Subgroups — C₁₇×#61422 #16919166

Order 4352.

1844 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3400	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3398	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3398	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3395	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3394	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3156	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3046	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3044	C₂	1	2	yes	maximal, complemented
13	C₁₇×#3035	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#2947	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₇×#137	C₂²	1	2	yes	—
19	C₂×C₁₇×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#137	C₂²	1	2	yes	—
21	C₂×C₁₇×#135	C₂²	1	2	yes	—
22	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	—
23	C₁₇×#559	C₂²	1	2	yes	—
24	C₁₇×#557	C₂²	1	2	yes	—
25	C₁₇×#557	C₂²	1	2	yes	—
26	C₁₇×#557	C₂²	1	2	yes	—
27	C₁₇×#556	—	2	1	no	—
28	C₁₇×#556	C₂²	1	4	yes	—
29	C₁₇×#556	C₂²	1	2	yes	—
30	C₁₇×#556	C₂²	1	2	yes	—
31	C₁₇×#554	—	2	1	no	—
32	C₁₇×#552	—	2	2	no	—
33	C₁₇×#552	—	2	2	no	—
34	C₁₇×#552	—	2	2	no	—
35	C₁₇×#541	—	2	2	no	—
36	C₁₇×#539	—	2	2	no	—
37	C₁₇×#536	C₂²	1	2	yes	—
38	C₁₇×#536	C₂²	1	2	yes	—
39	C₁₇×#533	—	2	1	no	—
40	C₁₇×#533	—	2	1	no	—
41	C₁₇×#533	C₂²	1	1	yes	characteristic
42	C₁₇×#532	C₂²	1	1	yes	characteristic
43	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₇×#529	—	2	2	no	—
45	C₁₇×#520	C₂²	1	2	yes	—
46	C₁₇×#519	C₂²	1	2	yes	—
47	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#497	C₂²	1	4	yes	—
50	C₁₇×#497	C₂²	1	4	yes	—
51	C₁₇×#497	C₂²	1	4	yes	—
52	C₁₇×#495	C₂²	1	4	yes	—
53	C₁₇×#494	C₂²	1	2	yes	—
54	C₁₇×#494	C₂²	1	4	yes	—
55	C₁₇×#492	C₂²	1	2	yes	—
56	C₁₇×#464	C₂²	1	2	yes	—
57	C₁₇×#464	C₂²	1	4	yes	—
58	C₁₇×#464	C₂²	1	4	yes	—
59	C₁₇×#464	C₂²	1	4	yes	—
60	C₁₇×#463	C₂²	1	2	yes	—
61	C₁₇×#463	C₂²	1	4	yes	—
62	C₁₇×#462	C₂²	1	2	yes	—
63	C₁₇×#462	C₂²	1	2	yes	—
64	C₁₇×#462	C₂²	1	4	yes	—
65	C₁₇×#462	C₂²	1	1	yes	characteristic
66	C₁₇×#462	C₂²	1	4	yes	—
67	C₁₇×#462	C₂²	1	4	yes	—
68	C₁₇×#462	C₂²	1	4	yes	—
69	C₁₇×#461	C₂²	1	1	yes	characteristic
70	C₁₇×#461	C₂²	1	4	yes	—
71	C₁₇×#460	C₂²	1	1	yes	characteristic
72	C₁₇×#459	C₂²	1	1	yes	characteristic
73	C₁₇×#446	C₂²	1	2	yes	—
74	C₁₇×#446	C₂²	1	4	yes	—
75	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
76	C₁₇×#441	C₂²	1	4	yes	—
77	C₁₇×#441	C₂²	1	2	yes	—
78	C₁₇×#440	C₂²	1	4	yes	—
79	C₁₇×#440	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
81	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
84	C₁₇×#428	C₂²	1	1	yes	characteristic
85	C₁₇×#424	C₂²	1	2	yes	—
86	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₇×#419	C₂²	1	1	yes	characteristic
88	C₁₇×#417	C₂²	1	1	yes	characteristic
89	C₁₇×#416	C₂²	1	2	yes	—
90	C₂×C₁₇×#103	C₂²	1	2	yes	—
91	C₁₇×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
94	C₂×#41×C₁₇	C₂³	1	2	yes	—
95	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
97	C₁₇×#137	—	2	8	no	—
98	C₁₇×#137	—	2	4	no	—
99	C₁₇×#137	—	4	4	no	—
100	C₁₇×#135	—	4	4	no	—
101	C₂×Q₁₆×C₁₇	—	4	4	no	—
102	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
107	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
113	C₂×D₈×C₁₇	C₂³	1	2	yes	—
114	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
117	C₁₇×C₄⋊Q₈	—	2	1	no	—
118	C₁₇×C₄⋊Q₈	—	2	1	no	—
119	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
120	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
121	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₇×#127	C₂³	1	1	yes	characteristic
127	C₁₇×#126	—	2	4	no	—
128	C₁₇×#126	—	2	4	no	—
129	C₁₇×#126	—	2	4	no	—
130	C₁₇×#126	—	2	4	no	—
131	C₁₇×#125	—	2	2	no	—
132	C₁₇×#125	—	2	2	no	—
133	C₁₇×#125	—	2	2	no	—
134	C₁₇×#125	—	2	4	no	—
135	C₁₇×#125	—	2	4	no	—
136	C₁₇×#125	—	2	4	no	—
137	C₁₇×#125	D₄	1	2	yes	—
138	C₁₇×#124	—	2	2	no	—
139	C₁₇×#124	C₂³	1	4	yes	—
140	C₁₇×#124	C₂³	1	4	yes	—
141	C₁₇×#124	C₂³	1	2	yes	—
142	C₁₇×#123	—	2	4	no	—
143	C₁₇×#123	—	2	4	no	—
144	C₁₇×#123	—	2	4	no	—
145	C₁₇×C₂²⋊Q₈	—	2	2	no	—
146	C₁₇×C₂²⋊Q₈	—	2	2	no	—
147	C₁₇×C₂²⋊Q₈	—	2	4	no	—
148	C₁₇×C₂²⋊Q₈	—	2	2	no	—
149	C₁₇×C₂²⋊Q₈	—	2	2	no	—
150	C₁₇×C₂²⋊Q₈	—	2	2	no	—
151	C₁₇×C₂²⋊Q₈	—	2	2	no	—
152	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
153	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
154	C₁₇×#121	—	2	1	no	—
155	C₁₇×#121	—	2	1	no	—
156	C₄×Q₈×C₁₇	—	2	2	no	—
157	C₄×Q₈×C₁₇	—	2	2	no	—
158	C₄×Q₈×C₁₇	—	2	2	no	—
159	C₄×Q₈×C₁₇	—	2	2	no	—
160	C₄×Q₈×C₁₇	—	2	2	no	—
161	C₄×Q₈×C₁₇	—	2	1	no	—
162	C₄×Q₈×C₁₇	—	2	1	no	—
163	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
169	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
170	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
172	C₄×D₄×C₁₇	—	2	1	no	—
173	C₄×D₄×C₁₇	—	2	1	no	—
174	C₄×D₄×C₁₇	—	2	2	no	—
175	C₄×D₄×C₁₇	—	2	4	no	—
176	C₄×D₄×C₁₇	—	2	1	no	—
177	C₄×D₄×C₁₇	—	2	1	no	—
178	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₇	C₂³	1	4	yes	—
181	C₁₇×#117	—	2	2	no	—
182	C₁₇×#117	—	2	4	no	—
183	C₁₇×#117	—	2	2	no	—
184	C₁₇×#117	—	2	2	no	—
185	C₁₇×#117	—	2	4	no	—
186	C₁₇×#117	—	2	1	no	—
187	C₁₇×#117	C₂³	1	1	yes	characteristic
188	C₁₇×#117	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
193	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₇	—	2	1	no	—
195	C₂×C₄²×C₁₇	—	2	1	no	—
196	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
197	C₁₇×#107	C₂³	1	2	yes	—
198	C₁₇×#106	C₂³	1	2	yes	—
199	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
204	C₁₇×#103	C₂³	1	4	yes	—
205	C₁₇×#103	C₂³	1	4	yes	—
206	C₁₇×#103	C₂³	1	2	yes	—
207	C₁₇×#103	C₂³	1	2	yes	—
208	C₁₇×#103	C₂³	1	2	yes	—
209	C₁₇×#103	C₂³	1	2	yes	—
210	C₁₇×#103	C₂³	1	2	yes	—
211	C₁₇×#102	C₂³	1	2	yes	—
212	C₁₇×#102	C₂³	1	2	yes	—
213	C₁₇×#102	C₂³	1	2	yes	—
214	C₁₇×#97	C₂³	1	2	yes	—
215	C₁₇×#97	C₂³	1	4	yes	—
216	C₄×C₈×C₁₇	C₂³	1	2	yes	—
217	C₄×C₈×C₁₇	C₂³	1	4	yes	—
218	#41×C₁₇	—	2	2	no	—
219	#41×C₁₇	—	2	4	no	—
220	#41×C₁₇	—	2	2	no	—
221	#41×C₁₇	—	2	4	no	—
222	C₂×Q₈×C₁₇	—	2	1	no	—
223	C₂×Q₈×C₁₇	—	2	2	no	—
224	C₂×Q₈×C₁₇	—	2	2	no	—
225	C₂×Q₈×C₁₇	—	2	4	no	—
226	C₂×Q₈×C₁₇	—	2	2	no	—
227	C₂×Q₈×C₁₇	—	2	4	no	—
228	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
234	C₂×D₄×C₁₇	—	2	1	no	—
235	C₂×D₄×C₁₇	—	2	2	no	—
236	C₂×D₄×C₁₇	—	2	1	no	—
237	C₂×D₄×C₁₇	—	2	1	no	—
238	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₇	—	2	1	no	—
241	C₂²×C₄×C₁₇	—	2	2	no	—
242	C₂²×C₄×C₁₇	—	2	1	no	—
243	C₂²×C₄×C₁₇	—	2	1	no	—
244	C₂²×C₄×C₁₇	—	2	2	no	—
245	C₂²×C₄×C₁₇	—	2	1	no	—
246	C₂²×C₄×C₁₇	—	2	1	no	—
247	C₂²×C₄×C₁₇	—	2	4	no	—
248	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
251	Q₁₆×C₁₇	—	2	4	no	—
252	Q₁₆×C₁₇	—	2	8	no	—
253	Q₁₆×C₁₇	—	4	4	no	—
254	Q₁₆×C₁₇	—	4	4	no	—
255	Q₁₆×C₁₇	—	4	2	no	—
256	Q₁₆×C₁₇	—	4	4	no	—
257	SD₁₆×C₁₇	—	2	8	no	—
258	SD₁₆×C₁₇	—	2	4	no	—
259	SD₁₆×C₁₇	—	4	2	no	—
260	SD₁₆×C₁₇	—	4	2	no	—
261	SD₁₆×C₁₇	—	4	4	no	—
262	D₈×C₁₇	—	4	2	no	—
263	M₁₆×C₁₇	—	2	2	no	—
264	M₁₆×C₁₇	#41	1	4	yes	—
265	C₂×C₈×C₁₇	—	2	4	no	—
266	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
269	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₁₇	—	2	4	no	—
271	C₄⋊C₄×C₁₇	—	2	2	no	—
272	C₄⋊C₄×C₁₇	—	2	4	no	—
273	C₄⋊C₄×C₁₇	—	2	4	no	—
274	C₄⋊C₄×C₁₇	—	2	4	no	—
275	C₄⋊C₄×C₁₇	—	2	4	no	—
276	C₄⋊C₄×C₁₇	—	2	4	no	—
277	C₄⋊C₄×C₁₇	—	2	4	no	—
278	C₄⋊C₄×C₁₇	—	2	2	no	—
279	C₄⋊C₄×C₁₇	—	2	2	no	—
280	C₄⋊C₄×C₁₇	—	2	2	no	—
281	C₄⋊C₄×C₁₇	—	2	1	no	—
282	C₄⋊C₄×C₁₇	—	2	1	no	—
283	C₄⋊C₄×C₁₇	—	2	1	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	1	no	—
288	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
291	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
293	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
297	C₂²⋊C₄×C₁₇	—	2	1	no	—
298	C₂²⋊C₄×C₁₇	—	2	4	no	—
299	C₂²⋊C₄×C₁₇	—	2	4	no	—
300	C₂²⋊C₄×C₁₇	—	2	4	no	—
301	C₂²⋊C₄×C₁₇	—	2	2	no	—
302	C₂²⋊C₄×C₁₇	—	2	4	no	—
303	C₂²⋊C₄×C₁₇	—	2	4	no	—
304	C₂²⋊C₄×C₁₇	—	2	2	no	—
305	C₂²⋊C₄×C₁₇	—	2	1	no	—
306	C₂²⋊C₄×C₁₇	—	2	1	no	—
307	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
308	C₄²×C₁₇	—	2	2	no	—
309	C₄²×C₁₇	—	2	1	no	—
310	C₄²×C₁₇	—	2	1	no	—
311	C₄²×C₁₇	—	2	4	no	—
312	C₄²×C₁₇	—	2	4	no	—
313	C₄²×C₁₇	—	2	4	no	—
314	C₄²×C₁₇	—	2	2	no	—
315	C₄²×C₁₇	—	2	1	no	—
316	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₇	C₂⁴	1	4	yes	—
319	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
320	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
321	#61422	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₁₇	—	2	1	no	—
323	C₂³×C₁₇	—	2	2	no	—
324	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₇	—	2	4	no	—
326	Q₈×C₁₇	—	2	2	no	—
327	Q₈×C₁₇	—	2	4	no	—
328	Q₈×C₁₇	—	2	2	no	—
329	Q₈×C₁₇	—	2	1	no	—
330	Q₈×C₁₇	—	2	1	no	—
331	Q₈×C₁₇	—	2	4	no	—
332	Q₈×C₁₇	—	2	2	no	—
333	Q₈×C₁₇	—	2	2	no	—
334	Q₈×C₁₇	—	4	2	no	—
335	Q₈×C₁₇	—	4	2	no	—
336	Q₈×C₁₇	—	4	4	no	—
337	D₄×C₁₇	—	2	1	no	—
338	D₄×C₁₇	—	2	2	no	—
339	D₄×C₁₇	—	2	1	no	—
340	D₄×C₁₇	—	2	2	no	—
341	D₄×C₁₇	—	4	2	no	—
342	D₄×C₁₇	—	4	4	no	—
343	D₄×C₁₇	—	4	2	no	—
344	D₄×C₁₇	—	8	1	no	—
345	C₂×C₄×C₁₇	—	2	2	no	—
346	C₂×C₄×C₁₇	—	2	1	no	—
347	C₂×C₄×C₁₇	—	2	1	no	—
348	C₂×C₄×C₁₇	—	2	2	no	—
349	C₂×C₄×C₁₇	—	2	2	no	—
350	C₂×C₄×C₁₇	—	2	2	no	—
351	C₂×C₄×C₁₇	—	2	4	no	—
352	C₂×C₄×C₁₇	—	2	1	no	—
353	C₂×C₄×C₁₇	—	4	1	no	—
354	C₂×C₄×C₁₇	—	4	2	no	—
355	C₂×C₄×C₁₇	—	4	2	no	—
356	C₂×C₄×C₁₇	—	4	4	no	—
357	C₂×C₄×C₁₇	—	4	2	no	—
358	C₂×C₄×C₁₇	—	4	4	no	—
359	C₂×C₄×C₁₇	—	4	2	no	—
360	C₂×C₄×C₁₇	—	8	4	no	—
361	C₂×C₄×C₁₇	—	8	1	no	—
362	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
366	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
370	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
371	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
372	C₈×C₁₇	—	2	2	no	—
373	C₈×C₁₇	—	2	2	no	—
374	C₈×C₁₇	—	2	2	no	—
375	C₈×C₁₇	C₂×#41	1	4	yes	—
376	#3509	C₂×C₁₇	1	1	yes	characteristic, complemented
377	#3507	C₂×C₁₇	1	1	yes	characteristic, complemented
378	#3402	C₂×C₁₇	1	4	yes	complemented
379	#3400	C₂×C₁₇	1	2	yes	complemented
380	#3398	C₂×C₁₇	1	2	yes	complemented
381	#3398	C₂×C₁₇	1	4	yes	complemented
382	#3395	C₂×C₁₇	1	2	yes	complemented
383	#3394	C₂×C₁₇	1	2	yes	complemented
384	#3156	C₂×C₁₇	1	2	yes	complemented
385	#3152	C₂×C₁₇	1	1	yes	characteristic, complemented
386	#3046	C₂×C₁₇	1	2	yes	complemented
387	#3044	C₂×C₁₇	1	2	yes	complemented
388	#3035	C₂×C₁₇	1	1	yes	characteristic
389	C₂×#462	C₂×C₁₇	1	1	yes	characteristic, complemented
390	#2962	C₂×C₁₇	1	1	yes	characteristic, complemented
391	#2947	C₂×C₁₇	1	2	yes	complemented
392	C₄×#137	C₂×C₁₇	1	1	yes	characteristic, complemented
393	C₂²×C₁₇	—	2	1	no	—
394	C₂²×C₁₇	—	2	1	no	—
395	C₂²×C₁₇	—	4	1	no	—
396	C₂²×C₁₇	—	4	2	no	—
397	C₂²×C₁₇	—	4	1	no	—
398	C₂²×C₁₇	—	4	2	no	—
399	C₂²×C₁₇	—	4	1	no	—
400	C₂²×C₁₇	—	4	2	no	—
401	C₂²×C₁₇	#550	1	2	yes	—
402	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₁₇	—	2	1	no	—
404	C₄×C₁₇	—	2	1	no	—
405	C₄×C₁₇	—	2	4	no	—
406	C₄×C₁₇	—	2	1	no	—
407	C₄×C₁₇	—	2	4	no	—
408	C₄×C₁₇	—	4	1	no	—
409	C₄×C₁₇	—	4	2	no	—
410	C₄×C₁₇	—	4	2	no	—
411	C₄×C₁₇	—	4	1	no	—
412	C₄×C₁₇	—	4	2	no	—
413	C₄×C₁₇	—	4	4	no	—
414	C₄×C₁₇	—	4	1	no	—
415	C₄×C₁₇	#550	1	2	yes	—
416	C₄×C₁₇	#578	1	2	yes	—
417	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
418	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×#137	C₂²×C₁₇	1	2	yes	—
420	C₂×#137	C₂²×C₁₇	1	1	yes	characteristic
421	C₂×#137	C₂²×C₁₇	1	2	yes	—
422	C₂×#135	C₂²×C₁₇	1	2	yes	—
423	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	—
424	#559	C₂²×C₁₇	1	2	yes	—
425	#557	C₂²×C₁₇	1	2	yes	—
426	#557	C₂²×C₁₇	1	2	yes	—
427	#557	C₂²×C₁₇	1	2	yes	—
428	#556	—	2	1	no	—
429	#556	C₂²×C₁₇	1	2	yes	—
430	#556	C₂²×C₁₇	1	4	yes	—
431	#556	C₂²×C₁₇	1	2	yes	—
432	#554	—	2	1	no	—
433	#552	—	2	2	no	—
434	#552	—	2	2	no	—
435	#552	—	2	2	no	—
436	#541	—	2	2	no	—
437	#539	—	2	2	no	—
438	#536	C₂²×C₁₇	1	2	yes	—
439	#536	C₂²×C₁₇	1	2	yes	—
440	#533	—	2	1	no	—
441	#533	—	2	1	no	—
442	#533	C₂²×C₁₇	1	1	yes	characteristic
443	#532	C₂²×C₁₇	1	1	yes	characteristic
444	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
445	#529	—	2	2	no	—
446	#520	C₂²×C₁₇	1	2	yes	—
447	#519	C₂²×C₁₇	1	2	yes	—
448	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
449	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
450	#497	C₂²×C₁₇	1	4	yes	—
451	#497	C₂²×C₁₇	1	4	yes	—
452	#497	C₂²×C₁₇	1	4	yes	—
453	#495	C₂²×C₁₇	1	4	yes	—
454	#494	C₂²×C₁₇	1	2	yes	—
455	#494	C₂²×C₁₇	1	4	yes	—
456	#492	C₂²×C₁₇	1	2	yes	—
457	#464	C₂²×C₁₇	1	4	yes	—
458	#464	C₂²×C₁₇	1	2	yes	—
459	#464	C₂²×C₁₇	1	4	yes	—
460	#464	C₂²×C₁₇	1	4	yes	—
461	#463	C₂²×C₁₇	1	4	yes	—
462	#463	C₂²×C₁₇	1	2	yes	—
463	#462	C₂²×C₁₇	1	2	yes	—
464	#462	C₂²×C₁₇	1	1	yes	characteristic
465	#462	C₂²×C₁₇	1	4	yes	—
466	#462	C₂²×C₁₇	1	4	yes	—
467	#462	C₂²×C₁₇	1	4	yes	—
468	#462	C₂²×C₁₇	1	2	yes	—
469	#462	C₂²×C₁₇	1	4	yes	—
470	#461	C₂²×C₁₇	1	1	yes	characteristic
471	#461	C₂²×C₁₇	1	4	yes	—
472	#460	C₂²×C₁₇	1	1	yes	characteristic
473	#459	C₂²×C₁₇	1	1	yes	characteristic
474	#446	C₂²×C₁₇	1	2	yes	—
475	#446	C₂²×C₁₇	1	4	yes	—
476	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
477	#441	C₂²×C₁₇	1	2	yes	—
478	#441	C₂²×C₁₇	1	4	yes	—
479	#440	C₂²×C₁₇	1	4	yes	—
480	#440	C₂²×C₁₇	1	2	yes	—
481	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
482	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
483	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
484	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	—
485	#428	C₂²×C₁₇	1	1	yes	characteristic
486	#424	C₂²×C₁₇	1	2	yes	—
487	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
488	#419	C₂²×C₁₇	1	1	yes	characteristic
489	#417	C₂²×C₁₇	1	1	yes	characteristic
490	#416	C₂²×C₁₇	1	2	yes	—
491	C₂×#103	C₂²×C₁₇	1	2	yes	—
492	#405	C₂²×C₁₇	1	2	yes	—
493	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
494	C₂×C₁₇	—	2	2	no	—
495	C₂×C₁₇	—	8	1	no	—
496	C₂×C₁₇	—	8	2	no	—
497	C₂×C₁₇	C₂×#550	1	1	yes	characteristic
498	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
499	C₂×C₁₇	#3586	1	1	yes	characteristic
500	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
501	C₂×#41	C₂³×C₁₇	1	2	yes	—
502	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
504	#137	—	2	8	no	—
505	#137	—	2	4	no	—
506	#137	—	4	4	no	—
507	#135	—	4	4	no	—
508	C₂×Q₁₆	—	4	4	no	—
509	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
510	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
511	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
512	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
513	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
514	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
517	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
518	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
519	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
520	C₂×D₈	C₂³×C₁₇	1	2	yes	—
521	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
522	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
527	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
532	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
533	#127	C₂³×C₁₇	1	1	yes	characteristic
534	#126	—	2	4	no	—
535	#126	—	2	4	no	—
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	4	no	—
542	#125	—	2	4	no	—
543	#125	—	2	4	no	—
544	#125	D₄×C₁₇	1	2	yes	—
545	#124	—	2	2	no	—
546	#124	C₂³×C₁₇	1	2	yes	—
547	#124	C₂³×C₁₇	1	4	yes	—
548	#124	C₂³×C₁₇	1	4	yes	—
549	#123	—	2	4	no	—
550	#123	—	2	4	no	—
551	#123	—	2	4	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	4	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
560	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
561	#121	—	2	1	no	—
562	#121	—	2	1	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
571	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
572	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
573	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
574	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
575	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
576	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
577	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
578	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	4	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
586	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
587	C₄×D₄	C₂³×C₁₇	1	4	yes	—
588	#117	—	2	2	no	—
589	#117	—	2	4	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	4	no	—
593	#117	—	2	1	no	—
594	#117	C₂³×C₁₇	1	1	yes	characteristic
595	#117	C₂³×C₁₇	1	2	yes	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	—	2	1	no	—
603	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
604	#107	C₂³×C₁₇	1	2	yes	—
605	#106	C₂³×C₁₇	1	2	yes	—
606	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
607	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
609	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
610	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
611	#103	C₂³×C₁₇	1	4	yes	—
612	#103	C₂³×C₁₇	1	4	yes	—
613	#103	C₂³×C₁₇	1	2	yes	—
614	#103	C₂³×C₁₇	1	2	yes	—
615	#103	C₂³×C₁₇	1	2	yes	—
616	#103	C₂³×C₁₇	1	2	yes	—
617	#103	C₂³×C₁₇	1	2	yes	—
618	#102	C₂³×C₁₇	1	2	yes	—
619	#102	C₂³×C₁₇	1	2	yes	—
620	#102	C₂³×C₁₇	1	2	yes	—
621	#97	C₂³×C₁₇	1	2	yes	—
622	#97	C₂³×C₁₇	1	4	yes	—
623	C₄×C₈	C₂³×C₁₇	1	2	yes	—
624	C₄×C₈	C₂³×C₁₇	1	4	yes	—
625	C₁₇	#61422	1	1	yes	characteristic, direct product factor, Sylow
626	#41	—	2	2	no	—
627	#41	—	2	4	no	—
628	#41	—	2	2	no	—
629	#41	—	2	4	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	2	4	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	4	no	—
636	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
637	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
638	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
639	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
640	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
641	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
647	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
659	Q₁₆	—	2	4	no	—
660	Q₁₆	—	2	8	no	—
661	Q₁₆	—	4	4	no	—
662	Q₁₆	—	4	4	no	—
663	Q₁₆	—	4	2	no	—
664	Q₁₆	—	4	4	no	—
665	SD₁₆	—	2	8	no	—
666	SD₁₆	—	2	4	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	4	no	—
670	D₈	—	4	2	no	—
671	M₁₆	—	2	2	no	—
672	M₁₆	#41×C₁₇	1	4	yes	—
673	C₂×C₈	—	2	4	no	—
674	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
675	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
676	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
677	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
697	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
699	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
700	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
702	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
703	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
704	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
726	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
727	C₄²	C₂⁴×C₁₇	1	4	yes	—
728	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
732	Q₈	—	2	4	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	4	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	4	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
771	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
776	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
777	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
778	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₈	C₂×#41×C₁₇	1	4	yes	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	2	no	—
791	C₂²	C₁₇×#550	1	2	yes	—
792	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
793	C₄	—	2	1	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	4	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	C₁₇×#550	1	2	yes	—
806	C₄	C₁₇×#578	1	2	yes	—
807	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
808	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
809	C₂	—	2	2	no	—
810	C₂	—	8	1	no	—
811	C₂	—	8	2	no	—
812	C₂	C₂×C₁₇×#550	1	1	yes	characteristic
813	C₂	C₂×C₁₇×#578	1	1	yes	characteristic
814	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3509	C₂	semidirect
2. C₁₇×#3507	C₂	semidirect
3. C₁₇×#3402	C₂	semidirect
4. C₁₇×#3400	C₂	semidirect
5. C₁₇×#3398	C₂	semidirect
6. C₁₇×#3398	C₂	semidirect
7. C₁₇×#3395	C₂	semidirect
8. C₁₇×#3394	C₂	semidirect
9. C₁₇×#3156	C₂	semidirect
10. C₁₇×#3152	C₂	semidirect
11. C₁₇×#3046	C₂	semidirect
12. C₁₇×#3044	C₂	semidirect
14. C₂×C₁₇×#462	C₂	semidirect
15. C₁₇×#2962	C₂	semidirect
16. C₁₇×#2947	C₂	semidirect
17. C₄×C₁₇×#137	C₂	semidirect
321. #61422	C₁₇	direct (N × H)
376. #3509	C₂×C₁₇	semidirect
377. #3507	C₂×C₁₇	semidirect
378. #3402	C₂×C₁₇	semidirect
379. #3400	C₂×C₁₇	semidirect
380. #3398	C₂×C₁₇	semidirect
381. #3398	C₂×C₁₇	semidirect
382. #3395	C₂×C₁₇	semidirect
383. #3394	C₂×C₁₇	semidirect
384. #3156	C₂×C₁₇	semidirect
385. #3152	C₂×C₁₇	semidirect
386. #3046	C₂×C₁₇	semidirect
387. #3044	C₂×C₁₇	semidirect
389. C₂×#462	C₂×C₁₇	semidirect
390. #2962	C₂×C₁₇	semidirect
391. #2947	C₂×C₁₇	semidirect
392. C₄×#137	C₂×C₁₇	semidirect
625. C₁₇	#61422	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×#3509	2
C₁₇×#3507	2
C₁₇×#3402	2
C₁₇×#3400	2
C₁₇×#3398	2
C₁₇×#3395	2
C₁₇×#3394	2
C₁₇×#3156	2
C₁₇×#3152	2
C₁₇×#3046	2
C₁₇×#3044	2
C₁₇×#3035	2
C₂×C₁₇×#462	2
C₁₇×#2962	2
C₁₇×#2947	2
C₄×C₁₇×#137	2
#61422	17

Subgroups — C17×#61422 #16919166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61422 #16919166