Subgroups — #17978829

Order 4352.

484 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545201	C₂	1	1	yes	maximal, characteristic, complemented
2	#14545200	C₂	1	1	yes	maximal, characteristic, complemented
3	#14545169	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545168	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545166	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545165	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545165	C₂	1	1	yes	maximal, characteristic, complemented
8	#14545164	C₂	1	1	yes	maximal, characteristic, complemented
9	#14545151	C₂	1	1	yes	maximal, characteristic, complemented
10	#14545150	C₂	1	1	yes	maximal, characteristic, complemented
11	#14545146	C₂	1	1	yes	maximal, characteristic, complemented
12	#14545121	C₂	1	1	yes	maximal, characteristic, complemented
13	#14545120	C₂	1	1	yes	maximal, characteristic, complemented
14	#14545118	C₂	1	1	yes	maximal, characteristic, complemented
15	#14537754	C₂	1	1	yes	maximal, characteristic
16	C₂×#10587530	C₂²	1	1	yes	characteristic
17	C₂×#10587538	C₂²	1	1	yes	characteristic
18	C₂×#10587538	C₂²	1	1	yes	characteristic
19	C₂×#10587538	C₂²	1	1	yes	characteristic
20	C₂×#10587529	C₂²	1	1	yes	characteristic
21	C₂²×#63216	C₂²	1	1	yes	characteristic
22	#11763730	C₂²	1	1	yes	characteristic
23	#11763730	C₂²	1	1	yes	characteristic
24	#11763730	C₂²	1	1	yes	characteristic
25	#11763730	C₂²	1	1	yes	characteristic
26	#11763730	C₂²	1	1	yes	characteristic
27	#11763730	C₂²	1	1	yes	characteristic
28	#11763730	C₂²	1	1	yes	characteristic
29	#11763730	C₂²	1	1	yes	characteristic
30	C₄⋊#63216	C₂²	1	1	yes	characteristic
31	C₄⋊#63216	C₂²	1	1	yes	characteristic
32	#11763704	C₂²	1	1	yes	characteristic
33	#11763704	C₂²	1	1	yes	characteristic
34	C₂²⋊#63216	C₂²	1	1	yes	characteristic
35	C₂²⋊#63216	C₂²	1	1	yes	characteristic
36	C₂²⋊#63216	C₂²	1	1	yes	characteristic
37	C₂²⋊#63216	C₂²	1	1	yes	characteristic
38	#11763698	C₂²	1	1	yes	characteristic
39	#11763698	C₂²	1	1	yes	characteristic
40	#11763698	C₂²	1	1	yes	characteristic
41	#11763697	C₂²	1	1	yes	characteristic
42	#11763695	C₂²	1	1	yes	characteristic
43	C₄×#63216	C₂²	1	1	yes	characteristic
44	#11763339	C₄	1	1	yes	characteristic
45	#11762937	C₄	1	1	yes	characteristic
46	#11762933	C₂²	1	1	yes	characteristic
47	#11762885	C₄	1	1	yes	characteristic
48	#11762880	C₄	1	1	yes	characteristic
49	D₄×#3622	C₂²	1	1	yes	characteristic
50	#11762872	C₂²	1	1	yes	characteristic
51	#11762872	C₂²	1	1	yes	characteristic
52	#11762869	C₄	1	1	yes	characteristic
53	#11762867	C₄	1	1	yes	characteristic
54	#11762863	C₄	1	1	yes	characteristic
55	#11762767	C₂²	1	1	yes	characteristic
56	#11762766	C₂²	1	1	yes	characteristic
57	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
58	C₁₇×#435	C₄	1	1	yes	characteristic
59	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
62	#10587625	C₈	1	1	yes	characteristic
63	#10587621	C₈	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
66	#10587612	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×#3622	C₂³	1	1	yes	characteristic
69	C₂²×#3622	C₂³	1	1	yes	characteristic
70	C₂×#63218	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
72	#10587584	C₈	1	1	yes	characteristic
73	#10587575	C₈	1	1	yes	characteristic
74	#10587572	C₈	1	1	yes	characteristic
75	#10587571	C₈	1	1	yes	characteristic
76	#10587565	C₈	1	1	yes	characteristic
77	#10587564	C₈	1	1	yes	characteristic
78	#10587558	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
80	#10587538	—	4	1	no	—
81	#10587538	—	4	1	no	—
82	#10587538	—	4	1	no	—
83	C₂×#63216	—	4	1	no	—
84	C₂×#63216	C₂³	1	1	yes	characteristic
85	C₂×#63216	C₂³	1	1	yes	characteristic
86	C₂×#63216	C₂³	1	1	yes	characteristic
87	C₂×#63216	C₂³	1	1	yes	characteristic
88	C₂×#63216	C₂³	1	1	yes	characteristic
89	C₂×#63216	C₂³	1	1	yes	characteristic
90	C₂×#63216	C₂³	1	1	yes	characteristic
91	C₂×#63216	C₂³	1	1	yes	characteristic
92	#10587530	—	4	1	no	—
93	#10587529	—	4	1	no	—
94	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
100	#10587491	C₂×C₄	1	1	yes	characteristic
101	#10587491	C₂×C₄	1	1	yes	characteristic
102	#10587486	C₂×C₄	1	1	yes	characteristic
103	#10587486	C₂×C₄	1	1	yes	characteristic
104	#10587486	C₂×C₄	1	1	yes	characteristic
105	#10587485	C₂×C₄	1	1	yes	characteristic
106	#10587485	C₂×C₄	1	1	yes	characteristic
107	#10587485	C₂×C₄	1	1	yes	characteristic
108	#10587485	C₂×C₄	1	1	yes	characteristic
109	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
112	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
113	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
114	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
115	C₄×#3622	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₁₇	C₂×C₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
125	M₁₆×C₁₇	—	4	1	no	—
126	C₂×C₈×C₁₇	—	4	1	no	—
127	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
132	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
133	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
134	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
136	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
137	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
138	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
139	#63227	C₂×C₈	1	1	yes	characteristic
140	#63227	C₂×C₈	1	1	yes	characteristic
141	#63227	C₂×C₈	1	1	yes	characteristic
142	#63227	C₂×C₈	1	1	yes	characteristic
143	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
144	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
145	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
146	#63225	C₂×C₈	1	1	yes	characteristic
147	#63225	C₂×C₈	1	1	yes	characteristic
148	#63225	C₂×C₈	1	1	yes	characteristic
149	#63225	C₂×C₈	1	1	yes	characteristic
150	#63225	C₂×C₈	1	1	yes	characteristic
151	#63225	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×#3622	—	2	1	no	—
158	C₂×#3622	—	2	1	no	—
159	C₂×#3622	—	2	1	no	—
160	C₂×#3622	—	2	1	no	—
161	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
162	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
163	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
164	C₂×#3622	C₂⁴	1	1	yes	characteristic
165	#63218	—	4	1	no	—
166	C₈×D₁₇	—	2	1	no	—
167	C₈×D₁₇	—	2	1	no	—
168	#63216	—	2	1	no	—
169	#63216	—	2	1	no	—
170	#63216	—	2	1	no	—
171	#63216	—	2	1	no	—
172	#63216	—	2	1	no	—
173	#63216	—	2	1	no	—
174	#63216	—	2	1	no	—
175	#63216	—	2	1	no	—
176	#33509	—	17	1	no	maximal, Sylow
177	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
178	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
179	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
180	D₄×C₁₇	—	4	1	no	—
181	C₂×C₄×C₁₇	—	2	1	no	—
182	C₂×C₄×C₁₇	—	2	1	no	—
183	C₂×C₄×C₁₇	—	2	1	no	—
184	C₂×C₄×C₁₇	—	2	1	no	—
185	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
189	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
190	C₂²⋊D₁₇	—	4	1	no	—
191	C₂²⋊D₁₇	—	4	1	no	—
192	C₂×Dic₁₇	—	4	1	no	—
193	C₂×Dic₁₇	—	4	1	no	—
194	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
195	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
201	C₄×D₁₇	—	2	1	no	—
202	C₄×D₁₇	—	2	1	no	—
203	Dic₃₄	—	4	1	no	—
204	C₈×C₁₇	—	2	1	no	—
205	C₈×C₁₇	—	2	1	no	—
206	C₈×C₁₇	—	2	1	no	—
207	C₈×C₁₇	—	2	1	no	—
208	#3622	—	2	1	no	—
209	#3622	—	2	1	no	—
210	#3622	—	2	1	no	—
211	#3622	H(5,𝔽₂)	1	1	yes	characteristic
212	#3622	2₋¹⁺⁴	1	1	yes	characteristic
213	#2966	—	17	1	no	—
214	#2183	—	17	1	no	—
215	#2183	—	17	1	no	—
216	#2169	—	17	1	no	—
217	#2169	—	17	1	no	—
218	#2168	—	17	1	no	—
219	#2168	—	17	1	no	—
220	#2168	—	17	1	no	—
221	#2168	—	17	1	no	—
222	#2164	—	17	1	no	—
223	#2164	—	17	1	no	—
224	#2163	—	17	1	no	—
225	#2151	—	17	1	no	—
226	#2151	—	17	1	no	—
227	#2150	—	17	1	no	—
228	C₂²×C₁₇	—	2	1	no	—
229	C₂²×C₁₇	—	2	1	no	—
230	C₂²×C₁₇	—	2	1	no	—
231	C₂²×C₁₇	—	2	1	no	—
232	C₂²×C₁₇	—	2	1	no	—
233	C₂²×C₁₇	—	2	1	no	—
234	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
235	C₂×D₁₇	—	2	1	no	—
236	C₂×D₁₇	—	2	1	no	—
237	C₂×D₁₇	—	2	1	no	—
238	C₄×C₁₇	—	2	1	no	—
239	C₄×C₁₇	—	2	1	no	—
240	C₄×C₁₇	—	2	1	no	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	#520	1	1	yes	characteristic
243	C₄×C₁₇	#568	1	1	yes	characteristic
244	Dic₁₇	—	2	1	no	—
245	Dic₁₇	—	2	1	no	—
246	Dic₁₇	—	2	1	no	—
247	Dic₁₇	—	2	1	no	—
248	Dic₁₇	—	2	1	no	—
249	Dic₁₇	—	2	1	no	—
250	Dic₁₇	—	2	1	no	—
251	#529	—	17	1	no	—
252	C₂×M₃₂	—	17	1	no	—
253	C₂×M₃₂	—	17	1	no	—
254	C₂×M₃₂	—	17	1	no	—
255	C₂×M₃₂	—	17	1	no	—
256	C₂²×C₁₆	—	17	1	no	—
257	C₂²×C₁₆	—	17	1	no	—
258	#446	—	17	1	no	—
259	C₈×Q₈	—	17	1	no	—
260	#436	—	17	1	no	—
261	#435	—	17	1	no	—
262	#435	#595	1	1	yes	characteristic
263	C₈×D₄	—	17	1	no	—
264	C₈×D₄	—	17	1	no	—
265	C₈×D₄	—	17	1	no	—
266	#433	—	17	1	no	—
267	#433	—	17	1	no	—
268	#432	—	17	1	no	—
269	#405	—	17	1	no	—
270	#405	—	17	1	no	—
271	C₂×C₄×C₈	—	17	1	no	—
272	C₄⋊C₁₆	—	17	1	no	—
273	C₄⋊C₁₆	—	17	1	no	—
274	C₄⋊C₁₆	—	17	1	no	—
275	C₄⋊C₁₆	—	17	1	no	—
276	C₄⋊C₁₆	—	17	1	no	—
277	C₄⋊C₁₆	—	17	1	no	—
278	C₄⋊C₁₆	—	17	1	no	—
279	C₄⋊C₁₆	—	17	1	no	—
280	C₄⋊C₁₆	—	17	1	no	—
281	C₄⋊C₁₆	—	17	1	no	—
282	C₂²⋊C₁₆	—	17	1	no	—
283	C₂²⋊C₁₆	—	17	1	no	—
284	C₂²⋊C₁₆	—	17	1	no	—
285	C₂²⋊C₁₆	—	17	1	no	—
286	C₂²⋊C₁₆	—	17	1	no	—
287	C₂²⋊C₁₆	—	17	1	no	—
288	#346	—	17	1	no	—
289	#346	—	17	1	no	—
290	#346	—	17	1	no	—
291	#346	—	17	1	no	—
292	C₄×C₁₆	—	17	1	no	—
293	C₄×C₁₆	—	17	1	no	—
294	C₂×C₁₇	—	4	1	no	—
295	C₂×C₁₇	—	4	1	no	—
296	C₂×C₁₇	#2988	1	1	yes	characteristic
297	C₂×C₁₇	#3407	1	1	yes	characteristic
298	C₂×C₁₇	#3407	1	1	yes	characteristic
299	D₁₇	—	4	1	no	—
300	C₂×M₁₆	—	17	1	no	—
301	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
302	C₂²×C₈	—	17	1	no	—
303	C₂²×C₈	—	17	1	no	—
304	C₂²×C₈	—	17	1	no	—
305	C₂²×C₈	C₂×#595	1	1	yes	characteristic
306	#126	—	17	1	no	—
307	#126	—	17	1	no	—
308	#125	—	17	1	no	—
309	#124	—	17	1	no	—
310	#123	—	17	1	no	—
311	#123	—	17	1	no	—
312	C₂²⋊Q₈	—	17	1	no	—
313	#121	—	17	1	no	—
314	C₄×Q₈	—	17	1	no	—
315	C₄×D₄	—	17	1	no	—
316	C₄×D₄	—	17	1	no	—
317	C₄×D₄	C₂×#595	1	1	yes	characteristic
318	#117	—	17	1	no	—
319	#117	—	17	1	no	—
320	C₂×C₄²	—	17	1	no	—
321	M₃₂	—	68	1	no	—
322	M₃₂	—	68	1	no	—
323	M₃₂	—	68	1	no	—
324	M₃₂	—	68	1	no	—
325	C₂×C₁₆	—	17	1	no	—
326	C₂×C₁₆	—	17	1	no	—
327	C₂×C₁₆	—	17	1	no	—
328	C₂×C₁₆	—	17	1	no	—
329	C₂×C₁₆	—	17	1	no	—
330	C₂×C₁₆	—	17	1	no	—
331	C₂×C₁₆	—	17	1	no	—
332	C₂×C₁₆	—	17	1	no	—
333	C₂×C₁₆	—	68	1	no	—
334	C₂×C₁₆	—	68	1	no	—
335	C₄⋊C₈	—	17	1	no	—
336	C₄⋊C₈	—	17	1	no	—
337	C₄⋊C₈	—	17	1	no	—
338	C₄⋊C₈	—	17	1	no	—
339	C₄⋊C₈	—	17	1	no	—
340	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
341	C₂²⋊C₈	—	17	1	no	—
342	C₂²⋊C₈	—	17	1	no	—
343	C₂²⋊C₈	—	17	1	no	—
344	C₂²⋊C₈	—	17	1	no	—
345	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
346	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
347	#97	—	17	1	no	—
348	#97	—	17	1	no	—
349	#97	—	17	1	no	—
350	#97	C₂×#595	1	1	yes	characteristic
351	C₄×C₈	—	17	1	no	—
352	C₄×C₈	—	17	1	no	—
353	C₄×C₈	—	17	1	no	—
354	C₄×C₈	—	17	1	no	—
355	C₄×C₈	—	17	1	no	—
356	C₄×C₈	—	17	1	no	—
357	C₁₇	#33509	1	1	yes	characteristic, complemented, Sylow
358	C₂×Q₈	—	17	1	no	—
359	C₂×D₄	—	17	1	no	—
360	C₂×D₄	—	17	1	no	—
361	C₂×D₄	#63242	1	1	yes	characteristic
362	C₂²×C₄	—	17	1	no	—
363	C₂²×C₄	—	17	1	no	—
364	C₂²×C₄	—	17	1	no	—
365	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
366	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
367	M₁₆	—	4	1	no	—
368	M₁₆	—	68	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	17	1	no	—
371	C₂×C₈	—	17	1	no	—
372	C₂×C₈	—	17	1	no	—
373	C₂×C₈	—	17	1	no	—
374	C₂×C₈	—	34	1	no	—
375	C₂×C₈	—	34	1	no	—
376	C₂×C₈	—	34	1	no	—
377	C₂×C₈	—	34	1	no	—
378	C₂×C₈	—	34	1	no	—
379	C₂×C₈	—	34	1	no	—
380	C₂×C₈	C₂²×#595	1	1	yes	characteristic
381	C₂×C₈	C₂²×#595	1	1	yes	characteristic
382	C₂×C₈	C₂²×#595	1	1	yes	characteristic
383	C₂×C₈	C₂²×#595	1	1	yes	characteristic
384	C₄⋊C₄	—	17	1	no	—
385	C₄⋊C₄	—	17	1	no	—
386	C₄⋊C₄	—	17	1	no	—
387	C₄⋊C₄	—	17	1	no	—
388	C₄⋊C₄	—	17	1	no	—
389	C₄⋊C₄	—	17	1	no	—
390	C₄⋊C₄	—	17	1	no	—
391	C₄⋊C₄	—	17	1	no	—
392	C₄⋊C₄	—	17	1	no	—
393	C₄⋊C₄	#63242	1	1	yes	characteristic
394	C₂²⋊C₄	—	17	1	no	—
395	C₂²⋊C₄	—	17	1	no	—
396	C₂²⋊C₄	—	17	1	no	—
397	C₂²⋊C₄	—	17	1	no	—
398	C₂²⋊C₄	—	17	1	no	—
399	C₂²⋊C₄	—	17	1	no	—
400	C₂²⋊C₄	—	17	1	no	—
401	C₂²⋊C₄	—	17	1	no	—
402	C₂²⋊C₄	#63242	1	1	yes	characteristic
403	C₂²⋊C₄	#63242	1	1	yes	characteristic
404	C₄²	—	17	1	no	—
405	C₄²	—	17	1	no	—
406	C₄²	—	17	1	no	—
407	C₄²	—	17	1	no	—
408	C₄²	—	17	1	no	—
409	C₄²	C₂²×#595	1	1	yes	characteristic
410	C₁₆	—	34	1	no	—
411	C₁₆	—	34	1	no	—
412	C₁₆	—	34	1	no	—
413	C₁₆	—	34	1	no	—
414	C₁₆	—	34	1	no	—
415	C₁₆	—	34	1	no	—
416	C₁₆	—	34	1	no	—
417	C₁₆	—	34	1	no	—
418	C₂³	—	17	1	no	—
419	C₂³	C₂×#63242	1	1	yes	characteristic
420	C₂³	C₂×#63242	1	1	yes	characteristic
421	Q₈	—	68	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	68	1	no	—
424	D₄	—	68	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	17	1	no	—
430	C₂×C₄	—	17	1	no	—
431	C₂×C₄	—	17	1	no	—
432	C₂×C₄	—	17	1	no	—
433	C₂×C₄	—	17	1	no	—
434	C₂×C₄	—	17	1	no	—
435	C₂×C₄	—	17	1	no	—
436	C₂×C₄	—	34	1	no	—
437	C₂×C₄	—	34	1	no	—
438	C₂×C₄	—	68	1	no	—
439	C₂×C₄	—	68	1	no	—
440	C₂×C₄	C₂×#63242	1	1	yes	characteristic
441	C₂×C₄	C₂×#63242	1	1	yes	characteristic
442	C₂×C₄	C₂×#63242	1	1	yes	characteristic
443	C₂×C₄	C₂×#63242	1	1	yes	characteristic
444	C₂×C₄	C₂³×#595	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	17	1	no	—
450	C₈	—	17	1	no	—
451	C₈	—	34	1	no	—
452	C₈	—	34	1	no	—
453	C₈	—	34	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	34	1	no	—
461	C₂²	—	34	1	no	—
462	C₂²	—	34	1	no	—
463	C₂²	C₂²×#63242	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	34	1	no	—
469	C₄	—	34	1	no	—
470	C₄	—	34	1	no	—
471	C₄	—	34	1	no	—
472	C₄	—	34	1	no	—
473	C₄	—	34	1	no	—
474	C₄	—	34	1	no	—
475	C₄	#11763878	1	1	yes	characteristic
476	C₄	#11763887	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	4	1	no	—
479	C₂	—	68	1	no	—
480	C₂	#14545700	1	1	yes	characteristic
481	C₂	#14545752	1	1	yes	characteristic
482	C₂	#14545753	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#435	C₄
prime radical	#10587625	C₈
cosocle	C₂×#3622	C₂⁴
hypercenter	#435	#595
hypocenter	C₁₇	#33509
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. #14545201	C₂	semidirect
2. #14545200	C₂	semidirect
3. #14545169	C₂	semidirect
4. #14545168	C₂	semidirect
5. #14545166	C₂	semidirect
6. #14545165	C₂	semidirect
7. #14545165	C₂	semidirect
8. #14545164	C₂	semidirect
9. #14545151	C₂	semidirect
10. #14545150	C₂	semidirect
11. #14545146	C₂	semidirect
12. #14545121	C₂	semidirect
13. #14545120	C₂	semidirect
14. #14545118	C₂	semidirect
357. C₁₇	#33509	semidirect

Maximal subgroups

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

subgroup	index
#14545201	2
#14545200	2
#14545169	2
#14545168	2
#14545166	2
#14545165	2
#14545164	2
#14545151	2
#14545150	2
#14545146	2
#14545121	2
#14545120	2
#14545118	2
#14537754	2
#33509	17