Subgroups — C₁₇×#61904 #16919648

Order 4352.

1788 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3401	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3400	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3394	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3373	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3371	C₂	1	4	yes	maximal, complemented
8	C₁₇×#3365	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3217	C₂	1	1	yes	maximal, characteristic
10	C₁₇×#3215	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3211	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3114	C₂	1	2	yes	maximal, complemented
14	C₁₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#3101	C₂	1	2	yes	maximal, complemented
17	C₁₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₇×#559	—	2	1	no	—
19	C₁₇×#559	—	2	2	no	—
20	C₁₇×#559	—	2	1	no	—
21	C₁₇×#559	C₂²	1	2	yes	—
22	C₁₇×#559	C₂²	1	4	yes	—
23	C₁₇×#559	C₂²	1	2	yes	—
24	C₁₇×#557	C₂²	1	1	yes	characteristic, complemented
25	C₁₇×#557	C₂²	1	1	yes	characteristic, complemented
26	C₁₇×#557	C₂²	1	2	yes	complemented
27	C₁₇×#556	C₂²	1	1	yes	characteristic, complemented
28	C₁₇×#556	C₂²	1	2	yes	complemented
29	C₁₇×#552	—	2	1	no	—
30	C₁₇×#552	—	2	2	no	—
31	D₄×Q₈×C₁₇	—	2	1	no	—
32	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
33	C₁₇×#541	—	2	1	no	—
34	C₁₇×#541	—	2	2	no	—
35	C₁₇×#533	C₂²	1	1	yes	characteristic
36	C₁₇×#533	C₂²	1	2	yes	—
37	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
38	C₁₇×#529	C₂²	1	2	yes	—
39	C₁₇×#529	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×#124	—	2	1	no	—
41	C₂×C₁₇×#124	C₂²	1	2	yes	—
42	C₂×C₁₇×#123	—	2	2	no	—
43	C₁₇×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₇	—	2	1	no	—
47	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
48	C₁₇×#497	C₂²	1	4	yes	complemented
49	C₁₇×#496	C₂²	1	2	yes	—
50	C₁₇×#495	C₂²	1	4	yes	complemented
51	C₁₇×#492	C₂²	1	2	yes	—
52	C₁₇×#490	C₂²	1	2	yes	—
53	C₁₇×#489	C₂²	1	4	yes	complemented
54	C₁₇×#488	C₂²	1	4	yes	complemented
55	C₁₇×#486	C₂²	1	2	yes	—
56	C₁₇×#483	C₂²	1	1	yes	characteristic
57	C₁₇×#483	C₂²	1	2	yes	—
58	C₁₇×#480	C₂²	1	1	yes	characteristic
59	C₁₇×#479	C₂²	1	2	yes	complemented
60	C₁₇×#478	C₂²	1	4	yes	complemented
61	C₁₇×#476	C₂²	1	4	yes	complemented
62	C₁₇×#475	C₂²	1	2	yes	complemented
63	C₁₇×#464	C₂²	1	4	yes	complemented
64	C₁₇×#464	C₂²	1	4	yes	complemented
65	C₁₇×#464	C₂²	1	4	yes	complemented
66	C₁₇×#464	C₂²	1	2	yes	complemented
67	C₁₇×#463	C₂²	1	4	yes	complemented
68	C₁₇×#463	C₂²	1	4	yes	complemented
69	C₁₇×#462	C₂²	1	2	yes	complemented
70	C₁₇×#461	C₂²	1	4	yes	complemented
71	C₁₇×#460	C₂²	1	4	yes	—
72	C₁₇×#460	C₂²	1	2	yes	—
73	C₁₇×#459	C₂²	1	2	yes	—
74	C₁₇×#451	C₂²	1	2	yes	—
75	C₁₇×#451	C₂²	1	1	yes	characteristic
76	C₁₇×#450	C₂²	1	2	yes	—
77	C₁₇×#450	C₂²	1	2	yes	—
78	C₁₇×#450	C₂²	1	2	yes	—
79	C₁₇×#448	C₂²	1	1	yes	characteristic
80	C₁₇×#447	C₂²	1	2	yes	—
81	C₁₇×#446	C₂²	1	4	yes	complemented
82	C₁₇×#446	C₂²	1	2	yes	complemented
83	C₈×Q₈×C₁₇	C₂²	1	2	yes	complemented
84	C₁₇×#442	C₂²	1	4	yes	complemented
85	C₁₇×#441	C₂²	1	4	yes	complemented
86	C₁₇×#440	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
88	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	complemented
90	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
91	C₁₇×#432	C₂²	1	2	yes	—
92	C₁₇×#432	C₂²	1	1	yes	characteristic
93	C₁₇×#431	C₂²	1	1	yes	characteristic
94	C₁₇×#431	C₂²	1	2	yes	—
95	C₂²×Q₈×C₁₇	—	2	1	no	—
96	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₇	—	2	1	no	—
99	C₂²×D₄×C₁₇	—	2	1	no	—
100	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₇	—	2	2	no	—
102	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
108	C₂×D₈×C₁₇	C₂³	1	4	yes	—
109	C₁₇×C₄⋊Q₈	—	2	1	no	—
110	C₁₇×C₄⋊Q₈	—	2	2	no	—
111	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₇×#127	—	2	1	no	—
116	C₁₇×#127	—	2	1	no	—
117	C₁₇×#127	C₂³	1	2	yes	—
118	C₁₇×#127	C₂³	1	2	yes	—
119	C₁₇×#126	—	2	2	no	—
120	C₁₇×#126	—	2	2	no	—
121	C₁₇×#126	—	2	2	no	—
122	C₁₇×#126	—	2	2	no	—
123	C₁₇×#126	—	2	1	no	—
124	C₁₇×#125	—	2	2	no	—
125	C₁₇×#125	—	2	2	no	—
126	C₁₇×#125	—	2	2	no	—
127	C₁₇×#125	—	2	2	no	—
128	C₁₇×#125	—	2	1	no	—
129	C₁₇×#125	—	2	2	no	—
130	C₁₇×#125	—	2	1	no	—
131	C₁₇×#125	C₂³	1	2	yes	—
132	C₁₇×#125	C₂³	1	1	yes	characteristic
133	C₁₇×#124	—	2	2	no	—
134	C₁₇×#124	—	2	2	no	—
135	C₁₇×#124	—	2	4	no	—
136	C₁₇×#124	—	2	2	no	—
137	C₁₇×#124	—	2	2	no	—
138	C₁₇×#124	C₂³	1	2	yes	—
139	C₁₇×#124	C₂³	1	4	yes	—
140	C₁₇×#124	C₂³	1	1	yes	characteristic
141	C₁₇×#124	C₂³	1	4	yes	—
142	C₁₇×#123	—	2	2	no	—
143	C₁₇×#123	—	2	1	no	—
144	C₁₇×#123	—	2	4	no	—
145	C₁₇×#123	—	2	4	no	—
146	C₁₇×#123	—	2	4	no	—
147	C₁₇×#123	—	2	4	no	—
148	C₁₇×C₂²⋊Q₈	—	2	1	no	—
149	C₁₇×C₂²⋊Q₈	—	2	2	no	—
150	C₁₇×C₂²⋊Q₈	—	2	1	no	—
151	C₁₇×C₂²⋊Q₈	—	2	2	no	—
152	C₁₇×C₂²⋊Q₈	—	2	2	no	—
153	C₁₇×C₂²⋊Q₈	—	2	1	no	—
154	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₇×#121	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₁₇	—	2	1	no	—
158	C₄×Q₈×C₁₇	—	2	2	no	—
159	C₄×Q₈×C₁₇	—	2	1	no	—
160	C₄×Q₈×C₁₇	—	2	1	no	—
161	C₄×Q₈×C₁₇	—	2	1	no	—
162	C₄×Q₈×C₁₇	—	2	2	no	—
163	C₄×Q₈×C₁₇	—	2	1	no	—
164	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₇	D₄	1	2	yes	—
167	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
177	C₄×D₄×C₁₇	—	2	1	no	—
178	C₄×D₄×C₁₇	—	2	2	no	—
179	C₄×D₄×C₁₇	—	2	2	no	—
180	C₄×D₄×C₁₇	—	2	4	no	—
181	C₄×D₄×C₁₇	—	2	2	no	—
182	C₄×D₄×C₁₇	—	2	2	no	—
183	C₄×D₄×C₁₇	—	2	2	no	—
184	C₄×D₄×C₁₇	C₂³	1	4	yes	—
185	C₄×D₄×C₁₇	C₂³	1	4	yes	—
186	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₇	C₂³	1	2	yes	—
188	C₁₇×#117	—	2	2	no	—
189	C₁₇×#117	—	2	1	no	—
190	C₁₇×#117	—	2	2	no	—
191	C₁₇×#117	—	2	1	no	—
192	C₁₇×#117	—	2	2	no	—
193	C₁₇×#117	—	2	1	no	—
194	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
195	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
201	C₂×C₄²×C₁₇	—	2	1	no	—
202	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
204	C₁₇×#107	C₂³	1	2	yes	—
205	C₁₇×#106	C₂³	1	2	yes	—
206	C₁₇×#106	C₂³	1	4	yes	—
207	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
211	C₁₇×#103	C₂³	1	2	yes	—
212	C₁₇×#103	C₂³	1	4	yes	—
213	C₁₇×#103	C₂³	1	2	yes	—
214	C₁₇×#103	C₂³	1	2	yes	—
215	C₁₇×#103	C₂³	1	4	yes	—
216	C₁₇×#102	C₂³	1	2	yes	—
217	C₁₇×#102	C₂³	1	4	yes	—
218	C₁₇×#102	C₂³	1	4	yes	—
219	C₁₇×#102	C₂³	1	4	yes	—
220	C₁₇×#102	C₂³	1	4	yes	—
221	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₁₇×#97	C₂³	1	2	yes	—
225	C₁₇×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₁₇	C₂³	1	2	yes	—
227	C₄×C₈×C₁₇	C₂³	1	4	yes	—
228	C₂⁴×C₁₇	—	2	2	no	—
229	C₂×Q₈×C₁₇	—	2	2	no	—
230	C₂×Q₈×C₁₇	—	2	1	no	—
231	C₂×Q₈×C₁₇	—	2	1	no	—
232	C₂×Q₈×C₁₇	—	4	2	no	—
233	C₂×Q₈×C₁₇	—	4	2	no	—
234	C₂×Q₈×C₁₇	—	4	4	no	—
235	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₇	—	2	1	no	—
242	C₂×D₄×C₁₇	—	2	2	no	—
243	C₂×D₄×C₁₇	—	2	2	no	—
244	C₂×D₄×C₁₇	—	2	2	no	—
245	C₂×D₄×C₁₇	—	2	2	no	—
246	C₂×D₄×C₁₇	—	2	2	no	—
247	C₂×D₄×C₁₇	—	4	4	no	—
248	C₂×D₄×C₁₇	—	4	4	no	—
249	C₂×D₄×C₁₇	—	8	2	no	—
250	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₇	—	2	1	no	—
253	C₂²×C₄×C₁₇	—	2	1	no	—
254	C₂²×C₄×C₁₇	—	2	2	no	—
255	C₂²×C₄×C₁₇	—	2	1	no	—
256	C₂²×C₄×C₁₇	—	2	4	no	—
257	C₂²×C₄×C₁₇	—	2	4	no	—
258	C₂²×C₄×C₁₇	—	8	4	no	—
259	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₁₇	—	4	4	no	—
265	Q₁₆×C₁₇	—	4	2	no	—
266	SD₁₆×C₁₇	—	4	4	no	—
267	SD₁₆×C₁₇	—	4	2	no	—
268	SD₁₆×C₁₇	—	4	4	no	—
269	SD₁₆×C₁₇	—	4	4	no	—
270	D₈×C₁₇	—	4	4	no	—
271	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
272	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
273	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₁₇	—	2	2	no	—
275	C₄⋊C₄×C₁₇	—	2	1	no	—
276	C₄⋊C₄×C₁₇	—	2	2	no	—
277	C₄⋊C₄×C₁₇	—	2	2	no	—
278	C₄⋊C₄×C₁₇	—	2	2	no	—
279	C₄⋊C₄×C₁₇	—	2	2	no	—
280	C₄⋊C₄×C₁₇	—	2	1	no	—
281	C₄⋊C₄×C₁₇	—	2	2	no	—
282	C₄⋊C₄×C₁₇	—	2	1	no	—
283	C₄⋊C₄×C₁₇	—	2	2	no	—
284	C₄⋊C₄×C₁₇	—	2	2	no	—
285	C₄⋊C₄×C₁₇	—	2	2	no	—
286	C₄⋊C₄×C₁₇	—	2	1	no	—
287	C₄⋊C₄×C₁₇	—	2	2	no	—
288	C₄⋊C₄×C₁₇	—	2	1	no	—
289	C₄⋊C₄×C₁₇	—	2	2	no	—
290	C₄⋊C₄×C₁₇	—	2	1	no	—
291	C₄⋊C₄×C₁₇	—	2	1	no	—
292	C₄⋊C₄×C₁₇	—	2	2	no	—
293	C₄⋊C₄×C₁₇	—	2	1	no	—
294	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₁₇	—	2	2	no	—
306	C₂²⋊C₄×C₁₇	—	2	1	no	—
307	C₂²⋊C₄×C₁₇	—	2	2	no	—
308	C₂²⋊C₄×C₁₇	—	2	1	no	—
309	C₂²⋊C₄×C₁₇	—	2	1	no	—
310	C₂²⋊C₄×C₁₇	—	2	2	no	—
311	C₂²⋊C₄×C₁₇	—	2	4	no	—
312	C₂²⋊C₄×C₁₇	—	2	4	no	—
313	C₂²⋊C₄×C₁₇	—	2	4	no	—
314	C₂²⋊C₄×C₁₇	—	2	4	no	—
315	C₂²⋊C₄×C₁₇	—	2	4	no	—
316	C₂²⋊C₄×C₁₇	—	2	4	no	—
317	C₂²⋊C₄×C₁₇	—	2	2	no	—
318	C₂²⋊C₄×C₁₇	—	2	1	no	—
319	C₂²⋊C₄×C₁₇	—	2	1	no	—
320	C₄²×C₁₇	—	2	2	no	—
321	C₄²×C₁₇	—	2	2	no	—
322	C₄²×C₁₇	—	2	2	no	—
323	C₄²×C₁₇	—	2	2	no	—
324	C₄²×C₁₇	—	2	2	no	—
325	C₄²×C₁₇	—	2	2	no	—
326	C₄²×C₁₇	—	2	1	no	—
327	C₄²×C₁₇	C₂×D₄	1	2	yes	—
328	C₄²×C₁₇	C₂×D₄	1	2	yes	—
329	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₇	C₂⁴	1	2	yes	—
332	C₄²×C₁₇	C₂⁴	1	2	yes	—
333	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
334	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
335	#61904	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₁₇	—	2	1	no	—
337	C₂³×C₁₇	—	2	4	no	—
338	C₂³×C₁₇	—	4	4	no	—
339	C₂³×C₁₇	—	4	4	no	—
340	C₂³×C₁₇	—	4	4	no	—
341	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₁₇	—	2	2	no	—
343	Q₈×C₁₇	—	2	2	no	—
344	Q₈×C₁₇	—	2	2	no	—
345	Q₈×C₁₇	—	2	4	no	—
346	Q₈×C₁₇	—	2	2	no	—
347	Q₈×C₁₇	—	2	2	no	—
348	Q₈×C₁₇	—	4	2	no	—
349	Q₈×C₁₇	—	4	2	no	—
350	Q₈×C₁₇	—	4	4	no	—
351	Q₈×C₁₇	—	4	2	no	—
352	D₄×C₁₇	—	2	2	no	—
353	D₄×C₁₇	—	2	4	no	—
354	D₄×C₁₇	—	2	4	no	—
355	D₄×C₁₇	—	4	4	no	—
356	D₄×C₁₇	—	4	4	no	—
357	D₄×C₁₇	—	4	2	no	—
358	D₄×C₁₇	—	4	4	no	—
359	D₄×C₁₇	—	8	2	no	—
360	D₄×C₁₇	—	8	2	no	—
361	C₂×C₄×C₁₇	—	2	4	no	—
362	C₂×C₄×C₁₇	—	2	2	no	—
363	C₂×C₄×C₁₇	—	2	2	no	—
364	C₂×C₄×C₁₇	—	2	2	no	—
365	C₂×C₄×C₁₇	—	2	1	no	—
366	C₂×C₄×C₁₇	—	2	2	no	—
367	C₂×C₄×C₁₇	—	2	1	no	—
368	C₂×C₄×C₁₇	—	2	2	no	—
369	C₂×C₄×C₁₇	—	2	2	no	—
370	C₂×C₄×C₁₇	—	2	2	no	—
371	C₂×C₄×C₁₇	—	2	1	no	—
372	C₂×C₄×C₁₇	—	4	2	no	—
373	C₂×C₄×C₁₇	—	4	4	no	—
374	C₂×C₄×C₁₇	—	4	2	no	—
375	C₂×C₄×C₁₇	—	4	2	no	—
376	C₂×C₄×C₁₇	—	4	2	no	—
377	C₂×C₄×C₁₇	—	8	4	no	—
378	C₂×C₄×C₁₇	—	8	4	no	—
379	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
389	C₈×C₁₇	—	2	4	no	—
390	C₈×C₁₇	—	2	2	no	—
391	C₈×C₁₇	—	2	2	no	—
392	#3523	C₂×C₁₇	1	1	yes	characteristic, complemented
393	C₂×#559	C₂×C₁₇	1	1	yes	characteristic, complemented
394	#3401	C₂×C₁₇	1	4	yes	complemented
395	#3400	C₂×C₁₇	1	2	yes	complemented
396	#3394	C₂×C₁₇	1	2	yes	complemented
397	#3373	C₂×C₁₇	1	2	yes	complemented
398	#3371	C₂×C₁₇	1	4	yes	complemented
399	#3365	C₂×C₁₇	1	2	yes	complemented
400	#3217	C₂×C₁₇	1	1	yes	characteristic
401	#3215	C₂×C₁₇	1	2	yes	complemented
402	#3211	C₂×C₁₇	1	2	yes	complemented
403	#3208	C₂×C₁₇	1	1	yes	characteristic, complemented
404	#3114	C₂×C₁₇	1	2	yes	complemented
405	#3113	C₂×C₁₇	1	1	yes	characteristic, complemented
406	#3108	C₂×C₁₇	1	1	yes	characteristic, complemented
407	#3101	C₂×C₁₇	1	2	yes	complemented
408	#2984	C₂×C₁₇	1	1	yes	characteristic, complemented
409	C₂²×C₁₇	—	2	1	no	—
410	C₂²×C₁₇	—	2	1	no	—
411	C₂²×C₁₇	—	4	4	no	—
412	C₂²×C₁₇	—	4	1	no	—
413	C₂²×C₁₇	—	4	1	no	—
414	C₂²×C₁₇	—	4	4	no	—
415	C₂²×C₁₇	—	4	4	no	—
416	C₂²×C₁₇	—	4	1	no	—
417	C₂²×C₁₇	—	8	8	no	—
418	C₂²×C₁₇	#577	1	2	yes	—
419	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
420	C₄×C₁₇	—	2	1	no	—
421	C₄×C₁₇	—	2	1	no	—
422	C₄×C₁₇	—	2	2	no	—
423	C₄×C₁₇	—	2	2	no	—
424	C₄×C₁₇	—	2	2	no	—
425	C₄×C₁₇	—	2	2	no	—
426	C₄×C₁₇	—	2	1	no	—
427	C₄×C₁₇	—	2	1	no	—
428	C₄×C₁₇	—	4	2	no	—
429	C₄×C₁₇	—	4	1	no	—
430	C₄×C₁₇	—	4	2	no	—
431	C₄×C₁₇	—	4	2	no	—
432	C₄×C₁₇	—	4	1	no	—
433	C₄×C₁₇	—	4	2	no	—
434	C₄×C₁₇	—	4	1	no	—
435	C₄×C₁₇	#575	1	2	yes	—
436	C₄×C₁₇	#585	1	2	yes	—
437	#559	—	2	1	no	—
438	#559	—	2	1	no	—
439	#559	—	2	2	no	—
440	#559	C₂²×C₁₇	1	2	yes	—
441	#559	C₂²×C₁₇	1	4	yes	—
442	#559	C₂²×C₁₇	1	2	yes	—
443	#557	C₂²×C₁₇	1	1	yes	characteristic, complemented
444	#557	C₂²×C₁₇	1	1	yes	characteristic, complemented
445	#557	C₂²×C₁₇	1	2	yes	complemented
446	#556	C₂²×C₁₇	1	1	yes	characteristic, complemented
447	#556	C₂²×C₁₇	1	2	yes	complemented
448	#552	—	2	1	no	—
449	#552	—	2	2	no	—
450	D₄×Q₈	—	2	1	no	—
451	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
452	#541	—	2	2	no	—
453	#541	—	2	1	no	—
454	#533	C₂²×C₁₇	1	2	yes	—
455	#533	C₂²×C₁₇	1	1	yes	characteristic
456	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
457	#529	C₂²×C₁₇	1	1	yes	characteristic
458	#529	C₂²×C₁₇	1	2	yes	—
459	C₂×#124	—	2	1	no	—
460	C₂×#124	C₂²×C₁₇	1	2	yes	—
461	C₂×#123	—	2	2	no	—
462	#519	—	2	1	no	—
463	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
465	C₂×C₄×D₄	—	2	1	no	—
466	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
467	#497	C₂²×C₁₇	1	4	yes	complemented
468	#496	C₂²×C₁₇	1	2	yes	—
469	#495	C₂²×C₁₇	1	4	yes	complemented
470	#492	C₂²×C₁₇	1	2	yes	—
471	#490	C₂²×C₁₇	1	2	yes	—
472	#489	C₂²×C₁₇	1	4	yes	complemented
473	#488	C₂²×C₁₇	1	4	yes	complemented
474	#486	C₂²×C₁₇	1	2	yes	—
475	#483	C₂²×C₁₇	1	1	yes	characteristic
476	#483	C₂²×C₁₇	1	2	yes	—
477	#480	C₂²×C₁₇	1	1	yes	characteristic
478	#479	C₂²×C₁₇	1	2	yes	complemented
479	#478	C₂²×C₁₇	1	4	yes	complemented
480	#476	C₂²×C₁₇	1	4	yes	complemented
481	#475	C₂²×C₁₇	1	2	yes	complemented
482	#464	C₂²×C₁₇	1	2	yes	complemented
483	#464	C₂²×C₁₇	1	4	yes	complemented
484	#464	C₂²×C₁₇	1	4	yes	complemented
485	#464	C₂²×C₁₇	1	4	yes	complemented
486	#463	C₂²×C₁₇	1	4	yes	complemented
487	#463	C₂²×C₁₇	1	4	yes	complemented
488	#462	C₂²×C₁₇	1	2	yes	complemented
489	#461	C₂²×C₁₇	1	4	yes	complemented
490	#460	C₂²×C₁₇	1	2	yes	—
491	#460	C₂²×C₁₇	1	4	yes	—
492	#459	C₂²×C₁₇	1	2	yes	—
493	#451	C₂²×C₁₇	1	1	yes	characteristic
494	#451	C₂²×C₁₇	1	2	yes	—
495	#450	C₂²×C₁₇	1	2	yes	—
496	#450	C₂²×C₁₇	1	2	yes	—
497	#450	C₂²×C₁₇	1	2	yes	—
498	#448	C₂²×C₁₇	1	1	yes	characteristic
499	#447	C₂²×C₁₇	1	2	yes	—
500	#446	C₂²×C₁₇	1	4	yes	complemented
501	#446	C₂²×C₁₇	1	2	yes	complemented
502	C₈×Q₈	C₂²×C₁₇	1	2	yes	complemented
503	#442	C₂²×C₁₇	1	4	yes	complemented
504	#441	C₂²×C₁₇	1	4	yes	complemented
505	#440	C₂²×C₁₇	1	4	yes	complemented
506	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
507	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	complemented
508	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	complemented
509	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
510	#432	C₂²×C₁₇	1	1	yes	characteristic
511	#432	C₂²×C₁₇	1	2	yes	—
512	#431	C₂²×C₁₇	1	2	yes	—
513	#431	C₂²×C₁₇	1	1	yes	characteristic
514	C₂×C₁₇	—	2	2	no	—
515	C₂×C₁₇	—	8	1	no	—
516	C₂×C₁₇	—	8	4	no	—
517	C₂×C₁₇	#3487	1	1	yes	characteristic
518	C₂×C₁₇	C₂×#575	1	1	yes	characteristic
519	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
526	C₂³×C₄	—	2	2	no	—
527	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
528	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
529	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
533	C₂×D₈	C₂³×C₁₇	1	4	yes	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	2	no	—
536	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
540	#127	—	2	1	no	—
541	#127	—	2	1	no	—
542	#127	C₂³×C₁₇	1	2	yes	—
543	#127	C₂³×C₁₇	1	2	yes	—
544	#126	—	2	2	no	—
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	1	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	—	2	1	no	—
556	#125	C₂³×C₁₇	1	2	yes	—
557	#125	C₂³×C₁₇	1	1	yes	characteristic
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#124	—	2	4	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	C₂³×C₁₇	1	4	yes	—
564	#124	C₂³×C₁₇	1	4	yes	—
565	#124	C₂³×C₁₇	1	2	yes	—
566	#124	C₂³×C₁₇	1	1	yes	characteristic
567	#123	—	2	2	no	—
568	#123	—	2	1	no	—
569	#123	—	2	4	no	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
580	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
581	#121	C₂³×C₁₇	1	1	yes	characteristic
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
590	C₄×Q₈	D₄×C₁₇	1	2	yes	—
591	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
593	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
594	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
596	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
597	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
598	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
599	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	C₂³×C₁₇	1	4	yes	—
610	C₄×D₄	C₂³×C₁₇	1	4	yes	—
611	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₁₇	1	2	yes	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	—	2	1	no	—
616	#117	—	2	2	no	—
617	#117	—	2	2	no	—
618	#117	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	—	2	2	no	—
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₄²	—	2	1	no	—
627	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
629	#107	C₂³×C₁₇	1	2	yes	—
630	#106	C₂³×C₁₇	1	2	yes	—
631	#106	C₂³×C₁₇	1	4	yes	—
632	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
633	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
634	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
635	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
636	#103	C₂³×C₁₇	1	2	yes	—
637	#103	C₂³×C₁₇	1	4	yes	—
638	#103	C₂³×C₁₇	1	2	yes	—
639	#103	C₂³×C₁₇	1	2	yes	—
640	#103	C₂³×C₁₇	1	4	yes	—
641	#102	C₂³×C₁₇	1	2	yes	—
642	#102	C₂³×C₁₇	1	4	yes	—
643	#102	C₂³×C₁₇	1	4	yes	—
644	#102	C₂³×C₁₇	1	4	yes	—
645	#102	C₂³×C₁₇	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
647	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
648	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
649	#97	C₂³×C₁₇	1	4	yes	—
650	#97	C₂³×C₁₇	1	2	yes	—
651	C₄×C₈	C₂³×C₁₇	1	4	yes	—
652	C₄×C₈	C₂³×C₁₇	1	2	yes	—
653	C₁₇	#61904	1	1	yes	characteristic, direct product factor, Sylow
654	C₂⁴	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
662	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
663	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
666	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	8	2	no	—
676	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
677	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	8	4	no	—
685	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
690	Q₁₆	—	4	4	no	—
691	Q₁₆	—	4	2	no	—
692	SD₁₆	—	4	4	no	—
693	SD₁₆	—	4	2	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	4	no	—
696	D₈	—	4	4	no	—
697	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
698	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
699	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
721	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
726	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
730	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	1	no	—
753	C₄²	C₂×D₄×C₁₇	1	2	yes	—
754	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₁₇	1	2	yes	—
756	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
757	C₄²	C₂⁴×C₁₇	1	2	yes	—
758	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
759	C₄²	C₂⁴×C₁₇	1	2	yes	—
760	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
761	C₂³	—	2	1	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	—	4	4	no	—
766	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	4	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	2	no	—
775	Q₈	—	4	4	no	—
776	Q₈	—	4	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	4	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	8	4	no	—
803	C₂×C₄	—	8	4	no	—
804	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
813	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
814	C₈	—	2	4	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	2	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	8	8	no	—
826	C₂²	C₁₇×#577	1	2	yes	—
827	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	C₁₇×#575	1	2	yes	—
844	C₄	C₁₇×#585	1	2	yes	—
845	C₂	—	2	2	no	—
846	C₂	—	8	4	no	—
847	C₂	—	8	1	no	—
848	C₂	C₁₇×#3487	1	1	yes	characteristic
849	C₂	C₂×C₁₇×#575	1	1	yes	characteristic
850	C₂	C₂×C₁₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3217	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3523	C₂	semidirect
2. C₂×C₁₇×#559	C₂	semidirect
3. C₁₇×#3401	C₂	semidirect
4. C₁₇×#3400	C₂	semidirect
5. C₁₇×#3394	C₂	semidirect
6. C₁₇×#3373	C₂	semidirect
7. C₁₇×#3371	C₂	semidirect
8. C₁₇×#3365	C₂	semidirect
10. C₁₇×#3215	C₂	semidirect
11. C₁₇×#3211	C₂	semidirect
12. C₁₇×#3208	C₂	semidirect
13. C₁₇×#3114	C₂	semidirect
14. C₁₇×#3113	C₂	semidirect
15. C₁₇×#3108	C₂	semidirect
16. C₁₇×#3101	C₂	semidirect
17. C₁₇×#2984	C₂	semidirect
24. C₁₇×#557	C₂²	semidirect
25. C₁₇×#557	C₂²	semidirect
26. C₁₇×#557	C₂²	semidirect
27. C₁₇×#556	C₂²	semidirect
28. C₁₇×#556	C₂²	semidirect
32. D₄×Q₈×C₁₇	C₂²	semidirect
48. C₁₇×#497	C₂²	semidirect
50. C₁₇×#495	C₂²	semidirect
53. C₁₇×#489	C₂²	semidirect
54. C₁₇×#488	C₂²	semidirect
59. C₁₇×#479	C₂²	semidirect
60. C₁₇×#478	C₂²	semidirect
61. C₁₇×#476	C₂²	semidirect
62. C₁₇×#475	C₂²	semidirect
63. C₁₇×#464	C₂²	semidirect
64. C₁₇×#464	C₂²	semidirect
65. C₁₇×#464	C₂²	semidirect
66. C₁₇×#464	C₂²	semidirect
67. C₁₇×#463	C₂²	semidirect
68. C₁₇×#463	C₂²	semidirect
69. C₁₇×#462	C₂²	semidirect
70. C₁₇×#461	C₂²	semidirect
81. C₁₇×#446	C₂²	semidirect
82. C₁₇×#446	C₂²	semidirect
83. C₈×Q₈×C₁₇	C₂²	semidirect
84. C₁₇×#442	C₂²	semidirect
85. C₁₇×#441	C₂²	semidirect
86. C₁₇×#440	C₂²	semidirect
87. C₄×Q₁₆×C₁₇	C₂²	semidirect
88. C₄×SD₁₆×C₁₇	C₂²	semidirect
89. C₄×SD₁₆×C₁₇	C₂²	semidirect
90. C₄×SD₁₆×C₁₇	C₂²	semidirect
335. #61904	C₁₇	direct (N × H)
392. #3523	C₂×C₁₇	semidirect
393. C₂×#559	C₂×C₁₇	semidirect
394. #3401	C₂×C₁₇	semidirect
395. #3400	C₂×C₁₇	semidirect
396. #3394	C₂×C₁₇	semidirect
397. #3373	C₂×C₁₇	semidirect
398. #3371	C₂×C₁₇	semidirect
399. #3365	C₂×C₁₇	semidirect
401. #3215	C₂×C₁₇	semidirect
402. #3211	C₂×C₁₇	semidirect
403. #3208	C₂×C₁₇	semidirect
404. #3114	C₂×C₁₇	semidirect
405. #3113	C₂×C₁₇	semidirect
406. #3108	C₂×C₁₇	semidirect
407. #3101	C₂×C₁₇	semidirect
408. #2984	C₂×C₁₇	semidirect
443. #557	C₂²×C₁₇	semidirect
444. #557	C₂²×C₁₇	semidirect
445. #557	C₂²×C₁₇	semidirect
446. #556	C₂²×C₁₇	semidirect
447. #556	C₂²×C₁₇	semidirect
451. D₄×Q₈	C₂²×C₁₇	semidirect
467. #497	C₂²×C₁₇	semidirect
469. #495	C₂²×C₁₇	semidirect
472. #489	C₂²×C₁₇	semidirect
473. #488	C₂²×C₁₇	semidirect
478. #479	C₂²×C₁₇	semidirect
479. #478	C₂²×C₁₇	semidirect
480. #476	C₂²×C₁₇	semidirect
481. #475	C₂²×C₁₇	semidirect
482. #464	C₂²×C₁₇	semidirect
483. #464	C₂²×C₁₇	semidirect
484. #464	C₂²×C₁₇	semidirect
485. #464	C₂²×C₁₇	semidirect
486. #463	C₂²×C₁₇	semidirect
487. #463	C₂²×C₁₇	semidirect
488. #462	C₂²×C₁₇	semidirect
489. #461	C₂²×C₁₇	semidirect
500. #446	C₂²×C₁₇	semidirect
501. #446	C₂²×C₁₇	semidirect
502. C₈×Q₈	C₂²×C₁₇	semidirect
503. #442	C₂²×C₁₇	semidirect
504. #441	C₂²×C₁₇	semidirect
505. #440	C₂²×C₁₇	semidirect
506. C₄×Q₁₆	C₂²×C₁₇	semidirect
507. C₄×SD₁₆	C₂²×C₁₇	semidirect
508. C₄×SD₁₆	C₂²×C₁₇	semidirect
509. C₄×SD₁₆	C₂²×C₁₇	semidirect
653. C₁₇	#61904	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3523	2
C₂×C₁₇×#559	2
C₁₇×#3401	2
C₁₇×#3400	2
C₁₇×#3394	2
C₁₇×#3373	2
C₁₇×#3371	2
C₁₇×#3365	2
C₁₇×#3217	2
C₁₇×#3215	2
C₁₇×#3211	2
C₁₇×#3208	2
C₁₇×#3114	2
C₁₇×#3113	2
C₁₇×#3108	2
C₁₇×#3101	2
C₁₇×#2984	2
#61904	17

Subgroups — C17×#61904 #16919648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61904 #16919648