Subgroups — #62300

Order 256.

919 conjugacy classes of subgroups.

The subgroup lattice has 574 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
2	#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	#3356	C₂	1	1	yes	maximal, characteristic, complemented
4	#3344	C₂	1	2	yes	maximal, complemented
5	#3335	C₂	1	1	yes	maximal, characteristic, complemented
6	#3331	C₂	1	1	yes	maximal, characteristic, complemented
7	#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	#3316	C₂	1	2	yes	maximal, complemented
9	#3312	C₂	1	2	yes	maximal, complemented
10	#3299	C₂	1	1	yes	maximal, characteristic, complemented
11	#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	#3270	C₂	1	2	yes	maximal, complemented
15	#3255	C₂	1	1	yes	maximal, characteristic, complemented
16	#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	#3196	C₂	1	2	yes	maximal, complemented
18	#3195	C₂	1	2	yes	maximal, complemented
19	#3185	C₂	1	1	yes	maximal, characteristic, complemented
20	#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	#3056	C₂	1	2	yes	maximal, complemented
22	C₂×#470	C₂	1	2	yes	maximal, complemented
23	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆	C₂²	1	2	yes	complemented
26	C₂²×M₁₆	C₂²	1	2	yes	—
27	#556	C₂²	1	1	yes	characteristic
28	#554	—	2	1	no	—
29	#554	—	2	2	no	—
30	#554	—	2	1	no	—
31	#554	—	2	1	no	—
32	#554	C₂²	1	1	yes	characteristic
33	#554	C₂²	1	1	yes	characteristic
34	#554	C₂²	1	2	yes	—
35	#552	C₂²	1	2	yes	—
36	#551	—	2	2	no	—
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	2	yes	—
39	D₄×Q₈	C₂²	1	1	yes	characteristic
40	D₄×Q₈	C₂²	1	1	yes	characteristic
41	#548	C₂²	1	2	yes	—
42	#547	C₂²	1	1	yes	characteristic
43	#547	C₂²	1	1	yes	characteristic
44	#546	—	2	1	no	—
45	#544	—	2	1	no	—
46	#543	—	2	2	no	—
47	#542	—	2	1	no	—
48	#539	—	2	2	no	—
49	#533	C₂²	1	1	yes	characteristic
50	#533	C₂²	1	1	yes	characteristic
51	#533	C₂²	1	1	yes	characteristic
52	#529	C₂²	1	1	yes	characteristic
53	#525	C₂²	1	2	yes	—
54	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
57	#520	—	2	1	no	—
58	#518	—	2	1	no	—
59	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
60	#501	C₂²	1	1	yes	characteristic, complemented
61	#498	C₂²	1	1	yes	characteristic, complemented
62	#497	C₂²	1	1	yes	characteristic, complemented
63	#494	C₂²	1	1	yes	characteristic, complemented
64	#491	C₂²	1	1	yes	characteristic, complemented
65	#489	C₂²	1	1	yes	characteristic, complemented
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#487	C₂²	1	1	yes	characteristic, complemented
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#484	C₂²	1	2	yes	complemented
71	#483	C₂²	1	2	yes	complemented
72	#483	C₂²	1	2	yes	complemented
73	#483	C₂²	1	2	yes	complemented
74	#483	C₂²	1	2	yes	complemented
75	#481	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#477	C₂²	1	1	yes	characteristic, complemented
78	#476	C₂²	1	1	yes	characteristic, complemented
79	#475	C₂²	1	1	yes	characteristic, complemented
80	#475	C₂²	1	2	yes	complemented
81	#475	C₂²	1	1	yes	characteristic, complemented
82	#470	C₂²	1	1	yes	characteristic
83	#470	C₂²	1	1	yes	characteristic
84	#470	C₂²	1	2	yes	—
85	#470	C₂²	1	2	yes	—
86	#470	C₂²	1	2	yes	—
87	#470	C₂²	1	2	yes	—
88	#470	C₂²	1	2	yes	—
89	#470	C₂²	1	2	yes	complemented
90	#470	C₂²	1	2	yes	complemented
91	#470	C₂²	1	2	yes	complemented
92	#470	C₂²	1	2	yes	complemented
93	#468	C₂²	1	1	yes	characteristic
94	#468	C₂²	1	1	yes	characteristic
95	#468	C₂²	1	2	yes	—
96	#467	C₂²	1	2	yes	complemented
97	#467	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#464	C₂²	1	2	yes	complemented
101	#462	C₂²	1	1	yes	characteristic, complemented
102	#462	C₂²	1	1	yes	characteristic, complemented
103	#462	C₂²	1	2	yes	complemented
104	#462	C₂²	1	1	yes	characteristic, complemented
105	#461	C₂²	1	1	yes	characteristic, complemented
106	#452	C₂²	1	2	yes	complemented
107	#452	C₂²	1	2	yes	complemented
108	#451	C₂²	1	2	yes	complemented
109	#451	C₂²	1	2	yes	complemented
110	#451	C₂²	1	2	yes	complemented
111	#451	C₂²	1	2	yes	complemented
112	#451	C₂²	1	2	yes	complemented
113	#448	C₂²	1	2	yes	complemented
114	#441	C₂²	1	2	yes	complemented
115	#441	C₂²	1	2	yes	complemented
116	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	#436	C₂²	1	1	yes	characteristic
121	#436	C₂²	1	1	yes	characteristic
122	#435	C₂²	1	2	yes	—
123	#435	C₂²	1	2	yes	—
124	C₈×D₄	C₂²	1	1	yes	characteristic
125	C₈×D₄	C₂²	1	1	yes	characteristic
126	#428	C₂²	1	2	yes	complemented
127	C₂×#106	C₂²	1	2	yes	complemented
128	#423	C₂²	1	1	yes	characteristic
129	#419	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	complemented
131	C₂×#103	C₂²	1	2	yes	complemented
132	C₂×#103	C₂²	1	2	yes	complemented
133	#407	C₂²	1	2	yes	—
134	C₄×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	1	no	—
136	C₂×#41	C₂³	1	2	yes	—
137	C₂²×Q₈	C₂³	1	2	yes	—
138	C₂²×Q₈	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	#137	—	4	4	no	—
143	C₂×Q₁₆	—	4	4	no	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×M₁₆	—	4	4	no	—
155	C₂×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂×M₁₆	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	1	no	—
175	#125	—	2	2	no	—
176	#125	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	—	2	1	no	—
181	#125	—	2	1	no	—
182	#125	C₂³	1	1	yes	characteristic
183	#124	—	2	1	no	—
184	#124	—	2	2	no	—
185	#124	C₂³	1	1	yes	characteristic
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	1	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	1	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂²⋊Q₈	C₂³	1	2	yes	—
223	#121	—	2	2	no	—
224	#121	—	2	1	no	—
225	#121	C₂³	1	1	yes	characteristic
226	#121	C₂³	1	2	yes	—
227	#120	—	2	2	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₄×Q₈	C₂³	1	2	yes	—
234	C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₄×Q₈	C₂³	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	D₄	1	1	yes	characteristic
249	C₄×D₄	D₄	1	2	yes	—
250	C₄×D₄	D₄	1	1	yes	characteristic
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	2	yes	—
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	—	2	2	no	—
259	#117	—	2	1	no	—
260	#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	D₄	1	2	yes	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	2	yes	—
282	#106	C₂³	1	1	yes	characteristic
283	#106	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	2	yes	—
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	1	yes	characteristic
300	#103	C₂³	1	1	yes	characteristic
301	#103	C₂³	1	1	yes	characteristic
302	#103	C₂³	1	2	yes	—
303	#103	C₂³	1	2	yes	—
304	#102	C₂³	1	1	yes	characteristic
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	1	yes	characteristic
312	#97	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂⁴	C₂×D₄	1	2	yes	—
316	#41	—	4	2	no	—
317	#41	—	4	2	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	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	2	yes	—
334	C₂×Q₈	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈	C₂⁴	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₂×D₄	1	2	yes	—
341	C₂×D₄	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄	1	2	yes	—
357	C₂²×C₄	C₂×D₄	1	2	yes	—
358	C₂²×C₄	C₂×D₄	1	2	yes	—
359	C₂²×C₄	C₂⁴	1	2	yes	—
360	C₂²×C₄	C₂⁴	1	2	yes	—
361	C₂²×C₄	C₂⁴	1	1	yes	characteristic
362	Q₁₆	—	2	2	no	—
363	Q₁₆	—	2	4	no	—
364	Q₁₆	—	4	2	no	—
365	Q₁₆	—	4	2	no	—
366	Q₁₆	—	4	1	no	—
367	Q₁₆	—	4	2	no	—
368	Q₁₆	—	4	2	no	—
369	SD₁₆	—	2	2	no	—
370	SD₁₆	—	4	1	no	—
371	SD₁₆	—	4	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	4	no	—
374	M₁₆	—	4	2	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	1	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	2	yes	—
383	C₂×C₈	C₂⁴	1	2	yes	—
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	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	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴	1	2	yes	—
421	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄	C₂⁴	1	2	yes	—
424	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	C₂×D₄	1	1	yes	characteristic
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂⁴	1	1	yes	characteristic
456	C₄²	C₂⁴	1	1	yes	characteristic
457	C₂³	—	2	4	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	C₂²×D₄	1	1	yes	characteristic
462	C₂³	C₂²×D₄	1	2	yes	—
463	C₂³	C₂²×D₄	1	2	yes	—
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	1	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	8	1	no	—
476	Q₈	—	8	1	no	—
477	Q₈	—	8	2	no	—
478	Q₈	—	8	2	no	—
479	Q₈	—	8	2	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	8	2	no	—
487	D₄	#137	1	4	yes	complemented
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	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	—	8	2	no	—
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄	1	2	yes	—
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄	1	2	yes	—
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂⁵	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	2	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	H(5,𝔽₂)	1	2	yes	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	8	4	no	—
544	C₂²	C₂×#137	1	4	yes	—
545	C₂²	C₂³×D₄	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	2	no	—
563	C₄	C₂×#137	1	2	yes	—
564	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	C₄	#585	1	1	yes	characteristic
566	C₂	—	2	4	no	—
567	C₂	—	4	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	8	1	no	—
570	C₂	#3496	1	1	yes	characteristic
571	C₂	C₂²×#137	1	1	yes	characteristic
572	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3520	C₂
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
2. #3501	C₂	semidirect
3. #3356	C₂	semidirect
4. #3344	C₂	semidirect
5. #3335	C₂	semidirect
6. #3331	C₂	semidirect
7. #3328	C₂	semidirect
8. #3316	C₂	semidirect
9. #3312	C₂	semidirect
10. #3299	C₂	semidirect
11. #3298	C₂	semidirect
12. D₄×Q₁₆	C₂	semidirect
13. #3276	C₂	semidirect
14. #3270	C₂	semidirect
15. #3255	C₂	semidirect
16. #3252	C₂	semidirect
17. #3196	C₂	semidirect
18. #3195	C₂	semidirect
19. #3185	C₂	semidirect
20. #3172	C₂	semidirect
21. #3056	C₂	semidirect
22. C₂×#470	C₂	semidirect
23. D₄×M₁₆	C₂	semidirect
24. C₂×#137	C₂²	semidirect
25. C₂²×Q₁₆	C₂²	semidirect
60. #501	C₂²	semidirect
61. #498	C₂²	semidirect
62. #497	C₂²	semidirect
63. #494	C₂²	semidirect
64. #491	C₂²	semidirect
65. #489	C₂²	semidirect
66. #487	C₂²	semidirect
67. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #484	C₂²	semidirect
71. #483	C₂²	semidirect
72. #483	C₂²	semidirect
73. #483	C₂²	semidirect
74. #483	C₂²	semidirect
75. #481	C₂²	semidirect
76. #479	C₂²	semidirect
77. #477	C₂²	semidirect
78. #476	C₂²	semidirect
79. #475	C₂²	semidirect
80. #475	C₂²	semidirect
81. #475	C₂²	semidirect
89. #470	C₂²	semidirect
90. #470	C₂²	semidirect
91. #470	C₂²	semidirect
92. #470	C₂²	semidirect
96. #467	C₂²	semidirect
97. #467	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #464	C₂²	semidirect
101. #462	C₂²	semidirect
102. #462	C₂²	semidirect
103. #462	C₂²	semidirect
104. #462	C₂²	semidirect
105. #461	C₂²	semidirect
106. #452	C₂²	semidirect
107. #452	C₂²	semidirect
108. #451	C₂²	semidirect
109. #451	C₂²	semidirect
110. #451	C₂²	semidirect
111. #451	C₂²	semidirect
112. #451	C₂²	semidirect
113. #448	C₂²	semidirect
114. #441	C₂²	semidirect
115. #441	C₂²	semidirect
116. C₄×Q₁₆	C₂²	semidirect
117. C₄×Q₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
119. C₄×SD₁₆	C₂²	semidirect
126. #428	C₂²	semidirect
127. C₂×#106	C₂²	semidirect
129. #419	C₂²	semidirect
130. #417	C₂²	semidirect
131. C₂×#103	C₂²	semidirect
132. C₂×#103	C₂²	semidirect
487. D₄	#137	semidirect

Maximal subgroups

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

subgroup	index
#3520	2
#3501	2
#3356	2
#3344	2
#3335	2
#3331	2
#3328	2
#3316	2
#3312	2
#3299	2
#3298	2
D₄×Q₁₆	2
#3276	2
#3270	2
#3255	2
#3252	2
#3196	2
#3195	2
#3185	2
#3172	2
#3056	2
C₂×#470	2
D₄×M₁₆	2