Subgroups — #60302

Order 256.

858 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3480	C₂	1	1	yes	maximal, characteristic
2	#2995	C₂	1	2	yes	maximal, complemented
3	#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	#2992	C₂	1	2	yes	maximal, complemented
6	#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	#2989	C₂	1	1	yes	maximal, characteristic, complemented
8	#2984	C₂	1	1	yes	maximal, characteristic, complemented
9	#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	#2981	C₂	1	1	yes	maximal, characteristic, complemented
11	#2981	C₂	1	2	yes	maximal, complemented
12	#2980	C₂	1	2	yes	maximal, complemented
13	#2979	C₂	1	1	yes	maximal, characteristic, complemented
14	#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	#2968	C₂	1	2	yes	maximal, complemented
17	#2967	C₂	1	2	yes	maximal, complemented
18	#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	#2925	C₂	1	1	yes	maximal, characteristic, complemented
21	#2925	C₂	1	2	yes	maximal, complemented
22	#2923	C₂	1	2	yes	maximal, complemented
23	#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	C₄	1	1	yes	characteristic
25	#559	C₄	1	2	yes	—
26	#557	C₄	1	1	yes	characteristic
27	#556	C₄	1	1	yes	characteristic
28	#556	C₄	1	2	yes	—
29	#553	C₄	1	1	yes	characteristic
30	#553	C₄	1	1	yes	characteristic
31	#553	C₄	1	2	yes	—
32	#553	C₄	1	2	yes	—
33	#550	C₄	1	1	yes	characteristic
34	#548	C₄	1	1	yes	characteristic
35	#548	C₄	1	1	yes	characteristic
36	#532	C₂²	1	1	yes	characteristic
37	#532	C₂²	1	2	yes	—
38	#529	C₂²	1	1	yes	characteristic
39	#529	C₂²	1	2	yes	—
40	#529	C₂²	1	2	yes	—
41	#529	C₂²	1	1	yes	characteristic
42	C₄×#41	C₂²	1	1	yes	characteristic
43	C₄×#41	C₂²	1	1	yes	characteristic
44	C₄×#41	C₂²	1	1	yes	characteristic
45	C₄×#41	C₂²	1	2	yes	—
46	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
47	#446	C₂²	1	1	yes	characteristic
48	#446	C₂²	1	1	yes	characteristic
49	#446	C₂²	1	1	yes	characteristic
50	#446	C₂²	1	2	yes	—
51	#446	C₂²	1	2	yes	—
52	#446	C₂²	1	2	yes	—
53	#446	C₂²	1	2	yes	—
54	#446	C₂²	1	1	yes	characteristic
55	#446	C₂²	1	1	yes	characteristic
56	#446	C₂²	1	1	yes	characteristic
57	C₈×Q₈	C₂²	1	1	yes	characteristic
58	C₈×Q₈	C₂²	1	1	yes	characteristic
59	#436	C₂²	1	1	yes	characteristic
60	#436	C₂²	1	1	yes	characteristic
61	#436	C₂²	1	1	yes	characteristic
62	#436	C₂²	1	2	yes	—
63	#436	C₂²	1	2	yes	—
64	#436	C₂²	1	1	yes	characteristic
65	#436	C₂²	1	2	yes	—
66	#435	C₂²	1	2	yes	—
67	#435	C₂²	1	2	yes	—
68	#435	C₂²	1	2	yes	—
69	#435	C₂²	1	2	yes	—
70	#435	C₂²	1	2	yes	—
71	#435	C₂²	1	2	yes	—
72	#435	C₂²	1	2	yes	—
73	#435	C₂²	1	2	yes	—
74	#435	C₂²	1	2	yes	—
75	#435	C₂²	1	2	yes	—
76	#435	C₂²	1	2	yes	—
77	#435	C₂²	1	2	yes	—
78	#435	C₂²	1	2	yes	—
79	#435	C₂²	1	2	yes	—
80	C₈×D₄	C₂²	1	1	yes	characteristic
81	C₈×D₄	C₂²	1	2	yes	—
82	C₈×D₄	C₂²	1	2	yes	—
83	C₈×D₄	C₂²	1	2	yes	—
84	C₈×D₄	C₂²	1	1	yes	characteristic
85	C₈×D₄	C₂²	1	1	yes	characteristic
86	C₈×D₄	C₂²	1	1	yes	characteristic
87	#433	C₂²	1	1	yes	characteristic
88	#433	C₂²	1	1	yes	characteristic
89	#433	C₂²	1	1	yes	characteristic
90	#433	C₂²	1	1	yes	characteristic
91	#433	C₂²	1	2	yes	—
92	#433	C₂²	1	2	yes	—
93	#433	C₂²	1	2	yes	—
94	#433	C₂²	1	2	yes	—
95	#433	C₂²	1	2	yes	—
96	#433	C₂²	1	2	yes	—
97	#432	C₂²	1	2	yes	—
98	#432	C₂²	1	2	yes	—
99	#432	C₂²	1	2	yes	—
100	#432	C₂²	1	2	yes	—
101	#432	C₂²	1	1	yes	characteristic
102	#432	C₂²	1	2	yes	—
103	#432	C₂²	1	2	yes	—
104	#432	C₂²	1	1	yes	characteristic
105	#431	C₂²	1	1	yes	characteristic
106	#431	C₂²	1	1	yes	characteristic
107	#431	C₂²	1	1	yes	characteristic
108	#431	C₂²	1	1	yes	characteristic
109	#431	C₂²	1	2	yes	—
110	#431	C₂²	1	1	yes	characteristic
111	#431	C₂²	1	1	yes	characteristic
112	#431	C₂²	1	2	yes	—
113	#424	C₂²	1	1	yes	characteristic
114	#424	C₂²	1	1	yes	characteristic
115	#424	C₂²	1	2	yes	—
116	#424	C₂²	1	2	yes	—
117	#423	C₂²	1	2	yes	—
118	#423	C₂²	1	1	yes	characteristic
119	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
120	C₂×C₄⋊C₈	C₂²	1	2	yes	—
121	#408	C₂²	1	1	yes	characteristic
122	#408	C₂²	1	1	yes	characteristic
123	#408	C₂²	1	2	yes	—
124	#408	C₂²	1	2	yes	—
125	#408	C₂²	1	2	yes	—
126	#408	C₂²	1	2	yes	—
127	#408	C₂²	1	2	yes	—
128	#405	C₂²	1	2	yes	—
129	#405	C₂²	1	2	yes	—
130	#405	C₂²	1	2	yes	—
131	C₄×M₁₆	C₂²	1	1	yes	characteristic
132	C₄×M₁₆	C₂²	1	2	yes	—
133	C₂×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂×C₄	1	1	yes	characteristic
136	C₂×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₂×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×M₁₆	C₂³	1	2	yes	—
143	C₂×M₁₆	C₂³	1	2	yes	—
144	C₂×M₁₆	C₂³	1	2	yes	—
145	C₂×M₁₆	C₂³	1	2	yes	—
146	C₂×M₁₆	C₂³	1	2	yes	—
147	C₂²×C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₈	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	C₂×C₄	1	1	yes	characteristic
155	C₄⋊Q₈	C₂×C₄	1	2	yes	—
156	#127	C₂×C₄	1	1	yes	characteristic
157	#127	C₂×C₄	1	2	yes	—
158	#126	C₂×C₄	1	2	yes	—
159	#126	C₂×C₄	1	2	yes	—
160	#126	C₂×C₄	1	2	yes	—
161	#126	C₂×C₄	1	2	yes	—
162	#126	C₂×C₄	1	2	yes	—
163	#126	C₂×C₄	1	2	yes	—
164	#125	C₂×C₄	1	1	yes	characteristic
165	#125	C₂×C₄	1	2	yes	—
166	#125	C₂×C₄	1	2	yes	—
167	#125	C₂×C₄	1	1	yes	characteristic
168	#124	C₂×C₄	1	1	yes	characteristic
169	#124	C₂×C₄	1	1	yes	characteristic
170	#124	C₂×C₄	1	2	yes	—
171	#124	C₂×C₄	1	2	yes	—
172	#124	C₂×C₄	1	2	yes	—
173	#124	C₂×C₄	1	2	yes	—
174	#124	C₂×C₄	1	2	yes	—
175	#123	C₂×C₄	1	2	yes	—
176	#123	C₂×C₄	1	2	yes	—
177	#123	C₂×C₄	1	2	yes	—
178	#123	C₂×C₄	1	2	yes	—
179	#123	C₂×C₄	1	2	yes	—
180	#123	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	#121	C₂×C₄	1	1	yes	characteristic
186	#121	C₂×C₄	1	1	yes	characteristic
187	#121	C₂×C₄	1	2	yes	—
188	#121	C₂×C₄	1	2	yes	—
189	#121	C₂×C₄	1	1	yes	characteristic
190	#121	C₂×C₄	1	1	yes	characteristic
191	#121	C₂×C₄	1	2	yes	—
192	#121	C₂×C₄	1	2	yes	—
193	#121	C₂×C₄	1	2	yes	—
194	#121	C₂×C₄	1	2	yes	—
195	#121	C₂×C₄	1	2	yes	—
196	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈	C₂×C₄	1	2	yes	—
199	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
200	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
201	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
202	C₄×Q₈	C₂×C₄	1	2	yes	—
203	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
204	C₄×Q₈	C₂×C₄	1	2	yes	—
205	C₄×Q₈	C₂³	1	1	yes	characteristic
206	C₄×Q₈	C₂³	1	1	yes	characteristic
207	C₄×Q₈	C₂³	1	2	yes	—
208	C₄×D₄	C₂×C₄	1	1	yes	characteristic
209	C₄×D₄	C₂×C₄	1	1	yes	characteristic
210	C₄×D₄	C₂×C₄	1	2	yes	—
211	C₄×D₄	C₂×C₄	1	2	yes	—
212	C₄×D₄	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄	C₂×C₄	1	2	yes	—
214	C₄×D₄	C₂×C₄	1	1	yes	characteristic
215	C₄×D₄	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄	C₂×C₄	1	2	yes	—
217	C₄×D₄	C₂×C₄	1	2	yes	—
218	C₄×D₄	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄	C₂×C₄	1	2	yes	—
221	C₄×D₄	C₂×C₄	1	2	yes	—
222	C₄×D₄	C₂×C₄	1	1	yes	characteristic
223	C₄×D₄	C₂×C₄	1	2	yes	—
224	C₄×D₄	C₂³	1	1	yes	characteristic
225	C₄×D₄	C₂³	1	1	yes	characteristic
226	C₄×D₄	C₂³	1	2	yes	—
227	C₄×D₄	C₂³	1	2	yes	—
228	C₄×D₄	C₂³	1	2	yes	—
229	C₄×D₄	C₂³	1	2	yes	—
230	C₄×D₄	C₂³	1	2	yes	—
231	#117	C₂×C₄	1	1	yes	characteristic
232	#117	C₂×C₄	1	1	yes	characteristic
233	#117	C₂×C₄	1	2	yes	—
234	#117	C₂×C₄	1	2	yes	—
235	#117	C₂³	1	1	yes	characteristic
236	#117	C₂³	1	1	yes	characteristic
237	#117	C₂³	1	2	yes	—
238	#117	C₂³	1	1	yes	characteristic
239	#117	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
242	C₂×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₄²	C₂³	1	2	yes	—
244	C₂×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₄²	C₂³	1	2	yes	—
246	C₂×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₄²	C₂³	1	2	yes	—
248	C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₄⋊C₈	C₂³	1	2	yes	—
250	C₄⋊C₈	C₂³	1	2	yes	—
251	C₄⋊C₈	C₂³	1	2	yes	—
252	C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₄⋊C₈	C₂³	1	2	yes	—
255	C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₄⋊C₈	C₂³	1	2	yes	—
259	C₄⋊C₈	C₂³	1	2	yes	—
260	C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₄⋊C₈	C₂³	1	2	yes	—
267	C₄⋊C₈	C₂³	1	2	yes	—
268	C₄⋊C₈	C₂³	1	2	yes	—
269	C₄⋊C₈	C₂³	1	2	yes	—
270	C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂²⋊C₈	C₂³	1	2	yes	—
276	C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂²⋊C₈	C₂³	1	2	yes	—
289	C₂²⋊C₈	C₂³	1	2	yes	—
290	#97	C₂³	1	1	yes	characteristic
291	#97	C₂³	1	2	yes	—
292	#97	C₂³	1	2	yes	—
293	#97	C₂³	1	2	yes	—
294	#97	C₂³	1	1	yes	characteristic
295	#97	C₂³	1	2	yes	—
296	#97	C₂³	1	2	yes	—
297	#97	C₂³	1	2	yes	—
298	#97	C₂³	1	2	yes	—
299	#97	C₂³	1	2	yes	—
300	C₄×C₈	C₂³	1	1	yes	characteristic
301	C₄×C₈	C₂³	1	1	yes	characteristic
302	C₄×C₈	C₂³	1	1	yes	characteristic
303	C₄×C₈	C₂³	1	1	yes	characteristic
304	C₄×C₈	C₂³	1	2	yes	—
305	C₄×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₈	C₂³	1	1	yes	characteristic
307	C₄×C₈	C₂³	1	2	yes	—
308	C₄×C₈	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	2	yes	—
310	#41	—	4	1	no	—
311	#41	—	4	2	no	—
312	#41	—	4	1	no	—
313	#41	—	4	2	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
319	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
320	C₂×Q₈	C₂²×C₄	1	2	yes	—
321	C₂×Q₈	C₂²×C₄	1	2	yes	—
322	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₄	1	2	yes	—
327	C₂×D₄	C₂²×C₄	1	2	yes	—
328	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₄	C₂²×C₄	1	2	yes	—
330	C₂×D₄	C₂²×C₄	1	2	yes	—
331	C₂×D₄	C₂²×C₄	1	2	yes	—
332	C₂×D₄	C₂²×C₄	1	2	yes	—
333	C₂×D₄	C₂²×C₄	1	2	yes	—
334	C₂×D₄	C₂²×C₄	1	2	yes	—
335	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄	1	2	yes	—
340	C₂²×C₄	C₂²×C₄	1	2	yes	—
341	C₂²×C₄	C₂²×C₄	1	2	yes	—
342	C₂²×C₄	C₂²×C₄	1	2	yes	—
343	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄	1	2	yes	—
345	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄	1	2	yes	—
347	C₂²×C₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴	1	2	yes	—
350	C₂²×C₄	C₂⁴	1	2	yes	—
351	C₂²×C₄	C₂⁴	1	1	yes	characteristic
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	4	1	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	—	4	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₈	C₂⁴	1	1	yes	characteristic
368	C₂×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₈	C₂⁴	1	2	yes	—
372	C₂×C₈	C₂⁴	1	2	yes	—
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₈	C₂⁴	1	2	yes	—
377	C₂×C₈	C₂⁴	1	2	yes	—
378	C₄⋊C₄	C₂²×C₄	1	2	yes	—
379	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄	C₂²×C₄	1	2	yes	—
386	C₄⋊C₄	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
390	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	C₄⋊C₄	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂²×C₄	1	2	yes	—
395	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄	C₂²×C₄	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
403	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
404	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
406	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
417	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
424	C₄²	C₂²×C₄	1	1	yes	characteristic
425	C₄²	C₂²×C₄	1	2	yes	—
426	C₄²	C₂²×C₄	1	1	yes	characteristic
427	C₄²	C₂²×C₄	1	2	yes	—
428	C₄²	C₂²×C₄	1	2	yes	—
429	C₄²	C₂²×C₄	1	2	yes	—
430	C₄²	C₂²×C₄	1	1	yes	characteristic
431	C₄²	C₂²×C₄	1	1	yes	characteristic
432	C₄²	C₂²×C₄	1	1	yes	characteristic
433	C₄²	C₂²×C₄	1	2	yes	—
434	C₄²	C₂²×C₄	1	2	yes	—
435	C₄²	C₂²×C₄	1	1	yes	characteristic
436	C₄²	C₂⁴	1	1	yes	characteristic
437	C₄²	C₂⁴	1	1	yes	characteristic
438	C₄²	C₂⁴	1	2	yes	—
439	C₄²	C₂⁴	1	1	yes	characteristic
440	C₄²	C₂⁴	1	2	yes	—
441	C₄²	C₂⁴	1	1	yes	characteristic
442	C₂³	C₂³×C₄	1	1	yes	characteristic
443	C₂³	C₂³×C₄	1	1	yes	characteristic
444	C₂³	C₂³×C₄	1	2	yes	—
445	C₂³	C₂³×C₄	1	2	yes	—
446	C₂³	C₂³×C₄	1	1	yes	characteristic
447	Q₈	—	2	2	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	1	no	—
451	Q₈	—	4	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄	C₂³×C₄	1	2	yes	—
492	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₄	1	2	yes	—
495	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄	C₂³×C₄	1	2	yes	—
497	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄	C₂³×C₄	1	2	yes	—
499	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
500	C₂×C₄	C₂³×C₄	1	2	yes	—
501	C₂×C₄	C₂³×C₄	1	2	yes	—
502	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
503	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
504	C₂×C₄	C₂⁵	1	1	yes	characteristic
505	C₈	—	2	1	no	—
506	C₈	—	2	2	no	—
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	2	1	no	—
510	C₈	—	2	2	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	2	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	C₂⁴×C₄	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	#568	1	2	yes	—
550	C₄	#585	1	1	yes	characteristic
551	C₄	#585	1	1	yes	characteristic
552	C₂	—	4	1	no	—
553	C₂	—	4	1	no	—
554	C₂	—	4	1	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	2	no	—
557	C₂	#3428	1	1	yes	characteristic
558	C₂	C₂×#568	1	1	yes	characteristic
559	C₂	#3573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3480	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2995	C₂	semidirect
3. #2994	C₂	semidirect
4. #2993	C₂	semidirect
5. #2992	C₂	semidirect
6. #2990	C₂	semidirect
7. #2989	C₂	semidirect
8. #2984	C₂	semidirect
9. #2983	C₂	semidirect
10. #2981	C₂	semidirect
11. #2981	C₂	semidirect
12. #2980	C₂	semidirect
13. #2979	C₂	semidirect
14. #2970	C₂	semidirect
15. #2969	C₂	semidirect
16. #2968	C₂	semidirect
17. #2967	C₂	semidirect
18. #2966	C₂	semidirect
19. #2965	C₂	semidirect
20. #2925	C₂	semidirect
21. #2925	C₂	semidirect
22. #2923	C₂	semidirect
23. #2922	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3480	2
#2995	2
#2994	2
#2993	2
#2992	2
#2990	2
#2989	2
#2984	2
#2983	2
#2981	2
#2980	2
#2979	2
#2970	2
#2969	2
#2968	2
#2967	2
#2966	2
#2965	2
#2925	2
#2923	2
#2922	2