Subgroups — #62126

Order 256.

888 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	#3481	C₂	1	1	yes	maximal, characteristic
3	#3388	C₂	1	2	yes	maximal, complemented
4	#3371	C₂	1	2	yes	maximal, complemented
5	#3350	C₂	1	2	yes	maximal, complemented
6	#3344	C₂	1	2	yes	maximal, complemented
7	#3337	C₂	1	2	yes	maximal, complemented
8	#3311	C₂	1	2	yes	maximal, complemented
9	#3310	C₂	1	2	yes	maximal, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	#3252	C₂	1	1	yes	maximal, characteristic, complemented
12	#3248	C₂	1	1	yes	maximal, characteristic, complemented
13	#3246	C₂	1	1	yes	maximal, characteristic, complemented
14	#3238	C₂	1	1	yes	maximal, characteristic, complemented
15	#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	C₂²	1	1	yes	characteristic
25	#557	—	2	1	no	—
26	#557	C₂²	1	2	yes	complemented
27	#556	—	2	1	no	—
28	#556	C₂²	1	2	yes	complemented
29	#554	C₂²	1	1	yes	characteristic
30	#554	C₂²	1	1	yes	characteristic
31	#553	—	2	1	no	—
32	#553	C₂²	1	1	yes	characteristic
33	#553	C₂²	1	1	yes	characteristic
34	#552	—	2	1	no	—
35	#552	—	2	1	no	—
36	#552	C₂²	1	2	yes	—
37	#552	C₂²	1	2	yes	complemented
38	#551	—	2	1	no	—
39	#551	—	2	1	no	—
40	#546	—	2	1	no	—
41	#546	C₂²	1	1	yes	characteristic
42	#546	C₂²	1	1	yes	characteristic
43	D₄²	C₂²	1	1	yes	characteristic
44	#541	—	2	1	no	—
45	#541	—	2	1	no	—
46	#536	—	2	1	no	—
47	#533	C₂²	1	1	yes	characteristic, complemented
48	#533	C₂²	1	1	yes	characteristic, complemented
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#533	C₂²	1	1	yes	characteristic, complemented
51	#533	C₂²	1	1	yes	characteristic, complemented
52	#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	#529	—	2	1	no	—
55	#529	C₂²	1	1	yes	characteristic
56	#529	C₂²	1	1	yes	characteristic
57	#525	—	2	1	no	—
58	#525	—	2	1	no	—
59	#519	—	2	1	no	—
60	C₄×#41	C₂²	1	1	yes	characteristic
61	C₄×#41	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄	—	2	1	no	—
63	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	2	yes	complemented
66	#501	C₂²	1	2	yes	complemented
67	#499	C₂²	1	2	yes	complemented
68	#490	C₂²	1	2	yes	—
69	#489	C₂²	1	2	yes	complemented
70	#488	C₂²	1	2	yes	complemented
71	#485	C₂²	1	2	yes	complemented
72	#485	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	2	yes	—
77	#482	C₂²	1	2	yes	complemented
78	#482	C₂²	1	2	yes	complemented
79	#480	C₂²	1	2	yes	—
80	#479	C₂²	1	2	yes	complemented
81	#479	C₂²	1	2	yes	complemented
82	#479	C₂²	1	2	yes	complemented
83	#478	C₂²	1	2	yes	—
84	#478	C₂²	1	2	yes	—
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
89	#476	C₂²	1	1	yes	characteristic
90	#476	C₂²	1	2	yes	—
91	#476	C₂²	1	1	yes	characteristic, complemented
92	#476	C₂²	1	2	yes	complemented
93	#476	C₂²	1	1	yes	characteristic, complemented
94	#476	C₂²	1	1	yes	characteristic, complemented
95	#476	C₂²	1	1	yes	characteristic, complemented
96	#475	C₂²	1	1	yes	characteristic, complemented
97	#475	C₂²	1	2	yes	complemented
98	#474	C₂²	1	1	yes	characteristic
99	#474	C₂²	1	1	yes	characteristic, complemented
100	#474	C₂²	1	1	yes	characteristic, complemented
101	#470	C₂²	1	2	yes	complemented
102	#468	C₂²	1	2	yes	—
103	#467	C₂²	1	2	yes	complemented
104	#465	C₂²	1	2	yes	—
105	#465	C₂²	1	2	yes	complemented
106	#465	C₂²	1	2	yes	complemented
107	#464	C₂²	1	2	yes	complemented
108	#464	C₂²	1	2	yes	complemented
109	#462	C₂²	1	1	yes	characteristic, complemented
110	#461	C₂²	1	1	yes	characteristic
111	#461	C₂²	1	1	yes	characteristic, complemented
112	#461	C₂²	1	1	yes	characteristic, complemented
113	#460	C₂²	1	2	yes	—
114	#452	C₂²	1	2	yes	—
115	#450	C₂²	1	2	yes	—
116	#450	C₂²	1	2	yes	—
117	#446	C₂²	1	2	yes	complemented
118	#441	C₂²	1	2	yes	complemented
119	#440	C₂²	1	2	yes	—
120	#440	C₂²	1	2	yes	—
121	#440	C₂²	1	2	yes	complemented
122	C₄×SD₁₆	C₂²	1	2	yes	—
123	C₄×SD₁₆	C₂²	1	2	yes	complemented
124	#435	C₂²	1	2	yes	—
125	#435	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	2	yes	complemented
127	#432	C₂²	1	1	yes	characteristic, complemented
128	#432	C₂²	1	1	yes	characteristic, complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#428	C₂²	1	2	yes	complemented
131	#427	C₂²	1	2	yes	complemented
132	C₂×#106	C₂²	1	2	yes	complemented
133	#423	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	#418	C₂²	1	2	yes	—
137	#416	C₂²	1	2	yes	—
138	C₂×#102	C₂²	1	2	yes	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	D₄	1	1	yes	characteristic
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	C₂³	1	1	yes	characteristic
145	C₂²×D₄	C₂³	1	1	yes	characteristic
146	C₂³×C₄	—	2	1	no	—
147	C₂³×C₄	—	2	1	no	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	2	yes	—
153	C₂²×C₈	C₂³	1	2	yes	—
154	C₂²×C₈	C₂³	1	2	yes	—
155	C₄⋊Q₈	—	2	2	no	—
156	C₄⋊Q₈	—	2	1	no	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	#127	C₂³	1	1	yes	characteristic
165	#126	—	2	1	no	—
166	#126	—	2	1	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	1	no	—
172	#126	—	2	1	no	—
173	#125	—	2	1	no	—
174	#125	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	2	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	—	2	1	no	—
181	#125	C₂³	1	1	yes	characteristic
182	#125	C₂³	1	1	yes	characteristic
183	#125	C₂³	1	2	yes	—
184	#125	C₂³	1	2	yes	—
185	#124	—	2	1	no	—
186	#124	—	2	2	no	—
187	#124	—	2	1	no	—
188	#124	C₂³	1	1	yes	characteristic
189	#124	C₂³	1	1	yes	characteristic
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	1	no	—
193	#123	—	2	1	no	—
194	#123	—	2	1	no	—
195	#123	—	2	1	no	—
196	#123	—	2	1	no	—
197	#123	—	2	1	no	—
198	#123	—	2	1	no	—
199	#123	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	1	no	—
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂²⋊Q₈	C₂³	1	2	yes	—
217	#121	—	2	1	no	—
218	#121	—	2	1	no	—
219	#121	—	2	1	no	—
220	#121	—	2	1	no	—
221	#121	—	2	1	no	—
222	#121	—	2	1	no	—
223	#121	C₂³	1	1	yes	characteristic
224	#121	C₂³	1	1	yes	characteristic
225	#121	C₂³	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#120	—	2	1	no	—
228	#120	—	2	1	no	—
229	#120	—	2	1	no	—
230	#120	—	2	1	no	—
231	C₄×Q₈	—	2	2	no	—
232	C₄×Q₈	—	2	2	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	D₄	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₄×Q₈	C₂³	1	2	yes	—
244	C₄×Q₈	C₂³	1	2	yes	—
245	C₄×Q₈	C₂³	1	2	yes	—
246	C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	D₄	1	1	yes	characteristic
261	C₄×D₄	D₄	1	1	yes	characteristic
262	C₄×D₄	D₄	1	1	yes	characteristic
263	C₄×D₄	C₂³	1	1	yes	characteristic
264	C₄×D₄	C₂³	1	1	yes	characteristic
265	C₄×D₄	C₂³	1	1	yes	characteristic
266	C₄×D₄	C₂³	1	1	yes	characteristic
267	C₄×D₄	C₂³	1	1	yes	characteristic
268	C₄×D₄	C₂³	1	1	yes	characteristic
269	C₄×D₄	C₂³	1	1	yes	characteristic
270	C₄×D₄	C₂³	1	1	yes	characteristic
271	C₄×D₄	C₂³	1	1	yes	characteristic
272	C₄×D₄	C₂³	1	1	yes	characteristic
273	C₄×D₄	C₂³	1	1	yes	characteristic
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	1	no	—
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	#117	D₄	1	1	yes	characteristic
283	#117	D₄	1	1	yes	characteristic
284	#117	D₄	1	1	yes	characteristic
285	#117	C₂³	1	1	yes	characteristic
286	#117	C₂³	1	2	yes	—
287	#117	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³	1	1	yes	characteristic
299	C₂×C₄²	C₂³	1	1	yes	characteristic
300	C₂×C₄²	C₂³	1	1	yes	characteristic
301	#107	C₂³	1	2	yes	—
302	#107	C₂³	1	2	yes	—
303	#107	C₂³	1	2	yes	—
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#106	C₂³	1	2	yes	—
307	#106	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	#106	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	#106	C₂³	1	2	yes	—
313	C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₄⋊C₈	C₂³	1	1	yes	characteristic
315	C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₄⋊C₈	C₂³	1	2	yes	—
317	C₄⋊C₈	C₂³	1	2	yes	—
318	C₄⋊C₈	C₂³	1	2	yes	—
319	C₄⋊C₈	C₂³	1	1	yes	characteristic
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#103	C₂³	1	2	yes	—
323	#103	C₂³	1	2	yes	—
324	#103	C₂³	1	2	yes	—
325	#103	C₂³	1	2	yes	—
326	#103	C₂³	1	2	yes	—
327	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	#102	C₂³	1	2	yes	—
333	#102	C₂³	1	2	yes	—
334	#102	C₂³	1	2	yes	—
335	#102	C₂³	1	2	yes	—
336	C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂²⋊C₈	C₂³	1	2	yes	—
338	C₂²⋊C₈	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	#97	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	#41	—	2	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	1	no	—
347	#41	—	8	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈	C₂⁴	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄	C₂⁴	1	1	yes	characteristic
375	C₂×D₄	C₂⁴	1	1	yes	characteristic
376	C₂×D₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	8	2	no	—
390	C₂²×C₄	—	8	2	no	—
391	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴	1	1	yes	characteristic
400	Q₁₆	—	4	2	no	—
401	SD₁₆	—	2	4	no	—
402	SD₁₆	—	4	2	no	—
403	SD₁₆	—	4	2	no	—
404	M₁₆	—	4	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂⁴	1	2	yes	—
408	C₂×C₈	C₂⁴	1	2	yes	—
409	C₂×C₈	C₂⁴	1	2	yes	—
410	C₂×C₈	C₂⁴	1	2	yes	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₄⋊C₄	C₂⁴	1	2	yes	—
447	C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	C₂×D₄	1	1	yes	characteristic
491	C₄²	C₂×D₄	1	1	yes	characteristic
492	C₄²	C₂×D₄	1	1	yes	characteristic
493	C₄²	C₂×D₄	1	1	yes	characteristic
494	C₄²	C₂×D₄	1	1	yes	characteristic
495	C₄²	C₂×D₄	1	1	yes	characteristic
496	C₄²	C₂⁴	1	1	yes	characteristic
497	C₄²	C₂⁴	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₄²	C₂⁴	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	8	1	no	—
508	C₂³	—	8	1	no	—
509	C₂³	C₂²×D₄	1	1	yes	characteristic
510	C₂³	C₂²×D₄	1	1	yes	characteristic
511	C₂³	C₂²×D₄	1	1	yes	characteristic
512	Q₈	—	2	2	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	8	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	1	no	—
538	D₄	—	8	1	no	—
539	D₄	2₋¹⁺⁴	1	2	yes	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	8	1	no	—
568	C₂×C₄	—	8	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄	C₂⁵	1	1	yes	characteristic
585	C₈	—	2	2	no	—
586	C₈	—	2	2	no	—
587	C₈	—	2	2	no	—
588	C₈	—	2	2	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	8	4	no	—
607	C₂²	—	8	4	no	—
608	C₂²	#575	1	2	yes	—
609	C₂²	C₂³×D₄	1	1	yes	characteristic
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	2	no	—
629	C₄	#577	1	2	yes	—
630	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
631	C₄	#585	1	1	yes	characteristic
632	C₂	—	2	2	no	—
633	C₂	—	4	1	no	—
634	C₂	—	4	1	no	—
635	C₂	—	4	2	no	—
636	C₂	—	8	1	no	—
637	C₂	—	8	1	no	—
638	C₂	#3489	1	1	yes	characteristic
639	C₂	C₂×#575	1	1	yes	characteristic
640	C₂	C₂×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3481	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3509	C₂	semidirect
3. #3388	C₂	semidirect
4. #3371	C₂	semidirect
5. #3350	C₂	semidirect
6. #3344	C₂	semidirect
7. #3337	C₂	semidirect
8. #3311	C₂	semidirect
9. #3310	C₂	semidirect
10. #3296	C₂	semidirect
11. #3252	C₂	semidirect
12. #3248	C₂	semidirect
13. #3246	C₂	semidirect
14. #3238	C₂	semidirect
15. #3235	C₂	semidirect
16. #3233	C₂	semidirect
17. #3116	C₂	semidirect
18. #3110	C₂	semidirect
19. #3101	C₂	semidirect
20. #3077	C₂	semidirect
21. #3076	C₂	semidirect
22. C₂×#476	C₂	semidirect
23. #2990	C₂	semidirect
26. #557	C₂²	semidirect
28. #556	C₂²	semidirect
37. #552	C₂²	semidirect
47. #533	C₂²	semidirect
48. #533	C₂²	semidirect
49. #533	C₂²	semidirect
50. #533	C₂²	semidirect
51. #533	C₂²	semidirect
53. C₂×C₄⋊Q₈	C₂²	semidirect
65. #501	C₂²	semidirect
66. #501	C₂²	semidirect
67. #499	C₂²	semidirect
69. #489	C₂²	semidirect
70. #488	C₂²	semidirect
71. #485	C₂²	semidirect
72. #485	C₂²	semidirect
73. #484	C₂²	semidirect
74. #483	C₂²	semidirect
75. #483	C₂²	semidirect
77. #482	C₂²	semidirect
78. #482	C₂²	semidirect
80. #479	C₂²	semidirect
81. #479	C₂²	semidirect
82. #479	C₂²	semidirect
85. #478	C₂²	semidirect
86. #477	C₂²	semidirect
87. #477	C₂²	semidirect
91. #476	C₂²	semidirect
92. #476	C₂²	semidirect
93. #476	C₂²	semidirect
94. #476	C₂²	semidirect
95. #476	C₂²	semidirect
96. #475	C₂²	semidirect
97. #475	C₂²	semidirect
99. #474	C₂²	semidirect
100. #474	C₂²	semidirect
101. #470	C₂²	semidirect
103. #467	C₂²	semidirect
105. #465	C₂²	semidirect
106. #465	C₂²	semidirect
107. #464	C₂²	semidirect
108. #464	C₂²	semidirect
109. #462	C₂²	semidirect
111. #461	C₂²	semidirect
112. #461	C₂²	semidirect
117. #446	C₂²	semidirect
118. #441	C₂²	semidirect
121. #440	C₂²	semidirect
123. C₄×SD₁₆	C₂²	semidirect
125. #435	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. #432	C₂²	semidirect
128. #432	C₂²	semidirect
129. #431	C₂²	semidirect
130. #428	C₂²	semidirect
131. #427	C₂²	semidirect
132. C₂×#106	C₂²	semidirect
133. #423	C₂²	semidirect
134. C₂×C₄⋊C₈	C₂²	semidirect
135. C₂×C₄⋊C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3509	2
#3481	2
#3388	2
#3371	2
#3350	2
#3344	2
#3337	2
#3311	2
#3310	2
#3296	2
#3252	2
#3248	2
#3246	2
#3238	2
#3235	2
#3233	2
#3116	2
#3110	2
#3101	2
#3077	2
#3076	2
C₂×#476	2
#2990	2