Subgroups — C₁₇×#25428 #16883172

Order 4352.

1086 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2428	C₂	1	1	yes	maximal, characteristic
7	C₁₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#2041	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#121	—	2	1	no	—
26	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#492	—	2	4	no	—
31	C₁₇×#468	—	2	4	no	—
32	C₁₇×#468	—	2	4	no	—
33	C₁₇×#440	—	2	4	no	—
34	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
47	C₁₇×#398	—	2	1	no	—
48	C₁₇×#396	—	2	1	no	—
49	C₁₇×#394	—	2	1	no	—
50	C₁₇×#392	—	2	1	no	—
51	C₁₇×#391	C₂²	1	1	yes	characteristic
52	C₁₇×#390	C₂²	1	1	yes	characteristic
53	C₁₇×#389	—	2	1	no	—
54	C₁₇×#389	C₂²	1	1	yes	characteristic
55	C₁₇×#389	C₂²	1	1	yes	characteristic
56	C₁₇×#388	—	2	1	no	—
57	C₁₇×#386	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#340	C₂²	1	1	yes	characteristic
60	C₁₇×#340	C₂²	1	1	yes	characteristic
61	C₁₇×#336	C₂²	1	1	yes	characteristic
62	C₁₇×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₇	—	2	1	no	—
66	C₂²×D₄×C₁₇	—	2	1	no	—
67	C₂²×D₄×C₁₇	—	2	1	no	—
68	C₂²×D₄×C₁₇	—	2	1	no	—
69	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₇	—	2	1	no	—
72	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
73	C₂×SD₁₆×C₁₇	—	2	2	no	—
74	C₂×SD₁₆×C₁₇	—	2	2	no	—
75	C₂×SD₁₆×C₁₇	—	2	2	no	—
76	C₂×SD₁₆×C₁₇	—	2	2	no	—
77	C₂×SD₁₆×C₁₇	—	2	2	no	—
78	C₂×SD₁₆×C₁₇	—	2	2	no	—
79	C₂×SD₁₆×C₁₇	—	2	2	no	—
80	C₂×SD₁₆×C₁₇	—	2	2	no	—
81	C₂×SD₁₆×C₁₇	—	2	2	no	—
82	C₂×SD₁₆×C₁₇	—	4	1	no	—
83	C₂×SD₁₆×C₁₇	—	4	1	no	—
84	C₂×SD₁₆×C₁₇	D₄	1	4	yes	complemented
85	C₂×M₁₆×C₁₇	—	2	2	no	—
86	C₂×M₁₆×C₁₇	—	2	2	no	—
87	C₂×M₁₆×C₁₇	—	2	2	no	—
88	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
92	C₁₇×C₄⋊Q₈	—	2	2	no	—
93	C₁₇×C₄⋊Q₈	—	4	1	no	—
94	C₁₇×#127	—	2	2	no	—
95	C₁₇×#127	—	4	1	no	—
96	C₁₇×C₂²⋊Q₈	—	2	2	no	—
97	C₁₇×C₂²⋊Q₈	—	2	2	no	—
98	C₁₇×C₂²⋊Q₈	—	4	1	no	—
99	C₁₇×C₂²⋊Q₈	—	4	1	no	—
100	C₁₇×#121	—	2	2	no	—
101	C₁₇×#121	—	2	2	no	—
102	C₁₇×#121	—	4	4	no	—
103	C₁₇×#121	—	4	1	no	—
104	C₁₇×#121	—	4	1	no	—
105	C₄×Q₈×C₁₇	—	2	2	no	—
106	C₄×Q₈×C₁₇	—	4	1	no	—
107	C₄×D₄×C₁₇	—	2	2	no	—
108	C₄×D₄×C₁₇	—	4	1	no	—
109	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₇	—	2	1	no	—
130	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
132	C₁₇×#107	—	2	2	no	—
133	C₁₇×#107	D₄	1	4	yes	complemented
134	C₁₇×#103	—	2	2	no	—
135	C₁₇×#103	—	2	2	no	—
136	C₁₇×#103	—	2	2	no	—
137	C₁₇×#103	—	4	1	no	—
138	C₁₇×#102	—	2	2	no	—
139	C₁₇×#102	—	2	2	no	—
140	C₁₇×#102	—	2	2	no	—
141	C₁₇×#102	—	4	1	no	—
142	C₁₇×C₂²⋊C₈	—	2	2	no	—
143	C₁₇×#97	—	2	2	no	—
144	C₄×C₈×C₁₇	—	2	2	no	—
145	C₁₇×#95	—	2	1	no	—
146	C₁₇×#95	—	2	1	no	—
147	C₁₇×#95	—	2	1	no	—
148	C₁₇×#95	—	2	1	no	—
149	C₁₇×#95	D₄	1	1	yes	characteristic
150	C₁₇×#95	D₄	1	1	yes	characteristic
151	C₂⁴×C₁₇	—	2	1	no	—
152	C₂⁴×C₁₇	—	2	1	no	—
153	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₇	—	2	1	no	—
155	C₂×Q₈×C₁₇	—	2	1	no	—
156	C₂×Q₈×C₁₇	—	2	1	no	—
157	C₂×Q₈×C₁₇	—	2	1	no	—
158	C₂×Q₈×C₁₇	—	2	1	no	—
159	C₂×Q₈×C₁₇	—	2	1	no	—
160	C₂×Q₈×C₁₇	—	2	1	no	—
161	C₂×Q₈×C₁₇	—	2	1	no	—
162	C₂×Q₈×C₁₇	—	2	1	no	—
163	C₂×Q₈×C₁₇	—	2	1	no	—
164	C₂×Q₈×C₁₇	—	2	1	no	—
165	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₁₇	—	2	1	no	—
167	C₂×D₄×C₁₇	—	2	1	no	—
168	C₂×D₄×C₁₇	—	2	1	no	—
169	C₂×D₄×C₁₇	—	2	1	no	—
170	C₂×D₄×C₁₇	—	2	1	no	—
171	C₂×D₄×C₁₇	—	2	1	no	—
172	C₂×D₄×C₁₇	—	2	1	no	—
173	C₂×D₄×C₁₇	—	2	1	no	—
174	C₂×D₄×C₁₇	—	2	1	no	—
175	C₂×D₄×C₁₇	—	2	1	no	—
176	C₂×D₄×C₁₇	—	2	1	no	—
177	C₂×D₄×C₁₇	—	4	2	no	—
178	C₂×D₄×C₁₇	—	4	2	no	—
179	C₂×D₄×C₁₇	—	4	2	no	—
180	C₂×D₄×C₁₇	—	4	2	no	—
181	C₂×D₄×C₁₇	—	4	2	no	—
182	C₂×D₄×C₁₇	—	4	2	no	—
183	C₂×D₄×C₁₇	—	4	2	no	—
184	C₂×D₄×C₁₇	—	4	2	no	—
185	C₂×D₄×C₁₇	—	8	1	no	—
186	C₂×D₄×C₁₇	—	8	1	no	—
187	C₂×D₄×C₁₇	—	8	1	no	—
188	C₂×D₄×C₁₇	—	8	1	no	—
189	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₁₇	—	2	1	no	—
191	C₂²×C₄×C₁₇	—	2	1	no	—
192	C₂²×C₄×C₁₇	—	2	1	no	—
193	C₂²×C₄×C₁₇	—	2	1	no	—
194	C₂²×C₄×C₁₇	—	2	1	no	—
195	C₂²×C₄×C₁₇	—	2	1	no	—
196	C₂²×C₄×C₁₇	—	2	1	no	—
197	C₂²×C₄×C₁₇	—	2	1	no	—
198	C₂²×C₄×C₁₇	—	2	1	no	—
199	C₂²×C₄×C₁₇	—	2	1	no	—
200	C₂²×C₄×C₁₇	—	2	1	no	—
201	C₂²×C₄×C₁₇	—	2	1	no	—
202	C₂²×C₄×C₁₇	—	4	2	no	—
203	C₂²×C₄×C₁₇	—	4	2	no	—
204	C₂²×C₄×C₁₇	—	8	1	no	—
205	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
211	SD₁₆×C₁₇	—	2	8	no	—
212	SD₁₆×C₁₇	—	4	4	no	—
213	SD₁₆×C₁₇	—	4	4	no	—
214	SD₁₆×C₁₇	—	4	4	no	—
215	M₁₆×C₁₇	—	4	4	no	—
216	C₂×C₈×C₁₇	—	2	1	no	—
217	C₂×C₈×C₁₇	—	2	1	no	—
218	C₂×C₈×C₁₇	—	2	1	no	—
219	C₂×C₈×C₁₇	—	2	1	no	—
220	C₂×C₈×C₁₇	—	2	1	no	—
221	C₂×C₈×C₁₇	—	2	1	no	—
222	C₂×C₈×C₁₇	—	2	1	no	—
223	C₂×C₈×C₁₇	—	2	1	no	—
224	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
225	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
226	C₂×C₈×C₁₇	#41	1	2	yes	—
227	C₂×C₈×C₁₇	#41	1	2	yes	—
228	C₄⋊C₄×C₁₇	—	2	1	no	—
229	C₄⋊C₄×C₁₇	—	2	1	no	—
230	C₄⋊C₄×C₁₇	—	2	1	no	—
231	C₄⋊C₄×C₁₇	—	2	1	no	—
232	C₄⋊C₄×C₁₇	—	2	1	no	—
233	C₄⋊C₄×C₁₇	—	2	1	no	—
234	C₄⋊C₄×C₁₇	—	4	2	no	—
235	C₄⋊C₄×C₁₇	—	4	2	no	—
236	C₄⋊C₄×C₁₇	—	4	2	no	—
237	C₄⋊C₄×C₁₇	—	4	2	no	—
238	C₄⋊C₄×C₁₇	—	4	2	no	—
239	C₄⋊C₄×C₁₇	—	4	2	no	—
240	C₄⋊C₄×C₁₇	—	4	2	no	—
241	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
243	C₂²⋊C₄×C₁₇	—	2	2	no	—
244	C₂²⋊C₄×C₁₇	—	2	2	no	—
245	C₂²⋊C₄×C₁₇	—	4	2	no	—
246	C₂²⋊C₄×C₁₇	—	4	2	no	—
247	C₂²⋊C₄×C₁₇	—	4	2	no	—
248	C₂²⋊C₄×C₁₇	—	4	2	no	—
249	C₂²⋊C₄×C₁₇	—	4	2	no	—
250	C₂²⋊C₄×C₁₇	—	4	2	no	—
251	C₂²⋊C₄×C₁₇	—	8	1	no	—
252	C₄²×C₁₇	—	2	1	no	—
253	C₄²×C₁₇	—	2	1	no	—
254	C₄²×C₁₇	—	2	1	no	—
255	C₄²×C₁₇	—	2	1	no	—
256	C₄²×C₁₇	—	4	2	no	—
257	#25428	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₁₇	—	2	1	no	—
259	C₂³×C₁₇	—	2	1	no	—
260	C₂³×C₁₇	—	2	1	no	—
261	C₂³×C₁₇	—	2	2	no	—
262	C₂³×C₁₇	—	2	1	no	—
263	C₂³×C₁₇	—	2	1	no	—
264	C₂³×C₁₇	—	2	1	no	—
265	C₂³×C₁₇	—	2	1	no	—
266	C₂³×C₁₇	—	4	1	no	—
267	C₂³×C₁₇	—	4	1	no	—
268	C₂³×C₁₇	—	4	1	no	—
269	C₂³×C₁₇	—	4	1	no	—
270	C₂³×C₁₇	—	4	1	no	—
271	C₂³×C₁₇	—	4	1	no	—
272	C₂³×C₁₇	—	4	1	no	—
273	C₂³×C₁₇	—	4	1	no	—
274	C₂³×C₁₇	—	4	1	no	—
275	C₂³×C₁₇	—	4	1	no	—
276	C₂³×C₁₇	—	4	1	no	—
277	C₂³×C₁₇	—	4	1	no	—
278	C₂³×C₁₇	—	4	1	no	—
279	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₁₇	—	2	2	no	—
281	Q₈×C₁₇	—	2	2	no	—
282	Q₈×C₁₇	—	4	1	no	—
283	Q₈×C₁₇	—	4	1	no	—
284	Q₈×C₁₇	—	4	1	no	—
285	Q₈×C₁₇	—	4	1	no	—
286	Q₈×C₁₇	—	4	1	no	—
287	Q₈×C₁₇	—	4	1	no	—
288	D₄×C₁₇	—	2	2	no	—
289	D₄×C₁₇	—	2	2	no	—
290	D₄×C₁₇	—	4	1	no	—
291	D₄×C₁₇	—	4	1	no	—
292	D₄×C₁₇	—	4	1	no	—
293	D₄×C₁₇	—	4	1	no	—
294	D₄×C₁₇	—	4	1	no	—
295	D₄×C₁₇	—	4	1	no	—
296	D₄×C₁₇	—	8	4	no	—
297	D₄×C₁₇	—	8	4	no	—
298	D₄×C₁₇	—	8	4	no	—
299	D₄×C₁₇	—	8	4	no	—
300	C₂×C₄×C₁₇	—	2	1	no	—
301	C₂×C₄×C₁₇	—	2	1	no	—
302	C₂×C₄×C₁₇	—	2	1	no	—
303	C₂×C₄×C₁₇	—	2	1	no	—
304	C₂×C₄×C₁₇	—	2	1	no	—
305	C₂×C₄×C₁₇	—	2	1	no	—
306	C₂×C₄×C₁₇	—	2	1	no	—
307	C₂×C₄×C₁₇	—	2	2	no	—
308	C₂×C₄×C₁₇	—	2	2	no	—
309	C₂×C₄×C₁₇	—	2	1	no	—
310	C₂×C₄×C₁₇	—	2	1	no	—
311	C₂×C₄×C₁₇	—	2	2	no	—
312	C₂×C₄×C₁₇	—	2	1	no	—
313	C₂×C₄×C₁₇	—	2	1	no	—
314	C₂×C₄×C₁₇	—	2	1	no	—
315	C₂×C₄×C₁₇	—	2	1	no	—
316	C₂×C₄×C₁₇	—	4	1	no	—
317	C₂×C₄×C₁₇	—	4	1	no	—
318	C₂×C₄×C₁₇	—	4	1	no	—
319	C₂×C₄×C₁₇	—	4	1	no	—
320	C₂×C₄×C₁₇	—	4	1	no	—
321	C₂×C₄×C₁₇	—	4	1	no	—
322	C₂×C₄×C₁₇	—	4	1	no	—
323	C₂×C₄×C₁₇	—	4	1	no	—
324	C₂×C₄×C₁₇	—	4	1	no	—
325	C₂×C₄×C₁₇	—	4	1	no	—
326	C₂×C₄×C₁₇	—	4	1	no	—
327	C₂×C₄×C₁₇	—	4	1	no	—
328	C₂×C₄×C₁₇	—	4	1	no	—
329	C₂×C₄×C₁₇	—	4	1	no	—
330	C₂×C₄×C₁₇	—	4	1	no	—
331	C₂×C₄×C₁₇	—	4	1	no	—
332	C₂×C₄×C₁₇	—	4	1	no	—
333	C₂×C₄×C₁₇	—	4	1	no	—
334	C₂×C₄×C₁₇	—	4	1	no	—
335	C₂×C₄×C₁₇	—	8	4	no	—
336	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
337	C₂×C₄×C₁₇	#137	1	2	yes	—
338	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
344	C₈×C₁₇	—	2	2	no	—
345	C₈×C₁₇	—	4	1	no	—
346	C₈×C₁₇	—	4	1	no	—
347	C₈×C₁₇	#121	1	4	yes	complemented
348	C₂×#492	C₂×C₁₇	1	1	yes	characteristic, complemented
349	C₂×#468	C₂×C₁₇	1	1	yes	characteristic, complemented
350	C₂×#468	C₂×C₁₇	1	1	yes	characteristic, complemented
351	C₂×#440	C₂×C₁₇	1	1	yes	characteristic, complemented
352	#2429	C₂×C₁₇	1	1	yes	characteristic, complemented
353	#2428	C₂×C₁₇	1	1	yes	characteristic
354	#2043	C₂×C₁₇	1	1	yes	characteristic, complemented
355	#2041	C₂×C₁₇	1	1	yes	characteristic, complemented
356	#2000	C₂×C₁₇	1	1	yes	characteristic, complemented
357	#2000	C₂×C₁₇	1	1	yes	characteristic, complemented
358	#1973	C₂×C₁₇	1	1	yes	characteristic, complemented
359	#1942	C₂×C₁₇	1	1	yes	characteristic, complemented
360	#1880	C₂×C₁₇	1	1	yes	characteristic, complemented
361	#1877	C₂×C₁₇	1	1	yes	characteristic, complemented
362	#1753	C₂×C₁₇	1	1	yes	characteristic, complemented
363	C₂²×C₁₇	—	4	1	no	—
364	C₂²×C₁₇	—	4	1	no	—
365	C₂²×C₁₇	—	4	1	no	—
366	C₂²×C₁₇	—	4	2	no	—
367	C₂²×C₁₇	—	4	1	no	—
368	C₂²×C₁₇	—	4	2	no	—
369	C₂²×C₁₇	—	4	2	no	—
370	C₂²×C₁₇	—	4	1	no	—
371	C₂²×C₁₇	—	4	1	no	—
372	C₂²×C₁₇	—	4	1	no	—
373	C₂²×C₁₇	—	8	1	no	—
374	C₂²×C₁₇	—	8	1	no	—
375	C₂²×C₁₇	—	8	1	no	—
376	C₂²×C₁₇	—	8	1	no	—
377	C₂²×C₁₇	—	8	1	no	—
378	C₂²×C₁₇	—	8	1	no	—
379	C₂²×C₁₇	—	8	1	no	—
380	C₂²×C₁₇	—	8	1	no	—
381	C₂²×C₁₇	—	8	1	no	—
382	C₂²×C₁₇	—	8	1	no	—
383	C₂²×C₁₇	—	8	1	no	—
384	C₂²×C₁₇	#532	1	1	yes	characteristic
385	C₂²×C₁₇	D₄²	1	1	yes	characteristic
386	C₂²×C₁₇	D₄²	1	1	yes	characteristic
387	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂²×C₁₇	C₂×#137	1	1	yes	characteristic
389	C₂²×C₁₇	#577	1	1	yes	characteristic
390	C₂²×C₁₇	#577	1	1	yes	characteristic
391	C₄×C₁₇	—	2	2	no	—
392	C₄×C₁₇	—	2	2	no	—
393	C₄×C₁₇	—	4	1	no	—
394	C₄×C₁₇	—	4	2	no	—
395	C₄×C₁₇	—	4	1	no	—
396	C₄×C₁₇	—	4	2	no	—
397	C₄×C₁₇	—	4	2	no	—
398	C₄×C₁₇	—	4	1	no	—
399	C₄×C₁₇	—	8	1	no	—
400	C₄×C₁₇	—	8	1	no	—
401	C₄×C₁₇	—	8	1	no	—
402	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
403	C₄×C₁₇	#540	1	1	yes	characteristic
404	C₄×C₁₇	#546	1	1	yes	characteristic
405	C₄×C₁₇	#550	1	1	yes	characteristic
406	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
407	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
409	C₂²×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
410	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
411	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
412	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
415	C₂×#121	—	2	1	no	—
416	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
417	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
420	#492	—	2	4	no	—
421	#468	—	2	4	no	—
422	#468	—	2	4	no	—
423	#440	—	2	4	no	—
424	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
425	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
426	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
427	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
428	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
429	C₂×#103	C₂²×C₁₇	1	1	yes	characteristic
430	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
431	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
432	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
433	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
435	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
436	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
437	#398	—	2	1	no	—
438	#396	—	2	1	no	—
439	#394	—	2	1	no	—
440	#392	—	2	1	no	—
441	#391	C₂²×C₁₇	1	1	yes	characteristic
442	#390	C₂²×C₁₇	1	1	yes	characteristic
443	#389	—	2	1	no	—
444	#389	C₂²×C₁₇	1	1	yes	characteristic
445	#389	C₂²×C₁₇	1	1	yes	characteristic
446	#388	—	2	1	no	—
447	#386	—	2	1	no	—
448	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
449	#340	C₂²×C₁₇	1	1	yes	characteristic
450	#340	C₂²×C₁₇	1	1	yes	characteristic
451	#336	C₂²×C₁₇	1	1	yes	characteristic
452	#336	C₂²×C₁₇	1	1	yes	characteristic
453	C₂×C₁₇	—	8	1	no	—
454	C₂×C₁₇	—	8	2	no	—
455	C₂×C₁₇	—	16	1	no	—
456	C₂×C₁₇	#2428	1	1	yes	characteristic
457	C₂×C₁₇	#3174	1	1	yes	characteristic
458	C₂×C₁₇	#3182	1	1	yes	characteristic
459	C₂×C₁₇	#3265	1	1	yes	characteristic
460	C₂×C₁₇	#3266	1	1	yes	characteristic
461	C₂×C₁₇	#3272	1	1	yes	characteristic
462	C₂×C₁₇	#3278	1	1	yes	characteristic
463	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	2	2	no	—
478	C₂×SD₁₆	—	2	2	no	—
479	C₂×SD₁₆	—	2	2	no	—
480	C₂×SD₁₆	—	2	2	no	—
481	C₂×SD₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	4	1	no	—
483	C₂×SD₁₆	—	4	1	no	—
484	C₂×SD₁₆	D₄×C₁₇	1	4	yes	complemented
485	C₂×M₁₆	—	2	2	no	—
486	C₂×M₁₆	—	2	2	no	—
487	C₂×M₁₆	—	2	2	no	—
488	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	—	4	1	no	—
494	#127	—	2	2	no	—
495	#127	—	4	1	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	4	1	no	—
499	C₂²⋊Q₈	—	4	1	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	4	4	no	—
503	#121	—	4	1	no	—
504	#121	—	4	1	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	4	1	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	4	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
532	#107	—	2	2	no	—
533	#107	D₄×C₁₇	1	4	yes	complemented
534	#103	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	—	2	2	no	—
537	#103	—	4	1	no	—
538	#102	—	2	2	no	—
539	#102	—	2	2	no	—
540	#102	—	2	2	no	—
541	#102	—	4	1	no	—
542	C₂²⋊C₈	—	2	2	no	—
543	#97	—	2	2	no	—
544	C₄×C₈	—	2	2	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	#95	—	2	1	no	—
549	#95	D₄×C₁₇	1	1	yes	characteristic
550	#95	D₄×C₁₇	1	1	yes	characteristic
551	C₁₇	#25428	1	1	yes	characteristic, direct product factor, Sylow
552	C₂⁴	—	2	1	no	—
553	C₂⁴	—	2	1	no	—
554	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	—	8	1	no	—
588	C₂×D₄	—	8	1	no	—
589	C₂×D₄	—	8	1	no	—
590	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	8	1	no	—
606	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
612	SD₁₆	—	2	8	no	—
613	SD₁₆	—	4	4	no	—
614	SD₁₆	—	4	4	no	—
615	SD₁₆	—	4	4	no	—
616	M₁₆	—	4	4	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
626	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
627	C₂×C₈	#41×C₁₇	1	2	yes	—
628	C₂×C₈	#41×C₁₇	1	2	yes	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
643	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	8	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	4	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	4	1	no	—
686	Q₈	—	4	1	no	—
687	Q₈	—	4	1	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	2	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	8	4	no	—
697	D₄	—	8	4	no	—
698	D₄	—	8	4	no	—
699	D₄	—	8	4	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
737	C₂×C₄	C₁₇×#137	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
740	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
742	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
743	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
744	C₈	—	2	2	no	—
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	C₁₇×#121	1	4	yes	complemented
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	C₁₇×#532	1	1	yes	characteristic
770	C₂²	D₄²×C₁₇	1	1	yes	characteristic
771	C₂²	D₄²×C₁₇	1	1	yes	characteristic
772	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
773	C₂²	C₂×C₁₇×#137	1	1	yes	characteristic
774	C₂²	C₁₇×#577	1	1	yes	characteristic
775	C₂²	C₁₇×#577	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	—	8	1	no	—
787	C₄	C₂×C₁₇×#121	1	1	yes	characteristic
788	C₄	C₁₇×#540	1	1	yes	characteristic
789	C₄	C₁₇×#546	1	1	yes	characteristic
790	C₄	C₁₇×#550	1	1	yes	characteristic
791	C₂	—	8	1	no	—
792	C₂	—	8	2	no	—
793	C₂	—	16	1	no	—
794	C₂	C₁₇×#2428	1	1	yes	characteristic
795	C₂	C₁₇×#3174	1	1	yes	characteristic
796	C₂	C₁₇×#3182	1	1	yes	characteristic
797	C₂	C₁₇×#3265	1	1	yes	characteristic
798	C₂	C₁₇×#3266	1	1	yes	characteristic
799	C₂	C₁₇×#3272	1	1	yes	characteristic
800	C₂	C₁₇×#3278	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#2428	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₄×C₂²⋊C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#492	C₂	semidirect
2. C₂×C₁₇×#468	C₂	semidirect
3. C₂×C₁₇×#468	C₂	semidirect
4. C₂×C₁₇×#440	C₂	semidirect
5. C₁₇×#2429	C₂	semidirect
7. C₁₇×#2043	C₂	semidirect
8. C₁₇×#2041	C₂	semidirect
9. C₁₇×#2000	C₂	semidirect
10. C₁₇×#2000	C₂	semidirect
11. C₁₇×#1973	C₂	semidirect
12. C₁₇×#1942	C₂	semidirect
13. C₁₇×#1880	C₂	semidirect
14. C₁₇×#1877	C₂	semidirect
15. C₁₇×#1753	C₂	semidirect
84. C₂×SD₁₆×C₁₇	D₄	semidirect
133. C₁₇×#107	D₄	semidirect
257. #25428	C₁₇	direct (N × H)
347. C₈×C₁₇	#121	semidirect
348. C₂×#492	C₂×C₁₇	semidirect
349. C₂×#468	C₂×C₁₇	semidirect
350. C₂×#468	C₂×C₁₇	semidirect
351. C₂×#440	C₂×C₁₇	semidirect
352. #2429	C₂×C₁₇	semidirect
354. #2043	C₂×C₁₇	semidirect
355. #2041	C₂×C₁₇	semidirect
356. #2000	C₂×C₁₇	semidirect
357. #2000	C₂×C₁₇	semidirect
358. #1973	C₂×C₁₇	semidirect
359. #1942	C₂×C₁₇	semidirect
360. #1880	C₂×C₁₇	semidirect
361. #1877	C₂×C₁₇	semidirect
362. #1753	C₂×C₁₇	semidirect
484. C₂×SD₁₆	D₄×C₁₇	semidirect
533. #107	D₄×C₁₇	semidirect
551. C₁₇	#25428	direct (N × H)
747. C₈	C₁₇×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×#492	2
C₂×C₁₇×#468	2
C₂×C₁₇×#440	2
C₁₇×#2429	2
C₁₇×#2428	2
C₁₇×#2043	2
C₁₇×#2041	2
C₁₇×#2000	2
C₁₇×#1973	2
C₁₇×#1942	2
C₁₇×#1880	2
C₁₇×#1877	2
C₁₇×#1753	2
#25428	17

Subgroups — C17×#25428 #16883172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25428 #16883172