Subgroups — #61724

Order 256.

878 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	#3353	C₂	1	1	yes	maximal, characteristic, complemented
6	#3353	C₂	1	1	yes	maximal, characteristic, complemented
7	#3352	C₂	1	2	yes	maximal, complemented
8	#3351	C₂	1	2	yes	maximal, complemented
9	#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	#3329	C₂	1	1	yes	maximal, characteristic, complemented
12	#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	#3327	C₂	1	2	yes	maximal, complemented
14	#3326	C₂	1	2	yes	maximal, complemented
15	#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	#3197	C₂	1	2	yes	maximal, complemented
18	#3196	C₂	1	2	yes	maximal, complemented
19	#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3095	C₂	1	2	yes	maximal, complemented
22	#3093	C₂	1	2	yes	maximal, complemented
23	#2975	C₂	1	1	yes	maximal, characteristic, complemented
24	#556	C₂²	1	1	yes	characteristic
25	#556	C₂²	1	1	yes	characteristic
26	#555	C₂²	1	1	yes	characteristic
27	#554	—	2	1	no	—
28	#554	C₂²	1	1	yes	characteristic
29	#553	C₂²	1	2	yes	—
30	#552	—	2	1	no	—
31	#552	C₂²	1	2	yes	—
32	#552	C₂²	1	2	yes	—
33	#551	—	2	2	no	—
34	#551	—	2	2	no	—
35	D₄×Q₈	C₂²	1	1	yes	characteristic
36	#548	C₂²	1	2	yes	—
37	#547	C₂²	1	1	yes	characteristic
38	#547	C₂²	1	1	yes	characteristic
39	#547	C₂²	1	1	yes	characteristic
40	#546	—	2	1	no	—
41	#546	—	2	1	no	—
42	#542	—	2	1	no	—
43	#539	—	2	2	no	—
44	#533	C₂²	1	1	yes	characteristic
45	#533	C₂²	1	1	yes	characteristic
46	#529	—	2	2	no	—
47	#529	—	2	1	no	—
48	#529	C₂²	1	1	yes	characteristic
49	#525	C₂²	1	2	yes	—
50	#525	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
52	#520	—	2	1	no	—
53	C₄×#41	—	2	1	no	—
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×#117	C₂²	1	2	yes	—
57	#500	C₂²	1	1	yes	characteristic, complemented
58	#499	C₂²	1	2	yes	complemented
59	#498	C₂²	1	1	yes	characteristic, complemented
60	#488	C₂²	1	2	yes	complemented
61	#487	C₂²	1	1	yes	characteristic, complemented
62	#487	C₂²	1	1	yes	characteristic, complemented
63	#485	C₂²	1	2	yes	—
64	#485	C₂²	1	2	yes	—
65	#485	C₂²	1	1	yes	characteristic
66	#485	C₂²	1	2	yes	—
67	#485	C₂²	1	2	yes	—
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#485	C₂²	1	2	yes	complemented
71	#484	C₂²	1	2	yes	complemented
72	#484	C₂²	1	2	yes	complemented
73	#484	C₂²	1	2	yes	complemented
74	#483	C₂²	1	2	yes	complemented
75	#483	C₂²	1	2	yes	complemented
76	#482	C₂²	1	1	yes	characteristic
77	#482	C₂²	1	2	yes	—
78	#482	C₂²	1	2	yes	complemented
79	#482	C₂²	1	2	yes	complemented
80	#482	C₂²	1	2	yes	complemented
81	#481	C₂²	1	2	yes	complemented
82	#479	C₂²	1	2	yes	complemented
83	#479	C₂²	1	1	yes	characteristic, complemented
84	#479	C₂²	1	2	yes	complemented
85	#478	C₂²	1	1	yes	characteristic, complemented
86	#477	C₂²	1	1	yes	characteristic, complemented
87	#476	C₂²	1	1	yes	characteristic, complemented
88	#475	C₂²	1	1	yes	characteristic, complemented
89	#475	C₂²	1	1	yes	characteristic, complemented
90	#474	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#470	C₂²	1	2	yes	complemented
93	#470	C₂²	1	2	yes	complemented
94	#470	C₂²	1	2	yes	complemented
95	#469	C₂²	1	2	yes	complemented
96	#468	C₂²	1	2	yes	complemented
97	#468	C₂²	1	2	yes	complemented
98	#468	C₂²	1	2	yes	complemented
99	#468	C₂²	1	2	yes	complemented
100	#464	C₂²	1	1	yes	characteristic, complemented
101	#463	C₂²	1	1	yes	characteristic, complemented
102	#462	C₂²	1	1	yes	characteristic, complemented
103	#461	C₂²	1	1	yes	characteristic, complemented
104	#452	C₂²	1	1	yes	characteristic
105	#452	C₂²	1	2	yes	—
106	#452	C₂²	1	2	yes	complemented
107	#451	C₂²	1	2	yes	complemented
108	#449	C₂²	1	1	yes	characteristic
109	#449	C₂²	1	2	yes	complemented
110	#448	C₂²	1	2	yes	complemented
111	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆	C₂²	1	2	yes	complemented
113	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
117	#436	C₂²	1	1	yes	characteristic
118	#436	C₂²	1	1	yes	characteristic
119	#436	C₂²	1	1	yes	characteristic
120	#436	C₂²	1	1	yes	characteristic
121	#436	C₂²	1	2	yes	—
122	#436	C₂²	1	2	yes	—
123	#431	C₂²	1	1	yes	characteristic
124	#431	C₂²	1	1	yes	characteristic
125	#428	C₂²	1	2	yes	complemented
126	#428	C₂²	1	2	yes	complemented
127	#428	C₂²	1	2	yes	complemented
128	#428	C₂²	1	2	yes	complemented
129	#419	C₂²	1	2	yes	complemented
130	#419	C₂²	1	2	yes	complemented
131	#417	C₂²	1	2	yes	complemented
132	#417	C₂²	1	2	yes	complemented
133	#407	C₂²	1	2	yes	—
134	#407	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×Q₈	C₂³	1	2	yes	—
140	C₂²×D₄	D₄	1	1	yes	characteristic
141	C₂³×C₄	C₂³	1	2	yes	—
142	C₂×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆	C₂³	1	2	yes	—
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×D₈	C₂³	1	1	yes	characteristic
148	C₂×M₁₆	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂×M₁₆	C₂³	1	2	yes	—
151	C₂×M₁₆	C₂³	1	2	yes	—
152	C₄⋊Q₈	—	2	1	no	—
153	C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	1	no	—
163	#125	—	2	2	no	—
164	#125	—	2	1	no	—
165	#125	—	2	2	no	—
166	#125	—	2	1	no	—
167	#125	C₂³	1	1	yes	characteristic
168	#125	C₂³	1	2	yes	—
169	#124	—	2	1	no	—
170	#124	—	2	1	no	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	C₂³	1	1	yes	characteristic
174	#123	—	2	2	no	—
175	#123	—	2	2	no	—
176	#123	—	2	2	no	—
177	#123	—	2	2	no	—
178	#123	—	2	1	no	—
179	#123	—	2	2	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	C₂²⋊Q₈	—	2	2	no	—
184	C₂²⋊Q₈	—	2	2	no	—
185	C₂²⋊Q₈	—	2	1	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	#121	—	2	2	no	—
201	#121	—	2	1	no	—
202	#121	—	2	2	no	—
203	#121	—	2	1	no	—
204	#121	C₂³	1	1	yes	characteristic
205	#121	C₂³	1	2	yes	—
206	#121	C₂³	1	2	yes	—
207	#121	C₂³	1	2	yes	—
208	#120	—	2	2	no	—
209	#120	—	2	2	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	—	2	1	no	—
212	C₄×Q₈	—	2	1	no	—
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₄×Q₈	C₂³	1	2	yes	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	D₄	1	1	yes	characteristic
231	C₄×D₄	D₄	1	1	yes	characteristic
232	C₄×D₄	D₄	1	2	yes	—
233	C₄×D₄	C₂³	1	1	yes	characteristic
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	1	yes	characteristic
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	2	yes	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	1	no	—
242	#117	—	2	1	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	1	no	—
246	#117	—	2	1	no	—
247	#117	C₂³	1	1	yes	characteristic
248	#117	C₂³	1	2	yes	—
249	#117	C₂³	1	2	yes	—
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	D₄	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	1	yes	characteristic
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	2	yes	—
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	C₂×D₄	1	2	yes	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	4	no	—
318	#41	—	4	4	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	2	yes	—
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄	C₂×D₄	1	2	yes	—
338	C₂×D₄	C₂⁴	1	1	yes	characteristic
339	C₂×D₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	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	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄	1	2	yes	—
353	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄	1	2	yes	—
355	C₂²×C₄	C₂×D₄	1	2	yes	—
356	C₂²×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴	1	2	yes	—
358	C₂²×C₄	C₂⁴	1	2	yes	—
359	Q₁₆	—	4	1	no	—
360	Q₁₆	—	4	2	no	—
361	SD₁₆	—	4	1	no	—
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	4	1	no	—
364	D₈	—	4	1	no	—
365	M₁₆	—	4	2	no	—
366	M₁₆	—	4	2	no	—
367	M₁₆	—	4	2	no	—
368	M₁₆	—	4	2	no	—
369	C₂×C₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₈	C₂⁴	1	2	yes	—
371	C₂×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₈	C₂⁴	1	2	yes	—
374	C₂×C₈	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	C₂×D₄	1	1	yes	characteristic
443	C₄²	C₂×D₄	1	1	yes	characteristic
444	C₄²	C₂⁴	1	1	yes	characteristic
445	C₄²	C₂⁴	1	1	yes	characteristic
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	C₂²×D₄	1	1	yes	characteristic
452	C₂³	C₂²×D₄	1	2	yes	—
453	C₂³	C₂²×D₄	1	2	yes	—
454	Q₈	—	2	1	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	1	no	—
458	Q₈	—	2	1	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	8	1	no	—
463	Q₈	—	8	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	8	1	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄	1	2	yes	—
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂⁵	1	1	yes	characteristic
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	2	no	—
519	C₈	—	2	2	no	—
520	C₈	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₂³×D₄	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	#575	1	2	yes	—
555	C₄	#585	1	1	yes	characteristic
556	C₄	#585	1	1	yes	characteristic
557	C₂	—	4	2	no	—
558	C₂	—	4	2	no	—
559	C₂	—	4	1	no	—
560	C₂	—	8	1	no	—
561	C₂	—	8	1	no	—
562	C₂	#3485	1	1	yes	characteristic
563	C₂	C₂×#575	1	1	yes	characteristic
564	C₂	#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #3520	C₂	semidirect
2. #3475	C₂	semidirect
3. #3356	C₂	semidirect
4. #3354	C₂	semidirect
5. #3353	C₂	semidirect
6. #3353	C₂	semidirect
7. #3352	C₂	semidirect
8. #3351	C₂	semidirect
9. #3331	C₂	semidirect
10. #3330	C₂	semidirect
11. #3329	C₂	semidirect
12. #3328	C₂	semidirect
13. #3327	C₂	semidirect
14. #3326	C₂	semidirect
15. #3233	C₂	semidirect
16. #3231	C₂	semidirect
17. #3197	C₂	semidirect
18. #3196	C₂	semidirect
19. #3107	C₂	semidirect
20. #3102	C₂	semidirect
21. #3095	C₂	semidirect
22. #3093	C₂	semidirect
23. #2975	C₂	semidirect
57. #500	C₂²	semidirect
58. #499	C₂²	semidirect
59. #498	C₂²	semidirect
60. #488	C₂²	semidirect
61. #487	C₂²	semidirect
62. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #485	C₂²	semidirect
71. #484	C₂²	semidirect
72. #484	C₂²	semidirect
73. #484	C₂²	semidirect
74. #483	C₂²	semidirect
75. #483	C₂²	semidirect
78. #482	C₂²	semidirect
79. #482	C₂²	semidirect
80. #482	C₂²	semidirect
81. #481	C₂²	semidirect
82. #479	C₂²	semidirect
83. #479	C₂²	semidirect
84. #479	C₂²	semidirect
85. #478	C₂²	semidirect
86. #477	C₂²	semidirect
87. #476	C₂²	semidirect
88. #475	C₂²	semidirect
89. #475	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
92. #470	C₂²	semidirect
93. #470	C₂²	semidirect
94. #470	C₂²	semidirect
95. #469	C₂²	semidirect
96. #468	C₂²	semidirect
97. #468	C₂²	semidirect
98. #468	C₂²	semidirect
99. #468	C₂²	semidirect
100. #464	C₂²	semidirect
101. #463	C₂²	semidirect
102. #462	C₂²	semidirect
103. #461	C₂²	semidirect
106. #452	C₂²	semidirect
107. #451	C₂²	semidirect
109. #449	C₂²	semidirect
110. #448	C₂²	semidirect
111. C₄×Q₁₆	C₂²	semidirect
112. C₄×Q₁₆	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
125. #428	C₂²	semidirect
126. #428	C₂²	semidirect
127. #428	C₂²	semidirect
128. #428	C₂²	semidirect
129. #419	C₂²	semidirect
130. #419	C₂²	semidirect
131. #417	C₂²	semidirect
132. #417	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3520	2
#3475	2
#3356	2
#3354	2
#3353	2
#3352	2
#3351	2
#3331	2
#3330	2
#3329	2
#3328	2
#3327	2
#3326	2
#3233	2
#3231	2
#3197	2
#3196	2
#3107	2
#3102	2
#3095	2
#3093	2
#2975	2