Subgroups — #60994

Order 256.

891 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	#3247	C₂	1	1	yes	maximal, characteristic, complemented
6	#3246	C₂	1	1	yes	maximal, characteristic, complemented
7	#3241	C₂	1	2	yes	maximal, complemented
8	#3237	C₂	1	1	yes	maximal, characteristic, complemented
9	#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	#3221	C₂	1	2	yes	maximal, complemented
11	#3217	C₂	1	1	yes	maximal, characteristic, complemented
12	#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	#3200	C₂	1	2	yes	maximal, complemented
14	#3198	C₂	1	2	yes	maximal, complemented
15	#3179	C₂	1	2	yes	maximal, complemented
16	#3174	C₂	1	2	yes	maximal, complemented
17	#3123	C₂	1	2	yes	maximal, complemented
18	#3118	C₂	1	2	yes	maximal, complemented
19	#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	—	2	1	no	—
25	#559	—	2	1	no	—
26	#550	—	2	1	no	—
27	#550	—	2	1	no	—
28	#546	—	2	1	no	—
29	#546	—	2	1	no	—
30	#546	—	2	1	no	—
31	#546	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic, complemented
33	#542	—	2	1	no	—
34	#542	C₂²	1	1	yes	characteristic
35	#542	C₂²	1	1	yes	characteristic, complemented
36	#541	—	2	1	no	—
37	#541	C₂²	1	1	yes	characteristic
38	#541	C₂²	1	1	yes	characteristic, complemented
39	#540	C₂²	1	2	yes	—
40	#540	C₂²	1	2	yes	—
41	#539	—	2	1	no	—
42	#539	—	2	1	no	—
43	#537	C₂²	1	1	yes	characteristic
44	#536	C₂²	1	1	yes	characteristic
45	#536	C₂²	1	1	yes	characteristic, complemented
46	#535	C₂²	1	2	yes	—
47	#533	—	2	1	no	—
48	#533	C₂²	1	1	yes	characteristic
49	#533	C₂²	1	1	yes	characteristic
50	#533	C₂²	1	1	yes	characteristic, complemented
51	#532	C₂²	1	1	yes	characteristic
52	#532	C₂²	1	1	yes	characteristic
53	#532	C₂²	1	1	yes	characteristic
54	#532	C₂²	1	1	yes	characteristic
55	C₂×#127	C₂²	1	1	yes	characteristic
56	#529	—	2	1	no	—
57	#529	—	2	1	no	—
58	#529	—	2	1	no	—
59	#529	C₂²	1	1	yes	characteristic
60	#529	C₂²	1	1	yes	characteristic, complemented
61	#518	C₂²	1	2	yes	—
62	C₄×#41	C₂²	1	1	yes	characteristic
63	C₄×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
65	#501	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#496	C₂²	1	2	yes	—
68	#492	C₂²	1	2	yes	—
69	#491	C₂²	1	2	yes	complemented
70	#490	C₂²	1	2	yes	—
71	#488	C₂²	1	2	yes	complemented
72	#486	C₂²	1	2	yes	—
73	#485	C₂²	1	2	yes	—
74	#485	C₂²	1	2	yes	—
75	#485	C₂²	1	2	yes	—
76	#482	C₂²	1	2	yes	—
77	#482	C₂²	1	2	yes	complemented
78	#482	C₂²	1	2	yes	complemented
79	#481	C₂²	1	2	yes	complemented
80	#480	C₂²	1	2	yes	complemented
81	#478	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#477	C₂²	1	1	yes	characteristic, complemented
84	#477	C₂²	1	1	yes	characteristic, complemented
85	#477	C₂²	1	1	yes	characteristic, complemented
86	#476	C₂²	1	1	yes	characteristic, complemented
87	#476	C₂²	1	2	yes	complemented
88	#475	C₂²	1	1	yes	characteristic, complemented
89	#475	C₂²	1	1	yes	characteristic, complemented
90	#475	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#474	C₂²	1	2	yes	complemented
93	#469	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	complemented
95	#468	C₂²	1	2	yes	complemented
96	#468	C₂²	1	2	yes	complemented
97	#466	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#465	C₂²	1	2	yes	complemented
101	#463	C₂²	1	2	yes	complemented
102	#463	C₂²	1	2	yes	complemented
103	#461	C₂²	1	2	yes	complemented
104	#461	C₂²	1	2	yes	complemented
105	#460	C₂²	1	1	yes	characteristic
106	#460	C₂²	1	1	yes	characteristic
107	#460	C₂²	1	1	yes	characteristic
108	#460	C₂²	1	1	yes	characteristic
109	#460	C₂²	1	1	yes	characteristic
110	#460	C₂²	1	1	yes	characteristic
111	#459	C₂²	1	1	yes	characteristic
112	#459	C₂²	1	1	yes	characteristic
113	#450	C₂²	1	2	yes	—
114	#450	C₂²	1	2	yes	—
115	#450	C₂²	1	2	yes	—
116	#449	C₂²	1	2	yes	complemented
117	#449	C₂²	1	2	yes	complemented
118	#448	C₂²	1	2	yes	complemented
119	#448	C₂²	1	2	yes	complemented
120	#447	C₂²	1	2	yes	—
121	#442	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	#440	C₂²	1	2	yes	complemented
124	#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆	C₂²	1	2	yes	complemented
126	C₄×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×SD₁₆	C₂²	1	2	yes	complemented
128	C₄×D₈	C₂²	1	2	yes	complemented
129	#433	C₂²	1	2	yes	—
130	#433	C₂²	1	2	yes	complemented
131	#432	C₂²	1	1	yes	characteristic
132	#432	C₂²	1	1	yes	characteristic, complemented
133	#431	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic, complemented
135	#423	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
137	#408	C₂²	1	2	yes	—
138	#405	C₂²	1	2	yes	complemented
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	2	1	no	—
142	C₂×#41	—	2	1	no	—
143	C₂×#41	C₂³	1	1	yes	characteristic
144	C₂×#41	C₂³	1	1	yes	characteristic
145	C₂²×Q₈	C₂³	1	1	yes	characteristic
146	C₂²×D₄	—	2	1	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	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×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₈	C₂³	1	2	yes	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	#127	—	2	2	no	—
168	#127	—	2	1	no	—
169	#127	—	2	1	no	—
170	#127	C₂³	1	1	yes	characteristic
171	#127	C₂³	1	1	yes	characteristic
172	#127	C₂³	1	2	yes	—
173	#126	—	2	1	no	—
174	#126	—	2	1	no	—
175	#126	—	2	1	no	—
176	#126	—	2	1	no	—
177	#126	—	2	1	no	—
178	#126	—	2	1	no	—
179	#126	—	2	1	no	—
180	#126	—	2	1	no	—
181	#125	—	2	1	no	—
182	#125	—	2	1	no	—
183	#125	—	2	1	no	—
184	#125	—	2	1	no	—
185	#125	—	2	1	no	—
186	#125	—	2	1	no	—
187	#125	—	2	1	no	—
188	#125	C₂³	1	1	yes	characteristic
189	#125	C₂³	1	1	yes	characteristic
190	#125	C₂³	1	2	yes	—
191	#124	—	2	2	no	—
192	#124	—	2	1	no	—
193	#124	—	2	1	no	—
194	#124	—	2	1	no	—
195	#124	—	2	1	no	—
196	#124	—	2	1	no	—
197	#124	—	2	1	no	—
198	#124	—	2	1	no	—
199	#124	C₂³	1	1	yes	characteristic
200	#124	C₂³	1	1	yes	characteristic
201	#123	—	2	1	no	—
202	#123	—	2	1	no	—
203	#123	—	2	1	no	—
204	#123	—	2	1	no	—
205	#123	—	2	2	no	—
206	#123	—	2	2	no	—
207	#123	—	2	2	no	—
208	#123	—	2	2	no	—
209	#123	—	2	1	no	—
210	#123	—	2	1	no	—
211	#123	—	2	1	no	—
212	#123	—	2	1	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	—	2	1	no	—
218	C₂²⋊Q₈	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	C₂²⋊Q₈	—	2	1	no	—
221	C₂²⋊Q₈	—	2	1	no	—
222	C₂²⋊Q₈	—	2	1	no	—
223	C₂²⋊Q₈	—	2	1	no	—
224	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	—	2	1	no	—
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	—	2	1	no	—
236	#121	—	2	1	no	—
237	#121	—	2	2	no	—
238	#121	—	2	2	no	—
239	#121	—	2	2	no	—
240	#121	—	2	2	no	—
241	#121	C₂³	1	1	yes	characteristic
242	#121	C₂³	1	1	yes	characteristic
243	#121	C₂³	1	2	yes	—
244	#121	C₂³	1	2	yes	—
245	#121	C₂³	1	2	yes	—
246	#121	C₂³	1	2	yes	—
247	#120	—	2	2	no	—
248	#120	—	2	2	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×Q₈	D₄	1	1	yes	characteristic
256	C₄×Q₈	D₄	1	1	yes	characteristic
257	C₄×Q₈	C₂³	1	1	yes	characteristic
258	C₄×Q₈	C₂³	1	1	yes	characteristic
259	C₄×Q₈	C₂³	1	1	yes	characteristic
260	C₄×Q₈	C₂³	1	1	yes	characteristic
261	C₄×Q₈	C₂³	1	1	yes	characteristic
262	C₄×Q₈	C₂³	1	1	yes	characteristic
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	D₄	1	1	yes	characteristic
274	C₄×D₄	D₄	1	1	yes	characteristic
275	C₄×D₄	D₄	1	1	yes	characteristic
276	C₄×D₄	D₄	1	1	yes	characteristic
277	C₄×D₄	D₄	1	1	yes	characteristic
278	C₄×D₄	D₄	1	1	yes	characteristic
279	C₄×D₄	C₂³	1	1	yes	characteristic
280	C₄×D₄	C₂³	1	1	yes	characteristic
281	C₄×D₄	C₂³	1	2	yes	—
282	C₄×D₄	C₂³	1	2	yes	—
283	C₄×D₄	C₂³	1	2	yes	—
284	C₄×D₄	C₂³	1	2	yes	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	C₂³	1	1	yes	characteristic
291	#117	C₂³	1	2	yes	—
292	#117	C₂³	1	1	yes	characteristic
293	#117	C₂³	1	1	yes	characteristic
294	#117	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	1	yes	characteristic
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#107	C₂³	1	2	yes	—
307	#107	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	C₄⋊C₈	C₂³	1	1	yes	characteristic
313	C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₄⋊C₈	C₂³	1	2	yes	—
315	C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₄⋊C₈	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
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	#102	C₂³	1	2	yes	—
325	#102	C₂³	1	2	yes	—
326	#102	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	C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂²⋊C₈	C₂³	1	2	yes	—
336	C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂²⋊C₈	C₂³	1	2	yes	—
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	C₄×C₈	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	2	no	—
343	#41	—	4	1	no	—
344	#41	—	4	1	no	—
345	#41	—	4	1	no	—
346	#41	—	4	1	no	—
347	#41	—	8	2	no	—
348	#41	—	8	2	no	—
349	#41	—	8	2	no	—
350	#41	—	8	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈	C₂⁴	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	8	2	no	—
379	C₂×D₄	—	8	2	no	—
380	C₂×D₄	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄	C₂⁴	1	1	yes	characteristic
384	C₂×D₄	C₂⁴	1	2	yes	—
385	C₂×D₄	C₂⁴	1	2	yes	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴	1	1	yes	characteristic
404	SD₁₆	—	4	2	no	—
405	SD₁₆	—	4	2	no	—
406	SD₁₆	—	4	2	no	—
407	SD₁₆	—	4	2	no	—
408	SD₁₆	—	4	2	no	—
409	SD₁₆	—	4	2	no	—
410	D₈	—	4	2	no	—
411	D₈	—	4	2	no	—
412	M₁₆	—	4	2	no	—
413	C₂×C₈	—	4	2	no	—
414	C₂×C₈	C₂⁴	1	2	yes	—
415	C₂×C₈	C₂⁴	1	2	yes	—
416	C₂×C₈	C₂⁴	1	2	yes	—
417	C₂×C₈	C₂⁴	1	2	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	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	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	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	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄	C₂⁴	1	2	yes	—
456	C₄⋊C₄	C₂⁴	1	2	yes	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	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	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	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	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	2	no	—
495	C₄²	C₂×D₄	1	1	yes	characteristic
496	C₄²	C₂×D₄	1	1	yes	characteristic
497	C₄²	C₂×D₄	1	1	yes	characteristic
498	C₄²	C₂×D₄	1	1	yes	characteristic
499	C₄²	C₂×D₄	1	1	yes	characteristic
500	C₄²	C₂×D₄	1	1	yes	characteristic
501	C₄²	C₂⁴	1	1	yes	characteristic
502	C₄²	C₂⁴	1	1	yes	characteristic
503	C₄²	C₂⁴	1	1	yes	characteristic
504	C₄²	C₂⁴	1	1	yes	characteristic
505	C₂³	—	2	1	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	8	2	no	—
510	C₂³	—	8	2	no	—
511	C₂³	C₂²×D₄	1	1	yes	characteristic
512	C₂³	C₂²×D₄	1	1	yes	characteristic
513	C₂³	C₂²×D₄	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	8	1	no	—
525	Q₈	—	8	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	8	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	1	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	2	no	—
546	D₄	—	8	2	no	—
547	D₄	—	8	2	no	—
548	D₄	—	8	2	no	—
549	C₂×C₄	—	2	2	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	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	8	1	no	—
574	C₂×C₄	—	8	2	no	—
575	C₂×C₄	—	8	2	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂⁵	1	1	yes	characteristic
591	C₈	—	2	2	no	—
592	C₈	—	2	2	no	—
593	C₈	—	2	2	no	—
594	C₈	—	2	2	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	16	4	no	—
614	C₂²	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	2	no	—
634	C₄	#577	1	2	yes	—
635	C₄	#585	1	1	yes	characteristic
636	C₄	#585	1	1	yes	characteristic
637	C₂	—	4	1	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	1	no	—
640	C₂	—	8	1	no	—
641	C₂	—	8	2	no	—
642	C₂	—	8	2	no	—
643	C₂	#3449	1	1	yes	characteristic
644	C₂	C₂×#577	1	1	yes	characteristic
645	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 ◁ 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. #3508	C₂	semidirect
2. #3461	C₂	semidirect
3. #3254	C₂	semidirect
4. #3251	C₂	semidirect
5. #3247	C₂	semidirect
6. #3246	C₂	semidirect
7. #3241	C₂	semidirect
8. #3237	C₂	semidirect
9. #3233	C₂	semidirect
10. #3221	C₂	semidirect
11. #3217	C₂	semidirect
12. #3208	C₂	semidirect
13. #3200	C₂	semidirect
14. #3198	C₂	semidirect
15. #3179	C₂	semidirect
16. #3174	C₂	semidirect
17. #3123	C₂	semidirect
18. #3118	C₂	semidirect
19. #3115	C₂	semidirect
20. #3112	C₂	semidirect
21. #3106	C₂	semidirect
22. #3103	C₂	semidirect
23. #2925	C₂	semidirect
32. #544	C₂²	semidirect
35. #542	C₂²	semidirect
38. #541	C₂²	semidirect
45. #536	C₂²	semidirect
50. #533	C₂²	semidirect
60. #529	C₂²	semidirect
63. C₄×#41	C₂²	semidirect
64. C₂×C₄×Q₈	C₂²	semidirect
65. #501	C₂²	semidirect
66. #499	C₂²	semidirect
69. #491	C₂²	semidirect
71. #488	C₂²	semidirect
77. #482	C₂²	semidirect
78. #482	C₂²	semidirect
79. #481	C₂²	semidirect
80. #480	C₂²	semidirect
81. #478	C₂²	semidirect
82. #478	C₂²	semidirect
83. #477	C₂²	semidirect
84. #477	C₂²	semidirect
85. #477	C₂²	semidirect
86. #476	C₂²	semidirect
87. #476	C₂²	semidirect
88. #475	C₂²	semidirect
89. #475	C₂²	semidirect
90. #475	C₂²	semidirect
91. #474	C₂²	semidirect
92. #474	C₂²	semidirect
93. #469	C₂²	semidirect
94. #468	C₂²	semidirect
95. #468	C₂²	semidirect
96. #468	C₂²	semidirect
97. #466	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #465	C₂²	semidirect
101. #463	C₂²	semidirect
102. #463	C₂²	semidirect
103. #461	C₂²	semidirect
104. #461	C₂²	semidirect
116. #449	C₂²	semidirect
117. #449	C₂²	semidirect
118. #448	C₂²	semidirect
119. #448	C₂²	semidirect
121. #442	C₂²	semidirect
122. #440	C₂²	semidirect
123. #440	C₂²	semidirect
124. #440	C₂²	semidirect
125. C₄×SD₁₆	C₂²	semidirect
126. C₄×SD₁₆	C₂²	semidirect
127. C₄×SD₁₆	C₂²	semidirect
128. C₄×D₈	C₂²	semidirect
130. #433	C₂²	semidirect
132. #432	C₂²	semidirect
134. #431	C₂²	semidirect
135. #423	C₂²	semidirect
136. C₂×C₄⋊C₈	C₂²	semidirect
138. #405	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3508	2
#3461	2
#3254	2
#3251	2
#3247	2
#3246	2
#3241	2
#3237	2
#3233	2
#3221	2
#3217	2
#3208	2
#3200	2
#3198	2
#3179	2
#3174	2
#3123	2
#3118	2
#3115	2
#3112	2
#3106	2
#3103	2
#2925	2