Subgroups — #61702

Order 256.

922 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	#3341	C₂	1	1	yes	maximal, characteristic, complemented
4	#3340	C₂	1	1	yes	maximal, characteristic, complemented
5	#3339	C₂	1	2	yes	maximal, complemented
6	#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	#3337	C₂	1	2	yes	maximal, complemented
8	#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	#3297	C₂	1	2	yes	maximal, complemented
12	#3296	C₂	1	2	yes	maximal, complemented
13	#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	#3191	C₂	1	2	yes	maximal, complemented
18	#3188	C₂	1	2	yes	maximal, complemented
19	#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3091	C₂	1	2	yes	maximal, complemented
22	C₂×#482	C₂	1	2	yes	maximal, complemented
23	#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	#556	C₂²	1	1	yes	characteristic, complemented
25	#555	C₂²	1	1	yes	characteristic
26	#555	C₂²	1	1	yes	characteristic, complemented
27	#554	C₂²	1	1	yes	characteristic
28	#554	C₂²	1	1	yes	characteristic
29	#553	—	2	1	no	—
30	#553	C₂²	1	2	yes	—
31	#553	C₂²	1	2	yes	complemented
32	#552	—	2	1	no	—
33	#552	C₂²	1	2	yes	complemented
34	#551	—	2	2	no	—
35	#550	C₂²	1	1	yes	characteristic
36	#547	C₂²	1	1	yes	characteristic
37	#546	—	2	1	no	—
38	#546	—	2	2	no	—
39	#546	C₂²	1	2	yes	—
40	D₄²	—	2	1	no	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#540	—	2	1	no	—
43	#538	—	2	2	no	—
44	#533	C₂²	1	1	yes	characteristic, complemented
45	#532	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	complemented
51	C₂×#121	C₂²	1	2	yes	—
52	#518	—	2	1	no	—
53	C₄×#41	—	2	1	no	—
54	C₄×#41	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×#117	C₂²	1	2	yes	complemented
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	#486	C₂²	1	1	yes	characteristic, complemented
62	#486	C₂²	1	1	yes	characteristic, complemented
63	#485	C₂²	1	2	yes	complemented
64	#485	C₂²	1	1	yes	characteristic, complemented
65	#485	C₂²	1	2	yes	complemented
66	#484	C₂²	1	2	yes	complemented
67	#484	C₂²	1	2	yes	complemented
68	#483	C₂²	1	2	yes	complemented
69	#482	C₂²	1	1	yes	characteristic
70	#482	C₂²	1	2	yes	—
71	#482	C₂²	1	2	yes	complemented
72	#482	C₂²	1	2	yes	complemented
73	#482	C₂²	1	2	yes	complemented
74	#482	C₂²	1	2	yes	complemented
75	#482	C₂²	1	2	yes	complemented
76	#482	C₂²	1	2	yes	complemented
77	#482	C₂²	1	2	yes	complemented
78	#482	C₂²	1	2	yes	complemented
79	#481	C₂²	1	2	yes	complemented
80	#481	C₂²	1	2	yes	complemented
81	#480	C₂²	1	2	yes	complemented
82	#479	C₂²	1	1	yes	characteristic, complemented
83	#478	C₂²	1	2	yes	complemented
84	#478	C₂²	1	1	yes	characteristic, complemented
85	#478	C₂²	1	2	yes	complemented
86	#477	C₂²	1	1	yes	characteristic, complemented
87	#477	C₂²	1	1	yes	characteristic, complemented
88	#476	C₂²	1	1	yes	characteristic, complemented
89	#476	C₂²	1	1	yes	characteristic, complemented
90	#475	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#467	C₂²	1	2	yes	complemented
93	#466	C₂²	1	2	yes	complemented
94	#466	C₂²	1	2	yes	complemented
95	#466	C₂²	1	2	yes	complemented
96	#465	C₂²	1	2	yes	complemented
97	#465	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#464	C₂²	1	1	yes	characteristic, complemented
101	#463	C₂²	1	1	yes	characteristic, complemented
102	#460	C₂²	1	1	yes	characteristic, complemented
103	#459	C₂²	1	1	yes	characteristic, complemented
104	#452	C₂²	1	1	yes	characteristic, complemented
105	#452	C₂²	1	2	yes	complemented
106	#450	C₂²	1	2	yes	complemented
107	#449	C₂²	1	1	yes	characteristic
108	#449	C₂²	1	2	yes	complemented
109	#449	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	complemented
111	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈	C₂²	1	2	yes	complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
117	C₈×D₄	C₂²	1	1	yes	characteristic
118	C₈×D₄	C₂²	1	1	yes	characteristic
119	C₈×D₄	C₂²	1	2	yes	complemented
120	C₈×D₄	C₂²	1	2	yes	complemented
121	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
123	#431	C₂²	1	1	yes	characteristic, complemented
124	#431	C₂²	1	1	yes	characteristic, complemented
125	#427	C₂²	1	2	yes	complemented
126	#427	C₂²	1	2	yes	complemented
127	C₂×#107	C₂²	1	2	yes	complemented
128	C₂×#106	C₂²	1	2	yes	complemented
129	#416	C₂²	1	2	yes	complemented
130	#416	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
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×D₄	—	2	2	no	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	D₄	1	1	yes	characteristic
142	C₂²×D₄	C₂³	1	2	yes	—
143	C₂³×C₄	C₂³	1	2	yes	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×D₈	C₂³	1	1	yes	characteristic
149	C₂×D₈	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	2	yes	—
152	C₂²×C₈	C₂³	1	2	yes	—
153	C₂²×C₈	C₂³	1	2	yes	—
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	#127	—	2	1	no	—
158	#127	C₂³	1	1	yes	characteristic
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	1	no	—
164	#125	—	2	2	no	—
165	#125	—	2	1	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	2	no	—
171	#124	—	2	2	no	—
172	#124	—	2	1	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	1	no	—
178	#123	—	2	2	no	—
179	#123	—	2	2	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	C₂²⋊Q₈	—	2	1	no	—
183	C₂²⋊Q₈	—	2	1	no	—
184	C₂²⋊Q₈	—	2	1	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
188	C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂²⋊Q₈	C₂³	1	2	yes	—
191	#121	—	2	2	no	—
192	#121	—	2	1	no	—
193	#121	—	2	2	no	—
194	#121	—	2	1	no	—
195	#121	—	2	2	no	—
196	#121	—	2	2	no	—
197	#121	—	2	1	no	—
198	#121	—	2	1	no	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	C₂³	1	1	yes	characteristic
202	#121	C₂³	1	2	yes	—
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	2	yes	—
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	#120	—	2	2	no	—
211	#120	—	2	2	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×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	2	no	—
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	—	2	1	no	—
231	C₄×D₄	D₄	1	1	yes	characteristic
232	C₄×D₄	D₄	1	2	yes	—
233	C₄×D₄	D₄	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	2	yes	—
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	2	yes	—
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	1	no	—
244	#117	—	2	1	no	—
245	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	2	1	no	—
248	#117	C₂³	1	1	yes	characteristic
249	#117	C₂³	1	2	yes	—
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
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	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#106	C₂³	1	1	yes	characteristic
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
283	#103	C₂³	1	1	yes	characteristic
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#102	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	1	yes	characteristic
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
313	C₂⁴	C₂×D₄	1	2	yes	—
314	#41	—	4	1	no	—
315	#41	—	4	1	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	4	no	—
319	#41	—	8	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	8	4	no	—
342	C₂×D₄	C₂×D₄	1	2	yes	—
343	C₂×D₄	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄	C₂⁴	1	1	yes	characteristic
346	C₂×D₄	C₂⁴	1	2	yes	—
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄	1	2	yes	—
361	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄	1	2	yes	—
363	C₂²×C₄	C₂×D₄	1	2	yes	—
364	C₂²×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴	1	2	yes	—
366	C₂²×C₄	C₂⁴	1	2	yes	—
367	Q₁₆	—	4	1	no	—
368	SD₁₆	—	4	1	no	—
369	SD₁₆	—	4	1	no	—
370	SD₁₆	—	4	2	no	—
371	D₈	—	4	2	no	—
372	D₈	—	4	1	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	4	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₈	C₂⁴	1	2	yes	—
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	2	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂×D₄	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	C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄	—	2	1	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	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	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	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	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	C₄²	—	2	1	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	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	C₂×D₄	1	1	yes	characteristic
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂⁴	1	1	yes	characteristic
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₂³	—	2	4	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	C₂²×D₄	1	2	yes	—
458	C₂³	C₂²×D₄	1	1	yes	characteristic
459	C₂³	C₂²×D₄	1	2	yes	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	1	no	—
466	Q₈	—	8	1	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	4	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	1	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	2	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	#135	1	4	yes	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄	1	2	yes	—
519	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	2	yes	—
523	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂⁵	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	2	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	8	4	no	—
549	C₂²	—	16	4	no	—
550	C₂²	C₂×#135	1	4	yes	—
551	C₂²	C₂³×D₄	1	1	yes	characteristic
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	C₂×#135	1	2	yes	—
568	C₄	#585	1	1	yes	characteristic
569	C₄	#585	1	1	yes	characteristic
570	C₂	—	2	4	no	—
571	C₂	—	4	2	no	—
572	C₂	—	4	1	no	—
573	C₂	—	8	1	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	1	no	—
576	C₂	#3485	1	1	yes	characteristic
577	C₂	C₂²×#135	1	1	yes	characteristic
578	C₂	#3585	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. #3519	C₂	semidirect
2. #3475	C₂	semidirect
3. #3341	C₂	semidirect
4. #3340	C₂	semidirect
5. #3339	C₂	semidirect
6. #3338	C₂	semidirect
7. #3337	C₂	semidirect
8. #3335	C₂	semidirect
9. #3305	C₂	semidirect
10. #3304	C₂	semidirect
11. #3297	C₂	semidirect
12. #3296	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3233	C₂	semidirect
16. #3228	C₂	semidirect
17. #3191	C₂	semidirect
18. #3188	C₂	semidirect
19. #3106	C₂	semidirect
20. #3102	C₂	semidirect
21. #3091	C₂	semidirect
22. C₂×#482	C₂	semidirect
23. #2972	C₂	semidirect
24. #556	C₂²	semidirect
26. #555	C₂²	semidirect
31. #553	C₂²	semidirect
33. #552	C₂²	semidirect
44. #533	C₂²	semidirect
50. #525	C₂²	semidirect
54. C₄×#41	C₂²	semidirect
56. C₂×#117	C₂²	semidirect
57. #500	C₂²	semidirect
58. #499	C₂²	semidirect
59. #498	C₂²	semidirect
60. #488	C₂²	semidirect
61. #486	C₂²	semidirect
62. #486	C₂²	semidirect
63. #485	C₂²	semidirect
64. #485	C₂²	semidirect
65. #485	C₂²	semidirect
66. #484	C₂²	semidirect
67. #484	C₂²	semidirect
68. #483	C₂²	semidirect
71. #482	C₂²	semidirect
72. #482	C₂²	semidirect
73. #482	C₂²	semidirect
74. #482	C₂²	semidirect
75. #482	C₂²	semidirect
76. #482	C₂²	semidirect
77. #482	C₂²	semidirect
78. #482	C₂²	semidirect
79. #481	C₂²	semidirect
80. #481	C₂²	semidirect
81. #480	C₂²	semidirect
82. #479	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #478	C₂²	semidirect
86. #477	C₂²	semidirect
87. #477	C₂²	semidirect
88. #476	C₂²	semidirect
89. #476	C₂²	semidirect
90. #475	C₂²	semidirect
91. #474	C₂²	semidirect
92. #467	C₂²	semidirect
93. #466	C₂²	semidirect
94. #466	C₂²	semidirect
95. #466	C₂²	semidirect
96. #465	C₂²	semidirect
97. #465	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #464	C₂²	semidirect
101. #463	C₂²	semidirect
102. #460	C₂²	semidirect
103. #459	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #450	C₂²	semidirect
108. #449	C₂²	semidirect
109. #449	C₂²	semidirect
110. #447	C₂²	semidirect
111. C₄×Q₁₆	C₂²	semidirect
112. C₄×SD₁₆	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
119. C₈×D₄	C₂²	semidirect
120. C₈×D₄	C₂²	semidirect
121. C₈×D₄	C₂²	semidirect
122. C₈×D₄	C₂²	semidirect
123. #431	C₂²	semidirect
124. #431	C₂²	semidirect
125. #427	C₂²	semidirect
126. #427	C₂²	semidirect
127. C₂×#107	C₂²	semidirect
128. C₂×#106	C₂²	semidirect
129. #416	C₂²	semidirect
130. #416	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. C₂×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₂²⋊C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3519	2
#3475	2
#3341	2
#3340	2
#3339	2
#3338	2
#3337	2
#3335	2
#3305	2
#3304	2
#3297	2
#3296	2
#3295	2
#3294	2
#3233	2
#3228	2
#3191	2
#3188	2
#3106	2
#3102	2
#3091	2
C₂×#482	2
#2972	2