteristic
148	C₂²×C₈	—	2	4	no	—
149	C₂²×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₈	C₂³	1	2	yes	—
155	C₂²×C₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	—	2	1	no	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	#127	—	2	1	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#125	—	2	1	no	—
169	#125	—	2	1	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	C₂³	1	2	yes	—
174	#125	C₂³	1	2	yes	—
175	#124	—	2	1	no	—
176	#124	—	2	1	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	—	2	2	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	D₄	1	2	yes	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	D₄	1	1	yes	characteristic
196	C₂²⋊Q₈	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	—	2	2	no	—
204	#121	—	2	1	no	—
205	#121	—	2	1	no	—
206	#121	D₄	1	1	yes	characteristic
207	#121	D₄	1	1	yes	characteristic
208	#121	C₂³	1	2	yes	—
209	#121	C₂³	1	2	yes	—
210	#121	C₂³	1	2	yes	—
211	#121	C₂³	1	2	yes	—
212	#120	—	2	2	no	—
213	#120	D₄	1	2	yes	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	1	no	—
217	C₄×Q₈	—	2	1	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×Q₈	C₂³	1	2	yes	—
220	C₄×Q₈	C₂³	1	2	yes	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	C₂³	1	2	yes	—
231	C₄×D₄	C₂³	1	2	yes	—
232	C₄×D₄	C₂³	1	2	yes	—
233	C₄×D₄	C₂³	1	2	yes	—
234	#117	—	2	1	no	—
235	#117	—	2	1	no	—
236	#117	—	2	1	no	—
237	#117	—	2	1	no	—
238	#117	—	2	2	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	C₂³	1	1	yes	characteristic
243	#117	C₂³	1	1	yes	characteristic
244	#117	C₂³	1	1	yes	characteristic
245	#117	C₂³	1	1	yes	characteristic
246	#117	C₂³	1	1	yes	characteristic
247	#117	C₂³	1	1	yes	characteristic
248	#117	C₂³	1	1	yes	characteristic
249	#117	C₂³	1	1	yes	characteristic
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	1	yes	characteristic
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	1	yes	characteristic
276	#107	C₂³	1	1	yes	characteristic
277	#107	C₂³	1	2	yes	—
278	#107	C₂³	1	2	yes	—
279	#107	C₂³	1	2	yes	—
280	#107	C₂³	1	2	yes	—
281	#106	C₂³	1	2	yes	—
282	#106	C₂³	1	2	yes	—
283	#106	C₂³	1	1	yes	characteristic
284	#106	C₂³	1	1	yes	characteristic
285	#106	C₂³	1	1	yes	characteristic
286	#106	C₂³	1	1	yes	characteristic
287	#106	C₂³	1	1	yes	characteristic
288	#106	C₂³	1	1	yes	characteristic
289	#106	C₂³	1	1	yes	characteristic
290	#106	C₂³	1	1	yes	characteristic
291	#106	C₂³	1	2	yes	—
292	#106	C₂³	1	2	yes	—
293	#106	C₂³	1	2	yes	—
294	#106	C₂³	1	2	yes	—
295	C₄⋊C₈	C₂³	1	2	yes	—
296	C₄⋊C₈	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	2	yes	—
301	#103	C₂³	1	2	yes	—
302	#103	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	#97	C₂³	1	2	yes	—
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	C₂⁴	C₂×D₄	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	8	4	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	8	2	no	—
335	C₂×D₄	C₂×D₄	1	2	yes	—
336	C₂×D₄	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄	C₂×D₄	1	2	yes	—
338	C₂×D₄	C₂×D₄	1	2	yes	—
339	C₂×D₄	C₂⁴	1	2	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴	1	2	yes	—
358	C₂²×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴	1	1	yes	characteristic
360	SD₁₆	—	2	4	no	—
361	SD₁₆	—	2	4	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	#41	1	4	yes	complemented
372	C₂×C₈	C₂⁴	1	2	yes	—
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	2	yes	—
375	C₂×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	2	yes	—
404	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	C₂⁴	1	2	yes	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	1	no	—
456	C₂³	—	8	1	no	—
457	C₂³	C₂²×D₄	1	1	yes	characteristic
458	C₂³	C₂²×D₄	1	2	yes	—
459	C₂³	C₂²×D₄	1	1	yes	characteristic
460	C₂³	C₂²×D₄	1	1	yes	characteristic
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	2	no	—
466	Q₈	—	8	2	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	1	no	—
505	C₂×C₄	—	8	1	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	—	8	1	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	2	yes	—
512	C₂×C₄	C₂²×D₄	1	2	yes	—
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂×#41	1	2	yes	—
516	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
517	C₂×C₄	C₂⁵	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	C₂×#41	1	2	yes	—
523	C₈	C₂×#41	1	2	yes	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	16	2	no	—
539	C₂²	#547	1	2	yes	—
540	C₂²	#577	1	2	yes	—
541	C₂²	C₂³×D₄	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	#547	1	2	yes	—
559	C₄	C₂²×#41	1	1	yes	characteristic
560	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	2	2	no	—
563	C₂	—	4	2	no	—
564	C₂	—	4	1	no	—
565	C₂	—	8	2	no	—
566	C₂	C₂×#547	1	1	yes	characteristic
567	C₂	C₂×#577	1	1	yes	characteristic
568	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #525 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3495	C₂	semidirect
3. #3350	C₂	semidirect
4. #3348	C₂	semidirect
5. #3346	C₂	semidirect
6. #3343	C₂	semidirect
7. #3340	C₂	semidirect
8. #3337	C₂	semidirect
9. #3337	C₂	semidirect
10. #3335	C₂	semidirect
11. #3163	C₂	semidirect
12. #3097	C₂	semidirect
13. #3096	C₂	semidirect
14. #3095	C₂	semidirect
15. #3094	C₂	semidirect
16. #3082	C₂	semidirect
17. #3081	C₂	semidirect
18. #3057	C₂	semidirect
19. C₂×#465	C₂	semidirect
20. #2949	C₂	semidirect
21. #2929	C₂	semidirect
22. #2912	C₂	semidirect
23. C₂×#427	C₂	semidirect
27. #556	C₂²	semidirect
29. #554	C₂²	semidirect
33. #552	C₂²	semidirect
34. #552	C₂²	semidirect
60. #501	C₂²	semidirect
61. #501	C₂²	semidirect
62. #499	C₂²	semidirect
63. #498	C₂²	semidirect
64. #485	C₂²	semidirect
65. #485	C₂²	semidirect
66. #485	C₂²	semidirect
67. #485	C₂²	semidirect
68. #484	C₂²	semidirect
69. #484	C₂²	semidirect
70. #483	C₂²	semidirect
71. #483	C₂²	semidirect
74. #482	C₂²	semidirect
75. #482	C₂²	semidirect
77. #481	C₂²	semidirect
79. #480	C₂²	semidirect
80. #479	C₂²	semidirect
81. #479	C₂²	semidirect
82. #478	C₂²	semidirect
83. #478	C₂²	semidirect
84. #477	C₂²	semidirect
85. #476	C₂²	semidirect
86. #475	C₂²	semidirect
87. #474	C₂²	semidirect
88. #468	C₂²	semidirect
89. #468	C₂²	semidirect
94. #465	C₂²	semidirect
95. #465	C₂²	semidirect
96. #440	C₂²	semidirect
97. #440	C₂²	semidirect
98. C₄×SD₁₆	C₂²	semidirect
99. C₄×SD₁₆	C₂²	semidirect
100. #435	C₂²	semidirect
101. #435	C₂²	semidirect
102. C₈×D₄	C₂²	semidirect
103. C₈×D₄	C₂²	semidirect
108. #428	C₂²	semidirect
109. #428	C₂²	semidirect
114. #427	C₂²	semidirect
115. #427	C₂²	semidirect
116. #427	C₂²	semidirect
117. #427	C₂²	semidirect
118. #427	C₂²	semidirect
119. C₂×#107	C₂²	semidirect
120. C₂×#107	C₂²	semidirect
122. C₂×#106	C₂²	semidirect
123. C₂×#106	C₂²	semidirect
124. C₂×#106	C₂²	semidirect
371. C₂×C₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3495	2
#3494	2
#3350	2
#3348	2
#3346	2
#3343	2
#3340	2
#3337	2
#3335	2
#3163	2
#3097	2
#3096	2
#3095	2
#3094	2
#3082	2
#3081	2
#3057	2
C₂×#465	2
#2949	2
#2929	2
#2912	2
C₂×#427	2