Subgroups — #62025

Order 256.

893 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	#3524	C₂	1	1	yes	maximal, characteristic, complemented
3	#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	#3321	C₂	1	1	yes	maximal, characteristic, complemented
8	#3320	C₂	1	1	yes	maximal, characteristic, complemented
9	#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	#3309	C₂	1	1	yes	maximal, characteristic, complemented
11	#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	#3300	C₂	1	1	yes	maximal, characteristic, complemented
13	#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	#3284	C₂	1	1	yes	maximal, characteristic, complemented
15	#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	#3271	C₂	1	1	yes	maximal, characteristic, complemented
17	#3270	C₂	1	1	yes	maximal, characteristic, complemented
18	#3269	C₂	1	1	yes	maximal, characteristic, complemented
19	#3263	C₂	1	1	yes	maximal, characteristic, complemented
20	#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	#3248	C₂	1	1	yes	maximal, characteristic, complemented
22	#3225	C₂	1	1	yes	maximal, characteristic, complemented
23	#3221	C₂	1	1	yes	maximal, characteristic, complemented
24	#3219	C₂	1	1	yes	maximal, characteristic, complemented
25	#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	#3121	C₂	1	1	yes	maximal, characteristic, complemented
27	#3116	C₂	1	1	yes	maximal, characteristic, complemented
28	#3046	C₂	1	1	yes	maximal, characteristic, complemented
29	#3044	C₂	1	1	yes	maximal, characteristic, complemented
30	#3035	C₂	1	1	yes	maximal, characteristic, complemented
31	#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic
33	C₂×#137	C₂²	1	1	yes	characteristic
34	C₂×#135	C₂²	1	1	yes	characteristic
35	C₂×#135	C₂²	1	1	yes	characteristic
36	C₂×#135	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆	C₂²	1	1	yes	characteristic
38	#562	—	2	1	no	—
39	#562	—	2	1	no	—
40	#559	—	2	1	no	—
41	#559	—	2	1	no	—
42	#559	C₂²	1	1	yes	characteristic
43	#559	C₂²	1	1	yes	characteristic
44	#557	C₂²	1	1	yes	characteristic
45	#557	C₂²	1	1	yes	characteristic
46	#555	—	2	1	no	—
47	#555	C₂²	1	1	yes	characteristic
48	#554	—	2	1	no	—
49	#553	—	2	1	no	—
50	#553	C₂²	1	1	yes	characteristic
51	#552	—	2	1	no	—
52	#552	C₂²	1	1	yes	characteristic
53	#550	C₂²	1	1	yes	characteristic
54	#550	C₂²	1	1	yes	characteristic
55	D₄×Q₈	C₂²	1	1	yes	characteristic
56	#548	C₂²	1	1	yes	characteristic
57	#548	C₂²	1	1	yes	characteristic
58	#548	C₂²	1	1	yes	characteristic
59	#548	C₂²	1	1	yes	characteristic
60	#547	C₂²	1	1	yes	characteristic
61	#547	C₂²	1	1	yes	characteristic
62	#542	—	2	1	no	—
63	#542	—	2	1	no	—
64	#542	C₂²	1	1	yes	characteristic
65	#542	C₂²	1	1	yes	characteristic
66	#542	C₂²	1	1	yes	characteristic
67	#540	—	2	1	no	—
68	#540	—	2	1	no	—
69	#540	C₂²	1	1	yes	characteristic
70	#539	—	2	1	no	—
71	#539	—	2	1	no	—
72	#536	C₂²	1	1	yes	characteristic
73	#536	C₂²	1	1	yes	characteristic
74	#533	C₂²	1	1	yes	characteristic
75	#532	C₂²	1	1	yes	characteristic
76	#529	—	2	1	no	—
77	#529	—	2	1	no	—
78	#529	C₂²	1	1	yes	characteristic
79	#529	C₂²	1	1	yes	characteristic
80	#520	C₂²	1	1	yes	characteristic
81	#519	C₂²	1	1	yes	characteristic
82	C₄×#41	C₂²	1	1	yes	characteristic
83	#497	C₂²	1	1	yes	characteristic
84	#497	C₂²	1	1	yes	characteristic
85	#496	C₂²	1	1	yes	characteristic
86	#496	C₂²	1	1	yes	characteristic
87	#495	C₂²	1	1	yes	characteristic
88	#492	C₂²	1	1	yes	characteristic
89	#491	C₂²	1	1	yes	characteristic
90	#491	C₂²	1	1	yes	characteristic
91	#490	C₂²	1	1	yes	characteristic
92	#489	C₂²	1	1	yes	characteristic
93	#488	C₂²	1	1	yes	characteristic
94	#487	C₂²	1	1	yes	characteristic
95	#485	C₂²	1	1	yes	characteristic
96	#485	C₂²	1	1	yes	characteristic
97	#485	C₂²	1	1	yes	characteristic
98	#484	C₂²	1	1	yes	characteristic
99	#482	C₂²	1	1	yes	characteristic
100	#480	C₂²	1	1	yes	characteristic
101	#479	C₂²	1	1	yes	characteristic
102	#479	C₂²	1	1	yes	characteristic
103	#479	C₂²	1	1	yes	characteristic
104	#478	C₂²	1	1	yes	characteristic
105	#477	C₂²	1	1	yes	characteristic
106	#476	C₂²	1	1	yes	characteristic
107	#476	C₂²	1	1	yes	characteristic
108	#475	C₂²	1	1	yes	characteristic
109	#475	C₂²	1	1	yes	characteristic
110	#474	C₂²	1	1	yes	characteristic
111	#470	C₂²	1	1	yes	characteristic
112	#469	C₂²	1	1	yes	characteristic
113	#469	C₂²	1	1	yes	characteristic
114	#468	C₂²	1	1	yes	characteristic
115	#467	C₂²	1	1	yes	characteristic
116	#467	C₂²	1	1	yes	characteristic
117	#466	C₂²	1	1	yes	characteristic
118	#465	C₂²	1	1	yes	characteristic
119	#465	C₂²	1	1	yes	characteristic
120	#465	C₂²	1	1	yes	characteristic
121	#465	C₂²	1	1	yes	characteristic
122	#465	C₂²	1	1	yes	characteristic
123	#464	C₂²	1	1	yes	characteristic
124	#464	C₂²	1	1	yes	characteristic
125	#464	C₂²	1	1	yes	characteristic
126	#464	C₂²	1	1	yes	characteristic
127	#464	C₂²	1	1	yes	characteristic
128	#464	C₂²	1	1	yes	characteristic
129	#464	C₂²	1	1	yes	characteristic
130	#464	C₂²	1	1	yes	characteristic
131	#464	C₂²	1	1	yes	characteristic
132	#464	C₂²	1	1	yes	characteristic
133	#463	C₂²	1	1	yes	characteristic
134	#463	C₂²	1	1	yes	characteristic
135	#463	C₂²	1	1	yes	characteristic
136	#463	C₂²	1	1	yes	characteristic
137	#463	C₂²	1	1	yes	characteristic
138	#463	C₂²	1	1	yes	characteristic
139	#462	C₂²	1	1	yes	characteristic
140	#462	C₂²	1	1	yes	characteristic
141	#462	C₂²	1	1	yes	characteristic
142	#462	C₂²	1	1	yes	characteristic
143	#462	C₂²	1	1	yes	characteristic
144	#462	C₂²	1	1	yes	characteristic
145	#461	C₂²	1	1	yes	characteristic
146	#461	C₂²	1	1	yes	characteristic
147	#461	C₂²	1	1	yes	characteristic
148	#461	C₂²	1	1	yes	characteristic
149	#460	C₂²	1	1	yes	characteristic
150	#460	C₂²	1	1	yes	characteristic
151	#459	C₂²	1	1	yes	characteristic
152	#459	C₂²	1	1	yes	characteristic
153	#452	C₂²	1	1	yes	characteristic
154	#452	C₂²	1	1	yes	characteristic
155	#452	C₂²	1	1	yes	characteristic
156	#452	C₂²	1	1	yes	characteristic
157	#452	C₂²	1	1	yes	characteristic
158	#452	C₂²	1	1	yes	characteristic
159	#451	C₂²	1	1	yes	characteristic
160	#451	C₂²	1	1	yes	characteristic
161	#449	C₂²	1	1	yes	characteristic
162	#449	C₂²	1	1	yes	characteristic
163	#449	C₂²	1	1	yes	characteristic
164	#449	C₂²	1	1	yes	characteristic
165	#449	C₂²	1	1	yes	characteristic
166	#449	C₂²	1	1	yes	characteristic
167	#448	C₂²	1	1	yes	characteristic
168	#448	C₂²	1	1	yes	characteristic
169	#448	C₂²	1	1	yes	characteristic
170	#448	C₂²	1	1	yes	characteristic
171	#446	C₂²	1	1	yes	characteristic
172	#446	C₂²	1	1	yes	characteristic
173	#441	C₂²	1	1	yes	characteristic
174	#441	C₂²	1	1	yes	characteristic
175	#441	C₂²	1	1	yes	characteristic
176	#440	C₂²	1	1	yes	characteristic
177	#440	C₂²	1	1	yes	characteristic
178	#440	C₂²	1	1	yes	characteristic
179	#440	C₂²	1	1	yes	characteristic
180	#440	C₂²	1	1	yes	characteristic
181	C₄×Q₁₆	C₂²	1	1	yes	characteristic
182	C₄×Q₁₆	C₂²	1	1	yes	characteristic
183	C₄×SD₁₆	C₂²	1	1	yes	characteristic
184	C₄×D₈	C₂²	1	1	yes	characteristic
185	#435	C₂²	1	1	yes	characteristic
186	#435	C₂²	1	1	yes	characteristic
187	#435	C₂²	1	1	yes	characteristic
188	#435	C₂²	1	1	yes	characteristic
189	C₈×D₄	C₂²	1	1	yes	characteristic
190	C₈×D₄	C₂²	1	1	yes	characteristic
191	#433	C₂²	1	1	yes	characteristic
192	#433	C₂²	1	1	yes	characteristic
193	#432	C₂²	1	1	yes	characteristic
194	#424	C₂²	1	1	yes	characteristic
195	#424	C₂²	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
197	#419	C₂²	1	1	yes	characteristic
198	#417	C₂²	1	1	yes	characteristic
199	#416	C₂²	1	1	yes	characteristic
200	#416	C₂²	1	1	yes	characteristic
201	#416	C₂²	1	1	yes	characteristic
202	C₂×#103	C₂²	1	1	yes	characteristic
203	C₂×#41	C₂³	1	1	yes	characteristic
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂×#41	C₂³	1	1	yes	characteristic
208	C₂×#41	C₂³	1	1	yes	characteristic
209	C₂²×Q₈	C₂³	1	1	yes	characteristic
210	C₂²×Q₈	C₂³	1	1	yes	characteristic
211	C₂²×Q₈	C₂³	1	1	yes	characteristic
212	#137	—	4	2	no	—
213	#137	—	4	2	no	—
214	#135	—	4	2	no	—
215	#135	—	4	2	no	—
216	#135	—	4	2	no	—
217	C₂×Q₁₆	—	4	2	no	—
218	C₂×Q₁₆	C₂³	1	1	yes	characteristic
219	C₂×Q₁₆	C₂³	1	1	yes	characteristic
220	C₂×Q₁₆	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆	C₂³	1	1	yes	characteristic
238	C₂×D₈	C₂³	1	1	yes	characteristic
239	C₂×D₈	C₂³	1	1	yes	characteristic
240	C₂×D₈	C₂³	1	1	yes	characteristic
241	C₂×D₈	C₂³	1	1	yes	characteristic
242	C₂×M₁₆	C₂³	1	1	yes	characteristic
243	C₂×M₁₆	C₂³	1	1	yes	characteristic
244	C₂²×C₈	C₂³	1	1	yes	characteristic
245	C₂²×C₈	C₂³	1	1	yes	characteristic
246	C₂²×C₈	C₂³	1	1	yes	characteristic
247	C₂²×C₈	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³	1	1	yes	characteristic
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	C₂³	1	1	yes	characteristic
259	#127	C₂³	1	1	yes	characteristic
260	#126	—	2	1	no	—
261	#126	—	2	1	no	—
262	#126	—	2	1	no	—
263	#126	—	2	1	no	—
264	#126	—	2	1	no	—
265	#126	—	2	1	no	—
266	#126	D₄	1	1	yes	characteristic
267	#126	D₄	1	1	yes	characteristic
268	#125	—	2	1	no	—
269	#125	—	2	1	no	—
270	#125	—	2	1	no	—
271	#125	—	2	1	no	—
272	#125	—	2	1	no	—
273	#125	—	2	1	no	—
274	#125	—	2	1	no	—
275	#125	D₄	1	1	yes	characteristic
276	#125	C₂³	1	1	yes	characteristic
277	#125	C₂³	1	1	yes	characteristic
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	—	2	1	no	—
281	#124	—	2	1	no	—
282	#124	—	2	1	no	—
283	#124	—	2	1	no	—
284	#124	—	2	1	no	—
285	#124	—	2	1	no	—
286	#124	—	2	1	no	—
287	#124	—	2	1	no	—
288	#124	—	2	1	no	—
289	#124	D₄	1	1	yes	characteristic
290	#124	C₂³	1	1	yes	characteristic
291	#124	C₂³	1	1	yes	characteristic
292	#124	C₂³	1	1	yes	characteristic
293	#124	C₂³	1	1	yes	characteristic
294	#124	C₂³	1	1	yes	characteristic
295	#124	C₂³	1	1	yes	characteristic
296	#123	—	2	1	no	—
297	#123	—	2	1	no	—
298	#123	—	2	1	no	—
299	#123	—	2	1	no	—
300	#123	—	2	1	no	—
301	#123	—	2	1	no	—
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	—	2	1	no	—
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	#123	—	2	1	no	—
311	#123	—	2	1	no	—
312	#123	—	2	1	no	—
313	#123	—	2	1	no	—
314	#123	—	2	1	no	—
315	#123	—	2	1	no	—
316	#123	D₄	1	1	yes	characteristic
317	#123	D₄	1	1	yes	characteristic
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	D₄	1	1	yes	characteristic
333	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
334	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
335	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
337	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
338	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#121	—	2	1	no	—
350	#121	—	2	1	no	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	D₄	1	1	yes	characteristic
356	#121	C₂³	1	1	yes	characteristic
357	#121	C₂³	1	1	yes	characteristic
358	#121	C₂³	1	1	yes	characteristic
359	#121	C₂³	1	1	yes	characteristic
360	#121	C₂³	1	1	yes	characteristic
361	#121	C₂³	1	1	yes	characteristic
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂³	1	1	yes	characteristic
368	C₄×Q₈	C₂³	1	1	yes	characteristic
369	C₄×Q₈	C₂³	1	1	yes	characteristic
370	C₄×Q₈	C₂³	1	1	yes	characteristic
371	C₄×Q₈	C₂³	1	1	yes	characteristic
372	C₄×Q₈	C₂³	1	1	yes	characteristic
373	C₄×Q₈	C₂³	1	1	yes	characteristic
374	C₄×Q₈	C₂³	1	1	yes	characteristic
375	C₄×Q₈	C₂³	1	1	yes	characteristic
376	C₄×Q₈	C₂³	1	1	yes	characteristic
377	C₄×Q₈	C₂³	1	1	yes	characteristic
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	C₂³	1	1	yes	characteristic
396	C₄×D₄	C₂³	1	1	yes	characteristic
397	C₄×D₄	C₂³	1	1	yes	characteristic
398	C₄×D₄	C₂³	1	1	yes	characteristic
399	C₄×D₄	C₂³	1	1	yes	characteristic
400	C₄×D₄	C₂³	1	1	yes	characteristic
401	C₄×D₄	C₂³	1	1	yes	characteristic
402	C₄×D₄	C₂³	1	1	yes	characteristic
403	C₄×D₄	C₂³	1	1	yes	characteristic
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	C₂³	1	1	yes	characteristic
413	#117	C₂³	1	1	yes	characteristic
414	#117	C₂³	1	1	yes	characteristic
415	#117	C₂³	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³	1	1	yes	characteristic
422	#107	C₂³	1	1	yes	characteristic
423	#107	C₂³	1	1	yes	characteristic
424	#107	C₂³	1	1	yes	characteristic
425	#107	C₂³	1	1	yes	characteristic
426	#106	C₂³	1	1	yes	characteristic
427	#106	C₂³	1	1	yes	characteristic
428	#106	C₂³	1	1	yes	characteristic
429	#106	C₂³	1	1	yes	characteristic
430	C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₄⋊C₈	C₂³	1	1	yes	characteristic
434	C₄⋊C₈	C₂³	1	1	yes	characteristic
435	C₄⋊C₈	C₂³	1	1	yes	characteristic
436	C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₄⋊C₈	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#103	C₂³	1	1	yes	characteristic
453	#103	C₂³	1	1	yes	characteristic
454	#103	C₂³	1	1	yes	characteristic
455	#103	C₂³	1	1	yes	characteristic
456	#103	C₂³	1	1	yes	characteristic
457	#103	C₂³	1	1	yes	characteristic
458	#103	C₂³	1	1	yes	characteristic
459	#103	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	#102	C₂³	1	1	yes	characteristic
467	#102	C₂³	1	1	yes	characteristic
468	#102	C₂³	1	1	yes	characteristic
469	#102	C₂³	1	1	yes	characteristic
470	#102	C₂³	1	1	yes	characteristic
471	#102	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	#97	C₂³	1	1	yes	characteristic
479	#97	C₂³	1	1	yes	characteristic
480	#97	C₂³	1	1	yes	characteristic
481	#97	C₂³	1	1	yes	characteristic
482	C₄×C₈	C₂³	1	1	yes	characteristic
483	C₄×C₈	C₂³	1	1	yes	characteristic
484	#41	—	2	2	no	—
485	#41	—	2	2	no	—
486	#41	—	4	1	no	—
487	#41	—	4	1	no	—
488	#41	—	4	1	no	—
489	#41	—	4	1	no	—
490	#41	—	4	1	no	—
491	#41	—	4	1	no	—
492	#41	—	4	1	no	—
493	#41	—	4	1	no	—
494	#41	—	4	1	no	—
495	#41	—	4	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	4	1	no	—
503	C₂×Q₈	—	4	1	no	—
504	C₂×Q₈	—	4	1	no	—
505	C₂×Q₈	—	4	1	no	—
506	C₂×Q₈	—	4	1	no	—
507	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
508	C₂×Q₈	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈	C₂⁴	1	1	yes	characteristic
512	C₂×Q₈	C₂⁴	1	1	yes	characteristic
513	C₂×Q₈	C₂⁴	1	1	yes	characteristic
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	C₂×D₄	1	1	yes	characteristic
531	C₂×D₄	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄	C₂⁴	1	1	yes	characteristic
534	C₂×D₄	C₂⁴	1	1	yes	characteristic
535	C₂×D₄	C₂⁴	1	1	yes	characteristic
536	C₂×D₄	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴	1	1	yes	characteristic
558	Q₁₆	—	2	2	no	—
559	Q₁₆	—	2	2	no	—
560	Q₁₆	—	2	2	no	—
561	Q₁₆	—	2	2	no	—
562	Q₁₆	—	4	1	no	—
563	Q₁₆	—	4	1	no	—
564	Q₁₆	—	4	1	no	—
565	Q₁₆	—	4	1	no	—
566	SD₁₆	—	2	2	no	—
567	SD₁₆	—	2	2	no	—
568	SD₁₆	—	4	1	no	—
569	SD₁₆	—	4	1	no	—
570	SD₁₆	—	4	1	no	—
571	SD₁₆	—	4	1	no	—
572	SD₁₆	—	4	1	no	—
573	SD₁₆	—	4	1	no	—
574	SD₁₆	—	4	1	no	—
575	SD₁₆	—	4	1	no	—
576	SD₁₆	—	4	1	no	—
577	SD₁₆	—	4	1	no	—
578	D₈	—	4	1	no	—
579	D₈	—	4	1	no	—
580	D₈	—	4	1	no	—
581	D₈	—	4	1	no	—
582	M₁₆	—	4	1	no	—
583	M₁₆	—	4	1	no	—
584	C₂×C₈	—	4	1	no	—
585	C₂×C₈	—	4	1	no	—
586	C₂×C₈	—	4	1	no	—
587	C₂×C₈	—	4	1	no	—
588	C₂×C₈	C₂⁴	1	1	yes	characteristic
589	C₂×C₈	C₂⁴	1	1	yes	characteristic
590	C₂×C₈	C₂⁴	1	1	yes	characteristic
591	C₂×C₈	C₂⁴	1	1	yes	characteristic
592	C₂×C₈	C₂⁴	1	1	yes	characteristic
593	C₂×C₈	C₂⁴	1	1	yes	characteristic
594	C₂×C₈	C₂⁴	1	1	yes	characteristic
595	C₂×C₈	C₂⁴	1	1	yes	characteristic
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
676	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
677	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
678	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
679	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
681	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	1	no	—
690	C₄²	—	2	1	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₄²	—	2	1	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	C₂×D₄	1	1	yes	characteristic
698	C₄²	C₂×D₄	1	1	yes	characteristic
699	C₄²	C₂⁴	1	1	yes	characteristic
700	C₄²	C₂⁴	1	1	yes	characteristic
701	C₄²	C₂⁴	1	1	yes	characteristic
702	C₄²	C₂⁴	1	1	yes	characteristic
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	C₂²×D₄	1	1	yes	characteristic
708	C₂³	C₂²×D₄	1	1	yes	characteristic
709	C₂³	C₂²×D₄	1	1	yes	characteristic
710	Q₈	—	2	1	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	2	1	no	—
713	Q₈	—	2	1	no	—
714	Q₈	—	2	1	no	—
715	Q₈	—	2	1	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	1	no	—
718	Q₈	—	2	1	no	—
719	Q₈	—	2	1	no	—
720	Q₈	—	2	1	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	8	1	no	—
724	Q₈	—	8	1	no	—
725	Q₈	—	8	1	no	—
726	Q₈	—	8	1	no	—
727	Q₈	H(5,𝔽₂)	1	2	yes	—
728	D₄	—	2	1	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	1	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	1	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	2	no	—
742	D₄	—	8	1	no	—
743	D₄	—	8	1	no	—
744	D₄	—	8	1	no	—
745	D₄	—	8	1	no	—
746	D₄	—	8	1	no	—
747	D₄	—	8	1	no	—
748	D₄	—	8	1	no	—
749	D₄	—	8	1	no	—
750	D₄	—	8	1	no	—
751	D₄	—	8	1	no	—
752	D₄	—	8	1	no	—
753	D₄	—	8	1	no	—
754	D₄	—	8	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	8	1	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	—	8	1	no	—
781	C₂×C₄	—	8	1	no	—
782	C₂×C₄	—	8	1	no	—
783	C₂×C₄	—	8	1	no	—
784	C₂×C₄	—	8	1	no	—
785	C₂×C₄	—	8	1	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	—	8	1	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	1	no	—
791	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂⁵	1	1	yes	characteristic
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	1	no	—
806	C₈	—	2	1	no	—
807	C₈	—	2	1	no	—
808	C₈	—	2	1	no	—
809	C₈	—	2	1	no	—
810	C₈	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	C₂³×D₄	1	1	yes	characteristic
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	2	1	no	—
837	C₄	—	2	1	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
857	C₄	#585	1	1	yes	characteristic
858	C₂	—	4	1	no	—
859	C₂	—	4	1	no	—
860	C₂	—	4	1	no	—
861	C₂	—	8	1	no	—
862	C₂	—	8	1	no	—
863	C₂	—	8	1	no	—
864	C₂	—	8	1	no	—
865	C₂	#3488	1	1	yes	characteristic
866	C₂	#3584	1	1	yes	characteristic
867	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3554	C₂	semidirect
2. #3524	C₂	semidirect
3. #3403	C₂	semidirect
4. #3400	C₂	semidirect
5. #3374	C₂	semidirect
6. #3371	C₂	semidirect
7. #3321	C₂	semidirect
8. #3320	C₂	semidirect
9. #3315	C₂	semidirect
10. #3309	C₂	semidirect
11. #3303	C₂	semidirect
12. #3300	C₂	semidirect
13. #3285	C₂	semidirect
14. #3284	C₂	semidirect
15. #3271	C₂	semidirect
16. #3271	C₂	semidirect
17. #3270	C₂	semidirect
18. #3269	C₂	semidirect
19. #3263	C₂	semidirect
20. #3257	C₂	semidirect
21. #3248	C₂	semidirect
22. #3225	C₂	semidirect
23. #3221	C₂	semidirect
24. #3219	C₂	semidirect
25. #3124	C₂	semidirect
26. #3121	C₂	semidirect
27. #3116	C₂	semidirect
28. #3046	C₂	semidirect
29. #3044	C₂	semidirect
30. #3035	C₂	semidirect
31. #2992	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3554	2
#3524	2
#3403	2
#3400	2
#3374	2
#3371	2
#3321	2
#3320	2
#3315	2
#3309	2
#3303	2
#3300	2
#3285	2
#3284	2
#3271	2
#3270	2
#3269	2
#3263	2
#3257	2
#3248	2
#3225	2
#3221	2
#3219	2
#3124	2
#3121	2
#3116	2
#3046	2
#3044	2
#3035	2
#2992	2