Subgroups — #60342

Order 256.

851 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3482	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	2	yes	maximal, complemented
8	#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	#2987	C₂	1	2	yes	maximal, complemented
10	#2985	C₂	1	1	yes	maximal, characteristic, complemented
11	#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	#2983	C₂	1	1	yes	maximal, characteristic, complemented
13	#2970	C₂	1	2	yes	maximal, 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	Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
21	#2962	C₂	1	1	yes	maximal, characteristic, complemented
22	#2961	C₂	1	2	yes	maximal, complemented
23	C₂×#446	C₂	1	1	yes	maximal, characteristic, complemented
24	#557	C₄	1	1	yes	characteristic
25	#556	C₄	1	2	yes	—
26	#556	C₄	1	1	yes	characteristic
27	#552	C₄	1	1	yes	characteristic
28	#552	C₄	1	2	yes	—
29	#552	C₄	1	1	yes	characteristic
30	#552	C₄	1	2	yes	—
31	D₄×Q₈	C₄	1	1	yes	characteristic
32	#548	C₄	1	1	yes	characteristic
33	#548	C₄	1	1	yes	characteristic
34	#547	C₄	1	1	yes	characteristic
35	#547	C₄	1	2	yes	—
36	#533	C₂²	1	2	yes	—
37	#533	C₂²	1	1	yes	characteristic
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	2	yes	—
44	C₄×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
47	#446	C₂²	1	2	yes	—
48	#446	C₂²	1	1	yes	characteristic
49	#446	C₂²	1	1	yes	characteristic
50	#446	C₂²	1	1	yes	characteristic
51	#446	C₂²	1	1	yes	characteristic
52	#446	C₂²	1	2	yes	—
53	#446	C₂²	1	1	yes	characteristic
54	#446	C₂²	1	2	yes	—
55	#446	C₂²	1	2	yes	—
56	#446	C₂²	1	2	yes	—
57	#446	C₂²	1	2	yes	—
58	#446	C₂²	1	2	yes	—
59	#446	C₂²	1	2	yes	—
60	#446	C₂²	1	1	yes	characteristic
61	#446	C₂²	1	2	yes	—
62	#446	C₂²	1	1	yes	characteristic
63	#446	C₂²	1	2	yes	—
64	#446	C₂²	1	1	yes	characteristic
65	#446	C₂²	1	1	yes	characteristic
66	#446	C₂²	1	2	yes	—
67	#446	C₂²	1	2	yes	—
68	#446	C₂²	1	1	yes	characteristic
69	#446	C₂²	1	2	yes	—
70	C₈×Q₈	C₂²	1	1	yes	characteristic
71	C₈×Q₈	C₂²	1	1	yes	characteristic
72	C₈×Q₈	C₂²	1	1	yes	characteristic
73	C₈×Q₈	C₂²	1	1	yes	characteristic
74	#436	C₂²	1	1	yes	characteristic
75	#436	C₂²	1	1	yes	characteristic
76	#436	C₂²	1	1	yes	characteristic
77	#436	C₂²	1	2	yes	—
78	#436	C₂²	1	1	yes	characteristic
79	#436	C₂²	1	2	yes	—
80	#435	C₂²	1	1	yes	characteristic
81	#435	C₂²	1	1	yes	characteristic
82	#435	C₂²	1	1	yes	characteristic
83	#435	C₂²	1	1	yes	characteristic
84	#435	C₂²	1	2	yes	—
85	#435	C₂²	1	2	yes	—
86	#435	C₂²	1	2	yes	—
87	#435	C₂²	1	2	yes	—
88	#435	C₂²	1	2	yes	—
89	#435	C₂²	1	2	yes	—
90	#435	C₂²	1	2	yes	—
91	#435	C₂²	1	2	yes	—
92	#435	C₂²	1	2	yes	—
93	#435	C₂²	1	2	yes	—
94	C₈×D₄	C₂²	1	2	yes	—
95	C₈×D₄	C₂²	1	1	yes	characteristic
96	C₈×D₄	C₂²	1	2	yes	—
97	C₈×D₄	C₂²	1	2	yes	—
98	C₈×D₄	C₂²	1	1	yes	characteristic
99	#433	C₂²	1	2	yes	—
100	#433	C₂²	1	2	yes	—
101	#433	C₂²	1	2	yes	—
102	#433	C₂²	1	2	yes	—
103	#433	C₂²	1	2	yes	—
104	#433	C₂²	1	2	yes	—
105	#432	C₂²	1	1	yes	characteristic
106	#432	C₂²	1	2	yes	—
107	#432	C₂²	1	2	yes	—
108	#432	C₂²	1	2	yes	—
109	#432	C₂²	1	1	yes	characteristic
110	#432	C₂²	1	2	yes	—
111	#432	C₂²	1	2	yes	—
112	#431	C₂²	1	1	yes	characteristic
113	#431	C₂²	1	1	yes	characteristic
114	#431	C₂²	1	1	yes	characteristic
115	#431	C₂²	1	2	yes	—
116	#431	C₂²	1	1	yes	characteristic
117	#424	C₂²	1	2	yes	—
118	#424	C₂²	1	2	yes	—
119	#424	C₂²	1	2	yes	—
120	#423	C₂²	1	2	yes	—
121	#423	C₂²	1	2	yes	—
122	#423	C₂²	1	1	yes	characteristic
123	C₂×C₄⋊C₈	C₂²	1	2	yes	—
124	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
125	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	#405	C₂²	1	2	yes	—
127	#405	C₂²	1	2	yes	—
128	#405	C₂²	1	2	yes	—
129	C₄×M₁₆	C₂²	1	1	yes	characteristic
130	C₄×M₁₆	C₂²	1	1	yes	characteristic
131	C₄×M₁₆	C₂²	1	2	yes	—
132	C₂×#97	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	2	yes	—
137	C₂×#41	C₂×C₄	1	1	yes	characteristic
138	C₂²×Q₈	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
144	C₂×M₁₆	C₂³	1	1	yes	characteristic
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	2	yes	—
149	C₂²×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	2	yes	—
152	C₂²×C₈	C₂³	1	2	yes	—
153	C₄⋊Q₈	C₂×C₄	1	2	yes	—
154	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
155	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	C₄⋊Q₈	C₂×C₄	1	2	yes	—
157	#126	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	#125	C₂×C₄	1	1	yes	characteristic
164	#125	C₂×C₄	1	2	yes	—
165	#125	C₂×C₄	1	2	yes	—
166	#125	C₂×C₄	1	1	yes	characteristic
167	#125	C₂×C₄	1	2	yes	—
168	#125	C₂×C₄	1	2	yes	—
169	#125	C₂×C₄	1	2	yes	—
170	#124	C₂×C₄	1	1	yes	characteristic
171	#124	C₂×C₄	1	1	yes	characteristic
172	#124	C₂×C₄	1	2	yes	—
173	#124	C₂×C₄	1	2	yes	—
174	#123	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	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
181	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
188	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
189	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	#121	C₂×C₄	1	1	yes	characteristic
192	#121	C₂×C₄	1	1	yes	characteristic
193	#121	C₂×C₄	1	2	yes	—
194	#121	C₂×C₄	1	2	yes	—
195	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
196	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
199	C₄×Q₈	C₂×C₄	1	2	yes	—
200	C₄×Q₈	C₂×C₄	1	2	yes	—
201	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
202	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
203	C₄×Q₈	C₂×C₄	1	2	yes	—
204	C₄×Q₈	C₂³	1	1	yes	characteristic
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×Q₈	C₂³	1	2	yes	—
209	C₄×Q₈	C₂³	1	1	yes	characteristic
210	C₄×Q₈	C₂³	1	2	yes	—
211	C₄×D₄	C₂×C₄	1	1	yes	characteristic
212	C₄×D₄	C₂×C₄	1	2	yes	—
213	C₄×D₄	C₂×C₄	1	1	yes	characteristic
214	C₄×D₄	C₂×C₄	1	2	yes	—
215	C₄×D₄	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄	C₂×C₄	1	1	yes	characteristic
217	C₄×D₄	C₂×C₄	1	2	yes	—
218	C₄×D₄	C₂×C₄	1	2	yes	—
219	C₄×D₄	C₂³	1	1	yes	characteristic
220	C₄×D₄	C₂³	1	1	yes	characteristic
221	C₄×D₄	C₂³	1	2	yes	—
222	C₄×D₄	C₂³	1	1	yes	characteristic
223	C₄×D₄	C₂³	1	2	yes	—
224	C₄×D₄	C₂³	1	1	yes	characteristic
225	C₄×D₄	C₂³	1	2	yes	—
226	#117	C₂×C₄	1	1	yes	characteristic
227	#117	C₂×C₄	1	2	yes	—
228	#117	C₂×C₄	1	1	yes	characteristic
229	#117	C₂×C₄	1	2	yes	—
230	#117	C₂×C₄	1	1	yes	characteristic
231	#117	C₂×C₄	1	2	yes	—
232	#117	C₂×C₄	1	1	yes	characteristic
233	#117	C₂×C₄	1	2	yes	—
234	#117	C₂³	1	2	yes	—
235	#117	C₂³	1	2	yes	—
236	#117	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
241	C₂×C₄²	C₂³	1	1	yes	characteristic
242	C₂×C₄²	C₂³	1	2	yes	—
243	C₂×C₄²	C₂³	1	1	yes	characteristic
244	C₂×C₄²	C₂³	1	2	yes	—
245	C₂×C₄²	C₂³	1	2	yes	—
246	C₂×C₄²	C₂³	1	1	yes	characteristic
247	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
254	C₄⋊C₈	C₂³	1	2	yes	—
255	C₄⋊C₈	C₂³	1	2	yes	—
256	C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₄⋊C₈	C₂³	1	2	yes	—
258	C₄⋊C₈	C₂³	1	2	yes	—
259	C₄⋊C₈	C₂³	1	2	yes	—
260	C₄⋊C₈	C₂³	1	2	yes	—
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₄⋊C₈	C₂³	1	2	yes	—
264	C₄⋊C₈	C₂³	1	2	yes	—
265	C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₄⋊C₈	C₂³	1	2	yes	—
268	C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₄⋊C₈	C₂³	1	2	yes	—
271	C₄⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
276	C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
283	C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂²⋊C₈	C₂³	1	2	yes	—
285	#97	C₂³	1	2	yes	—
286	#97	C₂³	1	1	yes	characteristic
287	#97	C₂³	1	2	yes	—
288	#97	C₂³	1	2	yes	—
289	#97	C₂³	1	2	yes	—
290	#97	C₂³	1	2	yes	—
291	#97	C₂³	1	2	yes	—
292	#97	C₂³	1	1	yes	characteristic
293	#97	C₂³	1	1	yes	characteristic
294	#97	C₂³	1	2	yes	—
295	#97	C₂³	1	1	yes	characteristic
296	#97	C₂³	1	2	yes	—
297	#97	C₂³	1	2	yes	—
298	#97	C₂³	1	2	yes	—
299	C₄×C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
304	C₄×C₈	C₂³	1	1	yes	characteristic
305	C₄×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₈	C₂³	1	2	yes	—
307	C₄×C₈	C₂³	1	2	yes	—
308	C₄×C₈	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	2	yes	—
310	#41	—	4	2	no	—
311	#41	—	4	4	no	—
312	#41	—	4	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
317	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈	C₂²×C₄	1	2	yes	—
319	C₂×Q₈	C₂²×C₄	1	2	yes	—
320	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
325	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄	C₂²×C₄	1	2	yes	—
328	C₂×D₄	C₂²×C₄	1	2	yes	—
329	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄	1	2	yes	—
331	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄	1	2	yes	—
336	C₂²×C₄	C₂²×C₄	1	2	yes	—
337	C₂²×C₄	C₂²×C₄	1	2	yes	—
338	C₂²×C₄	C₂²×C₄	1	2	yes	—
339	C₂²×C₄	C₂²×C₄	1	2	yes	—
340	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₄	C₂⁴	1	1	yes	characteristic
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	1	no	—
348	M₁₆	—	4	2	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	4	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₈	C₂⁴	1	2	yes	—
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₈	C₂⁴	1	1	yes	characteristic
365	C₂×C₈	C₂⁴	1	2	yes	—
366	C₂×C₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₈	C₂⁴	1	2	yes	—
368	C₂×C₈	C₂⁴	1	2	yes	—
369	C₂×C₈	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	C₄⋊C₄	C₂²×C₄	1	2	yes	—
377	C₄⋊C₄	C₂²×C₄	1	2	yes	—
378	C₄⋊C₄	C₂²×C₄	1	2	yes	—
379	C₄⋊C₄	C₂²×C₄	1	2	yes	—
380	C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄	C₂²×C₄	1	2	yes	—
382	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
389	C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	2	yes	—
396	C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
409	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
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	2	yes	—
415	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
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	C₄²	C₂²×C₄	1	2	yes	—
421	C₄²	C₂²×C₄	1	1	yes	characteristic
422	C₄²	C₂²×C₄	1	1	yes	characteristic
423	C₄²	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	2	yes	—
427	C₄²	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
433	C₄²	C₂⁴	1	1	yes	characteristic
434	C₄²	C₂⁴	1	2	yes	—
435	C₄²	C₂⁴	1	1	yes	characteristic
436	C₄²	C₂⁴	1	2	yes	—
437	C₄²	C₂⁴	1	2	yes	—
438	C₄²	C₂⁴	1	1	yes	characteristic
439	C₂³	C₂³×C₄	1	1	yes	characteristic
440	C₂³	C₂³×C₄	1	2	yes	—
441	C₂³	C₂³×C₄	1	1	yes	characteristic
442	C₂³	C₂³×C₄	1	1	yes	characteristic
443	Q₈	—	2	2	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	2	no	—
450	D₄	—	2	2	no	—
451	D₄	—	2	4	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
480	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
481	C₂×C₄	C₂³×C₄	1	2	yes	—
482	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
483	C₂×C₄	C₂³×C₄	1	2	yes	—
484	C₂×C₄	C₂³×C₄	1	2	yes	—
485	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
486	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
487	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄	C₂³×C₄	1	2	yes	—
489	C₂×C₄	C₂³×C₄	1	2	yes	—
490	C₂×C₄	C₂³×C₄	1	2	yes	—
491	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄	C₂³×C₄	1	2	yes	—
493	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄	C₂⁵	1	1	yes	characteristic
496	C₈	—	2	1	no	—
497	C₈	—	2	2	no	—
498	C₈	—	2	1	no	—
499	C₈	—	2	1	no	—
500	C₈	—	2	2	no	—
501	C₈	—	2	2	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	2	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	2₋¹⁺⁴	1	2	yes	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	#568	1	2	yes	—
520	C₂²	C₂⁴×C₄	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	#568	1	2	yes	—
539	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
540	C₄	#585	1	1	yes	characteristic
541	C₂	—	2	2	no	—
542	C₂	—	4	1	no	—
543	C₂	—	4	1	no	—
544	C₂	—	4	2	no	—
545	C₂	C₄×2₋¹⁺⁴	1	1	yes	characteristic
546	C₂	C₂×#568	1	1	yes	characteristic
547	C₂	C₂×#568	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3482	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. #2989	C₂	semidirect
9. #2987	C₂	semidirect
10. #2985	C₂	semidirect
11. #2984	C₂	semidirect
12. #2983	C₂	semidirect
13. #2970	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. Q₈×M₁₆	C₂	semidirect
21. #2962	C₂	semidirect
22. #2961	C₂	semidirect
23. C₂×#446	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3482	2
#2995	2
#2994	2
#2993	2
#2992	2
#2990	2
#2989	2
#2987	2
#2985	2
#2984	2
#2983	2
#2970	2
#2969	2
#2968	2
#2967	2
#2966	2
#2965	2
Q₈×M₁₆	2
#2962	2
#2961	2
C₂×#446	2